Unstructured Euler flow solutions using hexahedral cell refinement

NASA Technical Reports Server (NTRS)

Melton, John E.; Cappuccio, Gelsomina; Thomas, Scott D.

1991-01-01

An attempt is made to extend grid refinement into three dimensions by using unstructured hexahedral grids. The flow solver is developed using the TIGER (topologically Independent Grid, Euler Refinement) as the starting point. The program uses an unstructured hexahedral mesh and a modified version of the Jameson four-stage, finite-volume Runge-Kutta algorithm for integration of the Euler equations. The unstructured mesh allows for local refinement appropriate for each freestream condition, thereby concentrating mesh cells in the regions of greatest interest. This increases the computational efficiency because the refinement is not required to extend throughout the entire flow field.

Effect of Coannular Flow on Linearized Euler Equation Predictions of Jet Noise

NASA Technical Reports Server (NTRS)

Hixon, R.; Shih, S.-H.; Mankbadi, Reda R.

1997-01-01

An improved version of a previously validated linearized Euler equation solver is used to compute the noise generated by coannular supersonic jets. Results for a single supersonic jet are compared to the results from both a normal velocity profile and an inverted velocity profile supersonic jet.

Generation of unstructured grids and Euler solutions for complex geometries

NASA Technical Reports Server (NTRS)

Loehner, Rainald; Parikh, Paresh; Salas, Manuel D.

1989-01-01

Algorithms are described for the generation and adaptation of unstructured grids in two and three dimensions, as well as Euler solvers for unstructured grids. The main purpose is to demonstrate how unstructured grids may be employed advantageously for the economic simulation of both geometrically as well as physically complex flow fields.

Three-dimensional unstructured grid Euler computations using a fully-implicit, upwind method

NASA Technical Reports Server (NTRS)

Whitaker, David L.

1993-01-01

A method has been developed to solve the Euler equations on a three-dimensional unstructured grid composed of tetrahedra. The method uses an upwind flow solver with a linearized, backward-Euler time integration scheme. Each time step results in a sparse linear system of equations which is solved by an iterative, sparse matrix solver. Local-time stepping, switched evolution relaxation (SER), preconditioning and reuse of the Jacobian are employed to accelerate the convergence rate. Implicit boundary conditions were found to be extremely important for fast convergence. Numerical experiments have shown that convergence rates comparable to that of a multigrid, central-difference scheme are achievable on the same mesh. Results are presented for several grids about an ONERA M6 wing.

Numerical solution of the two-dimensional time-dependent incompressible Euler equations

NASA Technical Reports Server (NTRS)

Whitfield, David L.; Taylor, Lafayette K.

1994-01-01

A numerical method is presented for solving the artificial compressibility form of the 2D time-dependent incompressible Euler equations. The approach is based on using an approximate Riemann solver for the cell face numerical flux of a finite volume discretization. Characteristic variable boundary conditions are developed and presented for all boundaries and in-flow out-flow situations. The system of algebraic equations is solved using the discretized Newton-relaxation (DNR) implicit method. Numerical results are presented for both steady and unsteady flow.

Flow solution on a dual-block grid around an airplane

NASA Technical Reports Server (NTRS)

Eriksson, Lars-Erik

1987-01-01

The compressible flow around a complex fighter-aircraft configuration (fuselage, cranked delta wing, canard, and inlet) is simulated numerically using a novel grid scheme and a finite-volume Euler solver. The patched dual-block grid is generated by an algebraic procedure based on transfinite interpolation, and the explicit Runge-Kutta time-stepping Euler solver is implemented with a high degree of vectorization on a Cyber 205 processor. Results are presented in extensive graphs and diagrams and characterized in detail. The concentration of grid points near the wing apex in the present scheme is shown to facilitate capture of the vortex generated by the leading edge at high angles of attack and modeling of its interaction with the canard wake.

A perspective on unstructured grid flow solvers

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.

1995-01-01

This survey paper assesses the status of compressible Euler and Navier-Stokes solvers on unstructured grids. Different spatial and temporal discretization options for steady and unsteady flows are discussed. The integration of these components into an overall framework to solve practical problems is addressed. Issues such as grid adaptation, higher order methods, hybrid discretizations and parallel computing are briefly discussed. Finally, some outstanding issues and future research directions are presented.

Numerical simulation of unsteady rotational flow over propfan configurations

NASA Technical Reports Server (NTRS)

Srivastava, R.; Sankar, L. N.

1989-01-01

The objective is to develop efficient numerical techniques for the study of aeroelastic response of a propfan in an unsteady transonic flow. A three dimensional unsteady Euler solver is being modified to address this problem.

Developing and utilizing an Euler computational method for predicting the airframe/propulsion effects for an aft-mounted turboprop transport. Volume 1: Theory document

NASA Technical Reports Server (NTRS)

Chen, H. C.; Yu, N. Y.

1991-01-01

An Euler flow solver was developed for predicting the airframe/propulsion integration effects for an aft-mounted turboprop transport. This solver employs a highly efficient multigrid scheme, with a successive mesh-refinement procedure to accelerate the convergence of the solution. A new dissipation model was also implemented to render solutions that are grid insensitive. The propeller power effects are simulated by the actuator disk concept. An embedded flow solution method was developed for predicting the detailed flow characteristics in the local vicinity of an aft-mounted propfan engine in the presence of a flow field induced by a complete aircraft. Results from test case analysis are presented. A user's guide for execution of computer programs, including format of various input files, sample job decks, and sample input files, is provided in an accompanying volume.

Numerical Modelling and Prediction of Erosion Induced by Hydrodynamic Cavitation

NASA Astrophysics Data System (ADS)

Peters, A.; Lantermann, U.; el Moctar, O.

2015-12-01

The present work aims to predict cavitation erosion using a numerical flow solver together with a new developed erosion model. The erosion model is based on the hypothesis that collapses of single cavitation bubbles near solid boundaries form high velocity microjets, which cause sonic impacts with high pressure amplitudes damaging the surface. The erosion model uses information from a numerical Euler-Euler flow simulation to predict erosion sensitive areas and assess the erosion aggressiveness of the flow. The obtained numerical results were compared to experimental results from tests of an axisymmetric nozzle.

An Adaptively-Refined, Cartesian, Cell-Based Scheme for the Euler and Navier-Stokes Equations. Ph.D. Thesis - Michigan Univ.

NASA Technical Reports Server (NTRS)

Coirier, William John

1994-01-01

A Cartesian, cell-based scheme for solving the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal 'cut' cells are created. The geometry of the cut cells is computed using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded, with a limited linear reconstruction of the primitive variables used to provide input states to an approximate Riemann solver for computing the fluxes between neighboring cells. A multi-stage time-stepping scheme is used to reach a steady-state solution. Validation of the Euler solver with benchmark numerical and exact solutions is presented. An assessment of the accuracy of the approach is made by uniform and adaptive grid refinements for a steady, transonic, exact solution to the Euler equations. The error of the approach is directly compared to a structured solver formulation. A non smooth flow is also assessed for grid convergence, comparing uniform and adaptively refined results. Several formulations of the viscous terms are assessed analytically, both for accuracy and positivity. The two best formulations are used to compute adaptively refined solutions of the Navier-Stokes equations. These solutions are compared to each other, to experimental results and/or theory for a series of low and moderate Reynolds numbers flow fields. The most suitable viscous discretization is demonstrated for geometrically-complicated internal flows. For flows at high Reynolds numbers, both an altered grid-generation procedure and a different formulation of the viscous terms are shown to be necessary. A hybrid Cartesian/body-fitted grid generation approach is demonstrated. In addition, a grid-generation procedure based on body-aligned cell cutting coupled with a viscous stensil-construction procedure based on quadratic programming is presented.

A Solution Adaptive Structured/Unstructured Overset Grid Flow Solver with Applications to Helicopter Rotor Flows

NASA Technical Reports Server (NTRS)

Duque, Earl P. N.; Biswas, Rupak; Strawn, Roger C.

1995-01-01

This paper summarizes a method that solves both the three dimensional thin-layer Navier-Stokes equations and the Euler equations using overset structured and solution adaptive unstructured grids with applications to helicopter rotor flowfields. The overset structured grids use an implicit finite-difference method to solve the thin-layer Navier-Stokes/Euler equations while the unstructured grid uses an explicit finite-volume method to solve the Euler equations. Solutions on a helicopter rotor in hover show the ability to accurately convect the rotor wake. However, isotropic subdivision of the tetrahedral mesh rapidly increases the overall problem size.

Researched applied to transonic compressors in numerical fluid mechanics of inviscid flow and viscous flow

NASA Technical Reports Server (NTRS)

Thompkins, W. T., Jr.

1985-01-01

A streamline Euler solver which combines high accuracy and good convergence rates with capabilities for inverse or direct mode solution modes and an analysis technique for finite difference models of hyperbolic partial difference equations were developed.

Domain modeling and grid generation for multi-block structured grids with application to aerodynamic and hydrodynamic configurations

NASA Technical Reports Server (NTRS)

Spekreijse, S. P.; Boerstoel, J. W.; Vitagliano, P. L.; Kuyvenhoven, J. L.

1992-01-01

About five years ago, a joint development was started of a flow simulation system for engine-airframe integration studies on propeller as well as jet aircraft. The initial system was based on the Euler equations and made operational for industrial aerodynamic design work. The system consists of three major components: a domain modeller, for the graphical interactive subdivision of flow domains into an unstructured collection of blocks; a grid generator, for the graphical interactive computation of structured grids in blocks; and a flow solver, for the computation of flows on multi-block grids. The industrial partners of the collaboration and NLR have demonstrated that the domain modeller, grid generator and flow solver can be applied to simulate Euler flows around complete aircraft, including propulsion system simulation. Extension to Navier-Stokes flows is in progress. Delft Hydraulics has shown that both the domain modeller and grid generator can also be applied successfully for hydrodynamic configurations. An overview is given about the main aspects of both domain modelling and grid generation.

On unstructured grids and solvers

NASA Technical Reports Server (NTRS)

Barth, T. J.

1990-01-01

The fundamentals and the state-of-the-art technology for unstructured grids and solvers are highlighted. Algorithms and techniques pertinent to mesh generation are discussed. It is shown that grid generation and grid manipulation schemes rely on fast multidimensional searching. Flow solution techniques for the Euler equations, which can be derived from the integral form of the equations are discussed. Sample calculations are also provided.

Blade design and analysis using a modified Euler solver

NASA Technical Reports Server (NTRS)

Leonard, O.; Vandenbraembussche, R. A.

1991-01-01

An iterative method for blade design based on Euler solver and described in an earlier paper is used to design compressor and turbine blades providing shock free transonic flows. The method shows a rapid convergence, and indicates how much the flow is sensitive to small modifications of the blade geometry, that the classical iterative use of analysis methods might not be able to define. The relationship between the required Mach number distribution and the resulting geometry is discussed. Examples show how geometrical constraints imposed upon the blade shape can be respected by using free geometrical parameters or by relaxing the required Mach number distribution. The same code is used both for the design of the required geometry and for the off-design calculations. Examples illustrate the difficulty of designing blade shapes with optimal performance also outside of the design point.

Quality assessment of two- and three-dimensional unstructured meshes and validation of an upwind Euler flow solver

NASA Technical Reports Server (NTRS)

Woodard, Paul R.; Batina, John T.; Yang, Henry T. Y.

1992-01-01

Quality assessment procedures are described for two-dimensional unstructured meshes. The procedures include measurement of minimum angles, element aspect ratios, stretching, and element skewness. Meshes about the ONERA M6 wing and the Boeing 747 transport configuration are generated using an advancing front method grid generation package of programs. Solutions of Euler's equations for these meshes are obtained at low angle-of-attack, transonic conditions. Results for these cases, obtained as part of a validation study demonstrate accuracy of an implicit upwind Euler solution algorithm.

Conical Euler simulation and active suppression of delta wing rocking motion

NASA Technical Reports Server (NTRS)

Lee, Elizabeth M.; Batina, John T.

1990-01-01

A conical Euler code was developed to study unsteady vortex-dominated flows about rolling highly-swept delta wings, undergoing either forced or free-to-roll motions including active roll suppression. The flow solver of the code involves a multistage Runge-Kutta time-stepping scheme which uses a finite volume spatial discretization of the Euler equations on an unstructured grid of triangles. The code allows for the additional analysis of the free-to-roll case, by including the rigid-body equation of motion for its simultaneous time integration with the governing flow equations. Results are presented for a 75 deg swept sharp leading edge delta wing at a freestream Mach number of 1.2 and at alpha equal to 10 and 30 deg angle of attack. A forced harmonic analysis indicates that the rolling moment coefficient provides: (1) a positive damping at the lower angle of attack equal to 10 deg, which is verified in a free-to-roll calculation; (2) a negative damping at the higher angle of attack equal to 30 deg at the small roll amplitudes. A free-to-roll calculation for the latter case produces an initially divergent response, but as the amplitude of motion grows with time, the response transitions to a wing-rock type of limit cycle oscillation. The wing rocking motion may be actively suppressed, however, through the use of a rate-feedback control law and antisymmetrically deflected leading edge flaps. The descriptions of the conical Euler flow solver and the free-to-roll analysis are presented. Results are also presented which give insight into the flow physics associated with unsteady vortical flows about forced and free-to-roll delta wings, including the active roll suppression of this wing-rock phenomenon.

Conjugate Compressible Fluid Flow and Heat Transfer in Ducts

NASA Technical Reports Server (NTRS)

Cross, M. F.

2011-01-01

A computational approach to modeling transient, compressible fluid flow with heat transfer in long, narrow ducts is presented. The primary application of the model is for analyzing fluid flow and heat transfer in solid propellant rocket motor nozzle joints during motor start-up, but the approach is relevant to a wide range of analyses involving rapid pressurization and filling of ducts. Fluid flow is modeled through solution of the spatially one-dimensional, transient Euler equations. Source terms are included in the governing equations to account for the effects of wall friction and heat transfer. The equation solver is fully-implicit, thus providing greater flexibility than an explicit solver. This approach allows for resolution of pressure wave effects on the flow as well as for fast calculation of the steady-state solution when a quasi-steady approach is sufficient. Solution of the one-dimensional Euler equations with source terms significantly reduces computational run times compared to general purpose computational fluid dynamics packages solving the Navier-Stokes equations with resolved boundary layers. In addition, conjugate heat transfer is more readily implemented using the approach described in this paper than with most general purpose computational fluid dynamics packages. The compressible flow code has been integrated with a transient heat transfer solver to analyze heat transfer between the fluid and surrounding structure. Conjugate fluid flow and heat transfer solutions are presented. The author is unaware of any previous work available in the open literature which uses the same approach described in this paper.

A new stream function formulation for the Euler equations

NASA Technical Reports Server (NTRS)

Atkins, H. L.; Hassan, H. A.

1983-01-01

A new stream function formulation is developed for the solution of Euler's equations in the transonic flow region. The stream function and the density are the dependent variables in this method, while the governing equations for adiabatic flow are the momentum equations which are solved in the strong conservation law form. The application of this method does not require a knowledge of the vorticity. The algorithm is combined with the automatic grid solver (GRAPE) of Steger and Sorenson (1979) in order to study arbitrary geometries. Results of the application of this method are presented for the NACA 0012 airfoil at various Mach numbers and angles of attack, and cylinders. In addition, detailed comparisons are made with other solutions of the Euler equations.

Extension of lattice Boltzmann flux solver for simulation of compressible multi-component flows

NASA Astrophysics Data System (ADS)

Yang, Li-Ming; Shu, Chang; Yang, Wen-Ming; Wang, Yan

2018-05-01

The lattice Boltzmann flux solver (LBFS), which was presented by Shu and his coworkers for solving compressible fluid flow problems, is extended to simulate compressible multi-component flows in this work. To solve the two-phase gas-liquid problems, the model equations with stiffened gas equation of state are adopted. In this model, two additional non-conservative equations are introduced to represent the material interfaces, apart from the classical Euler equations. We first convert the interface equations into the full conservative form by applying the mass equation. After that, we calculate the numerical fluxes of the classical Euler equations by the existing LBFS and the numerical fluxes of the interface equations by the passive scalar approach. Once all the numerical fluxes at the cell interface are obtained, the conservative variables at cell centers can be updated by marching the equations in time and the material interfaces can be identified via the distributions of the additional variables. The numerical accuracy and stability of present scheme are validated by its application to several compressible multi-component fluid flow problems.

Quality assessment of two- and three-dimensional unstructured meshes and validation of an upwind Euler flow solver

NASA Technical Reports Server (NTRS)

Woodard, Paul R.; Yang, Henry T. Y.; Batina, John T.

1992-01-01

Quality assessment procedures are described for two-dimensional and three-dimensional unstructured meshes. The procedures include measurement of minimum angles, element aspect ratios, stretching, and element skewness. Meshes about the ONERA M6 wing and the Boeing 747 transport configuration are generated using an advancing front method grid generation package of programs. Solutions of Euler's equations for these meshes are obtained at low angle-of-attack, transonic conditions. Results for these cases, obtained as part of a validation study demonstrate the accuracy of an implicit upwind Euler solution algorithm.

Development of a Chemically Reacting Flow Solver on the Graphic Processing Units

DTIC Science & Technology

2011-05-10

been implemented on the GPU by Schive et al. (2010). The outcome of their work is the GAMER code for astrophysical simulation. Thibault and...Euler equations at each cell. For simplification, consider the Euler equations in one dimension with no source terms; the discretized form of the...is known to be more diffusive than the other fluxes due to the large bound of the numerical signal velocities: b+, b-. 3.4 Time Marching Methods

Solution algorithms for the two-dimensional Euler equations on unstructured meshes

NASA Technical Reports Server (NTRS)

Whitaker, D. L.; Slack, David C.; Walters, Robert W.

1990-01-01

The objective of the study was to analyze implicit techniques employed in structured grid algorithms for solving two-dimensional Euler equations and extend them to unstructured solvers in order to accelerate convergence rates. A comparison is made between nine different algorithms for both first-order and second-order accurate solutions. Higher-order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The discussion is illustrated by results for flow over a transonic circular arc.

Conical Euler analysis and active roll suppression for unsteady vortical flows about rolling delta wings

NASA Technical Reports Server (NTRS)

Lee-Rausch, Elizabeth M.; Batina, John T.

1993-01-01

A conical Euler code was developed to study unsteady vortex-dominated flows about rolling, highly swept delta wings undergoing either forced motions or free-to-roll motions that include active roll suppression. The flow solver of the code involves a multistage, Runge-Kutta time-stepping scheme that uses a cell-centered, finite-volume, spatial discretization of the Euler equations on an unstructured grid of triangles. The code allows for the additional analysis of the free to-roll case by simultaneously integrating in time the rigid-body equation of motion with the governing flow equations. Results are presented for a delta wing with a 75 deg swept, sharp leading edge at a free-stream Mach number of 1.2 and at 10 deg, 20 deg, and 30 deg angle of attack alpha. At the lower angles of attack (10 and 20 deg), forced-harmonic analyses indicate that the rolling-moment coefficients provide a positive damping, which is verified by free-to-roll calculations. In contrast, at the higher angle of attack (30 deg), a forced-harmonic analysis indicates that the rolling-moment coefficient provides negative damping at the small roll amplitudes. A free-to-roll calculation for this case produces an initially divergent response, but as the amplitude of motion grows with time, the response transitions to a wing-rock type of limit cycle oscillation, which is characteristic of highly swept delta wings. This limit cycle oscillation may be actively suppressed through the use of a rate-feedback control law and antisymmetrically deflected leading-edge flaps. Descriptions of the conical Euler flow solver and the free-to roll analysis are included in this report. Results are presented that demonstrate how the systematic analysis of the forced response of the delta wing can be used to predict the stable, neutrally stable, and unstable free response of the delta wing. These results also give insight into the flow physics associated with unsteady vortical flows about delta wings undergoing forced motions and free-to-roll motions, including the active suppression of the wing-rock type phenomenon. The conical Euler methodology developed is directly extend able to three-dimensional calculations.

Sonic Boom Prediction and Minimization of the Douglas Reference OPT5 Configuration

NASA Technical Reports Server (NTRS)

Siclari, Michael J.

1999-01-01

Conventional CFD methods and grids do not yield adequate resolution of the complex shock flow pattern generated by a real aircraft geometry. As a result, a unique grid topology and supersonic flow solver was developed at Northrop Grumman based on the characteristic behavior of supersonic wave patterns emanating from the aircraft. Using this approach, it was possible to compute flow fields with adequate resolution several body lengths below the aircraft. In this region, three-dimensional effects are diminished and conventional two-dimensional modified linear theory (MLT) can be applied to estimate ground pressure signatures or sonic booms. To accommodate real aircraft geometries and alleviate the burdensome grid generation task, an implicit marching multi-block, multi-grid finite-volume Euler code was developed as the basis for the sonic boom prediction methodology. The Thomas two-dimensional extrapolation method is built into the Euler code so that ground signatures can be obtained quickly and efficiently with minimum computational effort suitable to the aircraft design environment. The loudness levels of these signatures can then be determined using a NASA generated noise code. Since the Euler code is a three-dimensional flow field solver, the complete circumferential region below the aircraft is computed. The extrapolation of all this field data from a cylinder of constant radius leads to the definition of the entire boom corridor occurring directly below and off to the side of the aircraft's flight path yielding an estimate for the entire noise "annoyance" corridor in miles as well as its magnitude. An automated multidisciplinary sonic boom design optimization software system was developed during the latter part of HSR Phase 1. Using this system, it was found that sonic boom signatures could be reduced through optimization of a variety of geometric aircraft parameters. This system uses a gradient based nonlinear optimizer as the driver in conjunction with a computationally efficient Euler CFD solver (NIIM3DSB) for computing the three-dimensional near-field characteristics of the aircraft. The intent of the design system is to identify and optimize geometric design variables that have a beneficial impact on the ground sonic boom. The system uses a simple wave drag data format to specify the aircraft geometry. The geometry is internally enhanced and analytic methods are used to generate marching grids suitable for the multi-block Euler solver. The Thomas extrapolation method is integrated into this system, and hence, the aircraft's centerline ground sonic boom signature is also automatically computed for a specified cruise altitude and yields the parameters necessary to evaluate the design function. The entire design system has been automated since the gradient based optimization software requires many flow analyses in order to obtain the required sensitivity derivatives for each design variable in order to converge on an optimal solution. Hence, once the problem is defined which includes defining the objective function and geometric and aerodynamic constraints, the system will automatically regenerate the perturbed geometry, the necessary grids, the Euler solution, and finally the ground sonic boom signature at the request of the optimizer.

A multiblock multigrid three-dimensional Euler equation solver

NASA Technical Reports Server (NTRS)

Cannizzaro, Frank E.; Elmiligui, Alaa; Melson, N. Duane; Vonlavante, E.

1990-01-01

Current aerodynamic designs are often quite complex (geometrically). Flexible computational tools are needed for the analysis of a wide range of configurations with both internal and external flows. In the past, geometrically dissimilar configurations required different analysis codes with different grid topologies in each. The duplicity of codes can be avoided with the use of a general multiblock formulation which can handle any grid topology. Rather than hard wiring the grid topology into the program, it is instead dictated by input to the program. In this work, the compressible Euler equations, written in a body-fitted finite-volume formulation, are solved using a pseudo-time-marching approach. Two upwind methods (van Leer's flux-vector-splitting and Roe's flux-differencing) were investigated. Two types of explicit solvers (a two-step predictor-corrector and a modified multistage Runge-Kutta) were used with multigrid acceleration to enhance convergence. A multiblock strategy is used to allow greater geometric flexibility. A report on simple explicit upwind schemes for solving compressible flows is included.

A New Approximate Chimera Donor Cell Search Algorithm

NASA Technical Reports Server (NTRS)

Holst, Terry L.; Nixon, David (Technical Monitor)

1998-01-01

The objectives of this study were to develop chimera-based full potential methodology which is compatible with overflow (Euler/Navier-Stokes) chimera flow solver and to develop a fast donor cell search algorithm that is compatible with the chimera full potential approach. Results of this work included presenting a new donor cell search algorithm suitable for use with a chimera-based full potential solver. This algorithm was found to be extremely fast and simple producing donor cells as fast as 60,000 per second.

On modeling heterogeneous coastal sediment transport - A numerical study using multiphase Eulerian and Euler-Lagrangian approaches

NASA Astrophysics Data System (ADS)

Cheng, Z.; Yu, X.; Hsu, T. J.; Calantoni, J.; Chauchat, J.

2016-02-01

Regional scale coastal evolution models do not explicitly resolve wave-driven sediment transport and must rely on bedload/suspended modules that utilize empirical assumptions. Under extreme wave events or in regions of high sediment heterogeneity, these empirical bedload/suspended load modules may need to be reevaluated with detailed observation and more sophisticated small-scale models. In the past decade, significant research efforts have been devoted to modeling sediment transport using multiphase Eulerian or Euler-Lagrangian approaches. Recently, an open-source multi-dimensional Reynolds-averaged two-phase sediment transport model, SedFOAM is developed by the authors and it has been adopted by many researchers to study momentary bed failure, granular rheology in sheet flow and scour around structures. In this abstract, we further report our recent progress made in extending the model with 3D turbulence-resolving capability and to model the sediment phase with the Discrete Element method (DEM). Adopting the large-eddy simulation methodology, we validate the 3D model with measured fine sediment transport is oscillatory sheet flow and demonstrate that the model is able to resolve sediment burst events during flow reversals. To better resolve the intergranular interactions and to model heterogeneous properties of sediment (e.g., mixed grain sizes and grain shape), we use an Euler-Lagrangian solver called CFDEM, which couples OpenFOAM for the fluid phase and LIGGGHTS for the particle phase. We improve the model by better enforcing conservation of mass in the pressure solver. The modified CFDEM solver is validated with measured oscillatory sheet flow data for coarse sand and we demonstrated that the model can reproduce the well-known armoring effects. We show that under Stokes second-order wave forcing, the armoring effect is more significant during the energetic positive peak, and hence the net onshore transport is reduced. Preliminary results modeling the shape effects using composite particles will be presented. This research is supported by Office of Naval Research and National Science Foundation.

Some Approaches Towards Constructing Optimally Efficient Multigrid Solvers for the Inviscid Flow Equations

NASA Technical Reports Server (NTRS)

Sidilkover, David

1997-01-01

Some important advances took place during the last several years in the development of genuinely multidimensional upwind schemes for the compressible Euler equations. In particular, a robust, high-resolution genuinely multidimensional scheme which can be used for any of the flow regimes computations was constructed. This paper summarizes briefly these developments and outlines the fundamental advantages of this approach.

Prediction of Undsteady Flows in Turbomachinery Using the Linearized Euler Equations on Deforming Grids

NASA Technical Reports Server (NTRS)

Clark, William S.; Hall, Kenneth C.

1994-01-01

A linearized Euler solver for calculating unsteady flows in turbomachinery blade rows due to both incident gusts and blade motion is presented. The model accounts for blade loading, blade geometry, shock motion, and wake motion. Assuming that the unsteadiness in the flow is small relative to the nonlinear mean solution, the unsteady Euler equations can be linearized about the mean flow. This yields a set of linear variable coefficient equations that describe the small amplitude harmonic motion of the fluid. These linear equations are then discretized on a computational grid and solved using standard numerical techniques. For transonic flows, however, one must use a linear discretization which is a conservative linearization of the non-linear discretized Euler equations to ensure that shock impulse loads are accurately captured. Other important features of this analysis include a continuously deforming grid which eliminates extrapolation errors and hence, increases accuracy, and a new numerically exact, nonreflecting far-field boundary condition treatment based on an eigenanalysis of the discretized equations. Computational results are presented which demonstrate the computational accuracy and efficiency of the method and demonstrate the effectiveness of the deforming grid, far-field nonreflecting boundary conditions, and shock capturing techniques. A comparison of the present unsteady flow predictions to other numerical, semi-analytical, and experimental methods shows excellent agreement. In addition, the linearized Euler method presented requires one or two orders-of-magnitude less computational time than traditional time marching techniques making the present method a viable design tool for aeroelastic analyses.

An upwind, kinetic flux-vector splitting method for flows in chemical and thermal non-equilibrium

NASA Technical Reports Server (NTRS)

Eppard, W. M.; Grossman, B.

1993-01-01

We have developed new upwind kinetic difference schemes for flows with non-equilibrium thermodynamics and chemistry. These schemes are derived from the Boltzmann equation with the resulting Euler schemes developed as moments of the discretized Boltzmann scheme with a locally Maxwellian velocity distribution. Splitting the velocity distribution at the Boltzmann level is seen to result in a flux-split Euler scheme and is called Kinetic Flux Vector Splitting (KFVS). Extensions to flows with finite-rate chemistry and vibrational relaxation is accomplished utilizing nonequilibrium kinetic theory. Computational examples are presented comparing KFVS with the schemes of Van Leer and Roe for a quasi-one-dimensional flow through a supersonic diffuser, inviscid flow through two-dimensional inlet, and viscous flow over a cone at zero angle-of-attack. Calculations are also shown for the transonic flow over a bump in a channel and the transonic flow over an NACA 0012 airfoil. The results show that even though the KFVS scheme is a Riemann solver at the kinetic level, its behavior at the Euler level is more similar to the existing flux-vector splitting algorithms than to the flux-difference splitting scheme of Roe.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mendenhall, M.R.

The present volume discusses tactical missile aerodynamic drag, drag-prediction methods for axisymmetric missile bodies, an aerodynamic heating analysis for supersonic missiles, a component buildup method for engineering analysis of missiles at low-to-high angles of attack, experimental and analytical methods for missiles with noncircular fuselages, and a vortex-cloud model for body vortex shedding and tracking. Also discussed are panel methods with vorticity effects and corrections for nonlinear compressibility, supersonic full-potential methods for missile body analysis, space-marching Euler solvers, the time-asymptotic Euler/Navier-Stokes methods for subsonic and transonic flows, 3D boundary layers on missiles, Navier-Stokes analyses of flows over slender airframes, and themore » interaction of exhaust plumes with missile airframes.« less

Euler-euler anisotropic gaussian mesoscale simulation of homogeneous cluster-induced gas-particle turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kong, Bo; Fox, Rodney O.; Feng, Heng

An Euler–Euler anisotropic Gaussian approach (EE-AG) for simulating gas–particle flows, in which particle velocities are assumed to follow a multivariate anisotropic Gaussian distribution, is used to perform mesoscale simulations of homogeneous cluster-induced turbulence (CIT). A three-dimensional Gauss–Hermite quadrature formulation is used to calculate the kinetic flux for 10 velocity moments in a finite-volume framework. The particle-phase volume-fraction and momentum equations are coupled with the Eulerian solver for the gas phase. This approach is implemented in an open-source CFD package, OpenFOAM, and detailed simulation results are compared with previous Euler–Lagrange simulations in a domain size study of CIT. Here, these resultsmore » demonstrate that the proposed EE-AG methodology is able to produce comparable results to EL simulations, and this moment-based methodology can be used to perform accurate mesoscale simulations of dilute gas–particle flows.« less

Euler-euler anisotropic gaussian mesoscale simulation of homogeneous cluster-induced gas-particle turbulence

DOE PAGES

Kong, Bo; Fox, Rodney O.; Feng, Heng; ...

2017-02-16

An Euler–Euler anisotropic Gaussian approach (EE-AG) for simulating gas–particle flows, in which particle velocities are assumed to follow a multivariate anisotropic Gaussian distribution, is used to perform mesoscale simulations of homogeneous cluster-induced turbulence (CIT). A three-dimensional Gauss–Hermite quadrature formulation is used to calculate the kinetic flux for 10 velocity moments in a finite-volume framework. The particle-phase volume-fraction and momentum equations are coupled with the Eulerian solver for the gas phase. This approach is implemented in an open-source CFD package, OpenFOAM, and detailed simulation results are compared with previous Euler–Lagrange simulations in a domain size study of CIT. Here, these resultsmore » demonstrate that the proposed EE-AG methodology is able to produce comparable results to EL simulations, and this moment-based methodology can be used to perform accurate mesoscale simulations of dilute gas–particle flows.« less

Conical Euler solution for a highly-swept delta wing undergoing wing-rock motion

NASA Technical Reports Server (NTRS)

Lee, Elizabeth M.; Batina, John T.

1990-01-01

Modifications to an unsteady conical Euler code for the free-to-roll analysis of highly-swept delta wings are described. The modifications involve the addition of the rolling rigid-body equation of motion for its simultaneous time-integration with the governing flow equations. The flow solver utilized in the Euler code includes a multistage Runge-Kutta time-stepping scheme which uses a finite-volume spatial discretization on an unstructured mesh made up of triangles. Steady and unsteady results are presented for a 75 deg swept delta wing at a freestream Mach number of 1.2 and an angle of attack of 30 deg. The unsteady results consist of forced harmonic and free-to-roll calculations. The free-to-roll case exhibits a wing rock response produced by unsteady aerodynamics consistent with the aerodynamics of the forced harmonic results. Similarities are shown with a wing-rock time history from a low-speed wind tunnel test.

On the eddy-resolving capability of high-order discontinuous Galerkin approaches to implicit LES / under-resolved DNS of Euler turbulence

NASA Astrophysics Data System (ADS)

Moura, R. C.; Mengaldo, G.; Peiró, J.; Sherwin, S. J.

2017-02-01

We present estimates of spectral resolution power for under-resolved turbulent Euler flows obtained with high-order discontinuous Galerkin (DG) methods. The '1% rule' based on linear dispersion-diffusion analysis introduced by Moura et al. (2015) [10] is here adapted for 3D energy spectra and validated through the inviscid Taylor-Green vortex problem. The 1% rule estimates the wavenumber beyond which numerical diffusion induces an artificial dissipation range on measured energy spectra. As the original rule relies on standard upwinding, different Riemann solvers are tested. Very good agreement is found for solvers which treat the different physical waves in a consistent manner. Relatively good agreement is still found for simpler solvers. The latter however displayed spurious features attributed to the inconsistent treatment of different physical waves. It is argued that, in the limit of vanishing viscosity, such features might have a significant impact on robustness and solution quality. The estimates proposed are regarded as useful guidelines for no-model DG-based simulations of free turbulence at very high Reynolds numbers.

Comments regarding two upwind methods for solving two-dimensional external flows using unstructured grids

NASA Technical Reports Server (NTRS)

Kleb, W. L.

1994-01-01

Steady flow over the leading portion of a multicomponent airfoil section is studied using computational fluid dynamics (CFD) employing an unstructured grid. To simplify the problem, only the inviscid terms are retained from the Reynolds-averaged Navier-Stokes equations - leaving the Euler equations. The algorithm is derived using the finite-volume approach, incorporating explicit time-marching of the unsteady Euler equations to a time-asymptotic, steady-state solution. The inviscid fluxes are obtained through either of two approximate Riemann solvers: Roe's flux difference splitting or van Leer's flux vector splitting. Results are presented which contrast the solutions given by the two flux functions as a function of Mach number and grid resolution. Additional information is presented concerning code verification techniques, flow recirculation regions, convergence histories, and computational resources.

Parallel computational fluid dynamics '91; Conference Proceedings, Stuttgart, Germany, Jun. 10-12, 1991

NASA Technical Reports Server (NTRS)

Reinsch, K. G. (Editor); Schmidt, W. (Editor); Ecer, A. (Editor); Haeuser, Jochem (Editor); Periaux, J. (Editor)

1992-01-01

A conference was held on parallel computational fluid dynamics and produced related papers. Topics discussed in these papers include: parallel implicit and explicit solvers for compressible flow, parallel computational techniques for Euler and Navier-Stokes equations, grid generation techniques for parallel computers, and aerodynamic simulation om massively parallel systems.

SedFoam-2.0: a 3-D two-phase flow numerical model for sediment transport

NASA Astrophysics Data System (ADS)

Chauchat, Julien; Cheng, Zhen; Nagel, Tim; Bonamy, Cyrille; Hsu, Tian-Jian

2017-11-01

In this paper, a three-dimensional two-phase flow solver, SedFoam-2.0, is presented for sediment transport applications. The solver is extended from twoPhaseEulerFoam available in the 2.1.0 release of the open-source CFD (computational fluid dynamics) toolbox OpenFOAM. In this approach the sediment phase is modeled as a continuum, and constitutive laws have to be prescribed for the sediment stresses. In the proposed solver, two different intergranular stress models are implemented: the kinetic theory of granular flows and the dense granular flow rheology μ(I). For the fluid stress, laminar or turbulent flow regimes can be simulated and three different turbulence models are available for sediment transport: a simple mixing length model (one-dimensional configuration only), a k - ɛ, and a k - ω model. The numerical implementation is demonstrated on four test cases: sedimentation of suspended particles, laminar bed load, sheet flow, and scour at an apron. These test cases illustrate the capabilities of SedFoam-2.0 to deal with complex turbulent sediment transport problems with different combinations of intergranular stress and turbulence models.

A three-dimensional application with the numerical grid generation code: EAGLE (utilizing an externally generated surface)

NASA Technical Reports Server (NTRS)

Houston, Johnny L.

1990-01-01

Program EAGLE (Eglin Arbitrary Geometry Implicit Euler) is a multiblock grid generation and steady-state flow solver system. This system combines a boundary conforming surface generation, a composite block structure grid generation scheme, and a multiblock implicit Euler flow solver algorithm. The three codes are intended to be used sequentially from the definition of the configuration under study to the flow solution about the configuration. EAGLE was specifically designed to aid in the analysis of both freestream and interference flow field configurations. These configurations can be comprised of single or multiple bodies ranging from simple axisymmetric airframes to complex aircraft shapes with external weapons. Each body can be arbitrarily shaped with or without multiple lifting surfaces. Program EAGLE is written to compile and execute efficiently on any CRAY machine with or without Solid State Disk (SSD) devices. Also, the code uses namelist inputs which are supported by all CRAY machines using the FORTRAN Compiler CF177. The use of namelist inputs makes it easier for the user to understand the inputs and to operate Program EAGLE. Recently, the Code was modified to operate on other computers, especially the Sun Spare4 Workstation. Several two-dimensional grid configurations were completely and successfully developed using EAGLE. Currently, EAGLE is being used for three-dimension grid applications.

Time integration algorithms for the two-dimensional Euler equations on unstructured meshes

NASA Technical Reports Server (NTRS)

Slack, David C.; Whitaker, D. L.; Walters, Robert W.

1994-01-01

Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.

One-dimensional high-order compact method for solving Euler's equations

NASA Astrophysics Data System (ADS)

Mohamad, M. A. H.; Basri, S.; Basuno, B.

2012-06-01

In the field of computational fluid dynamics, many numerical algorithms have been developed to simulate inviscid, compressible flows problems. Among those most famous and relevant are based on flux vector splitting and Godunov-type schemes. Previously, this system was developed through computational studies by Mawlood [1]. However the new test cases for compressible flows, the shock tube problems namely the receding flow and shock waves were not investigated before by Mawlood [1]. Thus, the objective of this study is to develop a high-order compact (HOC) finite difference solver for onedimensional Euler equation. Before developing the solver, a detailed investigation was conducted to assess the performance of the basic third-order compact central discretization schemes. Spatial discretization of the Euler equation is based on flux-vector splitting. From this observation, discretization of the convective flux terms of the Euler equation is based on a hybrid flux-vector splitting, known as the advection upstream splitting method (AUSM) scheme which combines the accuracy of flux-difference splitting and the robustness of flux-vector splitting. The AUSM scheme is based on the third-order compact scheme to the approximate finite difference equation was completely analyzed consequently. In one-dimensional problem for the first order schemes, an explicit method is adopted by using time integration method. In addition to that, development and modification of source code for the one-dimensional flow is validated with four test cases namely, unsteady shock tube, quasi-one-dimensional supersonic-subsonic nozzle flow, receding flow and shock waves in shock tubes. From these results, it was also carried out to ensure that the definition of Riemann problem can be identified. Further analysis had also been done in comparing the characteristic of AUSM scheme against experimental results, obtained from previous works and also comparative analysis with computational results generated by van Leer, KFVS and AUSMPW schemes. Furthermore, there is a remarkable improvement with the extension of the AUSM scheme from first-order to third-order accuracy in terms of shocks, contact discontinuities and rarefaction waves.

The block adaptive multigrid method applied to the solution of the Euler equations

NASA Technical Reports Server (NTRS)

Pantelelis, Nikos

1993-01-01

In the present study, a scheme capable of solving very fast and robust complex nonlinear systems of equations is presented. The Block Adaptive Multigrid (BAM) solution method offers multigrid acceleration and adaptive grid refinement based on the prediction of the solution error. The proposed solution method was used with an implicit upwind Euler solver for the solution of complex transonic flows around airfoils. Very fast results were obtained (18-fold acceleration of the solution) using one fourth of the volumes of a global grid with the same solution accuracy for two test cases.

Inverse design of centrifugal compressor vaned diffusers in inlet shear flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zangeneh, M.

1996-04-01

A three-dimensional inverse design method in which the blade (or vane) geometry is designed for specified distributions of circulation and blade thickness is applied to the design of centrifugal compressor vaned diffusers. Two generic diffusers are designed, one with uniform inlet flow (equivalent to a conventional design) and the other with a sheared inlet flow. The inlet shear flow effects are modeled in the design method by using the so-called ``Secondary Flow Approximation`` in which the Bernoulli surfaces are convected by the tangentially mean inviscid flow field. The difference between the vane geometry of the uniform inlet flow and nonuniformmore » inlet flow diffusers is found to be most significant from 50 percent chord to the trailing edge region. The flows through both diffusers are computed by using Denton`s three-dimensional inviscid Euler solver and Dawes` three-dimensional Navier-Stokes solver under sheared in-flow conditions. The predictions indicate improved pressure recovery and internal flow field for the diffuser designed for shear inlet flow conditions.« less

A Lagrangian meshfree method applied to linear and nonlinear elasticity.

PubMed

Walker, Wade A

2017-01-01

The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code.

A Lagrangian meshfree method applied to linear and nonlinear elasticity

PubMed Central

2017-01-01

The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code. PMID:29045443

A higher-order conservation element solution element method for solving hyperbolic differential equations on unstructured meshes

NASA Astrophysics Data System (ADS)

Bilyeu, David

This dissertation presents an extension of the Conservation Element Solution Element (CESE) method from second- to higher-order accuracy. The new method retains the favorable characteristics of the original second-order CESE scheme, including (i) the use of the space-time integral equation for conservation laws, (ii) a compact mesh stencil, (iii) the scheme will remain stable up to a CFL number of unity, (iv) a fully explicit, time-marching integration scheme, (v) true multidimensionality without using directional splitting, and (vi) the ability to handle two- and three-dimensional geometries by using unstructured meshes. This algorithm has been thoroughly tested in one, two and three spatial dimensions and has been shown to obtain the desired order of accuracy for solving both linear and non-linear hyperbolic partial differential equations. The scheme has also shown its ability to accurately resolve discontinuities in the solutions. Higher order unstructured methods such as the Discontinuous Galerkin (DG) method and the Spectral Volume (SV) methods have been developed for one-, two- and three-dimensional application. Although these schemes have seen extensive development and use, certain drawbacks of these methods have been well documented. For example, the explicit versions of these two methods have very stringent stability criteria. This stability criteria requires that the time step be reduced as the order of the solver increases, for a given simulation on a given mesh. The research presented in this dissertation builds upon the work of Chang, who developed a fourth-order CESE scheme to solve a scalar one-dimensional hyperbolic partial differential equation. The completed research has resulted in two key deliverables. The first is a detailed derivation of a high-order CESE methods on unstructured meshes for solving the conservation laws in two- and three-dimensional spaces. The second is the code implementation of these numerical methods in a computer code. For code development, a one-dimensional solver for the Euler equations was developed. This work is an extension of Chang's work on the fourth-order CESE method for solving a one-dimensional scalar convection equation. A generic formulation for the nth-order CESE method, where n ≥ 4, was derived. Indeed, numerical implementation of the scheme confirmed that the order of convergence was consistent with the order of the scheme. For the two- and three-dimensional solvers, SOLVCON was used as the basic framework for code implementation. A new solver kernel for the fourth-order CESE method has been developed and integrated into the framework provided by SOLVCON. The main part of SOLVCON, which deals with unstructured meshes and parallel computing, remains intact. The SOLVCON code for data transmission between computer nodes for High Performance Computing (HPC). To validate and verify the newly developed high-order CESE algorithms, several one-, two- and three-dimensional simulations where conducted. For the arbitrary order, one-dimensional, CESE solver, three sets of governing equations were selected for simulation: (i) the linear convection equation, (ii) the linear acoustic equations, (iii) the nonlinear Euler equations. All three systems of equations were used to verify the order of convergence through mesh refinement. In addition the Euler equations were used to solve the Shu-Osher and Blastwave problems. These two simulations demonstrated that the new high-order CESE methods can accurately resolve discontinuities in the flow field.For the two-dimensional, fourth-order CESE solver, the Euler equation was employed in four different test cases. The first case was used to verify the order of convergence through mesh refinement. The next three cases demonstrated the ability of the new solver to accurately resolve discontinuities in the flows. This was demonstrated through: (i) the interaction between acoustic waves and an entropy pulse, (ii) supersonic flow over a circular blunt body, (iii) supersonic flow over a guttered wedge. To validate and verify the three-dimensional, fourth-order CESE solver, two different simulations where selected. The first used the linear convection equations to demonstrate fourth-order convergence. The second used the Euler equations to simulate supersonic flow over a spherical body to demonstrate the scheme's ability to accurately resolve shocks. All test cases used are well known benchmark problems and as such, there are multiple sources available to validate the numerical results. Furthermore, the simulations showed that the high-order CESE solver was stable at a CFL number near unity.

Implementation of a parallel unstructured Euler solver on shared and distributed memory architectures

NASA Technical Reports Server (NTRS)

Mavriplis, D. J.; Das, Raja; Saltz, Joel; Vermeland, R. E.

1992-01-01

An efficient three dimensional unstructured Euler solver is parallelized on a Cray Y-MP C90 shared memory computer and on an Intel Touchstone Delta distributed memory computer. This paper relates the experiences gained and describes the software tools and hardware used in this study. Performance comparisons between two differing architectures are made.

Verification and Validation Studies for the LAVA CFD Solver

NASA Technical Reports Server (NTRS)

Moini-Yekta, Shayan; Barad, Michael F; Sozer, Emre; Brehm, Christoph; Housman, Jeffrey A.; Kiris, Cetin C.

2013-01-01

The verification and validation of the Launch Ascent and Vehicle Aerodynamics (LAVA) computational fluid dynamics (CFD) solver is presented. A modern strategy for verification and validation is described incorporating verification tests, validation benchmarks, continuous integration and version control methods for automated testing in a collaborative development environment. The purpose of the approach is to integrate the verification and validation process into the development of the solver and improve productivity. This paper uses the Method of Manufactured Solutions (MMS) for the verification of 2D Euler equations, 3D Navier-Stokes equations as well as turbulence models. A method for systematic refinement of unstructured grids is also presented. Verification using inviscid vortex propagation and flow over a flat plate is highlighted. Simulation results using laminar and turbulent flow past a NACA 0012 airfoil and ONERA M6 wing are validated against experimental and numerical data.

Aerodynamic Shape Optimization of Complex Aircraft Configurations via an Adjoint Formulation

NASA Technical Reports Server (NTRS)

Reuther, James; Jameson, Antony; Farmer, James; Martinelli, Luigi; Saunders, David

1996-01-01

This work describes the implementation of optimization techniques based on control theory for complex aircraft configurations. Here control theory is employed to derive the adjoint differential equations, the solution of which allows for a drastic reduction in computational costs over previous design methods (13, 12, 43, 38). In our earlier studies (19, 20, 22, 23, 39, 25, 40, 41, 42) it was shown that this method could be used to devise effective optimization procedures for airfoils, wings and wing-bodies subject to either analytic or arbitrary meshes. Design formulations for both potential flows and flows governed by the Euler equations have been demonstrated, showing that such methods can be devised for various governing equations (39, 25). In our most recent works (40, 42) the method was extended to treat wing-body configurations with a large number of mesh points, verifying that significant computational savings can be gained for practical design problems. In this paper the method is extended for the Euler equations to treat complete aircraft configurations via a new multiblock implementation. New elements include a multiblock-multigrid flow solver, a multiblock-multigrid adjoint solver, and a multiblock mesh perturbation scheme. Two design examples are presented in which the new method is used for the wing redesign of a transonic business jet.

Nonlinear Conservation Laws and Finite Volume Methods

NASA Astrophysics Data System (ADS)

Leveque, Randall J.

Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References

Inlet Spillage Drag Predictions Using the AIRPLANE Code

NASA Technical Reports Server (NTRS)

Thomas, Scott D.; Won, Mark A.; Cliff, Susan E.

1999-01-01

AIRPLANE (Jameson/Baker) is a steady inviscid unstructured Euler flow solver. It has been validated on many HSR geometries. It is implemented as MESHPLANE, an unstructured mesh generator, and FLOPLANE, an iterative flow solver. The surface description from an Intergraph CAD system goes into MESHPLANE as collections of polygonal curves to generate the 3D mesh. The flow solver uses a multistage time stepping scheme with residual averaging to approach steady state, but R is not time accurate. The flow solver was ported from Cray to IBM SP2 by Wu-Sun Cheng (IBM); it could only be run on 4 CPUs at a time because of memory limitations. Meshes for the four cases had about 655,000 points in the flow field, about 3.9 million tetrahedra, about 77,500 points on the surface. The flow solver took about 23 wall seconds per iteration when using 4 CPUs. It took about eight and a half wall hours to run 1,300 iterations at a time (the queue limit is 10 hours). A revised version of FLOPLANE (Thomas) was used on up to 64 CPUs to finish up some calculations at the end. We had to turn on more communication when using more processors to eliminate noise that was contaminating the flow field; this added about 50% to the elapsed wall time per iteration when using 64 CPUs. This study involved computing lift and drag for a wing/body/nacelle configuration at Mach 0.9 and 4 degrees pitch. Four cases were considered, corresponding to four nacelle mass flow conditions.

The method of space-time conservation element and solution element-applications to one-dimensional and two-dimensional time-marching flow problems

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Wang, Xiao-Yen; Chow, Chuen-Yen

1995-01-01

A nontraditional numerical method for solving conservation laws is being developed. The new method is designed from a physicist's perspective, i.e., its development is based more on physics than numerics. Even though it uses only the simplest approximation techniques, a 2D time-marching Euler solver developed recently using the new method is capable of generating nearly perfect solutions for a 2D shock reflection problem used by Helen Yee and others. Moreover, a recent application of this solver to computational aeroacoustics (CAA) problems reveals that: (1) accuracy of its results is comparable to that of a 6th order compact difference scheme even though nominally the current solver is only of 2nd-order accuracy; (2) generally, the non-reflecting boundary condition can be implemented in a simple way without involving characteristic variables; and (3) most importantly, the current solver is capable of handling both continuous and discontinuous flows very well and thus provides a unique numerical tool for solving those flow problems where the interactions between sound waves and shocks are important, such as the noise field around a supersonic over- or under-expansion jet.

A Computational/Experimental Study of Two Optimized Supersonic Transport Designs and the Reference H Baseline

NASA Technical Reports Server (NTRS)

Cliff, Susan E.; Baker, Timothy J.; Hicks, Raymond M.; Reuther, James J.

1999-01-01

Two supersonic transport configurations designed by use of non-linear aerodynamic optimization methods are compared with a linearly designed baseline configuration. One optimized configuration, designated Ames 7-04, was designed at NASA Ames Research Center using an Euler flow solver, and the other, designated Boeing W27, was designed at Boeing using a full-potential method. The two optimized configurations and the baseline were tested in the NASA Langley Unitary Plan Supersonic Wind Tunnel to evaluate the non-linear design optimization methodologies. In addition, the experimental results are compared with computational predictions for each of the three configurations from the Enter flow solver, AIRPLANE. The computational and experimental results both indicate moderate to substantial performance gains for the optimized configurations over the baseline configuration. The computed performance changes with and without diverters and nacelles were in excellent agreement with experiment for all three models. Comparisons of the computational and experimental cruise drag increments for the optimized configurations relative to the baseline show excellent agreement for the model designed by the Euler method, but poorer comparisons were found for the configuration designed by the full-potential code.

An Approach to the Constrained Design of Natural Laminar Flow Airfoils

NASA Technical Reports Server (NTRS)

Green, Bradford E.

1997-01-01

A design method has been developed by which an airfoil with a substantial amount of natural laminar flow can be designed, while maintaining other aerodynamic and geometric constraints. After obtaining the initial airfoil's pressure distribution at the design lift coefficient using an Euler solver coupled with an integral turbulent boundary layer method, the calculations from a laminar boundary layer solver are used by a stability analysis code to obtain estimates of the transition location (using N-Factors) for the starting airfoil. A new design method then calculates a target pressure distribution that will increase the laminar flow toward the desired amount. An airfoil design method is then iteratively used to design an airfoil that possesses that target pressure distribution. The new airfoil's boundary layer stability characteristics are determined, and this iterative process continues until an airfoil is designed that meets the laminar flow requirement and as many of the other constraints as possible.

An approach to the constrained design of natural laminar flow airfoils

NASA Technical Reports Server (NTRS)

Green, Bradford Earl

1995-01-01

A design method has been developed by which an airfoil with a substantial amount of natural laminar flow can be designed, while maintaining other aerodynamic and geometric constraints. After obtaining the initial airfoil's pressure distribution at the design lift coefficient using an Euler solver coupled with an integml turbulent boundary layer method, the calculations from a laminar boundary layer solver are used by a stability analysis code to obtain estimates of the transition location (using N-Factors) for the starting airfoil. A new design method then calculates a target pressure distribution that will increase the larninar flow toward the desired amounl An airfoil design method is then iteratively used to design an airfoil that possesses that target pressure distribution. The new airfoil's boundary layer stability characteristics are determined, and this iterative process continues until an airfoil is designed that meets the laminar flow requirement and as many of the other constraints as possible.

An interactive adaptive remeshing algorithm for the two-dimensional Euler equations

NASA Technical Reports Server (NTRS)

Slack, David C.; Walters, Robert W.; Lohner, R.

1990-01-01

An interactive adaptive remeshing algorithm utilizing a frontal grid generator and a variety of time integration schemes for the two-dimensional Euler equations on unstructured meshes is presented. Several device dependent interactive graphics interfaces have been developed along with a device independent DI-3000 interface which can be employed on any computer that has the supporting software including the Cray-2 supercomputers Voyager and Navier. The time integration methods available include: an explicit four stage Runge-Kutta and a fully implicit LU decomposition. A cell-centered finite volume upwind scheme utilizing Roe's approximate Riemann solver is developed. To obtain higher order accurate results a monotone linear reconstruction procedure proposed by Barth is utilized. Results for flow over a transonic circular arc and flow through a supersonic nozzle are examined.

An Adaptive Flow Solver for Air-Borne Vehicles Undergoing Time-Dependent Motions/Deformations

NASA Technical Reports Server (NTRS)

Singh, Jatinder; Taylor, Stephen

1997-01-01

This report describes a concurrent Euler flow solver for flows around complex 3-D bodies. The solver is based on a cell-centered finite volume methodology on 3-D unstructured tetrahedral grids. In this algorithm, spatial discretization for the inviscid convective term is accomplished using an upwind scheme. A localized reconstruction is done for flow variables which is second order accurate. Evolution in time is accomplished using an explicit three-stage Runge-Kutta method which has second order temporal accuracy. This is adapted for concurrent execution using another proven methodology based on concurrent graph abstraction. This solver operates on heterogeneous network architectures. These architectures may include a broad variety of UNIX workstations and PCs running Windows NT, symmetric multiprocessors and distributed-memory multi-computers. The unstructured grid is generated using commercial grid generation tools. The grid is automatically partitioned using a concurrent algorithm based on heat diffusion. This results in memory requirements that are inversely proportional to the number of processors. The solver uses automatic granularity control and resource management techniques both to balance load and communication requirements, and deal with differing memory constraints. These ideas are again based on heat diffusion. Results are subsequently combined for visualization and analysis using commercial CFD tools. Flow simulation results are demonstrated for a constant section wing at subsonic, transonic, and a supersonic case. These results are compared with experimental data and numerical results of other researchers. Performance results are under way for a variety of network topologies.

A New Modular Approach for Tightly Coupled Fluid/Structure Analysis

NASA Technical Reports Server (NTRS)

Guruswamy, Guru

2003-01-01

Static aeroelastic computations are made using a C++ executive suitable for closely coupled fluid/structure interaction studies. The fluid flow is modeled using the Euler/Navier Stokes equations and the structure is modeled using finite elements. FORTRAN based fluids and structures codes are integrated under C++ environment. The flow and structural solvers are treated as separate object files. The data flow between fluids and structures is accomplished using I/O. Results are demonstrated for transonic flow over partially flexible surface that is important for aerospace vehicles. Use of this development to accurately predict flow induced structural failure will be demonstrated.

A package for 3-D unstructured grid generation, finite-element flow solution and flow field visualization

NASA Technical Reports Server (NTRS)

Parikh, Paresh; Pirzadeh, Shahyar; Loehner, Rainald

1990-01-01

A set of computer programs for 3-D unstructured grid generation, fluid flow calculations, and flow field visualization was developed. The grid generation program, called VGRID3D, generates grids over complex configurations using the advancing front method. In this method, the point and element generation is accomplished simultaneously, VPLOT3D is an interactive, menudriven pre- and post-processor graphics program for interpolation and display of unstructured grid data. The flow solver, VFLOW3D, is an Euler equation solver based on an explicit, two-step, Taylor-Galerkin algorithm which uses the Flux Corrected Transport (FCT) concept for a wriggle-free solution. Using these programs, increasingly complex 3-D configurations of interest to aerospace community were gridded including a complete Space Transportation System comprised of the space-shuttle orbitor, the solid-rocket boosters, and the external tank. Flow solutions were obtained on various configurations in subsonic, transonic, and supersonic flow regimes.

Three-dimensional elliptic grid generation for an F-16

NASA Technical Reports Server (NTRS)

Sorenson, Reese L.

1988-01-01

A case history depicting the effort to generate a computational grid for the simulation of transonic flow about an F-16 aircraft at realistic flight conditions is presented. The flow solver for which this grid is designed is a zonal one, using the Reynolds averaged Navier-Stokes equations near the surface of the aircraft, and the Euler equations in regions removed from the aircraft. A body conforming global grid, suitable for the Euler equation, is first generated using 3-D Poisson equations having inhomogeneous terms modeled after the 2-D GRAPE code. Regions of the global grid are then designated for zonal refinement as appropriate to accurately model the flow physics. Grid spacing suitable for solution of the Navier-Stokes equations is generated in the refinement zones by simple subdivision of the given coarse grid intervals. That grid generation project is described, with particular emphasis on the global coarse grid.

High Energy Boundary Conditions for a Cartesian Mesh Euler Solver

NASA Technical Reports Server (NTRS)

Pandya, Shishir; Murman, Scott; Aftosmis, Michael

2003-01-01

Inlets and exhaust nozzles are common place in the world of flight. Yet, many aerodynamic simulation packages do not provide a method of modelling such high energy boundaries in the flow field. For the purposes of aerodynamic simulation, inlets and exhausts are often fared over and it is assumed that the flow differences resulting from this assumption are minimal. While this is an adequate assumption for the prediction of lift, the lack of a plume behind the aircraft creates an evacuated base region thus effecting both drag and pitching moment values. In addition, the flow in the base region is often mis-predicted resulting in incorrect base drag. In order to accurately predict these quantities, a method for specifying inlet and exhaust conditions needs to be available in aerodynamic simulation packages. A method for a first approximation of a plume without accounting for chemical reactions is added to the Cartesian mesh based aerodynamic simulation package CART3D. The method consists of 3 steps. In the first step, a components approach where each triangle is assigned a component number is used. Here, a method for marking the inlet or exhaust plane triangles as separate components is discussed. In step two, the flow solver is modified to accept a reference state for the components marked inlet or exhaust. In the third step, the flow solver uses these separated components and the reference state to compute the correct flow condition at that triangle. The present method is implemented in the CART3D package which consists of a set of tools for generating a Cartesian volume mesh from a set of component triangulations. The Euler equations are solved on the resulting unstructured Cartesian mesh. The present methods is implemented in this package and its usefulness is demonstrated with two validation cases. A generic missile body is also presented to show the usefulness of the method on a real world geometry.

Numerical solution of fluid-structure interaction represented by human vocal folds in airflow

NASA Astrophysics Data System (ADS)

Valášek, J.; Sváček, P.; Horáček, J.

2016-03-01

The paper deals with the human vocal folds vibration excited by the fluid flow. The vocal fold is modelled as an elastic body assuming small displacements and therefore linear elasticity theory is used. The viscous incompressible fluid flow is considered. For purpose of numerical solution the arbitrary Lagrangian-Euler method (ALE) is used. The whole problem is solved by the finite element method (FEM) based solver. Results of numerical experiments with different boundary conditions are presented.

Turbulent Bubbly Flow in a Vertical Pipe Computed By an Eddy-Resolving Reynolds Stress Model

DTIC Science & Technology

2014-09-19

the numerical code OpenFOAM R©. 1 Introduction Turbulent bubbly flows are encountered in many industrially relevant applications, such as chemical in...performed using the OpenFOAM -2.2.2 computational code utilizing a cell- center-based finite volume method on an unstructured numerical grid. The...the mean Courant number is always below 0.4. The utilized turbulence models were implemented into the so-called twoPhaseEulerFoam solver in OpenFOAM , to

A multiple-block multigrid method for the solution of the three-dimensional Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Atkins, Harold

1991-01-01

A multiple block multigrid method for the solution of the three dimensional Euler and Navier-Stokes equations is presented. The basic flow solver is a cell vertex method which employs central difference spatial approximations and Runge-Kutta time stepping. The use of local time stepping, implicit residual smoothing, multigrid techniques and variable coefficient numerical dissipation results in an efficient and robust scheme is discussed. The multiblock strategy places the block loop within the Runge-Kutta Loop such that accuracy and convergence are not affected by block boundaries. This has been verified by comparing the results of one and two block calculations in which the two block grid is generated by splitting the one block grid. Results are presented for both Euler and Navier-Stokes computations of wing/fuselage combinations.

CFD Approaches for Simulation of Wing-Body Stage Separation

NASA Technical Reports Server (NTRS)

Buning, Pieter G.; Gomez, Reynaldo J.; Scallion, William I.

2004-01-01

A collection of computational fluid dynamics tools and techniques are being developed and tested for application to stage separation and abort simulation for next-generation launch vehicles. In this work, an overset grid Navier-Stokes flow solver has been enhanced and demonstrated on a matrix of proximity cases and on a dynamic separation simulation of a belly-to-belly wing-body configuration. Steady cases show excellent agreement between Navier-Stokes results, Cartesian grid Euler solutions, and wind tunnel data at Mach 3. Good agreement has been obtained between Navier-Stokes, Euler, and wind tunnel results at Mach 6. An analysis of a dynamic separation at Mach 3 demonstrates that unsteady aerodynamic effects are not important for this scenario. Results provide an illustration of the relative applicability of Euler and Navier-Stokes methods to these types of problems.

A new approach for solving the three-dimensional steady Euler equations. I - General theory

NASA Technical Reports Server (NTRS)

Chang, S.-C.; Adamczyk, J. J.

1986-01-01

The present iterative procedure combines the Clebsch potentials and the Munk-Prim (1947) substitution principle with an extension of a semidirect Cauchy-Riemann solver to three dimensions, in order to solve steady, inviscid three-dimensional rotational flow problems in either subsonic or incompressible flow regimes. This solution procedure can be used, upon discretization, to obtain inviscid subsonic flow solutions in a 180-deg turning channel. In addition to accurately predicting the behavior of weak secondary flows, the algorithm can generate solutions for strong secondary flows and will yield acceptable flow solutions after only 10-20 outer loop iterations.

A new approach for solving the three-dimensional steady Euler equations. I - General theory

NASA Astrophysics Data System (ADS)

Chang, S.-C.; Adamczyk, J. J.

1986-08-01

The present iterative procedure combines the Clebsch potentials and the Munk-Prim (1947) substitution principle with an extension of a semidirect Cauchy-Riemann solver to three dimensions, in order to solve steady, inviscid three-dimensional rotational flow problems in either subsonic or incompressible flow regimes. This solution procedure can be used, upon discretization, to obtain inviscid subsonic flow solutions in a 180-deg turning channel. In addition to accurately predicting the behavior of weak secondary flows, the algorithm can generate solutions for strong secondary flows and will yield acceptable flow solutions after only 10-20 outer loop iterations.

Upwind MacCormack Euler solver with non-equilibrium chemistry

NASA Technical Reports Server (NTRS)

Sherer, Scott E.; Scott, James N.

1993-01-01

A computer code, designated UMPIRE, is currently under development to solve the Euler equations in two dimensions with non-equilibrium chemistry. UMPIRE employs an explicit MacCormack algorithm with dissipation introduced via Roe's flux-difference split upwind method. The code also has the capability to employ a point-implicit methodology for flows where stiffness is introduced through the chemical source term. A technique consisting of diagonal sweeps across the computational domain from each corner is presented, which is used to reduce storage and execution requirements. Results depicting one dimensional shock tube flow for both calorically perfect gas and thermally perfect, dissociating nitrogen are presented to verify current capabilities of the program. Also, computational results from a chemical reactor vessel with no fluid dynamic effects are presented to check the chemistry capability and to verify the point implicit strategy.

The semi-discrete Galerkin finite element modelling of compressible viscous flow past an airfoil

NASA Technical Reports Server (NTRS)

Meade, Andrew J., Jr.

1992-01-01

A method is developed to solve the two-dimensional, steady, compressible, turbulent boundary-layer equations and is coupled to an existing Euler solver for attached transonic airfoil analysis problems. The boundary-layer formulation utilizes the semi-discrete Galerkin (SDG) method to model the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby permitting the use of a uniform finite element grid which provides high resolution near the wall and automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes, through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past NACA 0012 and RAE 2822 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack. All results show good agreement with experiment, and the coupled code proved to be a computationally-efficient and accurate airfoil analysis tool.

A 3D Unstructured Mesh Euler Solver Based on the Fourth-Order CESE Method

DTIC Science & Technology

2013-06-01

Form 298 (Rev. 8-98) Prescribed by ANSI Std. 239.18 A 3D Unstructured Mesh Euler Solver Based on the Fourth-Order CESE Method David L. Bilyeu ∗1,2...Similarly, the fluxes, f x,y,z i , and their derivatives inside a SE are also discretized by the Taylor series expansion: ∂ Cfx ,y,zi ∂xI∂yJ∂zK∂tL = A

Investigation of advanced counterrotation blade configuration concepts for high speed turboprop systems, task 1: Ducted propfan analysis

NASA Technical Reports Server (NTRS)

Hall, Edward J.; Delaney, Robert A.; Bettner, James L.

1990-01-01

The time-dependent three-dimensional Euler equations of gas dynamics were solved numerically to study the steady compressible transonic flow about ducted propfan propulsion systems. Aerodynamic calculations were based on a four-stage Runge-Kutta time-marching finite volume solution technique with added numerical dissipation. An implicit residual smoothing operator was used to aid convergence. Two calculation grids were employed in this study. The first grid utilized an H-type mesh network with a branch cut opening to represent the axisymmetric cowl. The second grid utilized a multiple-block mesh system with a C-type grid about the cowl. The individual blocks were numerically coupled in the Euler solver. Grid systems were generated by a combined algebraic/elliptic algortihm developed specifically for ducted propfans. Numerical calculations were initially performed for unducted propfans to verify the accuracy of the three-dimensional Euler formulation. The Euler analyses were then applied for the calculation of ducted propfan flows, and predicted results were compared with experimental data for two cases. The three-dimensional Euler analyses displayed exceptional accuracy, although certain parameters were observed to be very sensitive to geometric deflections. Both solution schemes were found to be very robust and demonstrated nearly equal efficiency and accuracy, although it was observed that the multi-block C-grid formulation provided somewhat better resolution of the cowl leading edge region.

Development of a High-Order Navier-Stokes Solver Using Flux Reconstruction to Simulate Three-Dimensional Vortex Structures in a Curved Artery Model

NASA Astrophysics Data System (ADS)

Cox, Christopher

Low-order numerical methods are widespread in academic solvers and ubiquitous in industrial solvers due to their robustness and usability. High-order methods are less robust and more complicated to implement; however, they exhibit low numerical dissipation and have the potential to improve the accuracy of flow simulations at a lower computational cost when compared to low-order methods. This motivates our development of a high-order compact method using Huynh's flux reconstruction scheme for solving unsteady incompressible flow on unstructured grids. We use Chorin's classic artificial compressibility formulation with dual time stepping to solve unsteady flow problems. In 2D, an implicit non-linear lower-upper symmetric Gauss-Seidel scheme with backward Euler discretization is used to efficiently march the solution in pseudo time, while a second-order backward Euler discretization is used to march in physical time. We verify and validate implementation of the high-order method coupled with our implicit time stepping scheme using both steady and unsteady incompressible flow problems. The current implicit time stepping scheme is proven effective in satisfying the divergence-free constraint on the velocity field in the artificial compressibility formulation. The high-order solver is extended to 3D and parallelized using MPI. Due to its simplicity, time marching for 3D problems is done explicitly. The feasibility of using the current implicit time stepping scheme for large scale three-dimensional problems with high-order polynomial basis still remains to be seen. We directly use the aforementioned numerical solver to simulate pulsatile flow of a Newtonian blood-analog fluid through a rigid 180-degree curved artery model. One of the most physiologically relevant forces within the cardiovascular system is the wall shear stress. This force is important because atherosclerotic regions are strongly correlated with curvature and branching in the human vasculature, where the shear stress is both oscillatory and multidirectional. Also, the combined effect of curvature and pulsatility in cardiovascular flows produces unsteady vortices. The aim of this research as it relates to cardiovascular fluid dynamics is to predict the spatial and temporal evolution of vortical structures generated by secondary flows, as well as to assess the correlation between multiple vortex pairs and wall shear stress. We use a physiologically (pulsatile) relevant flow rate and generate results using both fully developed and uniform entrance conditions, the latter being motivated by the fact that flow upstream of a curved artery may not have sufficient straight entrance length to become fully developed. Under the two pulsatile inflow conditions, we characterize the morphology and evolution of various vortex pairs and their subsequent effect on relevant haemodynamic wall shear stress metrics.

Euler Technology Assessment for Preliminary Aircraft Design-Unstructured/Structured Grid NASTD Application for Aerodynamic Analysis of an Advanced Fighter/Tailless Configuration

NASA Technical Reports Server (NTRS)

Michal, Todd R.

1998-01-01

This study supports the NASA Langley sponsored project aimed at determining the viability of using Euler technology for preliminary design use. The primary objective of this study was to assess the accuracy and efficiency of the Boeing, St. Louis unstructured grid flow field analysis system, consisting of the MACGS grid generation and NASTD flow solver codes. Euler solutions about the Aero Configuration/Weapons Fighter Technology (ACWFT) 1204 aircraft configuration were generated. Several variations of the geometry were investigated including a standard wing, cambered wing, deflected elevon, and deflected body flap. A wide range of flow conditions, most of which were in the non-linear regimes of the flight envelope, including variations in speed (subsonic, transonic, supersonic), angles of attack, and sideslip were investigated. Several flowfield non-linearities were present in these solutions including shock waves, vortical flows and the resulting interactions. The accuracy of this method was evaluated by comparing solutions with test data and Navier-Stokes solutions. The ability to accurately predict lateral-directional characteristics and control effectiveness was investigated by computing solutions with sideslip, and with deflected control surfaces. Problem set up times and computational resource requirements were documented and used to evaluate the efficiency of this approach for use in the fast paced preliminary design environment.

An assessment of computational fluid dynamic techniques in the analysis and design of turbomachinery - The 1990 Freeman Scholar Lecture

NASA Technical Reports Server (NTRS)

Lakshminarayana, B.

1991-01-01

Various computational fluid dynamic techniques are reviewed focusing on the Euler and Navier-Stokes solvers with a brief assessment of boundary layer solutions, and quasi-3D and quasi-viscous techniques. Particular attention is given to a pressure-based method, explicit and implicit time marching techniques, a pseudocompressibility technique for incompressible flow, and zonal techniques. Recommendations are presented with regard to the most appropriate technique for various flow regimes and types of turbomachinery, incompressible and compressible flows, cascades, rotors, stators, liquid-handling, and gas-handling turbomachinery.

Improvements to the Unstructured Mesh Generator MESH3D

NASA Technical Reports Server (NTRS)

Thomas, Scott D.; Baker, Timothy J.; Cliff, Susan E.

1999-01-01

The AIRPLANE process starts with an aircraft geometry stored in a CAD system. The surface is modeled with a mesh of triangles and then the flow solver produces pressures at surface points which may be integrated to find forces and moments. The biggest advantage is that the grid generation bottleneck of the CFD process is eliminated when an unstructured tetrahedral mesh is used. MESH3D is the key to turning around the first analysis of a CAD geometry in days instead of weeks. The flow solver part of AIRPLANE has proven to be robust and accurate over a decade of use at NASA. It has been extensively validated with experimental data and compares well with other Euler flow solvers. AIRPLANE has been applied to all the HSR geometries treated at Ames over the course of the HSR program in order to verify the accuracy of other flow solvers. The unstructured approach makes handling complete and complex geometries very simple because only the surface of the aircraft needs to be discretized, i.e. covered with triangles. The volume mesh is created automatically by MESH3D. AIRPLANE runs well on multiple platforms. Vectorization on the Cray Y-MP is reasonable for a code that uses indirect addressing. Massively parallel computers such as the IBM SP2, SGI Origin 2000, and the Cray T3E have been used with an MPI version of the flow solver and the code scales very well on these systems. AIRPLANE can run on a desktop computer as well. AIRPLANE has a future. The unstructured technologies developed as part of the HSR program are now targeting high Reynolds number viscous flow simulation. The pacing item in this effort is Navier-Stokes mesh generation.

GPU computing of compressible flow problems by a meshless method with space-filling curves

NASA Astrophysics Data System (ADS)

Ma, Z. H.; Wang, H.; Pu, S. H.

2014-04-01

A graphic processing unit (GPU) implementation of a meshless method for solving compressible flow problems is presented in this paper. Least-square fit is used to discretize the spatial derivatives of Euler equations and an upwind scheme is applied to estimate the flux terms. The compute unified device architecture (CUDA) C programming model is employed to efficiently and flexibly port the meshless solver from CPU to GPU. Considering the data locality of randomly distributed points, space-filling curves are adopted to re-number the points in order to improve the memory performance. Detailed evaluations are firstly carried out to assess the accuracy and conservation property of the underlying numerical method. Then the GPU accelerated flow solver is used to solve external steady flows over aerodynamic configurations. Representative results are validated through extensive comparisons with the experimental, finite volume or other available reference solutions. Performance analysis reveals that the running time cost of simulations is significantly reduced while impressive (more than an order of magnitude) speedups are achieved.

On multigrid solution of the implicit equations of hydrodynamics. Experiments for the compressible Euler equations in general coordinates

NASA Astrophysics Data System (ADS)

Kifonidis, K.; Müller, E.

2012-08-01

Aims: We describe and study a family of new multigrid iterative solvers for the multidimensional, implicitly discretized equations of hydrodynamics. Schemes of this class are free of the Courant-Friedrichs-Lewy condition. They are intended for simulations in which widely differing wave propagation timescales are present. A preferred solver in this class is identified. Applications to some simple stiff test problems that are governed by the compressible Euler equations, are presented to evaluate the convergence behavior, and the stability properties of this solver. Algorithmic areas are determined where further work is required to make the method sufficiently efficient and robust for future application to difficult astrophysical flow problems. Methods: The basic equations are formulated and discretized on non-orthogonal, structured curvilinear meshes. Roe's approximate Riemann solver and a second-order accurate reconstruction scheme are used for spatial discretization. Implicit Runge-Kutta (ESDIRK) schemes are employed for temporal discretization. The resulting discrete equations are solved with a full-coarsening, non-linear multigrid method. Smoothing is performed with multistage-implicit smoothers. These are applied here to the time-dependent equations by means of dual time stepping. Results: For steady-state problems, our results show that the efficiency of the present approach is comparable to the best implicit solvers for conservative discretizations of the compressible Euler equations that can be found in the literature. The use of red-black as opposed to symmetric Gauss-Seidel iteration in the multistage-smoother is found to have only a minor impact on multigrid convergence. This should enable scalable parallelization without having to seriously compromise the method's algorithmic efficiency. For time-dependent test problems, our results reveal that the multigrid convergence rate degrades with increasing Courant numbers (i.e. time step sizes). Beyond a Courant number of nine thousand, even complete multigrid breakdown is observed. Local Fourier analysis indicates that the degradation of the convergence rate is associated with the coarse-grid correction algorithm. An implicit scheme for the Euler equations that makes use of the present method was, nevertheless, able to outperform a standard explicit scheme on a time-dependent problem with a Courant number of order 1000. Conclusions: For steady-state problems, the described approach enables the construction of parallelizable, efficient, and robust implicit hydrodynamics solvers. The applicability of the method to time-dependent problems is presently restricted to cases with moderately high Courant numbers. This is due to an insufficient coarse-grid correction of the employed multigrid algorithm for large time steps. Further research will be required to help us to understand and overcome the observed multigrid convergence difficulties for time-dependent problems.

An efficient and accurate two-stage fourth-order gas-kinetic scheme for the Euler and Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Pan, Liang; Xu, Kun; Li, Qibing; Li, Jiequan

2016-12-01

For computational fluid dynamics (CFD), the generalized Riemann problem (GRP) solver and the second-order gas-kinetic scheme (GKS) provide a time-accurate flux function starting from a discontinuous piecewise linear flow distributions around a cell interface. With the adoption of time derivative of the flux function, a two-stage Lax-Wendroff-type (L-W for short) time stepping method has been recently proposed in the design of a fourth-order time accurate method for inviscid flow [21]. In this paper, based on the same time-stepping method and the second-order GKS flux function [42], a fourth-order gas-kinetic scheme is constructed for the Euler and Navier-Stokes (NS) equations. In comparison with the formal one-stage time-stepping third-order gas-kinetic solver [24], the current fourth-order method not only reduces the complexity of the flux function, but also improves the accuracy of the scheme. In terms of the computational cost, a two-dimensional third-order GKS flux function takes about six times of the computational time of a second-order GKS flux function. However, a fifth-order WENO reconstruction may take more than ten times of the computational cost of a second-order GKS flux function. Therefore, it is fully legitimate to develop a two-stage fourth order time accurate method (two reconstruction) instead of standard four stage fourth-order Runge-Kutta method (four reconstruction). Most importantly, the robustness of the fourth-order GKS is as good as the second-order one. In the current computational fluid dynamics (CFD) research, it is still a difficult problem to extend the higher-order Euler solver to the NS one due to the change of governing equations from hyperbolic to parabolic type and the initial interface discontinuity. This problem remains distinctively for the hypersonic viscous and heat conducting flow. The GKS is based on the kinetic equation with the hyperbolic transport and the relaxation source term. The time-dependent GKS flux function provides a dynamic process of evolution from the kinetic scale particle free transport to the hydrodynamic scale wave propagation, which provides the physics for the non-equilibrium numerical shock structure construction to the near equilibrium NS solution. As a result, with the implementation of the fifth-order WENO initial reconstruction, in the smooth region the current two-stage GKS provides an accuracy of O ((Δx) 5 ,(Δt) 4) for the Euler equations, and O ((Δx) 5 ,τ2 Δt) for the NS equations, where τ is the time between particle collisions. Many numerical tests, including difficult ones for the Navier-Stokes solvers, have been used to validate the current method. Perfect numerical solutions can be obtained from the high Reynolds number boundary layer to the hypersonic viscous heat conducting flow. Following the two-stage time-stepping framework, the third-order GKS flux function can be used as well to construct a fifth-order method with the usage of both first-order and second-order time derivatives of the flux function. The use of time-accurate flux function may have great advantages on the development of higher-order CFD methods.

Multidisciplinary Modeling Software for Analysis, Design, and Optimization of HRRLS Vehicles

NASA Technical Reports Server (NTRS)

Spradley, Lawrence W.; Lohner, Rainald; Hunt, James L.

2011-01-01

The concept for Highly Reliable Reusable Launch Systems (HRRLS) under the NASA Hypersonics project is a two-stage-to-orbit, horizontal-take-off / horizontal-landing, (HTHL) architecture with an air-breathing first stage. The first stage vehicle is a slender body with an air-breathing propulsion system that is highly integrated with the airframe. The light weight slender body will deflect significantly during flight. This global deflection affects the flow over the vehicle and into the engine and thus the loads and moments on the vehicle. High-fidelity multi-disciplinary analyses that accounts for these fluid-structures-thermal interactions are required to accurately predict the vehicle loads and resultant response. These predictions of vehicle response to multi physics loads, calculated with fluid-structural-thermal interaction, are required in order to optimize the vehicle design over its full operating range. This contract with ResearchSouth addresses one of the primary objectives of the Vehicle Technology Integration (VTI) discipline: the development of high-fidelity multi-disciplinary analysis and optimization methods and tools for HRRLS vehicles. The primary goal of this effort is the development of an integrated software system that can be used for full-vehicle optimization. This goal was accomplished by: 1) integrating the master code, FEMAP, into the multidiscipline software network to direct the coupling to assure accurate fluid-structure-thermal interaction solutions; 2) loosely-coupling the Euler flow solver FEFLO to the available and proven aeroelasticity and large deformation (FEAP) code; 3) providing a coupled Euler-boundary layer capability for rapid viscous flow simulation; 4) developing and implementing improved Euler/RANS algorithms into the FEFLO CFD code to provide accurate shock capturing, skin friction, and heat-transfer predictions for HRRLS vehicles in hypersonic flow, 5) performing a Reynolds-averaged Navier-Stokes computation on an HRRLS configuration; 6) integrating the RANS solver with the FEAP code for coupled fluid-structure-thermal capability; and 7) integrating the existing NASA SRGULL propulsion flow path prediction software with the FEFLO software for quasi-3D propulsion flow path predictions, 8) improving and integrating into the network, an existing adjoint-based design optimization code.

Use of the PARC code to estimate the off-design transonic performance of an over/under turboramjet nozzle

NASA Technical Reports Server (NTRS)

Lam, David W.

1995-01-01

The transonic performance of a dual-throat, single-expansion-ramp nozzle (SERN) was investigated with a PARC computational fluid dynamics (CFD) code, an external flow Navier-Stokes solver. The nozzle configuration was from a conceptual Mach 5 cruise aircraft powered by four air-breathing turboramjets. Initial test cases used the two-dimensional version of PARC in Euler mode to investigate the effect of geometric variation on transonic performance. Additional cases used the two-dimensional version in viscous mode and the three-dimensional version in both Euler and viscous modes. Results of the analysis indicate low nozzle performance and a highly three-dimensional nozzle flow at transonic conditions. In another comparative study using the PARC code, a single-throat SERN configuration for which experimental data were available at transonic conditions was used to validate the results of the over/under turboramjet nozzle.

Static aeroelastic analysis of wings using Euler/Navier-Stokes equations coupled with improved wing-box finite element structures

NASA Technical Reports Server (NTRS)

Guruswamy, Guru P.; MacMurdy, Dale E.; Kapania, Rakesh K.

1994-01-01

Strong interactions between flow about an aircraft wing and the wing structure can result in aeroelastic phenomena which significantly impact aircraft performance. Time-accurate methods for solving the unsteady Navier-Stokes equations have matured to the point where reliable results can be obtained with reasonable computational costs for complex non-linear flows with shock waves, vortices and separations. The ability to combine such a flow solver with a general finite element structural model is key to an aeroelastic analysis in these flows. Earlier work involved time-accurate integration of modal structural models based on plate elements. A finite element model was developed to handle three-dimensional wing boxes, and incorporated into the flow solver without the need for modal analysis. Static condensation is performed on the structural model to reduce the structural degrees of freedom for the aeroelastic analysis. Direct incorporation of the finite element wing-box structural model with the flow solver requires finding adequate methods for transferring aerodynamic pressures to the structural grid and returning deflections to the aerodynamic grid. Several schemes were explored for handling the grid-to-grid transfer of information. The complex, built-up nature of the wing-box complicated this transfer. Aeroelastic calculations for a sample wing in transonic flow comparing various simple transfer schemes are presented and discussed.

Effects of turbulence modelling on prediction of flow characteristics in a bench-scale anaerobic gas-lift digester.

PubMed

Coughtrie, A R; Borman, D J; Sleigh, P A

2013-06-01

Flow in a gas-lift digester with a central draft-tube was investigated using computational fluid dynamics (CFD) and different turbulence closure models. The k-ω Shear-Stress-Transport (SST), Renormalization-Group (RNG) k-∊, Linear Reynolds-Stress-Model (RSM) and Transition-SST models were tested for a gas-lift loop reactor under Newtonian flow conditions validated against published experimental work. The results identify that flow predictions within the reactor (where flow is transitional) are particularly sensitive to the turbulence model implemented; the Transition-SST model was found to be the most robust for capturing mixing behaviour and predicting separation reliably. Therefore, Transition-SST is recommended over k-∊ models for use in comparable mixing problems. A comparison of results obtained using multiphase Euler-Lagrange and singlephase approaches are presented. The results support the validity of the singlephase modelling assumptions in obtaining reliable predictions of the reactor flow. Solver independence of results was verified by comparing two independent finite-volume solvers (Fluent-13.0sp2 and OpenFOAM-2.0.1). Copyright © 2013 Elsevier Ltd. All rights reserved.

Preliminary Results from the Application of Automated Adjoint Code Generation to CFL3D

NASA Technical Reports Server (NTRS)

Carle, Alan; Fagan, Mike; Green, Lawrence L.

1998-01-01

This report describes preliminary results obtained using an automated adjoint code generator for Fortran to augment a widely-used computational fluid dynamics flow solver to compute derivatives. These preliminary results with this augmented code suggest that, even in its infancy, the automated adjoint code generator can accurately and efficiently deliver derivatives for use in transonic Euler-based aerodynamic shape optimization problems with hundreds to thousands of independent design variables.

Design and experimental evaluation of compact radial-inflow turbines

NASA Technical Reports Server (NTRS)

Fredmonski, A. J.; Huber, F. W.; Roelke, R. J.; Simonyi, S.

1991-01-01

The application of a multistage 3D Euler solver to the aerodynamic design of two compact radial-inflow turbines is presented, along with experimental results evaluating and validating the designs. The objectives of the program were to design, fabricate, and rig test compact radial-inflow turbines with equal or better efficiency relative to conventional designs, while having 40 percent less rotor length than current traditionally-sized radial turbines. The approach to achieving these objectives was to apply a calibrated 3D multistage Euler code to accurately predict and control the high rotor flow passage velocities and high aerodynamic loadings resulting from the reduction in rotor length. A comparison of the advanced compact designs to current state-of-the-art configurations is presented.

Development of a linearized unsteady Euler analysis for turbomachinery blade rows

NASA Technical Reports Server (NTRS)

Verdon, Joseph M.; Montgomery, Matthew D.; Kousen, Kenneth A.

1995-01-01

A linearized unsteady aerodynamic analysis for axial-flow turbomachinery blading is described in this report. The linearization is based on the Euler equations of fluid motion and is motivated by the need for an efficient aerodynamic analysis that can be used in predicting the aeroelastic and aeroacoustic responses of blade rows. The field equations and surface conditions required for inviscid, nonlinear and linearized, unsteady aerodynamic analyses of three-dimensional flow through a single, blade row operating within a cylindrical duct, are derived. An existing numerical algorithm for determining time-accurate solutions of the nonlinear unsteady flow problem is described, and a numerical model, based upon this nonlinear flow solver, is formulated for the first-harmonic linear unsteady problem. The linearized aerodynamic and numerical models have been implemented into a first-harmonic unsteady flow code, called LINFLUX. At present this code applies only to two-dimensional flows, but an extension to three-dimensions is planned as future work. The three-dimensional aerodynamic and numerical formulations are described in this report. Numerical results for two-dimensional unsteady cascade flows, excited by prescribed blade motions and prescribed aerodynamic disturbances at inlet and exit, are also provided to illustrate the present capabilities of the LINFLUX analysis.

The Prediction of Broadband Shock-Associated Noise Including Propagation Effects

NASA Technical Reports Server (NTRS)

Miller, Steven; Morris, Philip J.

2011-01-01

An acoustic analogy is developed based on the Euler equations for broadband shock- associated noise (BBSAN) that directly incorporates the vector Green's function of the linearized Euler equations and a steady Reynolds-Averaged Navier-Stokes solution (SRANS) as the mean flow. The vector Green's function allows the BBSAN propagation through the jet shear layer to be determined. The large-scale coherent turbulence is modeled by two-point second order velocity cross-correlations. Turbulent length and time scales are related to the turbulent kinetic energy and dissipation. An adjoint vector Green's function solver is implemented to determine the vector Green's function based on a locally parallel mean flow at streamwise locations of the SRANS solution. However, the developed acoustic analogy could easily be based on any adjoint vector Green's function solver, such as one that makes no assumptions about the mean flow. The newly developed acoustic analogy can be simplified to one that uses the Green's function associated with the Helmholtz equation, which is consistent with the formulation of Morris and Miller (AIAAJ 2010). A large number of predictions are generated using three different nozzles over a wide range of fully expanded Mach numbers and jet stagnation temperatures. These predictions are compared with experimental data from multiple jet noise labs. In addition, two models for the so-called 'fine-scale' mixing noise are included in the comparisons. Improved BBSAN predictions are obtained relative to other models that do not include the propagation effects, especially in the upstream direction of the jet.

Static Aeroelastic Predictions for a Transonic Transport Model Using an Unstructured-Grid Flow Solver Coupled With a Structural Plate Technique

NASA Technical Reports Server (NTRS)

Allison, Dennis O.; Cavallo, Peter A.

2003-01-01

An equivalent-plate structural deformation technique was coupled with a steady-state unstructured-grid three-dimensional Euler flow solver and a two-dimensional strip interactive boundary-layer technique. The objective of the research was to assess the extent to which a simple accounting for static model deformations could improve correlations with measured wing pressure distributions and lift coefficients at transonic speeds. Results were computed and compared to test data for a wing-fuselage model of a generic low-wing transonic transport at a transonic cruise condition over a range of Reynolds numbers and dynamic pressures. The deformations significantly improved correlations with measured wing pressure distributions and lift coefficients. This method provided a means of quantifying the role of dynamic pressure in wind-tunnel studies of Reynolds number effects for transonic transport models.

Euler Flow Computations on Non-Matching Unstructured Meshes

NASA Technical Reports Server (NTRS)

Gumaste, Udayan

1999-01-01

Advanced fluid solvers to predict aerodynamic performance-coupled treatment of multiple fields are described. The interaction between the fluid and structural components in the bladed regions of the engine is investigated with respect to known blade failures caused by either flutter or forced vibrations. Methods are developed to describe aeroelastic phenomena for internal flows in turbomachinery by accounting for the increased geometric complexity, mutual interaction between adjacent structural components and presence of thermal and geometric loading. The computer code developed solves the full three dimensional aeroelastic problem of-stage. The results obtained show that flow computations can be performed on non-matching finite-volume unstructured meshes with second order spatial accuracy.

Adaptive finite-volume WENO schemes on dynamically redistributed grids for compressible Euler equations

NASA Astrophysics Data System (ADS)

Pathak, Harshavardhana S.; Shukla, Ratnesh K.

2016-08-01

A high-order adaptive finite-volume method is presented for simulating inviscid compressible flows on time-dependent redistributed grids. The method achieves dynamic adaptation through a combination of time-dependent mesh node clustering in regions characterized by strong solution gradients and an optimal selection of the order of accuracy and the associated reconstruction stencil in a conservative finite-volume framework. This combined approach maximizes spatial resolution in discontinuous regions that require low-order approximations for oscillation-free shock capturing. Over smooth regions, high-order discretization through finite-volume WENO schemes minimizes numerical dissipation and provides excellent resolution of intricate flow features. The method including the moving mesh equations and the compressible flow solver is formulated entirely on a transformed time-independent computational domain discretized using a simple uniform Cartesian mesh. Approximations for the metric terms that enforce discrete geometric conservation law while preserving the fourth-order accuracy of the two-point Gaussian quadrature rule are developed. Spurious Cartesian grid induced shock instabilities such as carbuncles that feature in a local one-dimensional contact capturing treatment along the cell face normals are effectively eliminated through upwind flux calculation using a rotated Hartex-Lax-van Leer contact resolving (HLLC) approximate Riemann solver for the Euler equations in generalized coordinates. Numerical experiments with the fifth and ninth-order WENO reconstructions at the two-point Gaussian quadrature nodes, over a range of challenging test cases, indicate that the redistributed mesh effectively adapts to the dynamic flow gradients thereby improving the solution accuracy substantially even when the initial starting mesh is non-adaptive. The high adaptivity combined with the fifth and especially the ninth-order WENO reconstruction allows remarkably sharp capture of discontinuous propagating shocks with simultaneous resolution of smooth yet complex small scale unsteady flow features to an exceptional detail.

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1994-01-01

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells are created using polygon-clipping algorithms. The grid is stored in a binary-tree structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: a gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1995-01-01

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells are created using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: A gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment and other accepted computational results for a series of low and moderate Reynolds number flows.

Multiscale Numerical Methods for Non-Equilibrium Plasma

DTIC Science & Technology

2015-08-01

current paper reports on the implementation of a numerical solver on the Graphic Processing Units (GPUs) to model reactive gas mixtures with detailed...Governing equations The flow ismodeled as amixture of gas specieswhile neglecting viscous effects. The chemical reactions taken place between the gas ...components are to be modeled in great detail. The set of the Euler equations for a reactive gas mixture can be written as: ∂Q ∂t + ∇ · F̄ = Ω̇ (1) where Q

Computational aeroelasticity using a pressure-based solver

NASA Astrophysics Data System (ADS)

Kamakoti, Ramji

A computational methodology for performing fluid-structure interaction computations for three-dimensional elastic wing geometries is presented. The flow solver used is based on an unsteady Reynolds-Averaged Navier-Stokes (RANS) model. A well validated k-ε turbulence model with wall function treatment for near wall region was used to perform turbulent flow calculations. Relative merits of alternative flow solvers were investigated. The predictor-corrector-based Pressure Implicit Splitting of Operators (PISO) algorithm was found to be computationally economic for unsteady flow computations. Wing structure was modeled using Bernoulli-Euler beam theory. A fully implicit time-marching scheme (using the Newmark integration method) was used to integrate the equations of motion for structure. Bilinear interpolation and linear extrapolation techniques were used to transfer necessary information between fluid and structure solvers. Geometry deformation was accounted for by using a moving boundary module. The moving grid capability was based on a master/slave concept and transfinite interpolation techniques. Since computations were performed on a moving mesh system, the geometric conservation law must be preserved. This is achieved by appropriately evaluating the Jacobian values associated with each cell. Accurate computation of contravariant velocities for unsteady flows using the momentum interpolation method on collocated, curvilinear grids was also addressed. Flutter computations were performed for the AGARD 445.6 wing at subsonic, transonic and supersonic Mach numbers. Unsteady computations were performed at various dynamic pressures to predict the flutter boundary. Results showed favorable agreement of experiment and previous numerical results. The computational methodology exhibited capabilities to predict both qualitative and quantitative features of aeroelasticity.

Development of advanced Navier-Stokes solver

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan

1994-01-01

The objective of research was to develop and validate new computational algorithms for solving the steady and unsteady Euler and Navier-Stokes equations. The end-products are new three-dimensional Euler and Navier-Stokes codes that are faster, more reliable, more accurate, and easier to use. The three-dimensional Euler and full/thin-layer Reynolds-averaged Navier-Stokes equations for compressible/incompressible flows are solved on structured hexahedral grids. The Baldwin-Lomax algebraic turbulence model is used for closure. The space discretization is based on a cell-centered finite-volume method augmented by a variety of numerical dissipation models with optional total variation diminishing limiters. The governing equations are integrated in time by an implicit method based on lower-upper factorization and symmetric Gauss-Seidel relaxation. The algorithm is vectorized on diagonal planes of sweep using two-dimensional indices in three dimensions. Convergence rates and the robustness of the codes are enhanced by the use of an implicit full approximation storage multigrid method.

LINFLUX-AE: A Turbomachinery Aeroelastic Code Based on a 3-D Linearized Euler Solver

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Bakhle, M. A.; Trudell, J. J.; Mehmed, O.; Stefko, G. L.

2004-01-01

This report describes the development and validation of LINFLUX-AE, a turbomachinery aeroelastic code based on the linearized unsteady 3-D Euler solver, LINFLUX. A helical fan with flat plate geometry is selected as the test case for numerical validation. The steady solution required by LINFLUX is obtained from the nonlinear Euler/Navier Stokes solver TURBO-AE. The report briefly describes the salient features of LINFLUX and the details of the aeroelastic extension. The aeroelastic formulation is based on a modal approach. An eigenvalue formulation is used for flutter analysis. The unsteady aerodynamic forces required for flutter are obtained by running LINFLUX for each mode, interblade phase angle and frequency of interest. The unsteady aerodynamic forces for forced response analysis are obtained from LINFLUX for the prescribed excitation, interblade phase angle, and frequency. The forced response amplitude is calculated from the modal summation of the generalized displacements. The unsteady pressures, work done per cycle, eigenvalues and forced response amplitudes obtained from LINFLUX are compared with those obtained from LINSUB, TURBO-AE, ASTROP2, and ANSYS.

Application of computational aeroacoustic methodologies to advanced propeller configurations - A review

NASA Technical Reports Server (NTRS)

Korkan, Kenneth D.; Eagleson, Lisa A.; Griffiths, Robert C.

1991-01-01

Current research in the area of advanced propeller configurations for performance and acoustics are briefly reviewed. Particular attention is given to the techniques of Lock and Theodorsen modified for use in the design of counterrotating propeller configurations; a numerical method known as SSTAGE, which is a Euler solver for the unducted fan concept; the NASPROP-E numerical analysis also based on a Euler solver and used to study the near acoustic fields for the SR series propfan configurations; and a counterrotating propeller test rig designed to obtain an experimental performance/acoustic data base for various propeller configurations.

Nonlinear (time domain) and linearized (time and frequency domain) solutions to the compressible Euler equations in conservation law form

NASA Technical Reports Server (NTRS)

Sreenivas, Kidambi; Whitfield, David L.

1995-01-01

Two linearized solvers (time and frequency domain) based on a high resolution numerical scheme are presented. The basic approach is to linearize the flux vector by expressing it as a sum of a mean and a perturbation. This allows the governing equations to be maintained in conservation law form. A key difference between the time and frequency domain computations is that the frequency domain computations require only one grid block irrespective of the interblade phase angle for which the flow is being computed. As a result of this and due to the fact that the governing equations for this case are steady, frequency domain computations are substantially faster than the corresponding time domain computations. The linearized equations are used to compute flows in turbomachinery blade rows (cascades) arising due to blade vibrations. Numerical solutions are compared to linear theory (where available) and to numerical solutions of the nonlinear Euler equations.

Galerkin CFD solvers for use in a multi-disciplinary suite for modeling advanced flight vehicles

NASA Astrophysics Data System (ADS)

Moffitt, Nicholas J.

This work extends existing Galerkin CFD solvers for use in a multi-disciplinary suite. The suite is proposed as a means of modeling advanced flight vehicles, which exhibit strong coupling between aerodynamics, structural dynamics, controls, rigid body motion, propulsion, and heat transfer. Such applications include aeroelastics, aeroacoustics, stability and control, and other highly coupled applications. The suite uses NASA STARS for modeling structural dynamics and heat transfer. Aerodynamics, propulsion, and rigid body dynamics are modeled in one of the five CFD solvers below. Euler2D and Euler3D are Galerkin CFD solvers created at OSU by Cowan (2003). These solvers are capable of modeling compressible inviscid aerodynamics with modal elastics and rigid body motion. This work reorganized these solvers to improve efficiency during editing and at run time. Simple and efficient propulsion models were added, including rocket, turbojet, and scramjet engines. Viscous terms were added to the previous solvers to create NS2D and NS3D. The viscous contributions were demonstrated in the inertial and non-inertial frames. Variable viscosity (Sutherland's equation) and heat transfer boundary conditions were added to both solvers but not verified in this work. Two turbulence models were implemented in NS2D and NS3D: Spalart-Allmarus (SA) model of Deck, et al. (2002) and Menter's SST model (1994). A rotation correction term (Shur, et al., 2000) was added to the production of turbulence. Local time stepping and artificial dissipation were adapted to each model. CFDsol is a Taylor-Galerkin solver with an SA turbulence model. This work improved the time accuracy, far field stability, viscous terms, Sutherland?s equation, and SA model with NS3D as a guideline and added the propulsion models from Euler3D to CFDsol. Simple geometries were demonstrated to utilize current meshing and processing capabilities. Air-breathing hypersonic flight vehicles (AHFVs) represent the ultimate application of the suite. The current models are accurate at low supersonic speed and reasonable for engineering approximation at hypersonic speeds. Improvements to extend the models fully into the hypersonic regime are given in the Recommendations section.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thompson, S.

This report describes the use of several subroutines from the CORLIB core mathematical subroutine library for the solution of a model fluid flow problem. The model consists of the Euler partial differential equations. The equations are spatially discretized using the method of pseudo-characteristics. The resulting system of ordinary differential equations is then integrated using the method of lines. The stiff ordinary differential equation solver LSODE (2) from CORLIB is used to perform the time integration. The non-stiff solver ODE (4) is used to perform a related integration. The linear equation solver subroutines DECOMP and SOLVE are used to solve linearmore » systems whose solutions are required in the calculation of the time derivatives. The monotone cubic spline interpolation subroutines PCHIM and PCHFE are used to approximate water properties. The report describes the use of each of these subroutines in detail. It illustrates the manner in which modules from a standard mathematical software library such as CORLIB can be used as building blocks in the solution of complex problems of practical interest. 9 refs., 2 figs., 4 tabs.« less

Adaptively Refined Euler and Navier-Stokes Solutions with a Cartesian-Cell Based Scheme

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1995-01-01

A Cartesian-cell based scheme with adaptive mesh refinement for solving the Euler and Navier-Stokes equations in two dimensions has been developed and tested. Grids about geometrically complicated bodies were generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells were created using polygon-clipping algorithms. The grid was stored in a binary-tree data structure which provided a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations were solved on the resulting grids using an upwind, finite-volume formulation. The inviscid fluxes were found in an upwinded manner using a linear reconstruction of the cell primitives, providing the input states to an approximate Riemann solver. The viscous fluxes were formed using a Green-Gauss type of reconstruction upon a co-volume surrounding the cell interface. Data at the vertices of this co-volume were found in a linearly K-exact manner, which ensured linear K-exactness of the gradients. Adaptively-refined solutions for the inviscid flow about a four-element airfoil (test case 3) were compared to theory. Laminar, adaptively-refined solutions were compared to accepted computational, experimental and theoretical results.

Task III: Development of an Effective Computational Methodology for Body Force Representation of High-speed Rotor 37

NASA Technical Reports Server (NTRS)

Tan, Choon-Sooi; Suder, Kenneth (Technical Monitor)

2003-01-01

A framework for an effective computational methodology for characterizing the stability and the impact of distortion in high-speed multi-stage compressor is being developed. The methodology consists of using a few isolated-blade row Navier-Stokes solutions for each blade row to construct a body force database. The purpose of the body force database is to replace each blade row in a multi-stage compressor by a body force distribution to produce same pressure rise and flow turning. To do this, each body force database is generated in such a way that it can respond to the changes in local flow conditions. Once the database is generated, no hrther Navier-Stokes computations are necessary. The process is repeated for every blade row in the multi-stage compressor. The body forces are then embedded as source terms in an Euler solver. The method is developed to have the capability to compute the performance in a flow that has radial as well as circumferential non-uniformity with a length scale larger than a blade pitch; thus it can potentially be used to characterize the stability of a compressor under design. It is these two latter features as well as the accompanying procedure to obtain the body force representation that distinguish the present methodology from the streamline curvature method. The overall computational procedures have been developed. A dimensional analysis was carried out to determine the local flow conditions for parameterizing the magnitudes of the local body force representation of blade rows. An Euler solver was modified to embed the body forces as source terms. The results from the dimensional analysis show that the body forces can be parameterized in terms of the two relative flow angles, the relative Mach number, and the Reynolds number. For flow in a high-speed transonic blade row, they can be parameterized in terms of the local relative Mach number alone.

Development of a solution adaptive unstructured scheme for quasi-3D inviscid flows through advanced turbomachinery cascades

NASA Technical Reports Server (NTRS)

Usab, William J., Jr.; Jiang, Yi-Tsann

1991-01-01

The objective of the present research is to develop a general solution adaptive scheme for the accurate prediction of inviscid quasi-three-dimensional flow in advanced compressor and turbine designs. The adaptive solution scheme combines an explicit finite-volume time-marching scheme for unstructured triangular meshes and an advancing front triangular mesh scheme with a remeshing procedure for adapting the mesh as the solution evolves. The unstructured flow solver has been tested on a series of two-dimensional airfoil configurations including a three-element analytic test case presented here. Mesh adapted quasi-three-dimensional Euler solutions are presented for three spanwise stations of the NASA rotor 67 transonic fan. Computed solutions are compared with available experimental data.

Numerical simulation of the transonic flow past the blunted wedge in the diverging channel

NASA Astrophysics Data System (ADS)

Ryabinin, Anatoly

2018-05-01

Positions of shock waves in the 2D channel with a blunted wedge are studied numerically. Solutions of the Euler equations are obtained with finite-volume solver SU2 for 15 variants of channel geometry. Numerical simulations reveal a considerable hysteresis in the shock wave position versus the supersonic Mach number given at the inlet. In the certain range of inlet Mach number, there are asymmetrical solutions of the equations. Small change in the geometry of the channel leads to shift of boundaries of the hysteresis range.

A dynamic-solver-consistent minimum action method: With an application to 2D Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Wan, Xiaoliang; Yu, Haijun

2017-02-01

This paper discusses the necessity and strategy to unify the development of a dynamic solver and a minimum action method (MAM) for a spatially extended system when employing the large deviation principle (LDP) to study the effects of small random perturbations. A dynamic solver is used to approximate the unperturbed system, and a minimum action method is used to approximate the LDP, which corresponds to solving an Euler-Lagrange equation related to but more complicated than the unperturbed system. We will clarify possible inconsistencies induced by independent numerical approximations of the unperturbed system and the LDP, based on which we propose to define both the dynamic solver and the MAM on the same approximation space for spatial discretization. The semi-discrete LDP can then be regarded as the exact LDP of the semi-discrete unperturbed system, which is a finite-dimensional ODE system. We achieve this methodology for the two-dimensional Navier-Stokes equations using a divergence-free approximation space. The method developed can be used to study the nonlinear instability of wall-bounded parallel shear flows, and be generalized straightforwardly to three-dimensional cases. Numerical experiments are presented.

Solution-Adaptive Cartesian Cell Approach for Viscous and Inviscid Flows

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1996-01-01

A Cartesian cell-based approach for adaptively refined solutions of the Euler and Navier-Stokes equations in two dimensions is presented. Grids about geometrically complicated bodies are generated automatically, by the recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal cut cells are created using modified polygon-clipping algorithms. The grid is stored in a binary tree data structure that provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite volume formulation. The convective terms are upwinded: A linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The results of a study comparing the accuracy and positivity of two classes of cell-centered, viscous gradient reconstruction procedures is briefly summarized. Adaptively refined solutions of the Navier-Stokes equations are shown using the more robust of these gradient reconstruction procedures, where the results computed by the Cartesian approach are compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.

A third-order gas-kinetic CPR method for the Euler and Navier-Stokes equations on triangular meshes

NASA Astrophysics Data System (ADS)

Zhang, Chao; Li, Qibing; Fu, Song; Wang, Z. J.

2018-06-01

A third-order accurate gas-kinetic scheme based on the correction procedure via reconstruction (CPR) framework is developed for the Euler and Navier-Stokes equations on triangular meshes. The scheme combines the accuracy and efficiency of the CPR formulation with the multidimensional characteristics and robustness of the gas-kinetic flux solver. Comparing with high-order finite volume gas-kinetic methods, the current scheme is more compact and efficient by avoiding wide stencils on unstructured meshes. Unlike the traditional CPR method where the inviscid and viscous terms are treated differently, the inviscid and viscous fluxes in the current scheme are coupled and computed uniformly through the kinetic evolution model. In addition, the present scheme adopts a fully coupled spatial and temporal gas distribution function for the flux evaluation, achieving high-order accuracy in both space and time within a single step. Numerical tests with a wide range of flow problems, from nearly incompressible to supersonic flows with strong shocks, for both inviscid and viscous problems, demonstrate the high accuracy and efficiency of the present scheme.

Tetrahedral Finite-Volume Solutions to the Navier-Stokes Equations on Complex Configurations

NASA Technical Reports Server (NTRS)

Frink, Neal T.; Pirzadeh, Shahyar Z.

1998-01-01

A review of the algorithmic features and capabilities of the unstructured-grid flow solver USM3Dns is presented. This code, along with the tetrahedral grid generator, VGRIDns, is being extensively used throughout the U.S. for solving the Euler and Navier-Stokes equations on complex aerodynamic problems. Spatial discretization is accomplished by a tetrahedral cell-centered finite-volume formulation using Roe's upwind flux difference splitting. The fluxes are limited by either a Superbee or MinMod limiter. Solution reconstruction within the tetrahedral cells is accomplished with a simple, but novel, multidimensional analytical formula. Time is advanced by an implicit backward-Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the near-wall region of the boundary layer. The issues of accuracy and robustness of USM3Dns Navier-Stokes capabilities are addressed for a flat-plate boundary layer, and a full F-16 aircraft with external stores at transonic speed.

Entropy Analysis of Kinetic Flux Vector Splitting Schemes for the Compressible Euler Equations

NASA Technical Reports Server (NTRS)

Shiuhong, Lui; Xu, Jun

1999-01-01

Flux Vector Splitting (FVS) scheme is one group of approximate Riemann solvers for the compressible Euler equations. In this paper, the discretized entropy condition of the Kinetic Flux Vector Splitting (KFVS) scheme based on the gas-kinetic theory is proved. The proof of the entropy condition involves the entropy definition difference between the distinguishable and indistinguishable particles.

Aeroelastic Analyses of the SemiSpan SuperSonic Transport (S4T) Wind Tunnel Model at Mach 0.95

NASA Technical Reports Server (NTRS)

Hur, Jiyoung

2014-01-01

Detailed aeroelastic analyses of the SemiSpan SuperSonic Transport (S4T) wind tunnel model at Mach 0.95 with a 1.75deg fixed angle of attack are presented. First, a numerical procedure using the Computational Fluids Laboratory 3-Dimensional (CFL3D) Version 6.4 flow solver is investigated. The mesh update method for structured multi-block grids was successfully applied to the Navier-Stokes simulations. Second, the steady aerodynamic analyses with a rigid structure of the S4T wind tunnel model are reviewed in transonic flow. Third, the static analyses were performed for both the Euler and Navier-Stokes equations. Both the Euler and Navier-Stokes equations predicted a significant increase of lift forces, compared to the results from the rigid structure of the S4T wind-tunnel model, over various dynamic pressures. Finally, dynamic aeroelastic analyses were performed to investigate the flutter condition of the S4T wind tunnel model at the transonic Mach number. The condition of flutter was observed at a dynamic pressure of approximately 75.0-psf for the Navier-Stokes simulations. However, it was observed that the flutter condition occurred a dynamic pressure of approximately 47.27-psf for the Euler simulations. Also, the computational efficiency of the aeroelastic analyses for the S4T wind tunnel model has been assessed.

Numerical analysis of the three-dimensional swirling flow in centrifugal compressor volutes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ayder, E.; Van den Braembussche, R.

1994-07-01

The improvement of centrifugal compressor performance and the control of the radial forces acting on the impeller due to the circumferential variation of the static pressure caused by the volute require a good understanding of the flow mechanisms and an accurate prediction of the flow pattern inside the volute. A three-dimensional volute calculation method has been developed for this purpose. The volute is discretized by means of hexahedral elements. A cell vertex finite volume approach is used in combination with a time-marching procedure. The numerical procedure makes use of a central space discretization and a four-step Runge-Kutta time-stepping scheme. Themore » artificial dissipation used in the solver is based on the fourth-order differences of the conservative variables. Implicit residual smoothing improves the convergence rate. The loss model implemented in the code accounts for the losses due to internal shear and friction losses on the walls. A comparison of the calculated and measured results inside a volute with elliptical cross section reveals that the modified Euler solver accurately predicts the velocity and pressure distribution inside and upstream of the volute.« less

Development of iterative techniques for the solution of unsteady compressible viscous flows

NASA Technical Reports Server (NTRS)

Hixon, Duane; Sankar, L. N.

1993-01-01

During the past two decades, there has been significant progress in the field of numerical simulation of unsteady compressible viscous flows. At present, a variety of solution techniques exist such as the transonic small disturbance analyses (TSD), transonic full potential equation-based methods, unsteady Euler solvers, and unsteady Navier-Stokes solvers. These advances have been made possible by developments in three areas: (1) improved numerical algorithms; (2) automation of body-fitted grid generation schemes; and (3) advanced computer architectures with vector processing and massively parallel processing features. In this work, the GMRES scheme has been considered as a candidate for acceleration of a Newton iteration time marching scheme for unsteady 2-D and 3-D compressible viscous flow calculation; from preliminary calculations, this will provide up to a 65 percent reduction in the computer time requirements over the existing class of explicit and implicit time marching schemes. The proposed method has ben tested on structured grids, but is flexible enough for extension to unstructured grids. The described scheme has been tested only on the current generation of vector processor architecture of the Cray Y/MP class, but should be suitable for adaptation to massively parallel machines.

High speed corner and gap-seal computations using an LU-SGS scheme

NASA Technical Reports Server (NTRS)

Coirier, William J.

1989-01-01

The hybrid Lower-Upper Symmetric Gauss-Seidel (LU-SGS) algorithm was added to a widely used series of 2D/3D Euler/Navier-Stokes solvers and was demonstrated for a particular class of high-speed flows. A limited study was conducted to compare the hybrid LU-SGS for approximate Newton iteration and diagonalized Beam-Warming (DBW) schemes on a work and convergence history basis. The hybrid LU-SGS algorithm is more efficient and easier to implement than the DBW scheme originally present in the code for the cases considered. The code was validated for the hypersonic flow through two mutually perpendicular flat plates and then used to investigate the flow field in and around a simplified scramjet module gap seal configuration. Due to the similarities, the gap seal flow was compared to hypersonic corner flow at the same freestream conditions and Reynolds number.

A robust and contact resolving Riemann solver on unstructured mesh, Part I, Euler method

NASA Astrophysics Data System (ADS)

Shen, Zhijun; Yan, Wei; Yuan, Guangwei

2014-07-01

This article presents a new cell-centered numerical method for compressible flows on arbitrary unstructured meshes. A multi-dimensional Riemann solver based on the HLLC method (denoted by HLLC-2D solver) is established. The work is an extension from the cell-centered Lagrangian scheme of Maire et al. [27] to the Eulerian framework. Similarly to the work in [27], a two-dimensional contact velocity defined on a grid node is introduced, and the motivation is to keep an edge flux consistency with the node velocity connected to the edge intrinsically. The main new feature of the algorithm is to relax the condition that the contact pressures must be same in the traditional HLLC solver. The discontinuous fluxes are constructed across each wave sampling direction rather than only along the contact wave direction. The two-dimensional contact velocity of the grid node is determined via enforcing conservation of mass, momentum and total energy, and thus the new method satisfies these conservation properties at nodes rather than on grid edges. Other good properties of the HLLC-2d solver, such as the positivity and the contact preserving, are described, and the two-dimensional high-order extension is constructed employing MUSCL type reconstruction procedure. Numerical results based on both quadrilateral and triangular grids are presented to demonstrate the robustness and the accuracy of this new solver, which shows it has better performance than the existing HLLC method.

Multigrid Method for Modeling Multi-Dimensional Combustion with Detailed Chemistry

NASA Technical Reports Server (NTRS)

Zheng, Xiaoqing; Liu, Chaoqun; Liao, Changming; Liu, Zhining; McCormick, Steve

1996-01-01

A highly accurate and efficient numerical method is developed for modeling 3-D reacting flows with detailed chemistry. A contravariant velocity-based governing system is developed for general curvilinear coordinates to maintain simplicity of the continuity equation and compactness of the discretization stencil. A fully-implicit backward Euler technique and a third-order monotone upwind-biased scheme on a staggered grid are used for the respective temporal and spatial terms. An efficient semi-coarsening multigrid method based on line-distributive relaxation is used as the flow solver. The species equations are solved in a fully coupled way and the chemical reaction source terms are treated implicitly. Example results are shown for a 3-D gas turbine combustor with strong swirling inflows.

Wind-US Users Guide Version 3.0

NASA Technical Reports Server (NTRS)

Yoder, Dennis A.

2016-01-01

Wind-US is a computational platform which may be used to numerically solve various sets of equations governing physical phenomena. Currently, the code supports the solution of the Euler and Navier-Stokes equations of fluid mechanics, along with supporting equation sets governing turbulent and chemically reacting flows. Wind-US is a product of the NPARC Alliance, a partnership between the NASA Glenn Research Center (GRC) and the Arnold Engineering Development Complex (AEDC) dedicated to the establishment of a national, applications-oriented flow simulation capability. The Boeing Company has also been closely associated with the Alliance since its inception, and represents the interests of the NPARC User's Association. The "Wind-US User's Guide" describes the operation and use of Wind-US, including: a basic tutorial; the physical and numerical models that are used; the boundary conditions; monitoring convergence; the files that are read and/or written; parallel execution; and a complete list of input keywords and test options. For current information about Wind-US and the NPARC Alliance, please see the Wind-US home page at http://www.grc.nasa.gov/WWW/winddocs/ and the NPARC Alliance home page at http://www.grc.nasa.gov/WWW/wind/. This manual describes the operation and use of Wind-US, a computational platform which may be used to numerically solve various sets of equations governing physical phenomena. Wind-US represents a merger of the capabilities of four CFD codes - NASTD (a structured grid flow solver developed at McDonnell Douglas, now part of Boeing), NPARC (the original NPARC Alliance structured grid flow solver), NXAIR (an AEDC structured grid code used primarily for store separation analysis), and ICAT (an unstructured grid flow solver developed at the Rockwell Science Center and Boeing).

Numerical analysis and design of upwind sails

NASA Astrophysics Data System (ADS)

Shankaran, Sriram

The use of computational techniques that solve the Euler or the Navier-Stokes equations are increasingly being used by competing syndicates in races like the Americas Cup. For sail configurations, this desire stems from a need to understand the influence of the mast on the boundary layer and pressure distribution on the main sail, the effect of camber and planform variations of the sails on the driving and heeling force produced by them and the interaction of the boundary layer profile of the air over the surface of the water and the gap between the boom and the deck on the performance of the sail. Traditionally, experimental methods along with potential flow solvers have been widely used to quantify these effects. While these approaches are invaluable either for validation purposes or during the early stages of design, the potential advantages of high fidelity computational methods makes them attractive candidates during the later stages of the design process. The aim of this study is to develop and validate numerical methods that solve the inviscid field equations (Euler) to simulate and design upwind sails. The three dimensional compressible Euler equations are modified using the idea of artificial compressibility and discretized on unstructured tetrahedral grids to provide estimates of lift and drag for upwind sail configurations. Convergence acceleration techniques like multigrid and residual averaging are used along with parallel computing platforms to enable these simulations to be performed in a few minutes. To account for the elastic nature of the sail cloth, this flow solver was coupled to NASTRAN to provide estimates of the deflections caused by the pressure loading. The results of this aeroclastic simulation, showed that the major effect of the sail elasticity; was in altering the pressure distribution around the leading edge of the head and the main sail. Adjoint based design methods were developed next and were used to induce changes to the camber distribution of the main sail. The goal of the design process was to reduce the leading edge suction peaks that were considered to be detrimental to the growth of the boundary layer. The deflected shape of the sails obtained from the aeroelastic simulation were used by the design process. The design process resulted in an camber distribution that allowed smooth entry of the flow through the leading edge of the main sail thereby, reducing the leading edge suction peaks.

Automated Euler and Navier-Stokes Database Generation for a Glide-Back Booster

NASA Technical Reports Server (NTRS)

Chaderjian, Neal M.; Rogers, Stuart E.; Aftosmis, Mike J.; Pandya, Shishir A.; Ahmad, Jasim U.; Tejnil, Edward

2004-01-01

The past two decades have seen a sustained increase in the use of high fidelity Computational Fluid Dynamics (CFD) in basic research, aircraft design, and the analysis of post-design issues. As the fidelity of a CFD method increases, the number of cases that can be readily and affordably computed greatly diminishes. However, computer speeds now exceed 2 GHz, hundreds of processors are currently available and more affordable, and advances in parallel CFD algorithms scale more readily with large numbers of processors. All of these factors make it feasible to compute thousands of high fidelity cases. However, there still remains the overwhelming task of monitoring the solution process. This paper presents an approach to automate the CFD solution process. A new software tool, AeroDB, is used to compute thousands of Euler and Navier-Stokes solutions for a 2nd generation glide-back booster in one week. The solution process exploits a common job-submission grid environment, the NASA Information Power Grid (IPG), using 13 computers located at 4 different geographical sites. Process automation and web-based access to a MySql database greatly reduces the user workload, removing much of the tedium and tendency for user input errors. The AeroDB framework is shown. The user submits/deletes jobs, monitors AeroDB's progress, and retrieves data and plots via a web portal. Once a job is in the database, a job launcher uses an IPG resource broker to decide which computers are best suited to run the job. Job/code requirements, the number of CPUs free on a remote system, and queue lengths are some of the parameters the broker takes into account. The Globus software provides secure services for user authentication, remote shell execution, and secure file transfers over an open network. AeroDB automatically decides when a job is completed. Currently, the Cart3D unstructured flow solver is used for the Euler equations, and the Overflow structured overset flow solver is used for the Navier-Stokes equations. Other codes can be readily included into the AeroDB framework.

A Space-Time Conservation Element and Solution Element Method for Solving the Two- and Three-Dimensional Unsteady Euler Equations Using Quadrilateral and Hexahedral Meshes

NASA Technical Reports Server (NTRS)

Zhang, Zeng-Chan; Yu, S. T. John; Chang, Sin-Chung; Jorgenson, Philip (Technical Monitor)

2001-01-01

In this paper, we report a version of the Space-Time Conservation Element and Solution Element (CE/SE) Method in which the 2D and 3D unsteady Euler equations are simulated using structured or unstructured quadrilateral and hexahedral meshes, respectively. In the present method, mesh values of flow variables and their spatial derivatives are treated as independent unknowns to be solved for. At each mesh point, the value of a flow variable is obtained by imposing a flux conservation condition. On the other hand, the spatial derivatives are evaluated using a finite-difference/weighted-average procedure. Note that the present extension retains many key advantages of the original CE/SE method which uses triangular and tetrahedral meshes, respectively, for its 2D and 3D applications. These advantages include efficient parallel computing ease of implementing non-reflecting boundary conditions, high-fidelity resolution of shocks and waves, and a genuinely multidimensional formulation without using a dimensional-splitting approach. In particular, because Riemann solvers, the cornerstones of the Godunov-type upwind schemes, are not needed to capture shocks, the computational logic of the present method is considerably simpler. To demonstrate the capability of the present method, numerical results are presented for several benchmark problems including oblique shock reflection, supersonic flow over a wedge, and a 3D detonation flow.

Computation of an Underexpanded 3-D Rectangular Jet by the CE/SE Method

NASA Technical Reports Server (NTRS)

Loh, Ching Y.; Himansu, Ananda; Wang, Xiao Y.; Jorgenson, Philip C. E.

2000-01-01

Recently, an unstructured three-dimensional space-time conservation element and solution element (CE/SE) Euler solver was developed. Now it is also developed for parallel computation using METIS for domain decomposition and MPI (message passing interface). The method is employed here to numerically study the near-field of a typical 3-D rectangular under-expanded jet. For the computed case-a jet with Mach number Mj = 1.6. with a very modest grid of 1.7 million tetrahedrons, the flow features such as the shock-cell structures and the axis switching, are in good qualitative agreement with experimental results.

Implicit schemes and parallel computing in unstructured grid CFD

NASA Technical Reports Server (NTRS)

Venkatakrishnam, V.

1995-01-01

The development of implicit schemes for obtaining steady state solutions to the Euler and Navier-Stokes equations on unstructured grids is outlined. Applications are presented that compare the convergence characteristics of various implicit methods. Next, the development of explicit and implicit schemes to compute unsteady flows on unstructured grids is discussed. Next, the issues involved in parallelizing finite volume schemes on unstructured meshes in an MIMD (multiple instruction/multiple data stream) fashion are outlined. Techniques for partitioning unstructured grids among processors and for extracting parallelism in explicit and implicit solvers are discussed. Finally, some dynamic load balancing ideas, which are useful in adaptive transient computations, are presented.

An efficient direct solver for rarefied gas flows with arbitrary statistics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Diaz, Manuel A., E-mail: f99543083@ntu.edu.tw; Yang, Jaw-Yen, E-mail: yangjy@iam.ntu.edu.tw; Center of Advanced Study in Theoretical Science, National Taiwan University, Taipei 10167, Taiwan

2016-01-15

A new numerical methodology associated with a unified treatment is presented to solve the Boltzmann–BGK equation of gas dynamics for the classical and quantum gases described by the Bose–Einstein and Fermi–Dirac statistics. Utilizing a class of globally-stiffly-accurate implicit–explicit Runge–Kutta scheme for the temporal evolution, associated with the discrete ordinate method for the quadratures in the momentum space and the weighted essentially non-oscillatory method for the spatial discretization, the proposed scheme is asymptotic-preserving and imposes no non-linear solver or requires the knowledge of fugacity and temperature to capture the flow structures in the hydrodynamic (Euler) limit. The proposed treatment overcomes themore » limitations found in the work by Yang and Muljadi (2011) [33] due to the non-linear nature of quantum relations, and can be applied in studying the dynamics of a gas with internal degrees of freedom with correct values of the ratio of specific heat for the flow regimes for all Knudsen numbers and energy wave lengths. The present methodology is numerically validated with the unified treatment by the one-dimensional shock tube problem and the two-dimensional Riemann problems for gases of arbitrary statistics. Descriptions of ideal quantum gases including rotational degrees of freedom have been successfully achieved under the proposed methodology.« less

A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension

NASA Astrophysics Data System (ADS)

Garrick, Daniel P.; Owkes, Mark; Regele, Jonathan D.

2017-06-01

Shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization. Similar behavior occurs inside of supersonic combustors (scramjets) under startup conditions, but it is challenging to study these conditions experimentally. In order to investigate this phenomenon further, a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces. The flow field is solved via the compressible multicomponent Euler equations (i.e., the five equation model) discretized with the finite volume method on a uniform Cartesian grid. The solver utilizes a total variation diminishing (TVD) third-order Runge-Kutta method for time-marching and second order TVD spatial reconstruction. Surface tension is incorporated using the Continuum Surface Force (CSF) model. Fluxes are upwinded with a modified Harten-Lax-van Leer Contact (HLLC) approximate Riemann solver. An interface compression scheme is employed to counter numerical diffusion of the interface. The present work includes modifications to both the HLLC solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gas-liquid interface. A simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for the non-dimensionalization of the model. The model captures the surface tension induced pressure jump exactly if the exact curvature is known and is further verified with an oscillating elliptical droplet and Mach 1.47 and 3 shock-droplet interaction problems. The general characteristics of secondary atomization at a range of Weber numbers are also captured in a series of simulations.

A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garrick, Daniel P.; Owkes, Mark; Regele, Jonathan D., E-mail: jregele@iastate.edu

Shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization. Similar behavior occurs inside of supersonic combustors (scramjets) under startup conditions, but it is challenging to study these conditions experimentally. In order to investigate this phenomenon further, a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces. The flow field is solved via the compressible multicomponent Euler equations (i.e., the five equation model) discretized with the finite volume method on a uniform Cartesian grid. The solver utilizes a total variation diminishing (TVD) third-order Runge–Kuttamore » method for time-marching and second order TVD spatial reconstruction. Surface tension is incorporated using the Continuum Surface Force (CSF) model. Fluxes are upwinded with a modified Harten–Lax–van Leer Contact (HLLC) approximate Riemann solver. An interface compression scheme is employed to counter numerical diffusion of the interface. The present work includes modifications to both the HLLC solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gas–liquid interface. A simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for the non-dimensionalization of the model. The model captures the surface tension induced pressure jump exactly if the exact curvature is known and is further verified with an oscillating elliptical droplet and Mach 1.47 and 3 shock-droplet interaction problems. The general characteristics of secondary atomization at a range of Weber numbers are also captured in a series of simulations.« less

Transonic CFD applications at Boeing

NASA Technical Reports Server (NTRS)

Tinoco, E. N.

1989-01-01

The use of computational methods for three dimensional transonic flow design and analysis at the Boeing Company is presented. A range of computational tools consisting of production tools for every day use by project engineers, expert user tools for special applications by computational researchers, and an emerging tool which may see considerable use in the near future are described. These methods include full potential and Euler solvers, some coupled to three dimensional boundary layer analysis methods, for transonic flow analysis about nacelle, wing-body, wing-body-strut-nacelle, and complete aircraft configurations. As the examples presented show, such a toolbox of codes is necessary for the variety of applications typical of an industrial environment. Such a toolbox of codes makes possible aerodynamic advances not previously achievable in a timely manner, if at all.

Development of a grid-independent approximate Riemannsolver. Ph.D. Thesis - Michigan Univ.

NASA Technical Reports Server (NTRS)

Rumsey, Christopher Lockwood

1991-01-01

A grid-independent approximate Riemann solver for use with the Euler and Navier-Stokes equations was introduced and explored. The two-dimensional Euler and Navier-Stokes equations are described in Cartesian and generalized coordinates, as well as the traveling wave form of the Euler equations. The spatial and temporal discretization are described for both explicit and implicit time-marching schemes. The grid-aligned flux function of Roe is outlined, while the 5-wave grid-independent flux function is derived. The stability and monotonicity analysis of the 5-wave model are presented. Two-dimensional results are provided and extended to three dimensions. The corresponding results are presented.

TIGER: Turbomachinery interactive grid generation

NASA Technical Reports Server (NTRS)

Soni, Bharat K.; Shih, Ming-Hsin; Janus, J. Mark

1992-01-01

A three dimensional, interactive grid generation code, TIGER, is being developed for analysis of flows around ducted or unducted propellers. TIGER is a customized grid generator that combines new technology with methods from general grid generation codes. The code generates multiple block, structured grids around multiple blade rows with a hub and shroud for either C grid or H grid topologies. The code is intended for use with a Euler/Navier-Stokes solver also being developed, but is general enough for use with other flow solvers. TIGER features a silicon graphics interactive graphics environment that displays a pop-up window, graphics window, and text window. The geometry is read as a discrete set of points with options for several industrial standard formats and NASA standard formats. Various splines are available for defining the surface geometries. Grid generation is done either interactively or through a batch mode operation using history files from a previously generated grid. The batch mode operation can be done either with a graphical display of the interactive session or with no graphics so that the code can be run on another computer system. Run time can be significantly reduced by running on a Cray-YMP.

An explicit predictor-corrector solver with applications to Burgers' equation

NASA Technical Reports Server (NTRS)

Dey, S. K.; Dey, C.

1983-01-01

Forward Euler's explicit, finite-difference formula of extrapolation, is used as a predictor and a convex formula as a corrector to integrate differential equations numerically. An application has been made to Burger's equation.

An implicit scheme with memory reduction technique for steady state solutions of DVBE in all flow regimes

NASA Astrophysics Data System (ADS)

Yang, L. M.; Shu, C.; Yang, W. M.; Wu, J.

2018-04-01

High consumption of memory and computational effort is the major barrier to prevent the widespread use of the discrete velocity method (DVM) in the simulation of flows in all flow regimes. To overcome this drawback, an implicit DVM with a memory reduction technique for solving a steady discrete velocity Boltzmann equation (DVBE) is presented in this work. In the method, the distribution functions in the whole discrete velocity space do not need to be stored, and they are calculated from the macroscopic flow variables. As a result, its memory requirement is in the same order as the conventional Euler/Navier-Stokes solver. In the meantime, it is more efficient than the explicit DVM for the simulation of various flows. To make the method efficient for solving flow problems in all flow regimes, a prediction step is introduced to estimate the local equilibrium state of the DVBE. In the prediction step, the distribution function at the cell interface is calculated by the local solution of DVBE. For the flow simulation, when the cell size is less than the mean free path, the prediction step has almost no effect on the solution. However, when the cell size is much larger than the mean free path, the prediction step dominates the solution so as to provide reasonable results in such a flow regime. In addition, to further improve the computational efficiency of the developed scheme in the continuum flow regime, the implicit technique is also introduced into the prediction step. Numerical results showed that the proposed implicit scheme can provide reasonable results in all flow regimes and increase significantly the computational efficiency in the continuum flow regime as compared with the existing DVM solvers.

A Time-Accurate Upwind Unstructured Finite Volume Method for Compressible Flow with Cure of Pathological Behaviors

NASA Technical Reports Server (NTRS)

Loh, Ching Y.; Jorgenson, Philip C. E.

2007-01-01

A time-accurate, upwind, finite volume method for computing compressible flows on unstructured grids is presented. The method is second order accurate in space and time and yields high resolution in the presence of discontinuities. For efficiency, the Roe approximate Riemann solver with an entropy correction is employed. In the basic Euler/Navier-Stokes scheme, many concepts of high order upwind schemes are adopted: the surface flux integrals are carefully treated, a Cauchy-Kowalewski time-stepping scheme is used in the time-marching stage, and a multidimensional limiter is applied in the reconstruction stage. However even with these up-to-date improvements, the basic upwind scheme is still plagued by the so-called "pathological behaviors," e.g., the carbuncle phenomenon, the expansion shock, etc. A solution to these limitations is presented which uses a very simple dissipation model while still preserving second order accuracy. This scheme is referred to as the enhanced time-accurate upwind (ETAU) scheme in this paper. The unstructured grid capability renders flexibility for use in complex geometry; and the present ETAU Euler/Navier-Stokes scheme is capable of handling a broad spectrum of flow regimes from high supersonic to subsonic at very low Mach number, appropriate for both CFD (computational fluid dynamics) and CAA (computational aeroacoustics). Numerous examples are included to demonstrate the robustness of the methods.

Euler Calculations at Off-Design Conditions for an Inlet of Inward Turning RBCC-SSTO Vehicle

NASA Technical Reports Server (NTRS)

Takashima, N.; Kothari, A. P.

1998-01-01

The inviscid performance of an inward turning inlet design is calculated computationally for the first time. Hypersonic vehicle designs based on the inward turning inlets have been shown analytically to have increased effective specific impulse and lower heat load than comparably designed vehicles with two-dimensional inlets. The inward turning inlets are designed inversely from inviscid stream surfaces of known flow fields. The computational study is performed on a Mach 12 inlet design to validate the performance predicted by the design code (HAVDAC) and calculate its off-design Mach number performance. The three-dimensional Euler equations are solved for Mach 4, 8, and 12 using a software package called SAM, which consists of an unstructured mesh generator (SAMmesh), a three-dimensional unstructured mesh flow solver (SAMcfd), and a CAD-based software (SAMcad). The computed momentum averaged inlet throat pressure is within 6% of the design inlet throat pressure. The mass-flux at the inlet throat is also within 7 % of the value predicted by the design code thereby validating the accuracy of the design code. The off-design Mach number results show that flow spillage is minimal, and the variation in the mass capture ratio with Mach number is comparable to an ideal 2-D inlet. The results from the inviscid flow calculations of a Mach 12 inward turning inlet indicate that the inlet design has very good on and off-design performance which makes it a promising design candidate for future air-breathing hypersonic vehicles.

Aerodynamic Shape Optimization Using A Real-Number-Encoded Genetic Algorithm

NASA Technical Reports Server (NTRS)

Holst, Terry L.; Pulliam, Thomas H.

2001-01-01

A new method for aerodynamic shape optimization using a genetic algorithm with real number encoding is presented. The algorithm is used to optimize three different problems, a simple hill climbing problem, a quasi-one-dimensional nozzle problem using an Euler equation solver and a three-dimensional transonic wing problem using a nonlinear potential solver. Results indicate that the genetic algorithm is easy to implement and extremely reliable, being relatively insensitive to design space noise.

Prediction of Broadband Shock-Associated Noise Including Propagation Effects Originating NASA

NASA Technical Reports Server (NTRS)

Miller, Steven; Morris, Philip J.

2012-01-01

An acoustic analogy is developed based on the Euler equations for broadband shock-associated noise (BBSAN) that directly incorporates the vector Green s function of the linearized Euler equations and a steady Reynolds-Averaged Navier-Stokes solution (SRANS) to describe the mean flow. The vector Green s function allows the BBSAN propagation through the jet shear layer to be determined. The large-scale coherent turbulence is modeled by two-point second order velocity cross-correlations. Turbulent length and time scales are related to the turbulent kinetic energy and dissipation rate. An adjoint vector Green s function solver is implemented to determine the vector Green s function based on a locally parallel mean flow at different streamwise locations. The newly developed acoustic analogy can be simplified to one that uses the Green s function associated with the Helmholtz equation, which is consistent with a previous formulation by the authors. A large number of predictions are generated using three different nozzles over a wide range of fully-expanded jet Mach numbers and jet stagnation temperatures. These predictions are compared with experimental data from multiple jet noise experimental facilities. In addition, two models for the so-called fine-scale mixing noise are included in the comparisons. Improved BBSAN predictions are obtained relative to other models that do not include propagation effects.

An unstructured-grid software system for solving complex aerodynamic problems

NASA Technical Reports Server (NTRS)

Frink, Neal T.; Pirzadeh, Shahyar; Parikh, Paresh

1995-01-01

A coordinated effort has been underway over the past four years to elevate unstructured-grid methodology to a mature level. The goal of this endeavor is to provide a validated capability to non-expert users for performing rapid aerodynamic analysis and design of complex configurations. The Euler component of the system is well developed, and is impacting a broad spectrum of engineering needs with capabilities such as rapid grid generation and inviscid flow analysis, inverse design, interactive boundary layers, and propulsion effects. Progress is also being made in the more tenuous Navier-Stokes component of the system. A robust grid generator is under development for constructing quality thin-layer tetrahedral grids, along with a companion Navier-Stokes flow solver. This paper presents an overview of this effort, along with a perspective on the present and future status of the methodology.

Factorizable Schemes for the Equations of Fluid Flow

NASA Technical Reports Server (NTRS)

Sidilkover, David

1999-01-01

We present an upwind high-resolution factorizable (UHF) discrete scheme for the compressible Euler equations that allows to distinguish between full-potential and advection factors at the discrete level. The scheme approximates equations in their general conservative form and is related to the family of genuinely multidimensional upwind schemes developed previously and demonstrated to have good shock-capturing capabilities. A unique property of this scheme is that in addition to the aforementioned features it is also factorizable, i.e., it allows to distinguish between full-potential and advection factors at the discrete level. The latter property facilitates the construction of optimally efficient multigrid solvers. This is done through a relaxation procedure that utilizes the factorizability property.

Extension of the ADjoint Approach to a Laminar Navier-Stokes Solver

NASA Astrophysics Data System (ADS)

Paige, Cody

The use of adjoint methods is common in computational fluid dynamics to reduce the cost of the sensitivity analysis in an optimization cycle. The forward mode ADjoint is a combination of an adjoint sensitivity analysis method with a forward mode automatic differentiation (AD) and is a modification of the reverse mode ADjoint method proposed by Mader et al.[1]. A colouring acceleration technique is presented to reduce the computational cost increase associated with forward mode AD. The forward mode AD facilitates the implementation of the laminar Navier-Stokes (NS) equations. The forward mode ADjoint method is applied to a three-dimensional computational fluid dynamics solver. The resulting Euler and viscous ADjoint sensitivities are compared to the reverse mode Euler ADjoint derivatives and a complex-step method to demonstrate the reduced computational cost and accuracy. Both comparisons demonstrate the benefits of the colouring method and the practicality of using a forward mode AD. [1] Mader, C.A., Martins, J.R.R.A., Alonso, J.J., and van der Weide, E. (2008) ADjoint: An approach for the rapid development of discrete adjoint solvers. AIAA Journal, 46(4):863-873. doi:10.2514/1.29123.

Aerodynamic design of turbomachinery blading in three-dimensional flow - An application to radial inflow turbines

NASA Technical Reports Server (NTRS)

Yang, Y. L.; Tan, C. S.; Hawthorne, W. R.

1992-01-01

A computational method, based on a theory for turbomachinery blading design in three-dimensional inviscid flow, is applied to a parametric design study of a radial inflow turbine wheel. As the method requires the specification of swirl distribution, a technique for its smooth generation within the blade region is proposed. Excellent agreements have been obtained between the computed results from this design method and those from direct Euler computations, demonstrating the correspondence and consistency between the two. The computed results indicate the sensitivity of the pressure distribution to a lean in the stacking axis and a minor alteration in the hub/shroud profiles. Analysis based on Navier-Stokes solver shows no breakdown of flow within the designed blade passage and agreement with that from design calculation; thus the flow in the designed turbine rotor closely approximates that of an inviscid one. These calculations illustrate the use of a design method coupled to an analysis tool for establishing guidelines and criteria for designing turbomachinery blading.

An Empirical Temperature Variance Source Model in Heated Jets

NASA Technical Reports Server (NTRS)

Khavaran, Abbas; Bridges, James

2012-01-01

An acoustic analogy approach is implemented that models the sources of jet noise in heated jets. The equivalent sources of turbulent mixing noise are recognized as the differences between the fluctuating and Favre-averaged Reynolds stresses and enthalpy fluxes. While in a conventional acoustic analogy only Reynolds stress components are scrutinized for their noise generation properties, it is now accepted that a comprehensive source model should include the additional entropy source term. Following Goldstein s generalized acoustic analogy, the set of Euler equations are divided into two sets of equations that govern a non-radiating base flow plus its residual components. When the base flow is considered as a locally parallel mean flow, the residual equations may be rearranged to form an inhomogeneous third-order wave equation. A general solution is written subsequently using a Green s function method while all non-linear terms are treated as the equivalent sources of aerodynamic sound and are modeled accordingly. In a previous study, a specialized Reynolds-averaged Navier-Stokes (RANS) solver was implemented to compute the variance of thermal fluctuations that determine the enthalpy flux source strength. The main objective here is to present an empirical model capable of providing a reasonable estimate of the stagnation temperature variance in a jet. Such a model is parameterized as a function of the mean stagnation temperature gradient in the jet, and is evaluated using commonly available RANS solvers. The ensuing thermal source distribution is compared with measurements as well as computational result from a dedicated RANS solver that employs an enthalpy variance and dissipation rate model. Turbulent mixing noise predictions are presented for a wide range of jet temperature ratios from 1.0 to 3.20.

Towards a Comprehensive Model of Jet Noise Using an Acoustic Analogy and Steady RANS Solutions

NASA Technical Reports Server (NTRS)

Miller, Steven A. E.

2013-01-01

An acoustic analogy is developed to predict the noise from jet flows. It contains two source models that independently predict the noise from turbulence and shock wave shear layer interactions. The acoustic analogy is based on the Euler equations and separates the sources from propagation. Propagation effects are taken into account by calculating the vector Green's function of the linearized Euler equations. The sources are modeled following the work of Tam and Auriault, Morris and Boluriaan, and Morris and Miller. A statistical model of the two-point cross-correlation of the velocity fluctuations is used to describe the turbulence. The acoustic analogy attempts to take into account the correct scaling of the sources for a wide range of nozzle pressure and temperature ratios. It does not make assumptions regarding fine- or large-scale turbulent noise sources, self- or shear-noise, or convective amplification. The acoustic analogy is partially informed by three-dimensional steady Reynolds-Averaged Navier-Stokes solutions that include the nozzle geometry. The predictions are compared with experiments of jets operating subsonically through supersonically and at unheated and heated temperatures. Predictions generally capture the scaling of both mixing noise and BBSAN for the conditions examined, but some discrepancies remain that are due to the accuracy of the steady RANS turbulence model closure, the equivalent sources, and the use of a simplified vector Green's function solver of the linearized Euler equations.

Solution of steady and unsteady transonic-vortex flows using Euler and full-potential equations

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; Chuang, Andrew H.; Hu, Hong

1989-01-01

Two methods are presented for inviscid transonic flows: unsteady Euler equations in a rotating frame of reference for transonic-vortex flows and integral solution of full-potential equation with and without embedded Euler domains for transonic airfoil flows. The computational results covered: steady and unsteady conical vortex flows; 3-D steady transonic vortex flow; and transonic airfoil flows. The results are in good agreement with other computational results and experimental data. The rotating frame of reference solution is potentially efficient as compared with the space fixed reference formulation with dynamic gridding. The integral equation solution with embedded Euler domain is computationally efficient and as accurate as the Euler equations.

Explicit and implicit compact high-resolution shock-capturing methods for multidimensional Euler equations 1: Formulation

NASA Technical Reports Server (NTRS)

Yee, H. C.

1995-01-01

Two classes of explicit compact high-resolution shock-capturing methods for the multidimensional compressible Euler equations for fluid dynamics are constructed. Some of these schemes can be fourth-order accurate away from discontinuities. For the semi-discrete case their shock-capturing properties are of the total variation diminishing (TVD), total variation bounded (TVB), total variation diminishing in the mean (TVDM), essentially nonoscillatory (ENO), or positive type of scheme for 1-D scalar hyperbolic conservation laws and are positive schemes in more than one dimension. These fourth-order schemes require the same grid stencil as their second-order non-compact cousins. One class does not require the standard matrix inversion or a special numerical boundary condition treatment associated with typical compact schemes. Due to the construction, these schemes can be viewed as approximations to genuinely multidimensional schemes in the sense that they might produce less distortion in spherical type shocks and are more accurate in vortex type flows than schemes based purely on one-dimensional extensions. However, one class has a more desirable high-resolution shock-capturing property and a smaller operation count in 3-D than the other class. The extension of these schemes to coupled nonlinear systems can be accomplished using the Roe approximate Riemann solver, the generalized Steger and Warming flux-vector splitting or the van Leer type flux-vector splitting. Modification to existing high-resolution second- or third-order non-compact shock-capturing computer codes is minimal. High-resolution shock-capturing properties can also be achieved via a variant of the second-order Lax-Friedrichs numerical flux without the use of Riemann solvers for coupled nonlinear systems with comparable operations count to their classical shock-capturing counterparts. The simplest extension to viscous flows can be achieved by using the standard fourth-order compact or non-compact formula for the viscous terms.

A Computational Study of Shear Layer Receptivity

NASA Astrophysics Data System (ADS)

Barone, Matthew; Lele, Sanjiva

2002-11-01

The receptivity of two-dimensional, compressible shear layers to local and external excitation sources is examined using a computational approach. The family of base flows considered consists of a laminar supersonic stream separated from nearly quiescent fluid by a thin, rigid splitter plate with a rounded trailing edge. The linearized Euler and linearized Navier-Stokes equations are solved numerically in the frequency domain. The flow solver is based on a high order finite difference scheme, coupled with an overset mesh technique developed for computational aeroacoustics applications. Solutions are obtained for acoustic plane wave forcing near the most unstable shear layer frequency, and are compared to the existing low frequency theory. An adjoint formulation to the present problem is developed, and adjoint equation calculations are performed using the same numerical methods as for the regular equation sets. Solutions to the adjoint equations are used to shed light on the mechanisms which control the receptivity of finite-width compressible shear layers.

Methodology for CFD Design Analysis of National Launch System Nozzle Manifold

NASA Technical Reports Server (NTRS)

Haire, Scot L.

1993-01-01

The current design environment dictates that high technology CFD (Computational Fluid Dynamics) analysis produce quality results in a timely manner if it is to be integrated into the design process. The design methodology outlined describes the CFD analysis of an NLS (National Launch System) nozzle film cooling manifold. The objective of the analysis was to obtain a qualitative estimate for the flow distribution within the manifold. A complex, 3D, multiple zone, structured grid was generated from a 3D CAD file of the geometry. A Euler solution was computed with a fully implicit compressible flow solver. Post processing consisted of full 3D color graphics and mass averaged performance. The result was a qualitative CFD solution that provided the design team with relevant information concerning the flow distribution in and performance characteristics of the film cooling manifold within an effective time frame. Also, this design methodology was the foundation for a quick turnaround CFD analysis of the next iteration in the manifold design.

Development of a Navier-Stokes algorithm for parallel-processing supercomputers. Ph.D. Thesis - Colorado State Univ., Dec. 1988

NASA Technical Reports Server (NTRS)

Swisshelm, Julie M.

1989-01-01

An explicit flow solver, applicable to the hierarchy of model equations ranging from Euler to full Navier-Stokes, is combined with several techniques designed to reduce computational expense. The computational domain consists of local grid refinements embedded in a global coarse mesh, where the locations of these refinements are defined by the physics of the flow. Flow characteristics are also used to determine which set of model equations is appropriate for solution in each region, thereby reducing not only the number of grid points at which the solution must be obtained, but also the computational effort required to get that solution. Acceleration to steady-state is achieved by applying multigrid on each of the subgrids, regardless of the particular model equations being solved. Since each of these components is explicit, advantage can readily be taken of the vector- and parallel-processing capabilities of machines such as the Cray X-MP and Cray-2.

The design and implementation of a parallel unstructured Euler solver using software primitives

NASA Technical Reports Server (NTRS)

Das, R.; Mavriplis, D. J.; Saltz, J.; Gupta, S.; Ponnusamy, R.

1992-01-01

This paper is concerned with the implementation of a three-dimensional unstructured grid Euler-solver on massively parallel distributed-memory computer architectures. The goal is to minimize solution time by achieving high computational rates with a numerically efficient algorithm. An unstructured multigrid algorithm with an edge-based data structure has been adopted, and a number of optimizations have been devised and implemented in order to accelerate the parallel communication rates. The implementation is carried out by creating a set of software tools, which provide an interface between the parallelization issues and the sequential code, while providing a basis for future automatic run-time compilation support. Large practical unstructured grid problems are solved on the Intel iPSC/860 hypercube and Intel Touchstone Delta machine. The quantitative effect of the various optimizations are demonstrated, and we show that the combined effect of these optimizations leads to roughly a factor of three performance improvement. The overall solution efficiency is compared with that obtained on the CRAY-YMP vector supercomputer.

Some Developments of the Equilibrium Particle Simulation Method for the Direct Simulation of Compressible Flows

NASA Technical Reports Server (NTRS)

Macrossan, M. N.

1995-01-01

The direct simulation Monte Carlo (DSMC) method is the established technique for the simulation of rarefied gas flows. In some flows of engineering interest, such as occur for aero-braking spacecraft in the upper atmosphere, DSMC can become prohibitively expensive in CPU time because some regions of the flow, particularly on the windward side of blunt bodies, become collision dominated. As an alternative to using a hybrid DSMC and continuum gas solver (Euler or Navier-Stokes solver) this work is aimed at making the particle simulation method efficient in the high density regions of the flow. A high density, infinite collision rate limit of DSMC, the Equilibrium Particle Simulation method (EPSM) was proposed some 15 years ago. EPSM is developed here for the flow of a gas consisting of many different species of molecules and is shown to be computationally efficient (compared to DSMC) for high collision rate flows. It thus offers great potential as part of a hybrid DSMC/EPSM code which could handle flows in the transition regime between rarefied gas flows and fully continuum flows. As a first step towards this goal a pure EPSM code is described. The next step of combining DSMC and EPSM is not attempted here but should be straightforward. EPSM and DSMC are applied to Taylor-Couette flow with Kn = 0.02 and 0.0133 and S(omega) = 3). Toroidal vortices develop for both methods but some differences are found, as might be expected for the given flow conditions. EPSM appears to be less sensitive to the sequence of random numbers used in the simulation than is DSMC and may also be more dissipative. The question of the origin and the magnitude of the dissipation in EPSM is addressed. It is suggested that this analysis is also relevant to DSMC when the usual accuracy requirements on the cell size and decoupling time step are relaxed in the interests of computational efficiency.

Mathematical Investigation of Fluid Flow, Mass Transfer, and Slag-steel Interfacial Behavior in Gas-stirred Ladles

NASA Astrophysics Data System (ADS)

Cao, Qing; Nastac, Laurentiu

2018-06-01

In this study, the Euler-Euler and Euler-Lagrange modeling approaches were applied to simulate the multiphase flow in the water model and gas-stirred ladle systems. Detailed comparisons of the computational and experimental results were performed to establish which approach is more accurate for predicting the gas-liquid multiphase flow phenomena. It was demonstrated that the Euler-Lagrange approach is more accurate than the Euler-Euler approach. The Euler-Lagrange approach was applied to study the effects of the free surface setup, injected bubble size, gas flow rate, and slag layer thickness on the slag-steel interaction and mass transfer behavior. Detailed discussions on the flat/non-flat free surface assumption were provided. Significant inaccuracies in the prediction of the surface fluid flow characteristics were found when the flat free surface was assumed. The variations in the main controlling parameters (bubble size, gas flow rate, and slag layer thickness) and their potential impact on the multiphase fluid flow and mass transfer characteristics (turbulent intensity, mass transfer rate, slag-steel interfacial area, flow patterns, etc.,) in gas-stirred ladles were quantitatively determined to ensure the proper increase in the ladle refining efficiency. It was revealed that by injecting finer bubbles as well as by properly increasing the gas flow rate and the slag layer thickness, the ladle refining efficiency can be enhanced significantly.

Efficient Gradient-Based Shape Optimization Methodology Using Inviscid/Viscous CFD

NASA Technical Reports Server (NTRS)

Baysal, Oktay

1997-01-01

The formerly developed preconditioned-biconjugate-gradient (PBCG) solvers for the analysis and the sensitivity equations had resulted in very large error reductions per iteration; quadratic convergence was achieved whenever the solution entered the domain of attraction to the root. Its memory requirement was also lower as compared to a direct inversion solver. However, this memory requirement was high enough to preclude the realistic, high grid-density design of a practical 3D geometry. This limitation served as the impetus to the first-year activity (March 9, 1995 to March 8, 1996). Therefore, the major activity for this period was the development of the low-memory methodology for the discrete-sensitivity-based shape optimization. This was accomplished by solving all the resulting sets of equations using an alternating-direction-implicit (ADI) approach. The results indicated that shape optimization problems which required large numbers of grid points could be resolved with a gradient-based approach. Therefore, to better utilize the computational resources, it was recommended that a number of coarse grid cases, using the PBCG method, should initially be conducted to better define the optimization problem and the design space, and obtain an improved initial shape. Subsequently, a fine grid shape optimization, which necessitates using the ADI method, should be conducted to accurately obtain the final optimized shape. The other activity during this period was the interaction with the members of the Aerodynamic and Aeroacoustic Methods Branch of Langley Research Center during one stage of their investigation to develop an adjoint-variable sensitivity method using the viscous flow equations. This method had algorithmic similarities to the variational sensitivity methods and the control-theory approach. However, unlike the prior studies, it was considered for the three-dimensional, viscous flow equations. The major accomplishment in the second period of this project (March 9, 1996 to March 8, 1997) was the extension of the shape optimization methodology for the Thin-Layer Navier-Stokes equations. Both the Euler-based and the TLNS-based analyses compared with the analyses obtained using the CFL3D code. The sensitivities, again from both levels of the flow equations, also compared very well with the finite-differenced sensitivities. A fairly large set of shape optimization cases were conducted to study a number of issues previously not well understood. The testbed for these cases was the shaping of an arrow wing in Mach 2.4 flow. All the final shapes, obtained either from a coarse-grid-based or a fine-grid-based optimization, using either a Euler-based or a TLNS-based analysis, were all re-analyzed using a fine-grid, TLNS solution for their function evaluations. This allowed for a more fair comparison of their relative merits. From the aerodynamic performance standpoint, the fine-grid TLNS-based optimization produced the best shape, and the fine-grid Euler-based optimization produced the lowest cruise efficiency.

Development of an Aeroelastic Code Based on an Euler/Navier-Stokes Aerodynamic Solver

NASA Technical Reports Server (NTRS)

Bakhle, Milind A.; Srivastava, Rakesh; Keith, Theo G., Jr.; Stefko, George L.; Janus, Mark J.

1996-01-01

This paper describes the development of an aeroelastic code (TURBO-AE) based on an Euler/Navier-Stokes unsteady aerodynamic analysis. A brief review of the relevant research in the area of propulsion aeroelasticity is presented. The paper briefly describes the original Euler/Navier-Stokes code (TURBO) and then details the development of the aeroelastic extensions. The aeroelastic formulation is described. The modeling of the dynamics of the blade using a modal approach is detailed, along with the grid deformation approach used to model the elastic deformation of the blade. The work-per-cycle approach used to evaluate aeroelastic stability is described. Representative results used to verify the code are presented. The paper concludes with an evaluation of the development thus far, and some plans for further development and validation of the TURBO-AE code.

Boundary layer energization by means of optimized vortex generators

NASA Technical Reports Server (NTRS)

Barber, T. J.; Mounts, J. S.; Mccormick, D. C.

1993-01-01

A three-dimensional, multi-block, multi-zone, Euler analysis has been developed and applied to analyze the flow processes induced by a lateral array of low profile vortex generators (VG). These vortex generators have been shown to alleviate boundary layer separation through the generation of streamwise vorticity. The analysis has been applied to help develop improved VG configurations in an efficient manner. Special attention has been paid to determining the accuracy requirements of the solver for calculations in which vortical mechanisms are dominant. The analysis has been used to assess the effectiveness or boundary layer energization capacity of different VG's, including the effect of scale and shape variation. Finally, the analysis has been validated through comparisons with experimental data obtained in a large-scale low-speed wind tunnel.

Analysis of the Effects of Streamwise Lift Distribution on Sonic Boom Signature

NASA Technical Reports Server (NTRS)

Yoo, Seung Yeun (Paul)

2010-01-01

The streamwise lift distribution of a wing-canard-stabilator-body configuration was varied to study its effect on the near-field sonic boom signature. The investigation was carried out via solving the three-dimensional Euler equation with the OVERFLOW-2 flow solver. The computational meshes were created using the Chimera overset grid topology. The lift distribution was varied by first deflecting the canard then trimming the aircraft with the wing and the stabilator while maintaining constant lift coefficient of 0.05. A validation study using experimental results was also performed to determine required grid resolution and appropriate numerical scheme. A wide range of streamwise lift distribution was simulated. The result shows that the longitudinal wave propagation speed can be controlled through lift distribution thus controlling the shock coalescence.

Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

1992-01-01

One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology.

CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. II. GRAY RADIATION HYDRODYNAMICS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, W.; Almgren, A.; Bell, J.

We describe the development of a flux-limited gray radiation solver for the compressible astrophysics code, CASTRO. CASTRO uses an Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically rectangular variable-sized grids with simultaneous refinement in both space and time. The gray radiation solver is based on a mixed-frame formulation of radiation hydrodynamics. In our approach, the system is split into two parts, one part that couples the radiation and fluid in a hyperbolic subsystem, and another parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem is solved explicitly with a high-order Godunovmore » scheme, whereas the parabolic part is solved implicitly with a first-order backward Euler method.« less

Evaluation of a doubly-swept blade tip for rotorcraft noise reduction

NASA Technical Reports Server (NTRS)

Wake, Brian E.; Egolf, T. Alan

1992-01-01

A computational study was performed for a doubly-swept rotor blade tip to determine its benefit for high-speed impulsive (HSI) and blade-vortex interaction (BVI) noise. This design consists of aft and forward sweep. For the HSI-noise computations, unsteady Euler calculations were performed for several variations to a rotor blade geometry. A doubly-swept planform was predicted to increase the delocalizing Mach number to 0.94 (representative of a 200+ kt helicopter). For the BVI-noise problem, it had been hypothesized that the doubly-swept blade tip, by producing a leading-edge vortex, would reduce the tip-vortex effect on BVI noise. A procedure was used in which the tip vortex velocity profile computed by a Navier-Stokes solver was used to compute the inflow associated with BVI. This inflow was used by a Euler solver to compute the unsteady pressures for an acoustic analysis. The results of this study were inconclusive due to the difficulty in accurately predicting the viscous tip vortex downstream of the blade. Also, for the condition studied, no leading-edge vortex formed at the tip.

Development of computational methods for heavy lift launch vehicles

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan; Ryan, James S.

1993-01-01

The research effort has been focused on the development of an advanced flow solver for complex viscous turbulent flows with shock waves. The three-dimensional Euler and full/thin-layer Reynolds-averaged Navier-Stokes equations for compressible flows are solved on structured hexahedral grids. The Baldwin-Lomax algebraic turbulence model is used for closure. The space discretization is based on a cell-centered finite-volume method augmented by a variety of numerical dissipation models with optional total variation diminishing limiters. The governing equations are integrated in time by an implicit method based on lower-upper factorization and symmetric Gauss-Seidel relaxation. The algorithm is vectorized on diagonal planes of sweep using two-dimensional indices in three dimensions. A new computer program named CENS3D has been developed for viscous turbulent flows with discontinuities. Details of the code are described in Appendix A and Appendix B. With the developments of the numerical algorithm and dissipation model, the simulation of three-dimensional viscous compressible flows has become more efficient and accurate. The results of the research are expected to yield a direct impact on the design process of future liquid fueled launch systems.

A fast Chebyshev method for simulating flexible-wing propulsion

NASA Astrophysics Data System (ADS)

Moore, M. Nicholas J.

2017-09-01

We develop a highly efficient numerical method to simulate small-amplitude flapping propulsion by a flexible wing in a nearly inviscid fluid. We allow the wing's elastic modulus and mass density to vary arbitrarily, with an eye towards optimizing these distributions for propulsive performance. The method to determine the wing kinematics is based on Chebyshev collocation of the 1D beam equation as coupled to the surrounding 2D fluid flow. Through small-amplitude analysis of the Euler equations (with trailing-edge vortex shedding), the complete hydrodynamics can be represented by a nonlocal operator that acts on the 1D wing kinematics. A class of semi-analytical solutions permits fast evaluation of this operator with O (Nlog ⁡ N) operations, where N is the number of collocation points on the wing. This is in contrast to the minimum O (N2) cost of a direct 2D fluid solver. The coupled wing-fluid problem is thus recast as a PDE with nonlocal operator, which we solve using a preconditioned iterative method. These techniques yield a solver of near-optimal complexity, O (Nlog ⁡ N) , allowing one to rapidly search the infinite-dimensional parameter space of all possible material distributions and even perform optimization over this space.

Globalized Newton-Krylov-Schwarz Algorithms and Software for Parallel Implicit CFD

NASA Technical Reports Server (NTRS)

Gropp, W. D.; Keyes, D. E.; McInnes, L. C.; Tidriri, M. D.

1998-01-01

Implicit solution methods are important in applications modeled by PDEs with disparate temporal and spatial scales. Because such applications require high resolution with reasonable turnaround, "routine" parallelization is essential. The pseudo-transient matrix-free Newton-Krylov-Schwarz (Psi-NKS) algorithmic framework is presented as an answer. We show that, for the classical problem of three-dimensional transonic Euler flow about an M6 wing, Psi-NKS can simultaneously deliver: globalized, asymptotically rapid convergence through adaptive pseudo- transient continuation and Newton's method-, reasonable parallelizability for an implicit method through deferred synchronization and favorable communication-to-computation scaling in the Krylov linear solver; and high per- processor performance through attention to distributed memory and cache locality, especially through the Schwarz preconditioner. Two discouraging features of Psi-NKS methods are their sensitivity to the coding of the underlying PDE discretization and the large number of parameters that must be selected to govern convergence. We therefore distill several recommendations from our experience and from our reading of the literature on various algorithmic components of Psi-NKS, and we describe a freely available, MPI-based portable parallel software implementation of the solver employed here.

A Numerical Method of Calculating Propeller Noise Including Acoustic Nonlinear Effects

NASA Technical Reports Server (NTRS)

Korkan, K. D.

1985-01-01

Using the transonic flow fields(s) generated by the NASPROP-E computer code for an eight blade SR3-series propeller, a theoretical method is investigated to calculate the total noise values and frequency content in the acoustic near and far field without using the Ffowcs Williams - Hawkings equation. The flow field is numerically generated using an implicit three dimensional Euler equation solver in weak conservation law form. Numerical damping is required by the differencing method for stability in three dimensions, and the influence of the damping on the calculated acoustic values is investigated. The acoustic near field is solved by integrating with respect to time the pressure oscillations induced at a stationary observer location. The acoustic far field is calculated from the near field primitive variables as generated by NASPROP-E computer code using a method involving a perturbation velocity potential as suggested by Hawkings in the calculation of the acoustic pressure time-history at a specified far field observed location. the methodologies described are valid for calculating total noise levels and are applicable to any propeller geometry for which a flow field solution is available.

Progress in the Simulation of Steady and Time-Dependent Flows with 3D Parallel Unstructured Cartesian Methods

NASA Technical Reports Server (NTRS)

Aftosmis, M. J.; Berger, M. J.; Murman, S. M.; Kwak, Dochan (Technical Monitor)

2002-01-01

The proposed paper will present recent extensions in the development of an efficient Euler solver for adaptively-refined Cartesian meshes with embedded boundaries. The paper will focus on extensions of the basic method to include solution adaptation, time-dependent flow simulation, and arbitrary rigid domain motion. The parallel multilevel method makes use of on-the-fly parallel domain decomposition to achieve extremely good scalability on large numbers of processors, and is coupled with an automatic coarse mesh generation algorithm for efficient processing by a multigrid smoother. Numerical results are presented demonstrating parallel speed-ups of up to 435 on 512 processors. Solution-based adaptation may be keyed off truncation error estimates using tau-extrapolation or a variety of feature detection based refinement parameters. The multigrid method is extended to for time-dependent flows through the use of a dual-time approach. The extension to rigid domain motion uses an Arbitrary Lagrangian-Eulerlarian (ALE) formulation, and results will be presented for a variety of two- and three-dimensional example problems with both simple and complex geometry.

Time-Accurate, Unstructured-Mesh Navier-Stokes Computations with the Space-Time CESE Method

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan

2006-01-01

Application of the newly emerged space-time conservation element solution element (CESE) method to compressible Navier-Stokes equations is studied. In contrast to Euler equations solvers, several issues such as boundary conditions, numerical dissipation, and grid stiffness warrant systematic investigations and validations. Non-reflecting boundary conditions applied at the truncated boundary are also investigated from the stand point of acoustic wave propagation. Validations of the numerical solutions are performed by comparing with exact solutions for steady-state as well as time-accurate viscous flow problems. The test cases cover a broad speed regime for problems ranging from acoustic wave propagation to 3D hypersonic configurations. Model problems pertinent to hypersonic configurations demonstrate the effectiveness of the CESE method in treating flows with shocks, unsteady waves, and separations. Good agreement with exact solutions suggests that the space-time CESE method provides a viable alternative for time-accurate Navier-Stokes calculations of a broad range of problems.

A third-order implicit discontinuous Galerkin method based on a Hermite WENO reconstruction for time-accurate solution of the compressible Navier-Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xia, Yidong; Liu, Xiaodong; Luo, Hong

2015-06-01

Here, a space and time third-order discontinuous Galerkin method based on a Hermite weighted essentially non-oscillatory reconstruction is presented for the unsteady compressible Euler and Navier–Stokes equations. At each time step, a lower-upper symmetric Gauss–Seidel preconditioned generalized minimal residual solver is used to solve the systems of linear equations arising from an explicit first stage, single diagonal coefficient, diagonally implicit Runge–Kutta time integration scheme. The performance of the developed method is assessed through a variety of unsteady flow problems. Numerical results indicate that this method is able to deliver the designed third-order accuracy of convergence in both space and time,more » while requiring remarkably less storage than the standard third-order discontinous Galerkin methods, and less computing time than the lower-order discontinous Galerkin methods to achieve the same level of temporal accuracy for computing unsteady flow problems.« less

On the statistical mechanics of the 2D stochastic Euler equation

NASA Astrophysics Data System (ADS)

Bouchet, Freddy; Laurie, Jason; Zaboronski, Oleg

2011-12-01

The dynamics of vortices and large scale structures is qualitatively very different in two dimensional flows compared to its three dimensional counterparts, due to the presence of multiple integrals of motion. These are believed to be responsible for a variety of phenomena observed in Euler flow such as the formation of large scale coherent structures, the existence of meta-stable states and random abrupt changes in the topology of the flow. In this paper we study stochastic dynamics of the finite dimensional approximation of the 2D Euler flow based on Lie algebra su(N) which preserves all integrals of motion. In particular, we exploit rich algebraic structure responsible for the existence of Euler's conservation laws to calculate the invariant measures and explore their properties and also study the approach to equilibrium. Unexpectedly, we find deep connections between equilibrium measures of finite dimensional su(N) truncations of the stochastic Euler equations and random matrix models. Our work can be regarded as a preparation for addressing the questions of large scale structures, meta-stability and the dynamics of random transitions between different flow topologies in stochastic 2D Euler flows.

A linearized Euler analysis of unsteady flows in turbomachinery

NASA Technical Reports Server (NTRS)

Hall, Kenneth C.; Crawley, Edward F.

1987-01-01

A method for calculating unsteady flows in cascades is presented. The model, which is based on the linearized unsteady Euler equations, accounts for blade loading shock motion, wake motion, and blade geometry. The mean flow through the cascade is determined by solving the full nonlinear Euler equations. Assuming the unsteadiness in the flow is small, then the Euler equations are linearized about the mean flow to obtain a set of linear variable coefficient equations which describe the small amplitude, harmonic motion of the flow. These equations are discretized on a computational grid via a finite volume operator and solved directly subject to an appropriate set of linearized boundary conditions. The steady flow, which is calculated prior to the unsteady flow, is found via a Newton iteration procedure. An important feature of the analysis is the use of shock fitting to model steady and unsteady shocks. Use of the Euler equations with the unsteady Rankine-Hugoniot shock jump conditions correctly models the generation of steady and unsteady entropy and vorticity at shocks. In particular, the low frequency shock displacement is correctly predicted. Results of this method are presented for a variety of test cases. Predicted unsteady transonic flows in channels are compared to full nonlinear Euler solutions obtained using time-accurate, time-marching methods. The agreement between the two methods is excellent for small to moderate levels of flow unsteadiness. The method is also used to predict unsteady flows in cascades due to blade motion (flutter problem) and incoming disturbances (gust response problem).

Overview of Transonic to Hypersonic Stage Separation Tool Development for Multi-Stage-to-Orbit Concepts

NASA Technical Reports Server (NTRS)

Murphy, Kelly J.; Bunning, Pieter G.; Pamadi, Bandu N.; Scallion, William I.; Jones, Kenneth M.

2004-01-01

An overview of research efforts at NASA in support of the stage separation and ascent aerothermodynamics research program is presented. The objective of this work is to develop a synergistic suite of experimental, computational, and engineering tools and methods to apply to vehicle separation across the transonic to hypersonic speed regimes. Proximity testing of a generic bimese wing-body configuration is on-going in the transonic (Mach numbers 0.6, 1.05, and 1.1), supersonic (Mach numbers 2.3, 3.0, and 4.5) and hypersonic (Mach numbers 6 and 10) speed regimes in four wind tunnel facilities at the NASA Langley Research Center. An overset grid, Navier-Stokes flow solver has been enhanced and demonstrated on a matrix of proximity cases and on a dynamic separation simulation of the bimese configuration. Steady-state predictions with this solver were in excellent agreement with wind tunnel data at Mach 3 as were predictions via a Cartesian-grid Euler solver. Experimental and computational data have been used to evaluate multi-body enhancements to the widely-used Aerodynamic Preliminary Analysis System, an engineering methodology, and to develop a new software package, SepSim, for the simulation and visualization of vehicle motions in a stage separation scenario. Web-based software will be used for archiving information generated from this research program into a database accessible to the user community. Thus, a framework has been established to study stage separation problems using coordinated experimental, computational, and engineering tools.

QED multi-dimensional vacuum polarization finite-difference solver

NASA Astrophysics Data System (ADS)

Carneiro, Pedro; Grismayer, Thomas; Silva, Luís; Fonseca, Ricardo

2015-11-01

The Extreme Light Infrastructure (ELI) is expected to deliver peak intensities of 1023 - 1024 W/cm2 allowing to probe nonlinear Quantum Electrodynamics (QED) phenomena in an unprecedented regime. Within the framework of QED, the second order process of photon-photon scattering leads to a set of extended Maxwell's equations [W. Heisenberg and H. Euler, Z. Physik 98, 714] effectively creating nonlinear polarization and magnetization terms that account for the nonlinear response of the vacuum. To model this in a self-consistent way, we present a multi dimensional generalized Maxwell equation finite difference solver with significantly enhanced dispersive properties, which was implemented in the OSIRIS particle-in-cell code [R.A. Fonseca et al. LNCS 2331, pp. 342-351, 2002]. We present a detailed numerical analysis of this electromagnetic solver. As an illustration of the properties of the solver, we explore several examples in extreme conditions. We confirm the theoretical prediction of vacuum birefringence of a pulse propagating in the presence of an intense static background field [arXiv:1301.4918 [quant-ph

Aerodynamic shape optimization of a HSCT type configuration with improved surface definition

NASA Technical Reports Server (NTRS)

Thomas, Almuttil M.; Tiwari, Surendra N.

1994-01-01

Two distinct parametrization procedures of generating free-form surfaces to represent aerospace vehicles are presented. The first procedure is the representation using spline functions such as nonuniform rational b-splines (NURBS) and the second is a novel (geometrical) parametrization using solutions to a suitably chosen partial differential equation. The main idea is to develop a surface which is more versatile and can be used in an optimization process. Unstructured volume grid is generated by an advancing front algorithm and solutions obtained using an Euler solver. Grid sensitivity with respect to surface design parameters and aerodynamic sensitivity coefficients based on potential flow is obtained using an automatic differentiator precompiler software tool. Aerodynamic shape optimization of a complete aircraft with twenty four design variables is performed. High speed civil transport aircraft (HSCT) configurations are targeted to demonstrate the process.

Algorithm and code development for unsteady three-dimensional Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Obayashi, Shigeru

1994-01-01

Aeroelastic tests require extensive cost and risk. An aeroelastic wind-tunnel experiment is an order of magnitude more expensive than a parallel experiment involving only aerodynamics. By complementing the wind-tunnel experiments with numerical simulations, the overall cost of the development of aircraft can be considerably reduced. In order to accurately compute aeroelastic phenomenon it is necessary to solve the unsteady Euler/Navier-Stokes equations simultaneously with the structural equations of motion. These equations accurately describe the flow phenomena for aeroelastic applications. At ARC a code, ENSAERO, is being developed for computing the unsteady aerodynamics and aeroelasticity of aircraft, and it solves the Euler/Navier-Stokes equations. The purpose of this cooperative agreement was to enhance ENSAERO in both algorithm and geometric capabilities. During the last five years, the algorithms of the code have been enhanced extensively by using high-resolution upwind algorithms and efficient implicit solvers. The zonal capability of the code has been extended from a one-to-one grid interface to a mismatching unsteady zonal interface. The geometric capability of the code has been extended from a single oscillating wing case to a full-span wing-body configuration with oscillating control surfaces. Each time a new capability was added, a proper validation case was simulated, and the capability of the code was demonstrated.

Numerical simulation of steady three-dimensional flows in axial turbomachinery bladerows

NASA Astrophysics Data System (ADS)

Basson, Anton Herman

The formulation for and application of a numerical model for low Mach number steady three-dimensional flows in axial turbomachinery blade rows is presented. The formulation considered here includes an efficient grid generation scheme (particularly suited to computational grids for the analysis of turbulent turbomachinery flows) and a semi-implicit, pressure-based computational fluid dynamics scheme that directly includes artificial dissipation, applicable to viscous and inviscid flows. The grid generation technique uses a combination of algebraic and elliptic methods, in conjunction with the Minimal Residual Method, to economically generate smooth structured grids. For typical H-grids in turbomachinery bladerows, when compared to a purely elliptic grid generation scheme, the presented grid generation scheme produces grids with much improved smoothness near the leading and trailing edges, allows the use of small near wall grid spacing required by low Reynolds number turbulence models, and maintains orthogonality of the grid near the solid boundaries even for high flow angle cascades. A specialized embedded H-grid for application particularly to tip clearance flows is presented. This topology smoothly discretizes the domain without modifying the tip shape, while requiring only minor modifications to H-grid flow solvers. Better quantitative modeling of the tip clearance vortex structure than that obtained with a pinched tip approximation is demonstrated. The formulation of artificial dissipation terms for a semi-implicit, pressure-based (SIMPLE type) flow solver, is presented. It is applied to both the Euler and the Navier-Stokes equations, expressed in generalized coordinates using a non-staggered grid. This formulation is compared to some SIMPLE and time marching formulations, revealing the artificial dissipation inherent in some commonly used semi-implicit formulations. The effect of the amount of dissipation on the accuracy of the solution and the convergence rate is quantitatively demonstrated for a number of flow cases. The ability of the formulation to model complex steady turbomachinery flows is demonstrated, e.g. for pressure driven secondary flows, turbine nozzle wakes, turbulent boundary layers. The formulation's modeling of blade surface heat transfer is assessed. The numerical model is used to investigate the structure of phenomena associated with tip clearance flows in a turbine nozzle.

Airflow structures and nano-particle deposition in a human upper airway model

NASA Astrophysics Data System (ADS)

Zhang, Z.; Kleinstreuer, C.

2004-07-01

Considering a human upper airway model, or equivalently complex internal flow conduits, the transport and deposition of nano-particles in the 1-150 nm diameter range are simulated and analyzed for cyclic and steady flow conditions. Specifically, using a commercial finite-volume software with user-supplied programs as a solver, the Euler-Euler approach for the fluid-particle dynamics is employed with a low-Reynolds-number k- ω model for laminar-to-turbulent airflow and the mass transfer equation for dispersion of nano-particles or vapors. Presently, the upper respiratory system consists of two connected segments of a simplified human cast replica, i.e., the oral airways from the mouth to the trachea (Generation G0) and an upper tracheobronchial tree model of G0-G3. Experimentally validated computational fluid-particle dynamics results show the following: (i) transient effects in the oral airways appear most prominently during the decelerating phase of the inspiratory cycle; (ii) selecting matching flow rates, total deposition fractions of nano-size particles for cyclic inspiratory flow are not significantly different from those for steady flow; (iii) turbulent fluctuations which occur after the throat can persist downstream to at least Generation G3 at medium and high inspiratory flow rates (i.e., Qin⩾30 l/min) due to the enhancement of flow instabilities just upstream of the flow dividers; however, the effects of turbulent fluctuations on nano-particle deposition are quite minor in the human upper airways; (iv) deposition of nano-particles occurs to a relatively greater extent around the carinal ridges when compared to the straight tubular segments in the bronchial airways; (v) deposition distributions of nano-particles vary with airway segment, particle size, and inhalation flow rate, where the local deposition is more uniformly distributed for large-size particles (say, dp=100 nm) than for small-size particles (say, dp=1 nm); (vi) dilute 1 nm particle suspensions behave like certain (fuel) vapors which have the same diffusivities; and (vii) new correlations for particle deposition as a function of a diffusion parameter are most useful for global lung modeling.

Refinement Of Hexahedral Cells In Euler Flow Computations

NASA Technical Reports Server (NTRS)

Melton, John E.; Cappuccio, Gelsomina; Thomas, Scott D.

1996-01-01

Topologically Independent Grid, Euler Refinement (TIGER) computer program solves Euler equations of three-dimensional, unsteady flow of inviscid, compressible fluid by numerical integration on unstructured hexahedral coordinate grid refined where necessary to resolve shocks and other details. Hexahedral cells subdivided, each into eight smaller cells, as needed to refine computational grid in regions of high flow gradients. Grid Interactive Refinement and Flow-Field Examination (GIRAFFE) computer program written in conjunction with TIGER program to display computed flow-field data and to assist researcher in verifying specified boundary conditions and refining grid.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dumbser, Michael, E-mail: michael.dumbser@unitn.it; Balsara, Dinshaw S., E-mail: dbalsara@nd.edu

In this paper a new, simple and universal formulation of the HLLEM Riemann solver (RS) is proposed that works for general conservative and non-conservative systems of hyperbolic equations. For non-conservative PDE, a path-conservative formulation of the HLLEM RS is presented for the first time in this paper. The HLLEM Riemann solver is built on top of a novel and very robust path-conservative HLL method. It thus naturally inherits the positivity properties and the entropy enforcement of the underlying HLL scheme. However, with just the slight additional cost of evaluating eigenvectors and eigenvalues of intermediate characteristic fields, we can represent linearlymore » degenerate intermediate waves with a minimum of smearing. For conservative systems, our paper provides the easiest and most seamless path for taking a pre-existing HLL RS and quickly and effortlessly converting it to a RS that provides improved results, comparable with those of an HLLC, HLLD, Osher or Roe-type RS. This is done with minimal additional computational complexity, making our variant of the HLLEM RS also a very fast RS that can accurately represent linearly degenerate discontinuities. Our present HLLEM RS also transparently extends these advantages to non-conservative systems. For shallow water-type systems, the resulting method is proven to be well-balanced. Several test problems are presented for shallow water-type equations and two-phase flow models, as well as for gas dynamics with real equation of state, magnetohydrodynamics (MHD & RMHD), and nonlinear elasticity. Since our new formulation accommodates multiple intermediate waves and has a broader applicability than the original HLLEM method, it could alternatively be called the HLLI Riemann solver, where the “I” stands for the intermediate characteristic fields that can be accounted for. -- Highlights: •New simple and general path-conservative formulation of the HLLEM Riemann solver. •Application to general conservative and non-conservative hyperbolic systems. •Inclusion of sub-structure and resolution of intermediate characteristic fields. •Well-balanced for single- and two-layer shallow water equations and multi-phase flows. •Euler equations with real equation of state, MHD equations, nonlinear elasticity.« less

Dynamic mesh adaption for triangular and tetrahedral grids

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Strawn, Roger

1993-01-01

The following topics are discussed: requirements for dynamic mesh adaption; linked-list data structure; edge-based data structure; adaptive-grid data structure; three types of element subdivision; mesh refinement; mesh coarsening; additional constraints for coarsening; anisotropic error indicator for edges; unstructured-grid Euler solver; inviscid 3-D wing; and mesh quality for solution-adaptive grids. The discussion is presented in viewgraph form.

A hierarchical uniformly high order DG-IMEX scheme for the 1D BGK equation

NASA Astrophysics Data System (ADS)

Xiong, Tao; Qiu, Jing-Mei

2017-05-01

A class of high order nodal discontinuous Galerkin implicit-explicit (DG-IMEX) schemes with asymptotic preserving (AP) property has been developed for the one-dimensional (1D) BGK equation in Xiong et al. (2015) [40], based on a micro-macro reformulation. The schemes are globally stiffly accurate and asymptotically consistent, and as the Knudsen number becomes small or goes to zero, they recover first the compressible Navier-Stokes (CNS) and then the Euler limit. Motivated by the recent work of Filbet and Rey (2015) [27] and the references therein, in this paper, we propose a hierarchical high order AP method, namely kinetic, CNS and Euler solvers are automatically applied in regions where their corresponding models are appropriate. The numerical solvers for different regimes are coupled naturally by interface conditions. To the best of our knowledge, the resulting scheme is the very first hierarchical one being proposed in the literature, that enjoys AP property as well as uniform high order accuracy. Numerical experiments demonstrate the efficiency and effectiveness of the proposed approach. As time evolves, three different regimes are dynamically identified and naturally coupled, leading to significant CPU time savings (more than 80% for some of our test problems).

A family of high-order gas-kinetic schemes and its comparison with Riemann solver based high-order methods

NASA Astrophysics Data System (ADS)

Ji, Xing; Zhao, Fengxiang; Shyy, Wei; Xu, Kun

2018-03-01

Most high order computational fluid dynamics (CFD) methods for compressible flows are based on Riemann solver for the flux evaluation and Runge-Kutta (RK) time stepping technique for temporal accuracy. The advantage of this kind of space-time separation approach is the easy implementation and stability enhancement by introducing more middle stages. However, the nth-order time accuracy needs no less than n stages for the RK method, which can be very time and memory consuming due to the reconstruction at each stage for a high order method. On the other hand, the multi-stage multi-derivative (MSMD) method can be used to achieve the same order of time accuracy using less middle stages with the use of the time derivatives of the flux function. For traditional Riemann solver based CFD methods, the lack of time derivatives in the flux function prevents its direct implementation of the MSMD method. However, the gas kinetic scheme (GKS) provides such a time accurate evolution model. By combining the second-order or third-order GKS flux functions with the MSMD technique, a family of high order gas kinetic methods can be constructed. As an extension of the previous 2-stage 4th-order GKS, the 5th-order schemes with 2 and 3 stages will be developed in this paper. Based on the same 5th-order WENO reconstruction, the performance of gas kinetic schemes from the 2nd- to the 5th-order time accurate methods will be evaluated. The results show that the 5th-order scheme can achieve the theoretical order of accuracy for the Euler equations, and present accurate Navier-Stokes solutions as well due to the coupling of inviscid and viscous terms in the GKS formulation. In comparison with Riemann solver based 5th-order RK method, the high order GKS has advantages in terms of efficiency, accuracy, and robustness, for all test cases. The 4th- and 5th-order GKS have the same robustness as the 2nd-order scheme for the capturing of discontinuous solutions. The current high order MSMD GKS is a multi-dimensional scheme with incorporation of both normal and tangential spatial derivatives of flow variables at a cell interface in the flux evaluation. The scheme can be extended straightforwardly to viscous flow computation in unstructured mesh. It provides a promising direction for the development of high-order CFD methods for the computation of complex flows, such as turbulence and acoustics with shock interactions.

CFD analysis of multiphase blood flow within aorta and its thoracic branches of patient with coarctation of aorta using multiphase Euler - Euler approach

NASA Astrophysics Data System (ADS)

Ostrowski, Z.; Melka, B.; Adamczyk, W.; Rojczyk, M.; Golda, A.; Nowak, A. J.

2016-09-01

In the research a numerical Computational Fluid Dynamics (CFD) model of the pulsatile blood flow was created and analyzed. A real geometry of aorta and its thoracic branches of 8-year old patient diagnosed with a congenital heart defect - coarctation of aorta was used. The inlet boundary condition were implemented as the User Define Function according to measured values of volumetric blood flow. The blood flow was treated as multiphase: plasma, set as the primary fluid phase, was dominant with volume fraction of 0.585 and morphological elements of blood were treated in Euler-Euler approach as dispersed phases (with 90% Red Blood Cells and White Blood Cells as remaining solid volume fraction).

THOR: an open-source exo-GCM

NASA Astrophysics Data System (ADS)

Grosheintz, Luc; Mendonça, João; Käppeli, Roger; Lukas Grimm, Simon; Mishra, Siddhartha; Heng, Kevin

2015-12-01

In this talk, I will present THOR, the first fully conservative, GPU-accelerated exo-GCM (general circulation model) on a nearly uniform, global grid that treats shocks and is non-hydrostatic. THOR will be freely available to the community as a standard tool.Unlike most GCMs THOR solves the full, non-hydrostatic Euler equations instead of the primitive equations. The equations are solved on a global three-dimensional icosahedral grid by a second order Finite Volume Method (FVM). Icosahedral grids are nearly uniform refinements of an icosahedron. We've implemented three different versions of this grid. FVM conserves the prognostic variables (density, momentum and energy) exactly and doesn't require a diffusion term (artificial viscosity) in the Euler equations to stabilize our solver. Historically FVM was designed to treat discontinuities correctly. Hence it excels at resolving shocks, including those present in hot exoplanetary atmospheres.Atmospheres are generally in near hydrostatic equilibrium. We therefore implement a well-balancing technique recently developed at the ETH Zurich. This well-balancing ensures that our FVM maintains hydrostatic equilibrium to machine precision. Better yet, it is able to resolve pressure perturbations from this equilibrium as small as one part in 100'000. It is important to realize that these perturbations are significantly smaller than the truncation error of the same scheme without well-balancing. If during the course of the simulation (due to forcing) the atmosphere becomes non-hydrostatic, our solver continues to function correctly.THOR just passed an important mile stone. We've implemented the explicit part of the solver. The explicit solver is useful to study instabilities or local problems on relatively short time scales. I'll show some nice properties of the explicit THOR. An explicit solver is not appropriate for climate study because the time step is limited by the sound speed. Therefore, we are working on the first fully implicit GCM. By ESS3, I hope to present results for the advection equation.THOR is part of the Exoclimes Simulation Platform (ESP), a set of open-source community codes for simulating and understanding the atmospheres of exoplanets. The ESP also includes tools for radiative transfer and retrieval (HELIOS), an opacity calculator (HELIOS-K), and a chemical kinetics solver (VULCAN). We expect to publicly release an initial version of THOR in 2016 on www.exoclime.org.

Computational Assessment of Aft-Body Closure for the HSR Reference H Configuration

NASA Technical Reports Server (NTRS)

Londenberg, W. Kelly

1999-01-01

A study has been conducted to determine how well the USM3D unstructured Euler solver can be utilized to predict the flow over the High Speed Research (HSR) Reference H configuration with an ultimate goal of prediction of Sting interference so after body closure effects may be evaluated. This study has shown that the code can be used to predict the interference effects of a lower mounted blade sting with a high degree of confidence. It has been shown that wing and fuselage pressures, both levels and trends, can be predicted well. Force and moment levels are not predicted well but experimental trends are predicted. Based upon this, predicted force and moment increments are assumed to be predicted accurately. Deflection of the horizontal tail was found to cause a non-linear increment from the non-deflected sting interference effects.

Real Gas Computation Using an Energy Relaxation Method and High-Order WENO Schemes

NASA Technical Reports Server (NTRS)

Montarnal, Philippe; Shu, Chi-Wang

1998-01-01

In this paper, we use a recently developed energy relaxation theory by Coquel and Perthame and high order weighted essentially non-oscillatory (WENO) schemes to simulate the Euler equations of real gas. The main idea is an energy decomposition into two parts: one part is associated with a simpler pressure law and the other part (the nonlinear deviation) is convected with the flow. A relaxation process is performed for each time step to ensure that the original pressure law is satisfied. The necessary characteristic decomposition for the high order WENO schemes is performed on the characteristic fields based on the first part. The algorithm only calls for the original pressure law once per grid point per time step, without the need to compute its derivatives or any Riemann solvers. Both one and two dimensional numerical examples are shown to illustrate the effectiveness of this approach.

A new flux splitting scheme

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing; Steffen, Christopher J., Jr.

1993-01-01

A new flux splitting scheme is proposed. The scheme is remarkably simple and yet its accuracy rivals and in some cases surpasses that of Roe's solver in the Euler and Navier-Stokes solutions performed in this study. The scheme is robust and converges as fast as the Roe splitting. An approximately defined cell-face advection Mach number is proposed using values from the two straddling cells via associated characteristic speeds. This interface Mach number is then used to determine the upwind extrapolation for the convective quantities. Accordingly, the name of the scheme is coined as Advection Upstream Splitting Method (AUSM). A new pressure splitting is introduced which is shown to behave successfully, yielding much smoother results than other existing pressure splittings. Of particular interest is the supersonic blunt body problem in which the Roe scheme gives anomalous solutions. The AUSM produces correct solutions without difficulty for a wide range of flow conditions as well as grids.

A new flux splitting scheme

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing; Steffen, Christopher J., Jr.

1991-01-01

A new flux splitting scheme is proposed. The scheme is remarkably simple and yet its accuracy rivals and in some cases surpasses that of Roe's solver in the Euler and Navier-Stokes solutions performed in this study. The scheme is robust and converges as fast as the Roe splitting. An approximately defined cell-face advection Mach number is proposed using values from the two straddling cells via associated characteristic speeds. This interface Mach number is then used to determine the upwind extrapolation for the convective quantities. Accordingly, the name of the scheme is coined as Advection Upstream Splitting Method (AUSM). A new pressure splitting is introduced which is shown to behave successfully, yielding much smoother results than other existing pressure splittings. Of particular interest is the supersonic blunt body problem in which the Roe scheme gives anomalous solutions. The AUSM produces correct solutions without difficulty for a wide range of flow conditions as well as grids.

Implementation of density-based solver for all speeds in the framework of OpenFOAM

NASA Astrophysics Data System (ADS)

Shen, Chun; Sun, Fengxian; Xia, Xinlin

2014-10-01

In the framework of open source CFD code OpenFOAM, a density-based solver for all speeds flow field is developed. In this solver the preconditioned all speeds AUSM+(P) scheme is adopted and the dual time scheme is implemented to complete the unsteady process. Parallel computation could be implemented to accelerate the solving process. Different interface reconstruction algorithms are implemented, and their accuracy with respect to convection is compared. Three benchmark tests of lid-driven cavity flow, flow crossing over a bump, and flow over a forward-facing step are presented to show the accuracy of the AUSM+(P) solver for low-speed incompressible flow, transonic flow, and supersonic/hypersonic flow. Firstly, for the lid driven cavity flow, the computational results obtained by different interface reconstruction algorithms are compared. It is indicated that the one dimensional reconstruction scheme adopted in this solver possesses high accuracy and the solver developed in this paper can effectively catch the features of low incompressible flow. Then via the test cases regarding the flow crossing over bump and over forward step, the ability to capture characteristics of the transonic and supersonic/hypersonic flows are confirmed. The forward-facing step proves to be the most challenging for the preconditioned solvers with and without the dual time scheme. Nonetheless, the solvers described in this paper reproduce the main features of this flow, including the evolution of the initial transient.

An algebraic homotopy method for generating quasi-three-dimensional grids for high-speed configurations

NASA Technical Reports Server (NTRS)

Moitra, Anutosh

1989-01-01

A fast and versatile procedure for algebraically generating boundary conforming computational grids for use with finite-volume Euler flow solvers is presented. A semi-analytic homotopic procedure is used to generate the grids. Grids generated in two-dimensional planes are stacked to produce quasi-three-dimensional grid systems. The body surface and outer boundary are described in terms of surface parameters. An interpolation scheme is used to blend between the body surface and the outer boundary in order to determine the field points. The method, albeit developed for analytically generated body geometries is equally applicable to other classes of geometries. The method can be used for both internal and external flow configurations, the only constraint being that the body geometries be specified in two-dimensional cross-sections stationed along the longitudinal axis of the configuration. Techniques for controlling various grid parameters, e.g., clustering and orthogonality are described. Techniques for treating problems arising in algebraic grid generation for geometries with sharp corners are addressed. A set of representative grid systems generated by this method is included. Results of flow computations using these grids are presented for validation of the effectiveness of the method.

Numerical Simulation of Complex Turbomachinery Flows

NASA Technical Reports Server (NTRS)

Chernobrovkin, A. A.; Lakshiminarayana, B.

1999-01-01

An unsteady, multiblock, Reynolds Averaged Navier Stokes solver based on Runge-Kutta scheme and Pseudo-time step for turbo-machinery applications was developed. The code was validated and assessed against analytical and experimental data. It was used to study a variety of physical mechanisms of unsteady, three-dimensional, turbulent, transitional, and cooling flows in compressors and turbines. Flow over a cylinder has been used to study effects of numerical aspects on accuracy of prediction of wake decay and transition, and to modify K-epsilon models. The following simulations have been performed: (a) Unsteady flow in a compressor cascade: Three low Reynolds number turbulence models have been assessed and data compared with Euler/boundary layer predictions. Major flow features associated with wake induced transition were predicted and studied; (b) Nozzle wake-rotor interaction in a turbine: Results compared to LDV data in design and off-design conditions, and cause and effect of unsteady flow in turbine rotors were analyzed; (c) Flow in the low-pressure turbine: Assessed capability of the code to predict transitional, attached and separated flows at a wide range of low Reynolds numbers and inlet freestream turbulence intensity. Several turbulence and transition models have been employed and comparisons made to experiments; (d) leading edge film cooling at compound angle: Comparisons were made with experiments, and the flow physics of the associated vortical structures were studied; and (e) Tip leakage flow in a turbine. The physics of the secondary flow in a rotor was studied and sources of loss identified.

Three dimensional steady subsonic Euler flows in bounded nozzles

NASA Astrophysics Data System (ADS)

Chen, Chao; Xie, Chunjing

The existence and uniqueness of three dimensional steady subsonic Euler flows in rectangular nozzles were obtained when prescribing normal component of momentum at both the entrance and exit. If, in addition, the normal component of the voriticity and the variation of Bernoulli's function at the entrance are both zero, then there exists a unique subsonic potential flow when the magnitude of the normal component of the momentum is less than a critical number. As the magnitude of the normal component of the momentum approaches the critical number, the associated flows converge to a subsonic-sonic flow. Furthermore, when the normal component of vorticity and the variation of Bernoulli function are both small, the existence and uniqueness of subsonic Euler flows with non-zero vorticity are established. The proof of these results is based on a new formulation for the Euler system, a priori estimate for nonlinear elliptic equations with nonlinear boundary conditions, detailed study for a linear div-curl system, and delicate estimate for the transport equations.

Multigrid calculation of three-dimensional turbomachinery flows

NASA Technical Reports Server (NTRS)

Caughey, David A.

1989-01-01

Research was performed in the general area of computational aerodynamics, with particular emphasis on the development of efficient techniques for the solution of the Euler and Navier-Stokes equations for transonic flows through the complex blade passages associated with turbomachines. In particular, multigrid methods were developed, using both explicit and implicit time-stepping schemes as smoothing algorithms. The specific accomplishments of the research have included: (1) the development of an explicit multigrid method to solve the Euler equations for three-dimensional turbomachinery flows based upon the multigrid implementation of Jameson's explicit Runge-Kutta scheme (Jameson 1983); (2) the development of an implicit multigrid scheme for the three-dimensional Euler equations based upon lower-upper factorization; (3) the development of a multigrid scheme using a diagonalized alternating direction implicit (ADI) algorithm; (4) the extension of the diagonalized ADI multigrid method to solve the Euler equations of inviscid flow for three-dimensional turbomachinery flows; and also (5) the extension of the diagonalized ADI multigrid scheme to solve the Reynolds-averaged Navier-Stokes equations for two-dimensional turbomachinery flows.

Computational investigation of large-scale vortex interaction with flexible bodies

NASA Astrophysics Data System (ADS)

Connell, Benjamin; Yue, Dick K. P.

2003-11-01

The interaction of large-scale vortices with flexible bodies is examined with particular interest paid to the energy and momentum budgets of the system. Finite difference direct numerical simulation of the Navier-Stokes equations on a moving curvilinear grid is coupled with a finite difference structural solver of both a linear membrane under tension and linear Euler-Bernoulli beam. The hydrodynamics and structural dynamics are solved simultaneously using an iterative procedure with the external structural forcing calculated from the hydrodynamics at the surface and the flow-field velocity boundary condition given by the structural motion. We focus on an investigation into the canonical problem of a vortex-dipole impinging on a flexible membrane. It is discovered that the structural properties of the membrane direct the interaction in terms of the flow evolution and the energy budget. Pressure gradients associated with resonant membrane response are shown to sustain the oscillatory motion of the vortex pair. Understanding how the key mechanisms in vortex-body interactions are guided by the structural properties of the body is a prerequisite to exploiting these mechanisms.

The implementation of an aeronautical CFD flow code onto distributed memory parallel systems

NASA Astrophysics Data System (ADS)

Ierotheou, C. S.; Forsey, C. R.; Leatham, M.

2000-04-01

The parallelization of an industrially important in-house computational fluid dynamics (CFD) code for calculating the airflow over complex aircraft configurations using the Euler or Navier-Stokes equations is presented. The code discussed is the flow solver module of the SAUNA CFD suite. This suite uses a novel grid system that may include block-structured hexahedral or pyramidal grids, unstructured tetrahedral grids or a hybrid combination of both. To assist in the rapid convergence to a solution, a number of convergence acceleration techniques are employed including implicit residual smoothing and a multigrid full approximation storage scheme (FAS). Key features of the parallelization approach are the use of domain decomposition and encapsulated message passing to enable the execution in parallel using a single programme multiple data (SPMD) paradigm. In the case where a hybrid grid is used, a unified grid partitioning scheme is employed to define the decomposition of the mesh. The parallel code has been tested using both structured and hybrid grids on a number of different distributed memory parallel systems and is now routinely used to perform industrial scale aeronautical simulations. Copyright

Application of an unstructured grid flow solver to planes, trains and automobiles

NASA Technical Reports Server (NTRS)

Spragle, Gregory S.; Smith, Wayne A.; Yadlin, Yoram

1993-01-01

Rampant, an unstructured flow solver developed at Fluent Inc., is used to compute three-dimensional, viscous, turbulent, compressible flow fields within complex solution domains. Rampant is an explicit, finite-volume flow solver capable of computing flow fields using either triangular (2d) or tetrahedral (3d) unstructured grids. Local time stepping, implicit residual smoothing, and multigrid techniques are used to accelerate the convergence of the explicit scheme. The paper describes the Rampant flow solver and presents flow field solutions about a plane, train, and automobile.

3-D conditional hyperbolic method of moments for high-fidelity Euler-Euler simulations of particle-laden flows

NASA Astrophysics Data System (ADS)

Patel, Ravi; Kong, Bo; Capecelatro, Jesse; Fox, Rodney; Desjardins, Olivier

2017-11-01

Particle-laden turbulent flows are important features of many environmental and industrial processes. Euler-Euler (EE) simulations of these flows are more computationally efficient than Euler-Lagrange (EL) simulations. However, traditional EE methods, such as the two-fluid model, cannot faithfully capture dilute regions of flow with finite Stokes number particles. For this purpose, the multi-valued nature of the particle velocity field must be treated with a polykinetic description. Various quadrature-based moment methods (QBMM) can be used to approximate the full kinetic description by solving for a set of moments of the particle velocity distribution function (VDF) and providing closures for the higher-order moments. Early QBMM fail to maintain the strict hyperbolicity of the kinetic equations, producing unphysical delta shocks (i.e., mass accumulation at a point). In previous work, a 2-D conditional hyperbolic quadrature method of moments (CHyQMOM) was proposed as a fourth-order QBMM closure that maintains strict hyperbolicity. Here, we present the 3-D extension of CHyQMOM. We compare results from CHyQMOM to other QBMM and EL in the context of particle trajectory crossing, cluster-induced turbulence, and particle-laden channel flow. NSF CBET-1437903.

Numerical Capture of Wing-tip Vortex Using Vorticity Confinement

NASA Astrophysics Data System (ADS)

Zhang, Baili; Lou, Jing; Kang, Chang Wei; Wilson, Alexander; Lundberg, Johan; Bensow, Rickard

2012-11-01

Tracking vortices accurately over large distances is very important in many areas of engineering, for instance flow over rotating helicopter blades, ship propeller blades and aircraft wings. However, due to the inherent numerical dissipation in the advection step of flow simulation, current Euler and RANS field solvers tend to damp these vortices too fast. One possible solution to reduce the unphysical decay of these vortices is the application of vorticity confinement methods. In this study, a vorticity confinement term is added to the momentum conservation equations which is a function of the local element size, the vorticity and the gradient of the absolute value of vorticity. The approach has been evaluated by a systematic numerical study on the tip vortex trailing from a rectangular NACA0012 half-wing. The simulated structure and development of the wing-tip vortex agree well with experiments both qualitatively and quantitatively without any adverse effects on the global flow field. It is shown that vorticity confinement can negate the effect of numerical dissipation, leading to a more or less constant vortex strength. This is an approximate method in that genuine viscous diffusion of the vortex is not modeled, but it can be appropriate for vortex dominant flows over short to medium length scales where viscous diffusion can be neglected.

Gust Acoustics Computation with a Space-Time CE/SE Parallel 3D Solver

NASA Technical Reports Server (NTRS)

Wang, X. Y.; Himansu, A.; Chang, S. C.; Jorgenson, P. C. E.; Reddy, D. R. (Technical Monitor)

2002-01-01

The benchmark Problem 2 in Category 3 of the Third Computational Aero-Acoustics (CAA) Workshop is solved using the space-time conservation element and solution element (CE/SE) method. This problem concerns the unsteady response of an isolated finite-span swept flat-plate airfoil bounded by two parallel walls to an incident gust. The acoustic field generated by the interaction of the gust with the flat-plate airfoil is computed by solving the 3D (three-dimensional) Euler equations in the time domain using a parallel version of a 3D CE/SE solver. The effect of the gust orientation on the far-field directivity is studied. Numerical solutions are presented and compared with analytical solutions, showing a reasonable agreement.

Application of frequency-domain linearized Euler solutions to the prediction of aft fan tones and comparison with experimental measurements on model scale turbofan exhaust nozzles

NASA Astrophysics Data System (ADS)

Özyörük, Y.; Tester, B. J.

2011-08-01

Although it is widely accepted that aircraft noise needs to be further reduced, there is an equally important, on-going requirement to accurately predict the strengths of all the different aircraft noise sources, not only to ensure that a new aircraft is certifiable and can meet the ever more stringent local airport noise rules but also to prioritize and apply appropriate noise source reduction technologies at the design stage. As the bypass ratio of aircraft engines is increased - in order to reduce fuel consumption, emissions and jet mixing noise - the fan noise that radiates from the bypass exhaust nozzle is becoming one of the loudest engine sources, despite the large areas of acoustically absorptive treatment in the bypass duct. This paper addresses this 'aft fan' noise source, in particular the prediction of the propagation of fan noise through the bypass exhaust nozzle/jet exhaust flow and radiation out to the far-field observer. The proposed prediction method is equally applicable to fan tone and fan broadband noise (and also turbine and core noise) but here the method is validated with measured test data using simulated fan tones. The measured data had been previously acquired on two model scale turbofan engine exhausts with bypass and heated core flows typical of those found in a modern high bypass engine, but under static conditions (i.e. no flight simulation). The prediction method is based on frequency-domain solutions of the linearized Euler equations in conjunction with perfectly matched layer equations at the inlet and far-field boundaries using high-order finite differences. The discrete system of equations is inverted by the parallel sparse solver MUMPS. Far-field predictions are carried out by integrating Kirchhoff's formula in frequency domain. In addition to the acoustic modes excited and radiated, some non-acoustic waves within the cold stream-ambient shear layer are also captured by the computations at some flow and excitation frequencies. By extracting phase speed information from the near-field pressure solution, these non-acoustic waves are shown to be convective Kelvin-Helmholtz instability waves. Strouhal numbers computed along the shear layer, based on the local momentum thickness also confirm this in accordance with Michalke's instability criterion for incompressible round jets with a similar shear layer profile. Comparisons of the computed far-field results with the measured acoustic data reveal that, in general, the solver predicts the peak sound levels well when the farfield is dominated by the in-duct target mode (the target mode being the one specified to the in-duct mode generator). Calculations also show that the agreement can be considerably improved when the non-target modes are also included, despite their low in-duct levels. This is due to the fact that each duct mode has its own distinct directionality and a non-target low level mode may become dominant at angles where the higher-level target mode is directionally weak. The overall agreement between the computations and experiment strongly suggests that, at least for the range of mean flows and acoustic conditions considered, the physical aeroacoustic radiation processes are fully captured through the frequency-domain solutions to the linearized Euler equations and hence this could form the basis of a reliable aircraft noise prediction method.

New developments in the method of space-time conservation element and solution element: Applications to the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1993-01-01

A new numerical framework for solving conservation laws is being developed. This new approach differs substantially in both concept and methodology from the well-established methods--i.e., finite difference, finite volume, finite element, and spectral methods. It is conceptually simple and designed to avoid several key limitations to the above traditional methods. An explicit model scheme for solving a simple 1-D unsteady convection-diffusion equation is constructed and used to illuminate major differences between the current method and those mentioned above. Unexpectedly, its amplification factors for the pure convection and pure diffusion cases are identical to those of the Leapfrog and the DuFort-Frankel schemes, respectively. Also, this explicit scheme and its Navier-Stokes extension have the unusual property that their stabilities are limited only by the CFL condition. Moreover, despite the fact that it does not use any flux-limiter or slope-limiter, the Navier-Stokes solver is capable of generating highly accurate shock tube solutions with shock discontinuities being resolved within one mesh interval. An accurate Euler solver also is constructed through another extension. It has many unusual properties, e.g., numerical diffusion at all mesh points can be controlled by a set of local parameters.

Advanced Signal Processing for Integrated LES-RANS Simulations: Anti-aliasing Filters

NASA Technical Reports Server (NTRS)

Schlueter, J. U.

2003-01-01

Currently, a wide variety of flow phenomena are addressed with numerical simulations. Many flow solvers are optimized to simulate a limited spectrum of flow effects effectively, such as single parts of a flow system, but are either inadequate or too expensive to be applied to a very complex problem. As an example, the flow through a gas turbine can be considered. In the compressor and the turbine section, the flow solver has to be able to handle the moving blades, model the wall turbulence, and predict the pressure and density distribution properly. This can be done by a flow solver based on the Reynolds-Averaged Navier-Stokes (RANS) approach. On the other hand, the flow in the combustion chamber is governed by large scale turbulence, chemical reactions, and the presence of fuel spray. Experience shows that these phenomena require an unsteady approach. Hence, for the combustor, the use of a Large Eddy Simulation (LES) flow solver is desirable. While many design problems of a single flow passage can be addressed by separate computations, only the simultaneous computation of all parts can guarantee the proper prediction of multi-component phenomena, such as compressor/combustor instability and combustor/turbine hot-streak migration. Therefore, a promising strategy to perform full aero-thermal simulations of gas-turbine engines is the use of a RANS flow solver for the compressor sections, an LES flow solver for the combustor, and again a RANS flow solver for the turbine section.

New Developments in the Method of Space-Time Conservation Element and Solution Element-Applications to Two-Dimensional Time-Marching Problems

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Wang, Xiao-Yen; Chow, Chuen-Yen

1994-01-01

A new numerical discretization method for solving conservation laws is being developed. This new approach differs substantially in both concept and methodology from the well-established methods, i.e., finite difference, finite volume, finite element, and spectral methods. It is motivated by several important physical/numerical considerations and designed to avoid several key limitations of the above traditional methods. As a result of the above considerations, a set of key principles for the design of numerical schemes was put forth in a previous report. These principles were used to construct several numerical schemes that model a 1-D time-dependent convection-diffusion equation. These schemes were then extended to solve the time-dependent Euler and Navier-Stokes equations of a perfect gas. It was shown that the above schemes compared favorably with the traditional schemes in simplicity, generality, and accuracy. In this report, the 2-D versions of the above schemes, except the Navier-Stokes solver, are constructed using the same set of design principles. Their constructions are simplified greatly by the use of a nontraditional space-time mesh. Its use results in the simplest stencil possible, i.e., a tetrahedron in a 3-D space-time with a vertex at the upper time level and other three at the lower time level. Because of the similarity in their design, each of the present 2-D solvers virtually shares with its 1-D counterpart the same fundamental characteristics. Moreover, it is shown that the present Euler solver is capable of generating highly accurate solutions for a famous 2-D shock reflection problem. Specifically, both the incident and the reflected shocks can be resolved by a single data point without the presence of numerical oscillations near the discontinuity.

Comparison of two- and three-dimensional flow computations with laser anemometer measurements in a transonic compressor rotor

NASA Technical Reports Server (NTRS)

Chima, R. V.; Strazisar, A. J.

1982-01-01

Two and three dimensional inviscid solutions for the flow in a transonic axial compressor rotor at design speed are compared with probe and laser anemometers measurements at near-stall and maximum-flow operating points. Experimental details of the laser anemometer system and computational details of the two dimensional axisymmetric code and three dimensional Euler code are described. Comparisons are made between relative Mach number and flow angle contours, shock location, and shock strength. A procedure for using an efficient axisymmetric code to generate downstream pressure input for computationally expensive Euler codes is discussed. A film supplement shows the calculations of the two operating points with the time-marching Euler code.

A Riemann solver for single-phase and two-phase shallow flow models based on relaxation. Relations with Roe and VFRoe solvers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pelanti, Marica, E-mail: Marica.Pelanti@ens.f; Bouchut, Francois, E-mail: francois.bouchut@univ-mlv.f; Mangeney, Anne, E-mail: mangeney@ipgp.jussieu.f

2011-02-01

We present a Riemann solver derived by a relaxation technique for classical single-phase shallow flow equations and for a two-phase shallow flow model describing a mixture of solid granular material and fluid. Our primary interest is the numerical approximation of this two-phase solid/fluid model, whose complexity poses numerical difficulties that cannot be efficiently addressed by existing solvers. In particular, we are concerned with ensuring a robust treatment of dry bed states. The relaxation system used by the proposed solver is formulated by introducing auxiliary variables that replace the momenta in the spatial gradients of the original model systems. The resultingmore » relaxation solver is related to Roe solver in that its Riemann solution for the flow height and relaxation variables is formally computed as Roe's Riemann solution. The relaxation solver has the advantage of a certain degree of freedom in the specification of the wave structure through the choice of the relaxation parameters. This flexibility can be exploited to handle robustly vacuum states, which is a well known difficulty of standard Roe's method, while maintaining Roe's low diffusivity. For the single-phase model positivity of flow height is rigorously preserved. For the two-phase model positivity of volume fractions in general is not ensured, and a suitable restriction on the CFL number might be needed. Nonetheless, numerical experiments suggest that the proposed two-phase flow solver efficiently models wet/dry fronts and vacuum formation for a large range of flow conditions. As a corollary of our study, we show that for single-phase shallow flow equations the relaxation solver is formally equivalent to the VFRoe solver with conservative variables of Gallouet and Masella [T. Gallouet, J.-M. Masella, Un schema de Godunov approche C.R. Acad. Sci. Paris, Serie I, 323 (1996) 77-84]. The relaxation interpretation allows establishing positivity conditions for this VFRoe method.« less

Computation of three-dimensional multiphase flow dynamics by Fully-Coupled Immersed Flow (FCIF) solver

NASA Astrophysics Data System (ADS)

Miao, Sha; Hendrickson, Kelli; Liu, Yuming

2017-12-01

This work presents a Fully-Coupled Immersed Flow (FCIF) solver for the three-dimensional simulation of fluid-fluid interaction by coupling two distinct flow solvers using an Immersed Boundary (IB) method. The FCIF solver captures dynamic interactions between two fluids with disparate flow properties, while retaining the desirable simplicity of non-boundary-conforming grids. For illustration, we couple an IB-based unsteady Reynolds Averaged Navier Stokes (uRANS) simulator with a depth-integrated (long-wave) solver for the application of slug development with turbulent gas and laminar liquid. We perform a series of validations including turbulent/laminar flows over prescribed wavy boundaries and freely-evolving viscous fluids. These confirm the effectiveness and accuracy of both one-way and two-way coupling in the FCIF solver. Finally, we present a simulation example of the evolution from a stratified turbulent/laminar flow through the initiation of a slug that nearly bridges the channel. The results show both the interfacial wave dynamics excited by the turbulent gas forcing and the influence of the liquid on the gas turbulence. These results demonstrate that the FCIF solver effectively captures the essential physics of gas-liquid interaction and can serve as a useful tool for the mechanistic study of slug generation in two-phase gas/liquid flows in channels and pipes.

Advancing parabolic operators in thermodynamic MHD models: Explicit super time-stepping versus implicit schemes with Krylov solvers

NASA Astrophysics Data System (ADS)

Caplan, R. M.; Mikić, Z.; Linker, J. A.; Lionello, R.

2017-05-01

We explore the performance and advantages/disadvantages of using unconditionally stable explicit super time-stepping (STS) algorithms versus implicit schemes with Krylov solvers for integrating parabolic operators in thermodynamic MHD models of the solar corona. Specifically, we compare the second-order Runge-Kutta Legendre (RKL2) STS method with the implicit backward Euler scheme computed using the preconditioned conjugate gradient (PCG) solver with both a point-Jacobi and a non-overlapping domain decomposition ILU0 preconditioner. The algorithms are used to integrate anisotropic Spitzer thermal conduction and artificial kinematic viscosity at time-steps much larger than classic explicit stability criteria allow. A key component of the comparison is the use of an established MHD model (MAS) to compute a real-world simulation on a large HPC cluster. Special attention is placed on the parallel scaling of the algorithms. It is shown that, for a specific problem and model, the RKL2 method is comparable or surpasses the implicit method with PCG solvers in performance and scaling, but suffers from some accuracy limitations. These limitations, and the applicability of RKL methods are briefly discussed.

rhoCentralRfFoam: An OpenFOAM solver for high speed chemically active flows - Simulation of planar detonations -

NASA Astrophysics Data System (ADS)

Gutiérrez Marcantoni, L. F.; Tamagno, J.; Elaskar, S.

2017-10-01

A new solver developed within the framework of OpenFOAM 2.3.0, called rhoCentralRfFoam which can be interpreted like an evolution of rhoCentralFoam, is presented. Its use, performing numerical simulations on initiation and propagation of planar detonation waves in combustible mixtures H2-Air and H2-O2-Ar, is described. Unsteady one dimensional (1D) Euler equations coupled with sources to take into account chemical activity, are numerically solved using the Kurganov, Noelle and Petrova second order scheme in a domain discretized with finite volumes. The computational code can work with any number of species and its corresponding reactions, but here it was tested with 13 chemically active species (one species inert), and 33 elementary reactions. A gaseous igniter which acts like a shock-tube driver, and powerful enough to generate a strong shock capable of triggering exothermic chemical reactions in fuel mixtures, is used to start planar detonations. The following main aspects of planar detonations are here, treated: induction time of combustible mixtures cited above and required mesh resolutions; convergence of overdriven detonations to Chapman-Jouguet states; detonation structure (ZND model); and the use of reflected shocks to determine induction times experimentally. The rhoCentralRfFoam code was verified comparing numerical results and it was validated, through analytical results and experimental data.

A coupled sharp-interface immersed boundary-finite-element method for flow-structure interaction with application to human phonation.

PubMed

Zheng, X; Xue, Q; Mittal, R; Beilamowicz, S

2010-11-01

A new flow-structure interaction method is presented, which couples a sharp-interface immersed boundary method flow solver with a finite-element method based solid dynamics solver. The coupled method provides robust and high-fidelity solution for complex flow-structure interaction (FSI) problems such as those involving three-dimensional flow and viscoelastic solids. The FSI solver is used to simulate flow-induced vibrations of the vocal folds during phonation. Both two- and three-dimensional models have been examined and qualitative, as well as quantitative comparisons, have been made with established results in order to validate the solver. The solver is used to study the onset of phonation in a two-dimensional laryngeal model and the dynamics of the glottal jet in a three-dimensional model and results from these studies are also presented.

Transonic flow analysis for rotors. Part 3: Three-dimensional, quasi-steady, Euler calculation

NASA Technical Reports Server (NTRS)

Chang, I-Chung

1990-01-01

A new method is presented for calculating the quasi-steady transonic flow over a lifting or non-lifting rotor blade in both hover and forward flight by using Euler equations. The approach is to solve Euler equations in a rotor-fixed frame of reference using a finite volume method. A computer program was developed and was then verified by comparison with wind-tunnel data. In all cases considered, good agreement was found with published experimental data.

General Equation Set Solver for Compressible and Incompressible Turbomachinery Flows

NASA Technical Reports Server (NTRS)

Sondak, Douglas L.; Dorney, Daniel J.

2002-01-01

Turbomachines for propulsion applications operate with many different working fluids and flow conditions. The flow may be incompressible, such as in the liquid hydrogen pump in a rocket engine, or supersonic, such as in the turbine which may drive the hydrogen pump. Separate codes have traditionally been used for incompressible and compressible flow solvers. The General Equation Set (GES) method can be used to solve both incompressible and compressible flows, and it is not restricted to perfect gases, as are many compressible-flow turbomachinery solvers. An unsteady GES turbomachinery flow solver has been developed and applied to both air and water flows through turbines. It has been shown to be an excellent alternative to maintaining two separate codes.

Multidisciplinary design optimization for sonic boom mitigation

NASA Astrophysics Data System (ADS)

Ozcer, Isik A.

Automated, parallelized, time-efficient surface definition and grid generation and flow simulation methods are developed for sharp and accurate sonic boom signal computation in three dimensions in the near and mid-field of an aircraft using Euler/Full-Potential unstructured/structured computational fluid dynamics. The full-potential mid-field sonic boom prediction code is an accurate and efficient solver featuring automated grid generation, grid adaptation and shock fitting, and parallel processing. This program quickly marches the solution using a single nonlinear equation for large distances that cannot be covered with Euler solvers due to large memory and long computational time requirements. The solver takes into account variations in temperature and pressure with altitude. The far-field signal prediction is handled using the classical linear Thomas Waveform Parameter Method where the switching altitude from the nonlinear to linear prediction is determined by convergence of the ground signal pressure impulse value. This altitude is determined as r/L ≈ 10 from the source for a simple lifting wing, and r/L ≈ 40 for a real complex aircraft. Unstructured grid adaptation and shock fitting methodology developed for the near-field analysis employs an Hessian based anisotropic grid adaptation based on error equidistribution. A special field scalar is formulated to be used in the computation of the Hessian based error metric which enhances significantly the adaptation scheme for shocks. The entire cross-flow of a complex aircraft is resolved with high fidelity using only 500,000 grid nodes after only about 10 solution/adaptation cycles. Shock fitting is accomplished using Roe's Flux-Difference Splitting scheme which is an approximate Riemann type solver and by proper alignment of the cell faces with respect to shock surfaces. Simple to complex real aircraft geometries are handled with no user-interference required making the simulation methods suitable tools for product design. The simulation tools are used to optimize three geometries for sonic boom mitigation. The first is a simple axisymmetric shape to be used as a generic nose component, the second is a delta wing with lift, and the third is a real aircraft with nose and wing optimization. The objectives are to minimize the pressure impulse or the peak pressure in the sonic boom signal, while keeping the drag penalty under feasible limits. The design parameters for the meridian profile of the nose shape are the lengths and the half-cone angles of the linear segments that make up the profile. The design parameters for the lifting wing are the dihedral angle, angle of attack, non-linear span-wise twist and camber distribution. The test-bed aircraft is the modified F-5E aircraft built by Northrop Grumman, designated the Shaped Sonic Boom Demonstrator. This aircraft is fitted with an optimized axisymmetric nose, and the wings are optimized to demonstrate optimization for sonic boom mitigation for a real aircraft. The final results predict 42% reduction in bow shock strength, 17% reduction in peak Deltap, 22% reduction in pressure impulse, 10% reduction in foot print size, 24% reduction in inviscid drag, and no loss in lift for the optimized aircraft. Optimization is carried out using response surface methodology, and the design matrices are determined using standard DoE techniques for quadratic response modeling.

Generalized conjugate-gradient methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1991-01-01

A generalized conjugate-gradient method is used to solve the two-dimensional, compressible Navier-Stokes equations of fluid flow. The equations are discretized with an implicit, upwind finite-volume formulation. Preconditioning techniques are incorporated into the new solver to accelerate convergence of the overall iterative method. The superiority of the new solver is demonstrated by comparisons with a conventional line Gauss-Siedel Relaxation solver. Computational test results for transonic flow (trailing edge flow in a transonic turbine cascade) and hypersonic flow (M = 6.0 shock-on-shock phenoena on a cylindrical leading edge) are presented. When applied to the transonic cascade case, the new solver is 4.4 times faster in terms of number of iterations and 3.1 times faster in terms of CPU time than the Relaxation solver. For the hypersonic shock case, the new solver is 3.0 times faster in terms of number of iterations and 2.2 times faster in terms of CPU time than the Relaxation solver.

Numerical Analysis of the Cavity Flow subjected to Passive Controls Techniques

NASA Astrophysics Data System (ADS)

Melih Guleren, Kursad; Turk, Seyfettin; Mirza Demircan, Osman; Demir, Oguzhan

2018-03-01

Open-source flow solvers are getting more and more popular for the analysis of challenging flow problems in aeronautical and mechanical engineering applications. They are offered under the GNU General Public License and can be run, examined, shared and modified according to user’s requirements. SU2 and OpenFOAM are the two most popular open-source solvers in Computational Fluid Dynamics (CFD) community. In the present study, some passive control methods on the high-speed cavity flows are numerically simulated using these open-source flow solvers along with one commercial flow solver called ANSYS/Fluent. The results are compared with the available experimental data. The solver SU2 are seen to predict satisfactory the mean streamline velocity but not turbulent kinetic energy and overall averaged sound pressure level (OASPL). Whereas OpenFOAM predicts all these parameters nearly as the same levels of ANSYS/Fluent.

Development of axisymmetric lattice Boltzmann flux solver for complex multiphase flows

NASA Astrophysics Data System (ADS)

Wang, Yan; Shu, Chang; Yang, Li-Ming; Yuan, Hai-Zhuan

2018-05-01

This paper presents an axisymmetric lattice Boltzmann flux solver (LBFS) for simulating axisymmetric multiphase flows. In the solver, the two-dimensional (2D) multiphase LBFS is applied to reconstruct macroscopic fluxes excluding axisymmetric effects. Source terms accounting for axisymmetric effects are introduced directly into the governing equations. As compared to conventional axisymmetric multiphase lattice Boltzmann (LB) method, the present solver has the kinetic feature for flux evaluation and avoids complex derivations of external forcing terms. In addition, the present solver also saves considerable computational efforts in comparison with three-dimensional (3D) computations. The capability of the proposed solver in simulating complex multiphase flows is demonstrated by studying single bubble rising in a circular tube. The obtained results compare well with the published data.

Validation of a High-Order Prefactored Compact Scheme on Nonlinear Flows with Complex Geometries

NASA Technical Reports Server (NTRS)

Hixon, Ray; Mankbadi, Reda R.; Povinelli, L. A. (Technical Monitor)

2000-01-01

Three benchmark problems are solved using a sixth-order prefactored compact scheme employing an explicit 10th-order filter with optimized fourth-order Runge-Kutta time stepping. The problems solved are the following: (1) propagation of sound waves through a transonic nozzle; (2) shock-sound interaction; and (3) single airfoil gust response. In the first two problems, the spatial accuracy of the scheme is tested on a stretched grid, and the effectiveness of boundary conditions is shown. The solution stability and accuracy near a shock discontinuity is shown as well. Also, 1-D nonlinear characteristic boundary conditions will be evaluated. In the third problem, a nonlinear Euler solver will be used that solves the equations in generalized curvilinear coordinates using the chain rule transformation. This work, continuing earlier work on flat-plate cascades and Joukowski airfoils, will focus mainly on the effect of the grid and boundary conditions on the accuracy of the solution. The grids were generated using a commercially available grid generator, GridPro/az3000.

New multigrid approach for three-dimensional unstructured, adaptive grids

NASA Technical Reports Server (NTRS)

Parthasarathy, Vijayan; Kallinderis, Y.

1994-01-01

A new multigrid method with adaptive unstructured grids is presented. The three-dimensional Euler equations are solved on tetrahedral grids that are adaptively refined or coarsened locally. The multigrid method is employed to propagate the fine grid corrections more rapidly by redistributing the changes-in-time of the solution from the fine grid to the coarser grids to accelerate convergence. A new approach is employed that uses the parent cells of the fine grid cells in an adapted mesh to generate successively coaser levels of multigrid. This obviates the need for the generation of a sequence of independent, nonoverlapping grids as well as the relatively complicated operations that need to be performed to interpolate the solution and the residuals between the independent grids. The solver is an explicit, vertex-based, finite volume scheme that employs edge-based data structures and operations. Spatial discretization is of central-differencing type combined with a special upwind-like smoothing operators. Application cases include adaptive solutions obtained with multigrid acceleration for supersonic and subsonic flow over a bump in a channel, as well as transonic flow around the ONERA M6 wing. Two levels of multigrid resulted in reduction in the number of iterations by a factor of 5.

Semi-discrete Galerkin solution of the compressible boundary-layer equations with viscous-inviscid interaction

NASA Technical Reports Server (NTRS)

Day, Brad A.; Meade, Andrew J., Jr.

1993-01-01

A semi-discrete Galerkin (SDG) method is under development to model attached, turbulent, and compressible boundary layers for transonic airfoil analysis problems. For the boundary-layer formulation the method models the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby providing high resolution near the wall and permitting the use of a uniform finite element grid which automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past RAE 2822 and NACA 0012 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack.

Numerical Simulation of the Fluid-Structure Interaction of a Surface Effect Ship Bow Seal

NASA Astrophysics Data System (ADS)

Bloxom, Andrew L.

Numerical simulations of fluid-structure interaction (FSI) problems were performed in an effort to verify and validate a commercially available FSI tool. This tool uses an iterative partitioned coupling scheme between CD-adapco's STAR-CCM+ finite volume fluid solver and Simulia's Abaqus finite element structural solver to simulate the FSI response of a system. Preliminary verification and validation work (V&V) was carried out to understand the numerical behavior of the codes individually and together as a FSI tool. Verification and Validation work that was completed included code order verification of the respective fluid and structural solvers with Couette-Poiseuille flow and Euler-Bernoulli beam theory. These results confirmed the 2 nd order accuracy of the spatial discretizations used. Following that, a mixture of solution verifications and model calibrations was performed with the inclusion of the physics models implemented in the solution of the FSI problems. Solution verifications were completed for fluid and structural stand-alone models as well as for the coupled FSI solutions. These results re-confirmed the spatial order of accuracy but for more complex flows and physics models as well as the order of accuracy of the temporal discretizations. In lieu of a good material definition, model calibration is performed to reproduce the experimental results. This work used model calibration for both instances of hyperelastic materials which were presented in the literature as validation cases because these materials were defined as linear elastic. Calibrated, three dimensional models of the bow seal on the University of Michigan bow seal test platform showed the ability to reproduce the experimental results qualitatively through averaging of the forces and seal displacements. These simulations represent the only current 3D results for this case. One significant result of this study is the ability to visualize the flow around the seal and to directly measure the seal resistances at varying cushion pressures, seal immersions, forward speeds, and different seal materials. SES design analysis could greatly benefit from the inclusion of flexible seals in simulations, and this work is a positive step in that direction. In future work, the inclusion of more complex seal geometries and contact will further enhance the capability of this tool.

Euler force actuation mechanism for siphon valving in compact disk-like microfluidic chips.

PubMed

Deng, Yongbo; Fan, Jianhua; Zhou, Song; Zhou, Teng; Wu, Junfeng; Li, Yin; Liu, Zhenyu; Xuan, Ming; Wu, Yihui

2014-03-01

Based on the Euler force induced by the acceleration of compact disk (CD)-like microfluidic chip, this paper presents a novel actuation mechanism for siphon valving. At the preliminary stage of acceleration, the Euler force in the tangential direction of CD-like chip takes the primary place compared with the centrifugal force to function as the actuation of the flow, which fills the siphon and actuates the siphon valving. The Euler force actuation mechanism is demonstrated by the numerical solution of the phase-field based mathematical model for the flow in siphon valve. In addition, experimental validation is implemented in the polymethylmethacrylate-based CD-like microfluidic chip manufactured using CO2 laser engraving technique. To prove the application of the proposed Euler force actuation mechanism, whole blood separation and plasma extraction has been conducted using the Euler force actuated siphon valving. The newly introduced actuation mechanism overcomes the dependence on hydrophilic capillary filling of siphon by avoiding external manipulation or surface treatments of polymeric material. The sacrifice for highly integrated processing in pneumatic pumping technique is also prevented by excluding the volume-occupied compressed air chamber.

Convergence of the flow of a chemically reacting gaseous mixture to incompressible Euler equations in a unbounded domain

NASA Astrophysics Data System (ADS)

Kwon, Young-Sam

2017-12-01

The flow of chemically reacting gaseous mixture is associated with a variety of phenomena and processes. We study the combined quasineutral and inviscid limit from the flow of chemically reacting gaseous mixture governed by Poisson equation to incompressible Euler equations with the ill-prepared initial data in the unbounded domain R^2× T. Furthermore, the convergence rates are obtained.

Impulse propagation over a complex site: a comparison of experimental results and numerical predictions.

PubMed

Dragna, Didier; Blanc-Benon, Philippe; Poisson, Franck

2014-03-01

Results from outdoor acoustic measurements performed in a railway site near Reims in France in May 2010 are compared to those obtained from a finite-difference time-domain solver of the linearized Euler equations. During the experiments, the ground profile and the different ground surface impedances were determined. Meteorological measurements were also performed to deduce mean vertical profiles of wind and temperature. An alarm pistol was used as a source of impulse signals and three microphones were located along a propagation path. The various measured parameters are introduced as input data into the numerical solver. In the frequency domain, the numerical results are in good accordance with the measurements up to a frequency of 2 kHz. In the time domain, except a time shift, the predicted waveforms match the measured waveforms with a close agreement.

Prediction of a Densely Loaded Particle-Laden Jet using a Euler-Lagrange Dense Spray Model

NASA Astrophysics Data System (ADS)

Pakseresht, Pedram; Apte, Sourabh V.

2017-11-01

Modeling of a dense spray regime using an Euler-Lagrange discrete-element approach is challenging because of local high volume loading. A subgrid cluster of droplets can lead to locally high void fractions for the disperse phase. Under these conditions, spatio-temporal changes in the carrier phase volume fractions, which are commonly neglected in spray simulations in an Euler-Lagrange two-way coupling model, could become important. Accounting for the carrier phase volume fraction variations, leads to zero-Mach number, variable density governing equations. Using pressure-based solvers, this gives rise to a source term in the pressure Poisson equation and a non-divergence free velocity field. To test the validity and predictive capability of such an approach, a round jet laden with solid particles is investigated using Direct Numerical Simulation and compared with available experimental data for different loadings. Various volume fractions spanning from dilute to dense regimes are investigated with and without taking into account the volume displacement effects. The predictions of the two approaches are compared and analyzed to investigate the effectiveness of the dense spray model. Financial support was provided by National Aeronautics and Space Administration (NASA).

Adaptive Osher-type scheme for the Euler equations with highly nonlinear equations of state

NASA Astrophysics Data System (ADS)

Lee, Bok Jik; Toro, Eleuterio F.; Castro, Cristóbal E.; Nikiforakis, Nikolaos

2013-08-01

For the numerical simulation of detonation of condensed phase explosives, a complex equation of state (EOS), such as the Jones-Wilkins-Lee (JWL) EOS or the Cochran-Chan (C-C) EOS, are widely used. However, when a conservative scheme is used for solving the Euler equations with such equations of state, a spurious solution across the contact discontinuity, a well known phenomenon in multi-fluid systems, arises even for single materials. In this work, we develop a generalised Osher-type scheme in an adaptive primitive-conservative framework to overcome the aforementioned difficulties. Resulting numerical solutions are compared with the exact solutions and with the numerical solutions from the Godunov method in conjunction with the exact Riemann solver for the Euler equations with Mie-Grüneisen form of equations of state, such as the JWL and the C-C equations of state. The adaptive scheme is extended to second order and its empirical convergence rates are presented, verifying second order accuracy for smooth solutions. Through a suite of several tests problems in one and two space dimensions we illustrate the failure of conservative schemes and the capability of the methods of this paper to overcome the difficulties.

An Analysis of Elliptic Grid Generation Techniques Using an Implicit Euler Solver.

DTIC Science & Technology

1986-06-09

automatic determination of the control fu.nction, . elements of covariant metric tensor in the elliptic grid generation system , from the Cm = 1,2,3...computational fluid d’nan1-cs code. Tne code Inclues a tnree-dimensional current research is aimed primaril: at algebraic generation system based on transfinite...start the iterative solution of the f. ow, nea, transfer, and combustion proble:s. elliptic generation system . Tn13 feature also .:ven-.ts :.t be made

WIND Flow Solver Released

NASA Technical Reports Server (NTRS)

Towne, Charles E.

1999-01-01

The WIND code is a general-purpose, structured, multizone, compressible flow solver that can be used to analyze steady or unsteady flow for a wide range of geometric configurations and over a wide range of flow conditions. WIND is the latest product of the NPARC Alliance, a formal partnership between the NASA Lewis Research Center and the Air Force Arnold Engineering Development Center (AEDC). WIND Version 1.0 was released in February 1998, and Version 2.0 will be released in February 1999. The WIND code represents a merger of the capabilities of three existing computational fluid dynamics codes--NPARC (the original NPARC Alliance flow solver), NXAIR (an Air Force code used primarily for unsteady store separation problems), and NASTD (the primary flow solver at McDonnell Douglas, now part of Boeing).

A solution algorithm for fluid–particle flows across all flow regimes

DOE PAGES

Kong, Bo; Fox, Rodney O.

2017-05-12

Many fluid–particle flows occurring in nature and in technological applications exhibit large variations in the local particle volume fraction. For example, in circulating fluidized beds there are regions where the particles are closepacked as well as very dilute regions where particle–particle collisions are rare. Thus, in order to simulate such fluid–particle systems, it is necessary to design a flow solver that can accurately treat all flow regimes occurring simultaneously in the same flow domain. In this work, a solution algorithm is proposed for this purpose. The algorithm is based on splitting the free-transport flux solver dynamically and locally in themore » flow. In close-packed to moderately dense regions, a hydrodynamic solver is employed, while in dilute to very dilute regions a kinetic-based finite-volume solver is used in conjunction with quadrature-based moment methods. To illustrate the accuracy and robustness of the proposed solution algorithm, it is implemented in OpenFOAM for particle velocity moments up to second order, and applied to simulate gravity-driven, gas–particle flows exhibiting cluster-induced turbulence. By varying the average particle volume fraction in the flow domain, it is demonstrated that the flow solver can handle seamlessly all flow regimes present in fluid–particle flows.« less

A solution algorithm for fluid-particle flows across all flow regimes

NASA Astrophysics Data System (ADS)

Kong, Bo; Fox, Rodney O.

2017-09-01

Many fluid-particle flows occurring in nature and in technological applications exhibit large variations in the local particle volume fraction. For example, in circulating fluidized beds there are regions where the particles are close-packed as well as very dilute regions where particle-particle collisions are rare. Thus, in order to simulate such fluid-particle systems, it is necessary to design a flow solver that can accurately treat all flow regimes occurring simultaneously in the same flow domain. In this work, a solution algorithm is proposed for this purpose. The algorithm is based on splitting the free-transport flux solver dynamically and locally in the flow. In close-packed to moderately dense regions, a hydrodynamic solver is employed, while in dilute to very dilute regions a kinetic-based finite-volume solver is used in conjunction with quadrature-based moment methods. To illustrate the accuracy and robustness of the proposed solution algorithm, it is implemented in OpenFOAM for particle velocity moments up to second order, and applied to simulate gravity-driven, gas-particle flows exhibiting cluster-induced turbulence. By varying the average particle volume fraction in the flow domain, it is demonstrated that the flow solver can handle seamlessly all flow regimes present in fluid-particle flows.

A solution algorithm for fluid–particle flows across all flow regimes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kong, Bo; Fox, Rodney O.

Many fluid–particle flows occurring in nature and in technological applications exhibit large variations in the local particle volume fraction. For example, in circulating fluidized beds there are regions where the particles are closepacked as well as very dilute regions where particle–particle collisions are rare. Thus, in order to simulate such fluid–particle systems, it is necessary to design a flow solver that can accurately treat all flow regimes occurring simultaneously in the same flow domain. In this work, a solution algorithm is proposed for this purpose. The algorithm is based on splitting the free-transport flux solver dynamically and locally in themore » flow. In close-packed to moderately dense regions, a hydrodynamic solver is employed, while in dilute to very dilute regions a kinetic-based finite-volume solver is used in conjunction with quadrature-based moment methods. To illustrate the accuracy and robustness of the proposed solution algorithm, it is implemented in OpenFOAM for particle velocity moments up to second order, and applied to simulate gravity-driven, gas–particle flows exhibiting cluster-induced turbulence. By varying the average particle volume fraction in the flow domain, it is demonstrated that the flow solver can handle seamlessly all flow regimes present in fluid–particle flows.« less

An assessment of viscous effects in computational simulation of benign and burst vortex flows on generic fighter wind-tunnel models using TEAM code

NASA Technical Reports Server (NTRS)

Kinard, Tim A.; Harris, Brenda W.; Raj, Pradeep

1995-01-01

Vortex flows on a twin-tail and a single-tail modular transonic vortex interaction (MTVI) model, representative of a generic fighter configuration, are computationally simulated in this study using the Three-dimensional Euler/Navier-Stokes Aerodynamic Method (TEAM). The primary objective is to provide an assessment of viscous effects on benign (10 deg angle of attack) and burst (35 deg angle of attack) vortex flow solutions. This study was conducted in support of a NASA project aimed at assessing the viability of using Euler technology to predict aerodynamic characteristics of aircraft configurations at moderate-to-high angles of attack in a preliminary design environment. The TEAM code solves the Euler and Reynolds-average Navier-Stokes equations on patched multiblock structured grids. Its algorithm is based on a cell-centered finite-volume formulation with multistage time-stepping scheme. Viscous effects are assessed by comparing the computed inviscid and viscous solutions with each other and experimental data. Also, results of Euler solution sensitivity to grid density and numerical dissipation are presented for the twin-tail model. The results show that proper accounting of viscous effects is necessary for detailed design and optimization but Euler solutions can provide meaningful guidelines for preliminary design of flight vehicles which exhibit vortex flows in parts of their flight envelope.

CFD validation needs for advanced concepts at Northrop Corporation

NASA Technical Reports Server (NTRS)

George, Michael W.

1987-01-01

Information is given in viewgraph form on the Computational Fluid Dynamics (CFD) Workshop held July 14 - 16, 1987. Topics covered include the philosophy of CFD validation, current validation efforts, the wing-body-tail Euler code, F-20 Euler simulated oil flow, and Euler Navier-Stokes code validation for 2D and 3D nozzle afterbody applications.

Nonlinear Aeroacoustics Computations by the Space-Time CE/SE Method

NASA Technical Reports Server (NTRS)

Loh, Ching Y.

2003-01-01

The Space-Time Conservation Element and Solution Element Method, or CE/SE Method for short, is a recently developed numerical method for conservation laws. Despite its second order accuracy in space and time, it possesses low dispersion errors and low dissipation. The method is robust enough to cover a wide range of compressible flows: from weak linear acoustic waves to strong discontinuous waves (shocks). An outstanding feature of the CE/SE scheme is its truly multi-dimensional, simple but effective non-reflecting boundary condition (NRBC), which is particularly valuable for computational aeroacoustics (CAA). In nature, the method may be categorized as a finite volume method, where the conservation element (CE) is equivalent to a finite control volume (or cell) and the solution element (SE) can be understood as the cell interface. However, due to its careful treatment of the surface fluxes and geometry, it is different from the existing schemes. Currently, the CE/SE scheme has been developed to a matured stage that a 3-D unstructured CE/SE Navier-Stokes solver is already available. However, in the present review paper, as a general introduction to the CE/SE method, only the 2-D unstructured Euler CE/SE solver is chosen and sketched in section 2. Then applications of the 2-D and 3-D CE/SE schemes to linear, and in particular, nonlinear aeroacoustics are depicted in sections 3, 4, and 5 to demonstrate its robustness and capability.

A high-order gas-kinetic Navier-Stokes flow solver

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li Qibing, E-mail: lqb@tsinghua.edu.c; Xu Kun, E-mail: makxu@ust.h; Fu Song, E-mail: fs-dem@tsinghua.edu.c

2010-09-20

The foundation for the development of modern compressible flow solver is based on the Riemann solution of the inviscid Euler equations. The high-order schemes are basically related to high-order spatial interpolation or reconstruction. In order to overcome the low-order wave interaction mechanism due to the Riemann solution, the temporal accuracy of the scheme can be improved through the Runge-Kutta method, where the dynamic deficiencies in the first-order Riemann solution is alleviated through the sub-step spatial reconstruction in the Runge-Kutta process. The close coupling between the spatial and temporal evolution in the original nonlinear governing equations seems weakened due to itsmore » spatial and temporal decoupling. Many recently developed high-order methods require a Navier-Stokes flux function under piece-wise discontinuous high-order initial reconstruction. However, the piece-wise discontinuous initial data and the hyperbolic-parabolic nature of the Navier-Stokes equations seem inconsistent mathematically, such as the divergence of the viscous and heat conducting terms due to initial discontinuity. In this paper, based on the Boltzmann equation, we are going to present a time-dependent flux function from a high-order discontinuous reconstruction. The theoretical basis for such an approach is due to the fact that the Boltzmann equation has no specific requirement on the smoothness of the initial data and the kinetic equation has the mechanism to construct a dissipative wave structure starting from an initially discontinuous flow condition on a time scale being larger than the particle collision time. The current high-order flux evaluation method is an extension of the second-order gas-kinetic BGK scheme for the Navier-Stokes equations (BGK-NS). The novelty for the easy extension from a second-order to a higher order is due to the simple particle transport and collision mechanism on the microscopic level. This paper will present a hierarchy to construct such a high-order method. The necessity to couple spatial and temporal evolution nonlinearly in the flux evaluation can be clearly observed through the numerical performance of the scheme for the viscous flow computations.« less

Euler force actuation mechanism for siphon valving in compact disk-like microfluidic chips

PubMed Central

Deng, Yongbo; Fan, Jianhua; Zhou, Song; Zhou, Teng; Wu, Junfeng; Li, Yin; Liu, Zhenyu; Xuan, Ming; Wu, Yihui

2014-01-01

Based on the Euler force induced by the acceleration of compact disk (CD)-like microfluidic chip, this paper presents a novel actuation mechanism for siphon valving. At the preliminary stage of acceleration, the Euler force in the tangential direction of CD-like chip takes the primary place compared with the centrifugal force to function as the actuation of the flow, which fills the siphon and actuates the siphon valving. The Euler force actuation mechanism is demonstrated by the numerical solution of the phase-field based mathematical model for the flow in siphon valve. In addition, experimental validation is implemented in the polymethylmethacrylate-based CD-like microfluidic chip manufactured using CO2 laser engraving technique. To prove the application of the proposed Euler force actuation mechanism, whole blood separation and plasma extraction has been conducted using the Euler force actuated siphon valving. The newly introduced actuation mechanism overcomes the dependence on hydrophilic capillary filling of siphon by avoiding external manipulation or surface treatments of polymeric material. The sacrifice for highly integrated processing in pneumatic pumping technique is also prevented by excluding the volume-occupied compressed air chamber. PMID:24753736

MODFLOW-2000, The U.S. Geological Survey Modular Ground-Water Model -- GMG Linear Equation Solver Package Documentation

USGS Publications Warehouse

Wilson, John D.; Naff, Richard L.

2004-01-01

A geometric multigrid solver (GMG), based in the preconditioned conjugate gradient algorithm, has been developed for solving systems of equations resulting from applying the cell-centered finite difference algorithm to flow in porous media. This solver has been adapted to the U.S. Geological Survey ground-water flow model MODFLOW-2000. The documentation herein is a description of the solver and the adaptation to MODFLOW-2000.

Modelling gas dynamics in 1D ducts with abrupt area change

NASA Astrophysics Data System (ADS)

Menina, R.; Saurel, R.; Zereg, M.; Houas, L.

2011-09-01

Most gas dynamic computations in industrial ducts are done in one dimension with cross-section-averaged Euler equations. This poses a fundamental difficulty as soon as geometrical discontinuities are present. The momentum equation contains a non-conservative term involving a surface pressure integral, responsible for momentum loss. Definition of this integral is very difficult from a mathematical standpoint as the flow may contain other discontinuities (shocks, contact discontinuities). From a physical standpoint, geometrical discontinuities induce multidimensional vortices that modify the surface pressure integral. In the present paper, an improved 1D flow model is proposed. An extra energy (or entropy) equation is added to the Euler equations expressing the energy and turbulent pressure stored in the vortices generated by the abrupt area variation. The turbulent energy created by the flow-area change interaction is determined by a specific estimate of the surface pressure integral. Model's predictions are compared with 2D-averaged results from numerical solution of the Euler equations. Comparison with shock tube experiments is also presented. The new 1D-averaged model improves the conventional cross-section-averaged Euler equations and is able to reproduce the main flow features.

Modeling of Mixing Behavior in a Combined Blowing Steelmaking Converter with a Filter-Based Euler-Lagrange Model

NASA Astrophysics Data System (ADS)

Li, Mingming; Li, Lin; Li, Qiang; Zou, Zongshu

2018-05-01

A filter-based Euler-Lagrange multiphase flow model is used to study the mixing behavior in a combined blowing steelmaking converter. The Euler-based volume of fluid approach is employed to simulate the top blowing, while the Lagrange-based discrete phase model that embeds the local volume change of rising bubbles for the bottom blowing. A filter-based turbulence method based on the local meshing resolution is proposed aiming to improve the modeling of turbulent eddy viscosities. The model validity is verified through comparison with physical experiments in terms of mixing curves and mixing times. The effects of the bottom gas flow rate on bath flow and mixing behavior are investigated and the inherent reasons for the mixing result are clarified in terms of the characteristics of bottom-blowing plumes, the interaction between plumes and top-blowing jets, and the change of bath flow structure.

The international river interface cooperative: Public domain flow and morphodynamics software for education and applications

NASA Astrophysics Data System (ADS)

Nelson, Jonathan M.; Shimizu, Yasuyuki; Abe, Takaaki; Asahi, Kazutake; Gamou, Mineyuki; Inoue, Takuya; Iwasaki, Toshiki; Kakinuma, Takaharu; Kawamura, Satomi; Kimura, Ichiro; Kyuka, Tomoko; McDonald, Richard R.; Nabi, Mohamed; Nakatsugawa, Makoto; Simões, Francisco R.; Takebayashi, Hiroshi; Watanabe, Yasunori

2016-07-01

This paper describes a new, public-domain interface for modeling flow, sediment transport and morphodynamics in rivers and other geophysical flows. The interface is named after the International River Interface Cooperative (iRIC), the group that constructed the interface and many of the current solvers included in iRIC. The interface is entirely free to any user and currently houses thirteen models ranging from simple one-dimensional models through three-dimensional large-eddy simulation models. Solvers are only loosely coupled to the interface so it is straightforward to modify existing solvers or to introduce other solvers into the system. Six of the most widely-used solvers are described in detail including example calculations to serve as an aid for users choosing what approach might be most appropriate for their own applications. The example calculations range from practical computations of bed evolution in natural rivers to highly detailed predictions of the development of small-scale bedforms on an initially flat bed. The remaining solvers are also briefly described. Although the focus of most solvers is coupled flow and morphodynamics, several of the solvers are also specifically aimed at providing flood inundation predictions over large spatial domains. Potential users can download the application, solvers, manuals, and educational materials including detailed tutorials at www.-i-ric.org. The iRIC development group encourages scientists and engineers to use the tool and to consider adding their own methods to the iRIC suite of tools.

The international river interface cooperative: Public domain flow and morphodynamics software for education and applications

USGS Publications Warehouse

Nelson, Jonathan M.; Shimizu, Yasuyuki; Abe, Takaaki; Asahi, Kazutake; Gamou, Mineyuki; Inoue, Takuya; Iwasaki, Toshiki; Kakinuma, Takaharu; Kawamura, Satomi; Kimura, Ichiro; Kyuka, Tomoko; McDonald, Richard R.; Nabi, Mohamed; Nakatsugawa, Makoto; Simoes, Francisco J.; Takebayashi, Hiroshi; Watanabe, Yasunori

2016-01-01

This paper describes a new, public-domain interface for modeling flow, sediment transport and morphodynamics in rivers and other geophysical flows. The interface is named after the International River Interface Cooperative (iRIC), the group that constructed the interface and many of the current solvers included in iRIC. The interface is entirely free to any user and currently houses thirteen models ranging from simple one-dimensional models through three-dimensional large-eddy simulation models. Solvers are only loosely coupled to the interface so it is straightforward to modify existing solvers or to introduce other solvers into the system. Six of the most widely-used solvers are described in detail including example calculations to serve as an aid for users choosing what approach might be most appropriate for their own applications. The example calculations range from practical computations of bed evolution in natural rivers to highly detailed predictions of the development of small-scale bedforms on an initially flat bed. The remaining solvers are also briefly described. Although the focus of most solvers is coupled flow and morphodynamics, several of the solvers are also specifically aimed at providing flood inundation predictions over large spatial domains. Potential users can download the application, solvers, manuals, and educational materials including detailed tutorials at www.-i-ric.org. The iRIC development group encourages scientists and engineers to use the tool and to consider adding their own methods to the iRIC suite of tools.

A Study of Flow Separation in Transonic Flow Using Inviscid and Viscous Computational Fluid Dynamics (CFD) Schemes

NASA Technical Reports Server (NTRS)

Rhodes, J. A.; Tiwari, S. N.; Vonlavante, E.

1988-01-01

A comparison of flow separation in transonic flows is made using various computational schemes which solve the Euler and the Navier-Stokes equations of fluid mechanics. The flows examined are computed using several simple two-dimensional configurations including a backward facing step and a bump in a channel. Comparison of the results obtained using shock fitting and flux vector splitting methods are presented and the results obtained using the Euler codes are compared to results on the same configurations using a code which solves the Navier-Stokes equations.

Developing and utilizing an Euler computational method for predicting the airframe/propulsion effects for an aft-mounted turboprop transport. Volume 2: User guide

NASA Technical Reports Server (NTRS)

Chen, H. C.; Neback, H. E.; Kao, T. J.; Yu, N. Y.; Kusunose, K.

1991-01-01

This manual explains how to use an Euler based computational method for predicting the airframe/propulsion integration effects for an aft-mounted turboprop transport. The propeller power effects are simulated by the actuator disk concept. This method consists of global flow field analysis and the embedded flow solution for predicting the detailed flow characteristics in the local vicinity of an aft-mounted propfan engine. The computational procedure includes the use of several computer programs performing four main functions: grid generation, Euler solution, grid embedding, and streamline tracing. This user's guide provides information for these programs, including input data preparations with sample input decks, output descriptions, and sample Unix scripts for program execution in the UNICOS environment.

Euler Technology Assessment - SPLITFLOW Code Applications for Stability and Control Analysis on an Advanced Fighter Model Employing Innovative Control Concepts

NASA Technical Reports Server (NTRS)

Jordan, Keith J.

1998-01-01

This report documents results from the NASA-Langley sponsored Euler Technology Assessment Study conducted by Lockheed-Martin Tactical Aircraft Systems (LMTAS). The purpose of the study was to evaluate the ability of the SPLITFLOW code using viscous and inviscid flow models to predict aerodynamic stability and control of an advanced fighter model. The inviscid flow model was found to perform well at incidence angles below approximately 15 deg, but not as well at higher angles of attack. The results using a turbulent, viscous flow model matched the trends of the wind tunnel data, but did not show significant improvement over the Euler solutions. Overall, the predictions were found to be useful for stability and control design purposes.

Multimodel methods for optimal control of aeroacoustics.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Guoquan; Collis, Samuel Scott

2005-01-01

A new multidomain/multiphysics computational framework for optimal control of aeroacoustic noise has been developed based on a near-field compressible Navier-Stokes solver coupled with a far-field linearized Euler solver both based on a discontinuous Galerkin formulation. In this approach, the coupling of near- and far-field domains is achieved by weakly enforcing continuity of normal fluxes across a coupling surface that encloses all nonlinearities and noise sources. For optimal control, gradient information is obtained by the solution of an appropriate adjoint problem that involves the propagation of adjoint information from the far-field to the near-field. This computational framework has been successfully appliedmore » to study optimal boundary-control of blade-vortex interaction, which is a significant noise source for helicopters on approach to landing. In the model-problem presented here, the noise propagated toward the ground is reduced by 12dB.« less

Gas-Kinetic Theory Based Flux Splitting Method for Ideal Magnetohydrodynamics

NASA Technical Reports Server (NTRS)

Xu, Kun

1998-01-01

A gas-kinetic solver is developed for the ideal magnetohydrodynamics (MHD) equations. The new scheme is based on the direct splitting of the flux function of the MHD equations with the inclusion of "particle" collisions in the transport process. Consequently, the artificial dissipation in the new scheme is much reduced in comparison with the MHD Flux Vector Splitting Scheme. At the same time, the new scheme is compared with the well-developed Roe-type MHD solver. It is concluded that the kinetic MHD scheme is more robust and efficient than the Roe- type method, and the accuracy is competitive. In this paper the general principle of splitting the macroscopic flux function based on the gas-kinetic theory is presented. The flux construction strategy may shed some light on the possible modification of AUSM- and CUSP-type schemes for the compressible Euler equations, as well as to the development of new schemes for a non-strictly hyperbolic system.

An approximate Riemann solver for hypervelocity flows

NASA Technical Reports Server (NTRS)

Jacobs, Peter A.

1991-01-01

We describe an approximate Riemann solver for the computation of hypervelocity flows in which there are strong shocks and viscous interactions. The scheme has three stages, the first of which computes the intermediate states assuming isentropic waves. A second stage, based on the strong shock relations, may then be invoked if the pressure jump across either wave is large. The third stage interpolates the interface state from the two initial states and the intermediate states. The solver is used as part of a finite-volume code and is demonstrated on two test cases. The first is a high Mach number flow over a sphere while the second is a flow over a slender cone with an adiabatic boundary layer. In both cases the solver performs well.

Analysis Tools for CFD Multigrid Solvers

NASA Technical Reports Server (NTRS)

Mineck, Raymond E.; Thomas, James L.; Diskin, Boris

2004-01-01

Analysis tools are needed to guide the development and evaluate the performance of multigrid solvers for the fluid flow equations. Classical analysis tools, such as local mode analysis, often fail to accurately predict performance. Two-grid analysis tools, herein referred to as Idealized Coarse Grid and Idealized Relaxation iterations, have been developed and evaluated within a pilot multigrid solver. These new tools are applicable to general systems of equations and/or discretizations and point to problem areas within an existing multigrid solver. Idealized Relaxation and Idealized Coarse Grid are applied in developing textbook-efficient multigrid solvers for incompressible stagnation flow problems.

Splitting methods for low Mach number Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Abarbanel, Saul; Dutt, Pravir; Gottlieb, David

1987-01-01

Examined are some splitting techniques for low Mach number Euler flows. Shortcomings of some of the proposed methods are pointed out and an explanation for their inadequacy suggested. A symmetric splitting for both the Euler and Navier-Stokes equations is then presented which removes the stiffness of these equations when the Mach number is small. The splitting is shown to be stable.

A dual potential formulation of the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Gegg, S. G.; Pletcher, R. H.; Steger, J. L.

1989-01-01

A dual potential formulation for numerically solving the Navier-Stokes equations is developed and presented. The velocity field is decomposed using a scalar and vector potential. Vorticity and dilatation are used as the dependent variables in the momentum equations. Test cases in two dimensions verify the capability to solve flows using approximations from potential flow to full Navier-Stokes simulations. A three-dimensional incompressible flow formulation is also described. An interesting feature of this approach to solving the Navier-Stokes equations is the decomposition of the velocity field into a rotational part (vector potential) and an irrotational part (scalar potential). The Helmholtz decomposition theorem allows this splitting of the velocity field. This approach has had only limited use since it increases the number of dependent variables in the solution. However, it has often been used for incompressible flows where the solution scheme is known to be fast and accurate. This research extends the usage of this method to fully compressible Navier-Stokes simulations by using the dilatation variable along with vorticity. A time-accurate, iterative algorithm is used for the uncoupled solution of the governing equations. Several levels of flow approximation are available within the framework of this method. Potential flow, Euler and full Navier-Stokes solutions are possible using the dual potential formulation. Solution efficiency can be enhanced in a straightforward way. For some flows, the vorticity and/or dilatation may be negligible in certain regions (e.g., far from a viscous boundary in an external flow). It is possible to drop the calculation of these variables then and optimize the solution speed. Also, efficient Poisson solvers are available for the potentials. The relative merits of non-primitive variables versus primitive variables for solution of the Navier-Stokes equations are also discussed.

Nearly Interactive Parabolized Navier-Stokes Solver for High Speed Forebody and Inlet Flows

NASA Technical Reports Server (NTRS)

Benson, Thomas J.; Liou, May-Fun; Jones, William H.; Trefny, Charles J.

2009-01-01

A system of computer programs is being developed for the preliminary design of high speed inlets and forebodies. The system comprises four functions: geometry definition, flow grid generation, flow solver, and graphics post-processor. The system runs on a dedicated personal computer using the Windows operating system and is controlled by graphical user interfaces written in MATLAB (The Mathworks, Inc.). The flow solver uses the Parabolized Navier-Stokes equations to compute millions of mesh points in several minutes. Sample two-dimensional and three-dimensional calculations are demonstrated in the paper.

Adding Complex Terrain and Stable Atmospheric Condition Capability to the OpenFOAM-based Flow Solver of the Simulator for On/Offshore Wind Farm Applications (SOWFA): Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Churchfield, M. J.; Sang, L.; Moriarty, P. J.

This paper describes changes made to NREL's OpenFOAM-based wind plant aerodynamics solver such that it can compute the stably stratified atmospheric boundary layer and flow over terrain. Background about the flow solver, the Simulator for Off/Onshore Wind Farm Applications (SOWFA) is given, followed by details of the stable stratification/complex terrain modifications to SOWFA, along with somepreliminary results calculations of a stable atmospheric boundary layer and flow over a simply set of hills.

A general multiblock Euler code for propulsion integration. Volume 3: User guide for the Euler code

NASA Technical Reports Server (NTRS)

Chen, H. C.; Su, T. Y.; Kao, T. J.

1991-01-01

This manual explains the procedures for using the general multiblock Euler (GMBE) code developed under NASA contract NAS1-18703. The code was developed for the aerodynamic analysis of geometrically complex configurations in either free air or wind tunnel environments (vol. 1). The complete flow field is divided into a number of topologically simple blocks within each of which surface fitted grids and efficient flow solution algorithms can easily be constructed. The multiblock field grid is generated with the BCON procedure described in volume 2. The GMBE utilizes a finite volume formulation with an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. This user guide provides information on the GMBE code, including input data preparations with sample input files and a sample Unix script for program execution in the UNICOS environment.

Toward an optimal solver for time-spectral fluid-dynamic and aeroelastic solutions on unstructured meshes

NASA Astrophysics Data System (ADS)

Mundis, Nathan L.; Mavriplis, Dimitri J.

2017-09-01

The time-spectral method applied to the Euler and coupled aeroelastic equations theoretically offers significant computational savings for purely periodic problems when compared to standard time-implicit methods. However, attaining superior efficiency with time-spectral methods over traditional time-implicit methods hinges on the ability rapidly to solve the large non-linear system resulting from time-spectral discretizations which become larger and stiffer as more time instances are employed or the period of the flow becomes especially short (i.e. the maximum resolvable wave-number increases). In order to increase the efficiency of these solvers, and to improve robustness, particularly for large numbers of time instances, the Generalized Minimal Residual Method (GMRES) is used to solve the implicit linear system over all coupled time instances. The use of GMRES as the linear solver makes time-spectral methods more robust, allows them to be applied to a far greater subset of time-accurate problems, including those with a broad range of harmonic content, and vastly improves the efficiency of time-spectral methods. In previous work, a wave-number independent preconditioner that mitigates the increased stiffness of the time-spectral method when applied to problems with large resolvable wave numbers has been developed. This preconditioner, however, directly inverts a large matrix whose size increases in proportion to the number of time instances. As a result, the computational time of this method scales as the cube of the number of time instances. In the present work, this preconditioner has been reworked to take advantage of an approximate-factorization approach that effectively decouples the spatial and temporal systems. Once decoupled, the time-spectral matrix can be inverted in frequency space, where it has entries only on the main diagonal and therefore can be inverted quite efficiently. This new GMRES/preconditioner combination is shown to be over an order of magnitude more efficient than the previous wave-number independent preconditioner for problems with large numbers of time instances and/or large reduced frequencies.

IRMHD: an implicit radiative and magnetohydrodynamical solver for self-gravitating systems

NASA Astrophysics Data System (ADS)

Hujeirat, A.

1998-07-01

The 2D implicit hydrodynamical solver developed by Hujeirat & Rannacher is now modified to include the effects of radiation, magnetic fields and self-gravity in different geometries. The underlying numerical concept is based on the operator splitting approach, and the resulting 2D matrices are inverted using different efficient preconditionings such as ADI (alternating direction implicit), the approximate factorization method and Line-Gauss-Seidel or similar iteration procedures. Second-order finite volume with third-order upwinding and second-order time discretization is used. To speed up convergence and enhance efficiency we have incorporated an adaptive time-step control and monotonic multilevel grid distributions as well as vectorizing the code. Test calculations had shown that it requires only 38 per cent more computational effort than its explicit counterpart, whereas its range of application to astrophysical problems is much larger. For example, strongly time-dependent, quasi-stationary and steady-state solutions for the set of Euler and Navier-Stokes equations can now be sought on a non-linearly distributed and strongly stretched mesh. As most of the numerical techniques used to build up this algorithm have been described by Hujeirat & Rannacher in an earlier paper, we focus in this paper on the inclusion of self-gravity, radiation and magnetic fields. Strategies for satisfying the condition ∇.B=0 in the implicit evolution of MHD flows are given. A new discretization strategy for the vector potential which allows alternating use of the direct method is prescribed. We investigate the efficiencies of several 2D solvers for a Poisson-like equation and compare their convergence rates. We provide a splitting approach for the radiative flux within the FLD (flux-limited diffusion) approximation to enhance consistency and accuracy between regions of different optical depths. The results of some test problems are presented to demonstrate the accuracy and robustness of the code.

An approximate Riemann solver for real gas parabolized Navier-Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Urbano, Annafederica, E-mail: annafederica.urbano@uniroma1.it; Nasuti, Francesco, E-mail: francesco.nasuti@uniroma1.it

2013-01-15

Under specific assumptions, parabolized Navier-Stokes equations are a suitable mean to study channel flows. A special case is that of high pressure flow of real gases in cooling channels where large crosswise gradients of thermophysical properties occur. To solve the parabolized Navier-Stokes equations by a space marching approach, the hyperbolicity of the system of governing equations is obtained, even for very low Mach number flow, by recasting equations such that the streamwise pressure gradient is considered as a source term. For this system of equations an approximate Roe's Riemann solver is developed as the core of a Godunov type finitemore » volume algorithm. The properties of the approximated Riemann solver, which is a modification of Roe's Riemann solver for the parabolized Navier-Stokes equations, are presented and discussed with emphasis given to its original features introduced to handle fluids governed by a generic real gas EoS. Sample solutions are obtained for low Mach number high compressible flows of transcritical methane, heated in straight long channels, to prove the solver ability to describe flows dominated by complex thermodynamic phenomena.« less

Generic Wing-Body Aerodynamics Data Base

NASA Technical Reports Server (NTRS)

Holst, Terry L.; Olsen, Thomas H.; Kwak, Dochan (Technical Monitor)

2001-01-01

The wing-body aerodynamics data base consists of a series of CFD (Computational Fluid Dynamics) simulations about a generic wing body configuration consisting of a ogive-circular-cylinder fuselage and a simple symmetric wing mid-mounted on the fuselage. Solutions have been obtained for Nonlinear Potential (P), Euler (E) and Navier-Stokes (N) solvers over a range of subsonic and transonic Mach numbers and angles of attack. In addition, each solution has been computed on a series of grids, coarse, medium and fine to permit an assessment of grid refinement errors.

CFD Simulation on the J-2X Engine Exhaust in the Center-Body Diffuser and Spray Chamber at the B-2 Facility

NASA Technical Reports Server (NTRS)

Wang, Xiao-Yen; Wey, Thomas; Buehrle, Robert

2009-01-01

A computational fluid dynamic (CFD) code is used to simulate the J-2X engine exhaust in the center-body diffuser and spray chamber at the Spacecraft Propulsion Facility (B-2). The CFD code is named as the space-time conservation element and solution element (CESE) Euler solver and is very robust at shock capturing. The CESE results are compared with independent analysis results obtained by using the National Combustion Code (NCC) and show excellent agreement.

Application of an Unstructured Grid Navier-Stokes Solver to a Generic Helicopter Boby: Comparison of Unstructured Grid Results with Structured Grid Results and Experimental Results

NASA Technical Reports Server (NTRS)

Mineck, Raymond E.

1999-01-01

An unstructured-grid Navier-Stokes solver was used to predict the surface pressure distribution, the off-body flow field, the surface flow pattern, and integrated lift and drag coefficients on the ROBIN configuration (a generic helicopter) without a rotor at four angles of attack. The results are compared to those predicted by two structured- grid Navier-Stokes solvers and to experimental surface pressure distributions. The surface pressure distributions from the unstructured-grid Navier-Stokes solver are in good agreement with the results from the structured-grid Navier-Stokes solvers. Agreement with the experimental pressure coefficients is good over the forward portion of the body. However, agreement is poor on the lower portion of the mid-section of the body. Comparison of the predicted surface flow patterns showed similar regions of separated flow. Predicted lift and drag coefficients were in fair agreement with each other.

Unsteady transonic viscous-inviscid interaction using Euler and boundary-layer equations

NASA Technical Reports Server (NTRS)

Pirzadeh, Shahyar; Whitfield, Dave

1989-01-01

The Euler code is used extensively for computation of transonic unsteady aerodynamics. The boundary layer code solves the 3-D, compressible, unsteady, mean flow kinetic energy integral boundary layer equations in the direct mode. Inviscid-viscous coupling is handled using porosity boundary conditions. Some of the advantages and disadvantages of using the Euler and boundary layer equations for investigating unsteady viscous-inviscid interaction is examined.

Combining the Vortex Particle-Mesh method with a Multi-Body System solver for the simulation of self-propelled articulated swimmers

NASA Astrophysics Data System (ADS)

Bernier, Caroline; Gazzola, Mattia; Ronsse, Renaud; Chatelain, Philippe

2017-11-01

We present a 2D fluid-structure interaction simulation method with a specific focus on articulated and actuated structures. The proposed algorithm combines a viscous Vortex Particle-Mesh (VPM) method based on a penalization technique and a Multi-Body System (MBS) solver. The hydrodynamic forces and moments acting on the structure parts are not computed explicitly from the surface stresses; they are rather recovered from the projection and penalization steps within the VPM method. The MBS solver accounts for the body dynamics via the Euler-Lagrange formalism. The deformations of the structure are dictated by the hydrodynamic efforts and actuation torques. Here, we focus on simplified swimming structures composed of neutrally buoyant ellipses connected by virtual joints. The joints are actuated through a simple controller in order to reproduce the swimming patterns of an eel-like swimmer. The method enables to recover the histories of torques applied on each hinge along the body. The method is verified on several benchmarks: an impulsively started elastically mounted cylinder and free swimming articulated fish-like structures. Validation will be performed by means of an experimental swimming robot that reproduces the 2D articulated ellipses.

Numerical Investigation of Vertical Plunging Jet Using a Hybrid Multifluid–VOF Multiphase CFD Solver

DOE PAGES

Shonibare, Olabanji Y.; Wardle, Kent E.

2015-06-28

A novel hybrid multiphase flow solver has been used to conduct simulations of a vertical plunging liquid jet. This solver combines a multifluid methodology with selective interface sharpening to enable simulation of both the initial jet impingement and the long-time entrained bubble plume phenomena. Models are implemented for variable bubble size capturing and dynamic switching of interface sharpened regions to capture transitions between the initially fully segregated flow types into the dispersed bubbly flow regime. It was found that the solver was able to capture the salient features of the flow phenomena under study and areas for quantitative improvement havemore » been explored and identified. In particular, a population balance approach is employed and detailed calibration of the underlying models with experimental data is required to enable quantitative prediction of bubble size and distribution to capture the transition between segregated and dispersed flow types with greater fidelity.« less

Singular flow dynamics in three space dimensions driven by advection

NASA Astrophysics Data System (ADS)

Karimov, A. R.; Schamel, H.

2002-03-01

The initial value problem of an ideal, compressible fluid is investigated in three space dimensions (3D). Starting from a situation where the inertia terms dominate over the force terms in Euler's equation we explore by means of the Lagrangian flow description the basic flow properties. Special attention is drawn to the appearance of singularities in the flow pattern at finite time. Classes of initial velocity profiles giving rise to collapses of density and vorticity are found. This paper, hence, furnishes evidence of focused singularities for coherent structures obeying the 3D Euler equation and applies to potential as well as vortex flows.

The development of an intelligent interface to a computational fluid dynamics flow-solver code

NASA Technical Reports Server (NTRS)

Williams, Anthony D.

1988-01-01

Researchers at NASA Lewis are currently developing an 'intelligent' interface to aid in the development and use of large, computational fluid dynamics flow-solver codes for studying the internal fluid behavior of aerospace propulsion systems. This paper discusses the requirements, design, and implementation of an intelligent interface to Proteus, a general purpose, 3-D, Navier-Stokes flow solver. The interface is called PROTAIS to denote its introduction of artificial intelligence (AI) concepts to the Proteus code.

The development of an intelligent interface to a computational fluid dynamics flow-solver code

NASA Technical Reports Server (NTRS)

Williams, Anthony D.

1988-01-01

Researchers at NASA Lewis are currently developing an 'intelligent' interface to aid in the development and use of large, computational fluid dynamics flow-solver codes for studying the internal fluid behavior of aerospace propulsion systems. This paper discusses the requirements, design, and implementation of an intelligent interface to Proteus, a general purpose, three-dimensional, Navier-Stokes flow solver. The interface is called PROTAIS to denote its introduction of artificial intelligence (AI) concepts to the Proteus code.

Convergence Acceleration of a Navier-Stokes Solver for Efficient Static Aeroelastic Computations

NASA Technical Reports Server (NTRS)

Obayashi, Shigeru; Guruswamy, Guru P.

1995-01-01

New capabilities have been developed for a Navier-Stokes solver to perform steady-state simulations more efficiently. The flow solver for solving the Navier-Stokes equations is based on a combination of the lower-upper factored symmetric Gauss-Seidel implicit method and the modified Harten-Lax-van Leer-Einfeldt upwind scheme. A numerically stable and efficient pseudo-time-marching method is also developed for computing steady flows over flexible wings. Results are demonstrated for transonic flows over rigid and flexible wings.

Solution of the Euler equations with viscous-inviscid interaction for high Reynolds number transonic flow past wing/body configurations

NASA Technical Reports Server (NTRS)

Koenig, Keith

1986-01-01

The theoretical and numerical bases of a program for the solution of the Euler equations with viscous-inviscid interaction for high Reynolds number transonic flow past wing/body configurations are explained. The emphasis is upon the logic behind the equation development. The program is fully detailed so that the user can quickly become familiar with its operation.

Comparison of a Convected Helmholtz and Euler Model for Impedance Eduction in Flow

NASA Technical Reports Server (NTRS)

Watson, Willie R.; Jones, Michael G.

2006-01-01

Impedances educed from a well-tested convected Helmholtz model are compared to that of a recently developed linearized Euler model using two ceramic test liners under the assumed conditions or uniform flow and a plane wave source. The convected Helmholtz model is restricted to uniform mean flow whereas the linearized Euler model can account for the effect or the shear layer. Test data to educe the impedance is acquired from measurements obtained in the NASA Langley Research Center Grazing Incidence Tube for mean flow Mach numbers ranging from 0.0 to 0.5 and source frequencies ranging from 0.5 kHz to 3.0 kHz. The unknown impedance of the liner b educed by judiciously chooingth e impedance via an optimization method to match the measured acoustic pressure on the wall opposite the test liner. Results are presented on four spatial grids using three different optimization methods (contour deformation, Davidon-Fletcher Powell, and the Genetic Algorithm). All three optimization methods converge to the same impedance when used with the same model and to nearly identical impedances when used on different models. h anomaly was observed only at 0.5 kHz for high mean flow speeds. The anomaly is likely due to the use of measured data in a flow regime where shear layer effects are important but are neglected in the math models. Consistency between the impedances educed using the two models provides confidence that the linearized Euler model is ready For application to more realistic flows, such as those containing shear layers.

Static Aeroelastic Analysis with an Inviscid Cartesian Method

NASA Technical Reports Server (NTRS)

Rodriguez, David L.; Aftosmis, Michael J.; Nemec, Marian; Smith, Stephen C.

2014-01-01

An embedded-boundary, Cartesian-mesh flow solver is coupled with a three degree-of-freedom structural model to perform static, aeroelastic analysis of complex aircraft geometries. The approach solves a nonlinear, aerostructural system of equations using a loosely-coupled strategy. An open-source, 3-D discrete-geometry engine is utilized to deform a triangulated surface geometry according to the shape predicted by the structural model under the computed aerodynamic loads. The deformation scheme is capable of modeling large deflections and is applicable to the design of modern, very-flexible transport wings. The coupling interface is modular so that aerodynamic or structural analysis methods can be easily swapped or enhanced. After verifying the structural model with comparisons to Euler beam theory, two applications of the analysis method are presented as validation. The first is a relatively stiff, transport wing model which was a subject of a recent workshop on aeroelasticity. The second is a very flexible model recently tested in a low speed wind tunnel. Both cases show that the aeroelastic analysis method produces results in excellent agreement with experimental data.

Research in Parallel Algorithms and Software for Computational Aerosciences

NASA Technical Reports Server (NTRS)

Domel, Neal D.

1996-01-01

Phase I is complete for the development of a Computational Fluid Dynamics parallel code with automatic grid generation and adaptation for the Euler analysis of flow over complex geometries. SPLITFLOW, an unstructured Cartesian grid code developed at Lockheed Martin Tactical Aircraft Systems, has been modified for a distributed memory/massively parallel computing environment. The parallel code is operational on an SGI network, Cray J90 and C90 vector machines, SGI Power Challenge, and Cray T3D and IBM SP2 massively parallel machines. Parallel Virtual Machine (PVM) is the message passing protocol for portability to various architectures. A domain decomposition technique was developed which enforces dynamic load balancing to improve solution speed and memory requirements. A host/node algorithm distributes the tasks. The solver parallelizes very well, and scales with the number of processors. Partially parallelized and non-parallelized tasks consume most of the wall clock time in a very fine grain environment. Timing comparisons on a Cray C90 demonstrate that Parallel SPLITFLOW runs 2.4 times faster on 8 processors than its non-parallel counterpart autotasked over 8 processors.

Distributed Relaxation for Conservative Discretizations

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2001-01-01

A multigrid method is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work that is a small (less than 10) multiple of the operation count in one target-grid residual evaluation. The way to achieve this efficiency is the distributed relaxation approach. TME solvers employing distributed relaxation have already been demonstrated for nonconservative formulations of high-Reynolds-number viscous incompressible and subsonic compressible flow regimes. The purpose of this paper is to provide foundations for applications of distributed relaxation to conservative discretizations. A direct correspondence between the primitive variable interpolations for calculating fluxes in conservative finite-volume discretizations and stencils of the discretized derivatives in the nonconservative formulation has been established. Based on this correspondence, one can arrive at a conservative discretization which is very efficiently solved with a nonconservative relaxation scheme and this is demonstrated for conservative discretization of the quasi one-dimensional Euler equations. Formulations for both staggered and collocated grid arrangements are considered and extensions of the general procedure to multiple dimensions are discussed.

Large calculation of the flow over a hypersonic vehicle using a GPU

NASA Astrophysics Data System (ADS)

Elsen, Erich; LeGresley, Patrick; Darve, Eric

2008-12-01

Graphics processing units are capable of impressive computing performance up to 518 Gflops peak performance. Various groups have been using these processors for general purpose computing; most efforts have focussed on demonstrating relatively basic calculations, e.g. numerical linear algebra, or physical simulations for visualization purposes with limited accuracy. This paper describes the simulation of a hypersonic vehicle configuration with detailed geometry and accurate boundary conditions using the compressible Euler equations. To the authors' knowledge, this is the most sophisticated calculation of this kind in terms of complexity of the geometry, the physical model, the numerical methods employed, and the accuracy of the solution. The Navier-Stokes Stanford University Solver (NSSUS) was used for this purpose. NSSUS is a multi-block structured code with a provably stable and accurate numerical discretization which uses a vertex-based finite-difference method. A multi-grid scheme is used to accelerate the solution of the system. Based on a comparison of the Intel Core 2 Duo and NVIDIA 8800GTX, speed-ups of over 40× were demonstrated for simple test geometries and 20× for complex geometries.

Supersonic Coaxial Jets: Noise Predictions and Measurements

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Papamoschou, Dimitri; Hixon, Ray

1998-01-01

The noise from perfectly expanded coaxial jets was measured in an anechoic chamber for different operating conditions with the same total thrust, mass flow, and exit area. The shape of the measured noise spectrum at different angles to the jet axis was found to agree with spectral shapes for single, axisymmetric jets. Based on these spectra, the sound was characterized as being generated by large turbulent structures or fine-scale turbulence. Modeling the large scale structures as instability waves, a stability analysis was conducted for the coaxial jets to identify the growing and decaying instability waves in each shear layer and predict their noise radiation pattern outside the jet. When compared to measured directivity, the analysis identified the region downstream of the outer potential core, where the two shear layers were merging, as the source of the peak radiated noise where instability waves, with their origin in the inner shear layer, reach their maximum amplitude. Numerical computations were also performed using a linearized Euler equation solver. Those results were compared to both the results from the instability wave analysis and to measured data.

Research in Parallel Algorithms and Software for Computational Aerosciences

NASA Technical Reports Server (NTRS)

Domel, Neal D.

1996-01-01

Phase 1 is complete for the development of a computational fluid dynamics CFD) parallel code with automatic grid generation and adaptation for the Euler analysis of flow over complex geometries. SPLITFLOW, an unstructured Cartesian grid code developed at Lockheed Martin Tactical Aircraft Systems, has been modified for a distributed memory/massively parallel computing environment. The parallel code is operational on an SGI network, Cray J90 and C90 vector machines, SGI Power Challenge, and Cray T3D and IBM SP2 massively parallel machines. Parallel Virtual Machine (PVM) is the message passing protocol for portability to various architectures. A domain decomposition technique was developed which enforces dynamic load balancing to improve solution speed and memory requirements. A host/node algorithm distributes the tasks. The solver parallelizes very well, and scales with the number of processors. Partially parallelized and non-parallelized tasks consume most of the wall clock time in a very fine grain environment. Timing comparisons on a Cray C90 demonstrate that Parallel SPLITFLOW runs 2.4 times faster on 8 processors than its non-parallel counterpart autotasked over 8 processors.

Hypersonic flow analysis

NASA Technical Reports Server (NTRS)

Chow, Chuen-Yen; Ryan, James S.

1987-01-01

While the zonal grid system of Transonic Navier-Stokes (TNS) provides excellent modeling of complex geometries, improved shock capturing, and a higher Mach number range will be required if flows about hypersonic aircraft are to be modeled accurately. A computational fluid dynamics (CFD) code, the Compressible Navier-Stokes (CNS), is under development to combine the required high Mach number capability with the existing TNS geometry capability. One of several candidate flow solvers for inclusion in the CNS is that of F3D. This upwinding flow solver promises improved shock capturing, and more accurate hypersonic solutions overall, compared to the solver currently used in TNS.

Tangent Adjoint Methods In a Higher-Order Space-Time Discontinuous-Galerkin Solver For Turbulent Flows

NASA Technical Reports Server (NTRS)

Diosady, Laslo; Murman, Scott; Blonigan, Patrick; Garai, Anirban

2017-01-01

Presented space-time adjoint solver for turbulent compressible flows. Confirmed failure of traditional sensitivity methods for chaotic flows. Assessed rate of exponential growth of adjoint for practical 3D turbulent simulation. Demonstrated failure of short-window sensitivity approximations.

A Survey of the Isentropic Euler Vortex Problem Using High-Order Methods

NASA Technical Reports Server (NTRS)

Spiegel, Seth C.; Huynh, H. T.; DeBonis, James R.

2015-01-01

The flux reconstruction (FR) method offers a simple, efficient, and easy to implement method, and it has been shown to equate to a differential approach to discontinuous Galerkin (DG) methods. The FR method is also accurate to an arbitrary order and the isentropic Euler vortex problem is used here to empirically verify this claim. This problem is widely used in computational fluid dynamics (CFD) to verify the accuracy of a given numerical method due to its simplicity and known exact solution at any given time. While verifying our FR solver, multiple obstacles emerged that prevented us from achieving the expected order of accuracy over short and long amounts of simulation time. It was found that these complications stemmed from a few overlooked details in the original problem definition combined with the FR and DG methods achieving high-accuracy with minimal dissipation. This paper is intended to consolidate the many versions of the vortex problem found in literature and to highlight some of the consequences if these overlooked details remain neglected.

Modeling of Cluster-Induced Turbulence in Particle-Laden Channel Flow

NASA Astrophysics Data System (ADS)

Baker, Michael; Capecelatro, Jesse; Kong, Bo; Fox, Rodney; Desjardins, Olivier

2017-11-01

A phenomenon often observed in gas-solid flows is the formation of mesoscale clusters of particles due to the relative motion between the solid and fluid phases that is sustained through the dampening of collisional particle motion from interphase momentum coupling inside these clusters. The formation of such sustained clusters, leading to cluster-induced turbulence (CIT), can have a significant impact in industrial processes, particularly in regards to mixing, reaction progress, and heat transfer. Both Euler-Lagrange (EL) and Euler-Euler anisotropic Gaussian (EE-AG) approaches are used in this work to perform mesoscale simulations of CIT in fully developed gas-particle channel flow. The results from these simulations are applied in the development of a two-phase Reynolds-Averaged Navier-Stokes (RANS) model to capture the wall-normal flow characteristics in a less computationally expensive manner. Parameters such as mass loading, particle size, and gas velocity are varied to examine their respective impact on cluster formation and turbulence statistics. Acknowledging support from the NSF (AN:1437865).

Embedding methods for the steady Euler equations

NASA Technical Reports Server (NTRS)

Chang, S. H.; Johnson, G. M.

1983-01-01

An approach to the numerical solution of the steady Euler equations is to embed the first-order Euler system in a second-order system and then to recapture the original solution by imposing additional boundary conditions. Initial development of this approach and computational experimentation with it were previously based on heuristic physical reasoning. This has led to the construction of a relaxation procedure for the solution of two-dimensional steady flow problems. The theoretical justification for the embedding approach is addressed. It is proven that, with the appropriate choice of embedding operator and additional boundary conditions, the solution to the embedded system is exactly the one to the original Euler equations. Hence, solving the embedded version of the Euler equations will not produce extraneous solutions.

On Riemann solvers and kinetic relations for isothermal two-phase flows with surface tension

NASA Astrophysics Data System (ADS)

Rohde, Christian; Zeiler, Christoph

2018-06-01

We consider a sharp interface approach for the inviscid isothermal dynamics of compressible two-phase flow that accounts for phase transition and surface tension effects. Kinetic relations are frequently used to fix the mass exchange and entropy dissipation rate across the interface. The complete unidirectional dynamics can then be understood by solving generalized two-phase Riemann problems. We present new well-posedness theorems for the Riemann problem and corresponding computable Riemann solvers that cover quite general equations of state, metastable input data and curvature effects. The new Riemann solver is used to validate different kinetic relations on physically relevant problems including a comparison with experimental data. Riemann solvers are building blocks for many numerical schemes that are used to track interfaces in two-phase flow. It is shown that the new Riemann solver enables reliable and efficient computations for physical situations that could not be treated before.

Euler/Navier-Stokes calculations of transonic flow past fixed- and rotary-wing aircraft configurations

NASA Technical Reports Server (NTRS)

Deese, J. E.; Agarwal, R. K.

1989-01-01

Computational fluid dynamics has an increasingly important role in the design and analysis of aircraft as computer hardware becomes faster and algorithms become more efficient. Progress is being made in two directions: more complex and realistic configurations are being treated and algorithms based on higher approximations to the complete Navier-Stokes equations are being developed. The literature indicates that linear panel methods can model detailed, realistic aircraft geometries in flow regimes where this approximation is valid. As algorithms including higher approximations to the Navier-Stokes equations are developed, computer resource requirements increase rapidly. Generation of suitable grids become more difficult and the number of grid points required to resolve flow features of interest increases. Recently, the development of large vector computers has enabled researchers to attempt more complex geometries with Euler and Navier-Stokes algorithms. The results of calculations for transonic flow about a typical transport and fighter wing-body configuration using thin layer Navier-Stokes equations are described along with flow about helicopter rotor blades using both Euler/Navier-Stokes equations.

Computational Aeroacoustics by the Space-time CE/SE Method

NASA Technical Reports Server (NTRS)

Loh, Ching Y.

2001-01-01

In recent years, a new numerical methodology for conservation laws-the Space-Time Conservation Element and Solution Element Method (CE/SE), was developed by Dr. Chang of NASA Glenn Research Center and collaborators. In nature, the new method may be categorized as a finite volume method, where the conservation element (CE) is equivalent to a finite control volume (or cell) and the solution element (SE) can be understood as the cell interface. However, due to its rigorous treatment of the fluxes and geometry, it is different from the existing schemes. The CE/SE scheme features: (1) space and time treated on the same footing, the integral equations of conservation laws are solve( for with second order accuracy, (2) high resolution, low dispersion and low dissipation, (3) novel, truly multi-dimensional, simple but effective non-reflecting boundary condition, (4) effortless implementation of computation, no numerical fix or parameter choice is needed, an( (5) robust enough to cover a wide spectrum of compressible flow: from weak linear acoustic waves to strong, discontinuous waves (shocks) appropriate for linear and nonlinear aeroacoustics. Currently, the CE/SE scheme has been developed to such a stage that a 3-13 unstructured CE/SE Navier-Stokes solver is already available. However, in the present paper, as a general introduction to the CE/SE method, only the 2-D unstructured Euler CE/SE solver is chosen as a prototype and is sketched in Section 2. Then applications of the CE/SE scheme to linear, nonlinear aeroacoustics and airframe noise are depicted in Sections 3, 4, and 5 respectively to demonstrate its robustness and capability.

Numerical simulation of vortical ideal fluid flow through curved channel

NASA Astrophysics Data System (ADS)

Moshkin, N. P.; Mounnamprang, P.

2003-04-01

A numerical algorithm to study the boundary-value problem in which the governing equations are the steady Euler equations and the vorticity is given on the inflow parts of the domain boundary is developed. The Euler equations are implemented in terms of the stream function and vorticity. An irregular physical domain is transformed into a rectangle in the computational domain and the Euler equations are rewritten with respect to a curvilinear co-ordinate system. The convergence of the finite-difference equations to the exact solution is shown experimentally for the test problems by comparing the computational results with the exact solutions on the sequence of grids. To find the pressure from the known vorticity and stream function, the Euler equations are utilized in the Gromeka-Lamb form. The numerical algorithm is illustrated with several examples of steady flow through a two-dimensional channel with curved walls. The analysis of calculations shows strong dependence of the pressure field on the vorticity given at the inflow parts of the boundary. Plots of the flow structure and isobars, for different geometries of channel and for different values of vorticity on entrance, are also presented.

Recent Advances in Agglomerated Multigrid

NASA Technical Reports Server (NTRS)

Nishikawa, Hiroaki; Diskin, Boris; Thomas, James L.; Hammond, Dana P.

2013-01-01

We report recent advancements of the agglomerated multigrid methodology for complex flow simulations on fully unstructured grids. An agglomerated multigrid solver is applied to a wide range of test problems from simple two-dimensional geometries to realistic three- dimensional configurations. The solver is evaluated against a single-grid solver and, in some cases, against a structured-grid multigrid solver. Grid and solver issues are identified and overcome, leading to significant improvements over single-grid solvers.

Improved numerical methods for turbulent viscous recirculating flows

NASA Technical Reports Server (NTRS)

Turan, A.; Vandoormaal, J. P.

1988-01-01

The performance of discrete methods for the prediction of fluid flows can be enhanced by improving the convergence rate of solvers and by increasing the accuracy of the discrete representation of the equations of motion. This report evaluates the gains in solver performance that are available when various acceleration methods are applied. Various discretizations are also examined and two are recommended because of their accuracy and robustness. Insertion of the improved discretization and solver accelerator into a TEACH mode, that has been widely applied to combustor flows, illustrates the substantial gains to be achieved.

Preconditioned conjugate gradient methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1994-01-01

A preconditioned Krylov subspace method (GMRES) is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux-split formulation. Several preconditioning techniques are investigated to enhance the efficiency and convergence rate of the implicit solver based on the GMRES algorithm. The superiority of the new solver is established by comparisons with a conventional implicit solver, namely line Gauss-Seidel relaxation (LGSR). Computational test results for low-speed (incompressible flow over a backward-facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade), and hypersonic flow (shock-on-shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the Mach 0.1 case, overall speedup factors of up to 17 (in terms of time-steps) and 15 (in terms of CPU time on a CRAY-YMP/8) are found in favor of the preconditioned GMRES solver, when compared with the LGSR solver. The corresponding speedup factors for the transonic flow case are 17 and 23, respectively. The hypersonic flow case shows slightly lower speedup factors of 9 and 13, respectively. The study of preconditioners conducted in this research reveals that a new LUSGS-type preconditioner is much more efficient than a conventional incomplete LU-type preconditioner.

Towards a Coupled Vortex Particle and Acoustic Boundary Element Solver to Predict the Noise Production of Bio-Inspired Propulsion

NASA Astrophysics Data System (ADS)

Wagenhoffer, Nathan; Moored, Keith; Jaworski, Justin

2016-11-01

The design of quiet and efficient bio-inspired propulsive concepts requires a rapid, unified computational framework that integrates the coupled fluid dynamics with the noise generation. Such a framework is developed where the fluid motion is modeled with a two-dimensional unsteady boundary element method that includes a vortex-particle wake. The unsteady surface forces from the potential flow solver are then passed to an acoustic boundary element solver to predict the radiated sound in low-Mach-number flows. The use of the boundary element method for both the hydrodynamic and acoustic solvers permits dramatic computational acceleration by application of the fast multiple method. The reduced order of calculations due to the fast multipole method allows for greater spatial resolution of the vortical wake per unit of computational time. The coupled flow-acoustic solver is validated against canonical vortex-sound problems. The capability of the coupled solver is demonstrated by analyzing the performance and noise production of an isolated bio-inspired swimmer and of tandem swimmers.

Vortex methods for separated flows

NASA Technical Reports Server (NTRS)

Spalart, Philippe R.

1988-01-01

The numerical solution of the Euler or Navier-Stokes equations by Lagrangian vortex methods is discussed. The mathematical background is presented and includes the relationship with traditional point-vortex studies, convergence to smooth solutions of the Euler equations, and the essential differences between two and three-dimensional cases. The difficulties in extending the method to viscous or compressible flows are explained. Two-dimensional flows around bluff bodies are emphasized. Robustness of the method and the assessment of accuracy, vortex-core profiles, time-marching schemes, numerical dissipation, and efficient programming are treated. Operation counts for unbounded and periodic flows are given, and two algorithms designed to speed up the calculations are described.

Preconditioned conjugate-gradient methods for low-speed flow calculations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1993-01-01

An investigation is conducted into the viability of using a generalized Conjugate Gradient-like method as an iterative solver to obtain steady-state solutions of very low-speed fluid flow problems. Low-speed flow at Mach 0.1 over a backward-facing step is chosen as a representative test problem. The unsteady form of the two dimensional, compressible Navier-Stokes equations is integrated in time using discrete time-steps. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. The new iterative solver is used to solve a linear system of equations at each step of the time-integration. Preconditioning techniques are used with the new solver to enhance the stability and convergence rate of the solver and are found to be critical to the overall success of the solver. A study of various preconditioners reveals that a preconditioner based on the Lower-Upper Successive Symmetric Over-Relaxation iterative scheme is more efficient than a preconditioner based on Incomplete L-U factorizations of the iteration matrix. The performance of the new preconditioned solver is compared with a conventional Line Gauss-Seidel Relaxation (LGSR) solver. Overall speed-up factors of 28 (in terms of global time-steps required to converge to a steady-state solution) and 20 (in terms of total CPU time on one processor of a CRAY-YMP) are found in favor of the new preconditioned solver, when compared with the LGSR solver.

Preconditioned Conjugate Gradient methods for low speed flow calculations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1993-01-01

An investigation is conducted into the viability of using a generalized Conjugate Gradient-like method as an iterative solver to obtain steady-state solutions of very low-speed fluid flow problems. Low-speed flow at Mach 0.1 over a backward-facing step is chosen as a representative test problem. The unsteady form of the two dimensional, compressible Navier-Stokes equations are integrated in time using discrete time-steps. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. The new iterative solver is used to solve a linear system of equations at each step of the time-integration. Preconditioning techniques are used with the new solver to enhance the stability and the convergence rate of the solver and are found to be critical to the overall success of the solver. A study of various preconditioners reveals that a preconditioner based on the lower-upper (L-U)-successive symmetric over-relaxation iterative scheme is more efficient than a preconditioner based on incomplete L-U factorizations of the iteration matrix. The performance of the new preconditioned solver is compared with a conventional line Gauss-Seidel relaxation (LGSR) solver. Overall speed-up factors of 28 (in terms of global time-steps required to converge to a steady-state solution) and 20 (in terms of total CPU time on one processor of a CRAY-YMP) are found in favor of the new preconditioned solver, when compared with the LGSR solver.

LEM-CF Premixed Tool Kit

DOE Office of Scientific and Technical Information (OSTI.GOV)

2015-01-19

The purpose of LEM-CF Premixed Tool Kit is to process premixed flame simulation data from the LEM-CF solver (https://fileshare.craft-tech.com/clusters/view/lem-cf) into a large-eddy simulation (LES) subgrid model database. These databases may be used with a user-defined-function (UDF) that is included in the Tool Kit. The subgrid model UDF may be used with the ANSYS FLUENT flow solver or other commercial flow solvers.

Mathematical Fluid Dynamic Modeling of Plasma Stall-Spin Departure Control

DTIC Science & Technology

2007-04-01

filter (4), is appropriate for further CSN modeling of the vortical flow. The CNS solver reproduces symmetric and asymmetric vortex fields (Figure 11...calculations conducted for laminar flow showed that the CNS solver reproduces symmetric and asymmetric vortex fields and can be used for estimation of the...Galilean-invariant leeward vortex filter. The modified k-F EASM model was incorporated into our CSN solver. Parametric calculations showed that numerical

A Conformal, Fully-Conservative Approach for Predicting Blast Effects on Ground Vehicles

DTIC Science & Technology

2014-04-01

time integration  Approximate Riemann Fluxes (HLLE, HLLC) ◦ Robust mixture model for multi-material flows  Multiple Equations of State ◦ Perfect Gas...Loci/CHEM: Chemically reacting compressible flow solver . ◦ Currently in production use by NASA for the simulation of rocket motors, plumes, and...vehicles  Loci/DROPLET: Eulerian and Lagrangian multiphase solvers  Loci/STREAM: pressure-based solver ◦ Developed by Streamline Numerics and

Noise Production of an Idealized Two-Dimensional Fish School

NASA Astrophysics Data System (ADS)

Wagenhoffer, Nathan; Moored, Keith; Jaworski, Justin

2017-11-01

The analysis of quiet bio-inspired propulsive concepts requires a rapid, unified computational framework that integrates the coupled fluid-solid dynamics of swimmers and their wakes with the resulting noise generation. Such a framework is presented for two-dimensional flows, where the fluid motion is modeled by an unsteady boundary element method with a vortex-particle wake. The unsteady surface forces from the potential flow solver are then passed to an acoustic boundary element solver to predict the radiated sound in low-Mach-number flows. The coupled flow-acoustic solver is validated against canonical vortex-sound problems. A diamond arrangement of four airfoils are subjected to traveling wave kinematics representing a known idealized pattern for a school of fish, and the airfoil motion and inflow values are derived from the range of Strouhal values common to many natural swimmers. The coupled flow-acoustic solver estimates and analyzes the hydrodynamic performance and noise production of the idealized school of swimmers.

A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow

NASA Astrophysics Data System (ADS)

Krank, Benjamin; Fehn, Niklas; Wall, Wolfgang A.; Kronbichler, Martin

2017-11-01

We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration as well as nodal equal-order discretizations for velocity and pressure. The non-linear convective term is treated explicitly while a linear system is solved for the pressure Poisson equation and the viscous term. The key feature of our solver is a consistent penalty term reducing the local divergence error in order to overcome recently reported instabilities in spatially under-resolved high-Reynolds-number flows as well as small time steps. This penalty method is similar to the grad-div stabilization widely used in continuous finite elements. We further review and compare our method to several other techniques recently proposed in literature to stabilize the method for such flow configurations. The solver is specifically designed for large-scale computations through matrix-free linear solvers including efficient preconditioning strategies and tensor-product elements, which have allowed us to scale this code up to 34.4 billion degrees of freedom and 147,456 CPU cores. We validate our code and demonstrate optimal convergence rates with laminar flows present in a vortex problem and flow past a cylinder and show applicability of our solver to direct numerical simulation as well as implicit large-eddy simulation of turbulent channel flow at Reτ = 180 as well as 590.

Algorithms for the Euler and Navier-Stokes equations for supercomputers

NASA Technical Reports Server (NTRS)

Turkel, E.

1985-01-01

The steady state Euler and Navier-Stokes equations are considered for both compressible and incompressible flow. Methods are found for accelerating the convergence to a steady state. This acceleration is based on preconditioning the system so that it is no longer time consistent. In order that the acceleration technique be scheme-independent, this preconditioning is done at the differential equation level. Applications are presented for very slow flows and also for the incompressible equations.

A Depth-Averaged 2-D Simulation for Coastal Barrier Breaching Processes

DTIC Science & Technology

2011-05-01

including bed change and variable flow density in the flow continuity and momentum equations. The model adopts the HLL approximate Riemann solver to handle...flow density in the flow continuity and momentum equations. The model adopts the HLL approximate Riemann solver to handle the mixed-regime flows near...18 547 Keulegan equation or the Bernoulli equation, and the breach morphological change is determined using simplified sediment transport models

Simulation of all-scale atmospheric dynamics on unstructured meshes

NASA Astrophysics Data System (ADS)

Smolarkiewicz, Piotr K.; Szmelter, Joanna; Xiao, Feng

2016-10-01

The advance of massively parallel computing in the nineteen nineties and beyond encouraged finer grid intervals in numerical weather-prediction models. This has improved resolution of weather systems and enhanced the accuracy of forecasts, while setting the trend for development of unified all-scale atmospheric models. This paper first outlines the historical background to a wide range of numerical methods advanced in the process. Next, the trend is illustrated with a technical review of a versatile nonoscillatory forward-in-time finite-volume (NFTFV) approach, proven effective in simulations of atmospheric flows from small-scale dynamics to global circulations and climate. The outlined approach exploits the synergy of two specific ingredients: the MPDATA methods for the simulation of fluid flows based on the sign-preserving properties of upstream differencing; and the flexible finite-volume median-dual unstructured-mesh discretisation of the spatial differential operators comprising PDEs of atmospheric dynamics. The paper consolidates the concepts leading to a family of generalised nonhydrostatic NFTFV flow solvers that include soundproof PDEs of incompressible Boussinesq, anelastic and pseudo-incompressible systems, common in large-eddy simulation of small- and meso-scale dynamics, as well as all-scale compressible Euler equations. Such a framework naturally extends predictive skills of large-eddy simulation to the global atmosphere, providing a bottom-up alternative to the reverse approach pursued in the weather-prediction models. Theoretical considerations are substantiated by calculations attesting to the versatility and efficacy of the NFTFV approach. Some prospective developments are also discussed.

Numerical aspects and implementation of a two-layer zonal wall model for LES of compressible turbulent flows on unstructured meshes

NASA Astrophysics Data System (ADS)

Park, George Ilhwan; Moin, Parviz

2016-01-01

This paper focuses on numerical and practical aspects associated with a parallel implementation of a two-layer zonal wall model for large-eddy simulation (LES) of compressible wall-bounded turbulent flows on unstructured meshes. A zonal wall model based on the solution of unsteady three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations on a separate near-wall grid is implemented in an unstructured, cell-centered finite-volume LES solver. The main challenge in its implementation is to couple two parallel, unstructured flow solvers for efficient boundary data communication and simultaneous time integrations. A coupling strategy with good load balancing and low processors underutilization is identified. Face mapping and interpolation procedures at the coupling interface are explained in detail. The method of manufactured solution is used for verifying the correct implementation of solver coupling, and parallel performance of the combined wall-modeled LES (WMLES) solver is investigated. The method has successfully been applied to several attached and separated flows, including a transitional flow over a flat plate and a separated flow over an airfoil at an angle of attack.

Development of an Aerodynamic Analysis Method and Database for the SLS Service Module Panel Jettison Event Utilizing Inviscid CFD and MATLAB

NASA Technical Reports Server (NTRS)

Applebaum, Michael P.; Hall, Leslie, H.; Eppard, William M.; Purinton, David C.; Campbell, John R.; Blevins, John A.

2015-01-01

This paper describes the development, testing, and utilization of an aerodynamic force and moment database for the Space Launch System (SLS) Service Module (SM) panel jettison event. The database is a combination of inviscid Computational Fluid Dynamic (CFD) data and MATLAB code written to query the data at input values of vehicle/SM panel parameters and return the aerodynamic force and moment coefficients of the panels as they are jettisoned from the vehicle. The database encompasses over 5000 CFD simulations with the panels either in the initial stages of separation where they are hinged to the vehicle, in close proximity to the vehicle, or far enough from the vehicle that body interference effects are neglected. A series of viscous CFD check cases were performed to assess the accuracy of the Euler solutions for this class of problem and good agreement was obtained. The ultimate goal of the panel jettison database was to create a tool that could be coupled with any 6-Degree-Of-Freedom (DOF) dynamics model to rapidly predict SM panel separation from the SLS vehicle in a quasi-unsteady manner. Results are presented for panel jettison simulations that utilize the database at various SLS flight conditions. These results compare favorably to an approach that directly couples a 6-DOF model with the Cart3D Euler flow solver and obtains solutions for the panels at exact locations. This paper demonstrates a method of using inviscid CFD simulations coupled with a 6-DOF model that provides adequate fidelity to capture the physics of this complex multiple moving-body panel separation event.

Numerical study of MHD supersonic flow control

NASA Astrophysics Data System (ADS)

Ryakhovskiy, A. I.; Schmidt, A. A.

2017-11-01

Supersonic MHD flow around a blunted body with a constant external magnetic field has been simulated for a number of geometries as well as a range of the flow parameters. Solvers based on Balbas-Tadmor MHD schemes and HLLC-Roe Godunov-type method have been developed within the OpenFOAM framework. The stability of the solution varies depending on the intensity of magnetic interaction The obtained solutions show the potential of MHD flow control and provide insights into for the development of the flow control system. The analysis of the results proves the applicability of numerical schemes, that are being used in the solvers. A number of ways to improve both the mathematical model of the process and the developed solvers are proposed.

Computation of transonic viscous-inviscid interacting flow

NASA Technical Reports Server (NTRS)

Whitfield, D. L.; Thomas, J. L.; Jameson, A.; Schmidt, W.

1983-01-01

Transonic viscous-inviscid interaction is considered using the Euler and inverse compressible turbulent boundary-layer equations. Certain improvements in the inverse boundary-layer method are mentioned, along with experiences in using various Runge-Kutta schemes to solve the Euler equations. Numerical conditions imposed on the Euler equations at a surface for viscous-inviscid interaction using the method of equivalent sources are developed, and numerical solutions are presented and compared with experimental data to illustrate essential points. Previously announced in STAR N83-17829

On the prediction of far field computational aeroacoustics of advanced propellers

NASA Technical Reports Server (NTRS)

Jaeger, Stephen M.; Korkan, Kenneth D.

1990-01-01

A numerical method for determining the acoustic far field generated by a high-speed subsonic aircraft propeller was developed. The approach used in this method was to generate the entire three-dimensional pressure field about the propeller (using an Euler flowfield solver) and then to apply a solution of the wave equation on a cylindrical surface enveloping the propeller. The method is applied to generate the three-dimensional flowfield between two blades of an advanced propeller. The results are compared with experimental data obtained in a wind-tunnel test at a Mach number of 0.6.

Status of parallel Python-based implementation of UEDGE

NASA Astrophysics Data System (ADS)

Umansky, M. V.; Pankin, A. Y.; Rognlien, T. D.; Dimits, A. M.; Friedman, A.; Joseph, I.

2017-10-01

The tokamak edge transport code UEDGE has long used the code-development and run-time framework Basis. However, with the support for Basis expected to terminate in the coming years, and with the advent of the modern numerical language Python, it has become desirable to move UEDGE to Python, to ensure its long-term viability. Our new Python-based UEDGE implementation takes advantage of the portable build system developed for FACETS. The new implementation gives access to Python's graphical libraries and numerical packages for pre- and post-processing, and support of HDF5 simplifies exchanging data. The older serial version of UEDGE has used for time-stepping the Newton-Krylov solver NKSOL. The renovated implementation uses backward Euler discretization with nonlinear solvers from PETSc, which has the promise to significantly improve the UEDGE parallel performance. We will report on assessment of some of the extended UEDGE capabilities emerging in the new implementation, and will discuss the future directions. Work performed for U.S. DOE by LLNL under contract DE-AC52-07NA27344.

An Implicit Solver on A Parallel Block-Structured Adaptive Mesh Grid for FLASH

NASA Astrophysics Data System (ADS)

Lee, D.; Gopal, S.; Mohapatra, P.

2012-07-01

We introduce a fully implicit solver for FLASH based on a Jacobian-Free Newton-Krylov (JFNK) approach with an appropriate preconditioner. The main goal of developing this JFNK-type implicit solver is to provide efficient high-order numerical algorithms and methodology for simulating stiff systems of differential equations on large-scale parallel computer architectures. A large number of natural problems in nonlinear physics involve a wide range of spatial and time scales of interest. A system that encompasses such a wide magnitude of scales is described as "stiff." A stiff system can arise in many different fields of physics, including fluid dynamics/aerodynamics, laboratory/space plasma physics, low Mach number flows, reactive flows, radiation hydrodynamics, and geophysical flows. One of the big challenges in solving such a stiff system using current-day computational resources lies in resolving time and length scales varying by several orders of magnitude. We introduce FLASH's preliminary implementation of a time-accurate JFNK-based implicit solver in the framework of FLASH's unsplit hydro solver.

Preconditioned implicit solvers for the Navier-Stokes equations on distributed-memory machines

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Liou, Meng-Sing; Dyson, Rodger W.

1994-01-01

The GMRES method is parallelized, and combined with local preconditioning to construct an implicit parallel solver to obtain steady-state solutions for the Navier-Stokes equations of fluid flow on distributed-memory machines. The new implicit parallel solver is designed to preserve the convergence rate of the equivalent 'serial' solver. A static domain-decomposition is used to partition the computational domain amongst the available processing nodes of the parallel machine. The SPMD (Single-Program Multiple-Data) programming model is combined with message-passing tools to develop the parallel code on a 32-node Intel Hypercube and a 512-node Intel Delta machine. The implicit parallel solver is validated for internal and external flow problems, and is found to compare identically with flow solutions obtained on a Cray Y-MP/8. A peak computational speed of 2300 MFlops/sec has been achieved on 512 nodes of the Intel Delta machine,k for a problem size of 1024 K equations (256 K grid points).

Evaluation of new techniques for the calculation of internal recirculating flows

NASA Technical Reports Server (NTRS)

Van Doormaal, J. P.; Turan, A.; Raithby, G. D.

1987-01-01

The performance of discrete methods for the prediction of fluid flows can be enhanced by improving the convergence rate of solvers and by increasing the accuracy of the discrete representation of the equations of motion. This paper evaluates the gains in solver performance that are available when various acceleration methods are applied. Various discretizations are also examined and two are recommended because of their accuracy and robustness. Insertion of the improved discretization and solver accelerator into a TEACH code, that has been widely applied to combustor flows, illustrates the substantial gains that can be achieved.

Wind-US Unstructured Flow Solutions for a Transonic Diffuser

NASA Technical Reports Server (NTRS)

Mohler, Stanley R., Jr.

2005-01-01

The Wind-US Computational Fluid Dynamics flow solver computed flow solutions for a transonic diffusing duct. The calculations used an unstructured (hexahedral) grid. The Spalart-Allmaras turbulence model was used. Static pressures along the upper and lower wall agreed well with experiment, as did velocity profiles. The effect of the smoothing input parameters on convergence and solution accuracy was investigated. The meaning and proper use of these parameters are discussed for the benefit of Wind-US users. Finally, the unstructured solver is compared to the structured solver in terms of run times and solution accuracy.

Progress and supercomputing in computational fluid dynamics; Proceedings of U.S.-Israel Workshop, Jerusalem, Israel, December 1984

NASA Technical Reports Server (NTRS)

Murman, E. M. (Editor); Abarbanel, S. S. (Editor)

1985-01-01

Current developments and future trends in the application of supercomputers to computational fluid dynamics are discussed in reviews and reports. Topics examined include algorithm development for personal-size supercomputers, a multiblock three-dimensional Euler code for out-of-core and multiprocessor calculations, simulation of compressible inviscid and viscous flow, high-resolution solutions of the Euler equations for vortex flows, algorithms for the Navier-Stokes equations, and viscous-flow simulation by FEM and related techniques. Consideration is given to marching iterative methods for the parabolized and thin-layer Navier-Stokes equations, multigrid solutions to quasi-elliptic schemes, secondary instability of free shear flows, simulation of turbulent flow, and problems connected with weather prediction.

Lagrangian averaging with geodesic mean

NASA Astrophysics Data System (ADS)

Oliver, Marcel

2017-11-01

This paper revisits the derivation of the Lagrangian averaged Euler (LAE), or Euler-α equations in the light of an intrinsic definition of the averaged flow map as the geodesic mean on the volume-preserving diffeomorphism group. Under the additional assumption that first-order fluctuations are statistically isotropic and transported by the mean flow as a vector field, averaging of the kinetic energy Lagrangian of an ideal fluid yields the LAE Lagrangian. The derivation presented here assumes a Euclidean spatial domain without boundaries.

Lagrangian averaging with geodesic mean.

PubMed

Oliver, Marcel

2017-11-01

This paper revisits the derivation of the Lagrangian averaged Euler (LAE), or Euler- α equations in the light of an intrinsic definition of the averaged flow map as the geodesic mean on the volume-preserving diffeomorphism group. Under the additional assumption that first-order fluctuations are statistically isotropic and transported by the mean flow as a vector field, averaging of the kinetic energy Lagrangian of an ideal fluid yields the LAE Lagrangian. The derivation presented here assumes a Euclidean spatial domain without boundaries.

Concepts for radically increasing the numerical convergence rate of the Euler equations

NASA Technical Reports Server (NTRS)

Nixon, David; Tzuoo, Keh-Lih; Caruso, Steven C.; Farshchi, Mohammad; Klopfer, Goetz H.; Ayoub, Alfred

1987-01-01

Integral equation and finite difference methods have been developed for solving transonic flow problems using linearized forms of the transonic small disturbance and Euler equations. A key element is the use of a strained coordinate system in which the shock remains fixed. Additional criteria are developed to determine the free parameters in the coordinate straining; these free parameters are functions of the shock location. An integral equation analysis showed that the shock is located by ensuring that no expansion shocks exist in the solution. The expansion shock appears as oscillations in the solution near the sonic line, and the correct shock location is determined by removing these oscillations. A second objective was to study the ability of the Euler equation to model separated flow.

Numerical studies of laminar and turbulent drag reduction, part 2

NASA Technical Reports Server (NTRS)

Balasubramanian, R.; Orszag, S. A.

1983-01-01

The flow over wave shaped surfaces is studied using a Navier Stokes solver. Detailed comparisons with theoretical results are presented, including the stability of a laminar flow over wavy surfaces. Drag characteristics of nonplanar surfaces are predicted using the Navier-Stokes solver. The secondary instabilities of wall bounded and free shear flows are also discussed.

OVERSMART Reporting Tool for Flow Computations Over Large Grid Systems

NASA Technical Reports Server (NTRS)

Kao, David L.; Chan, William M.

2012-01-01

Structured grid solvers such as NASA's OVERFLOW compressible Navier-Stokes flow solver can generate large data files that contain convergence histories for flow equation residuals, turbulence model equation residuals, component forces and moments, and component relative motion dynamics variables. Most of today's large-scale problems can extend to hundreds of grids, and over 100 million grid points. However, due to the lack of efficient tools, only a small fraction of information contained in these files is analyzed. OVERSMART (OVERFLOW Solution Monitoring And Reporting Tool) provides a comprehensive report of solution convergence of flow computations over large, complex grid systems. It produces a one-page executive summary of the behavior of flow equation residuals, turbulence model equation residuals, and component forces and moments. Under the automatic option, a matrix of commonly viewed plots such as residual histograms, composite residuals, sub-iteration bar graphs, and component forces and moments is automatically generated. Specific plots required by the user can also be prescribed via a command file or a graphical user interface. Output is directed to the user s computer screen and/or to an html file for archival purposes. The current implementation has been targeted for the OVERFLOW flow solver, which is used to obtain a flow solution on structured overset grids. The OVERSMART framework allows easy extension to other flow solvers.

Modelling atmospheric flows with adaptive moving meshes

NASA Astrophysics Data System (ADS)

Kühnlein, Christian; Smolarkiewicz, Piotr K.; Dörnbrack, Andreas

2012-04-01

An anelastic atmospheric flow solver has been developed that combines semi-implicit non-oscillatory forward-in-time numerics with a solution-adaptive mesh capability. A key feature of the solver is the unification of a mesh adaptation apparatus, based on moving mesh partial differential equations (PDEs), with the rigorous formulation of the governing anelastic PDEs in generalised time-dependent curvilinear coordinates. The solver development includes an enhancement of the flux-form multidimensional positive definite advection transport algorithm (MPDATA) - employed in the integration of the underlying anelastic PDEs - that ensures full compatibility with mass continuity under moving meshes. In addition, to satisfy the geometric conservation law (GCL) tensor identity under general moving meshes, a diagnostic approach is proposed based on the treatment of the GCL as an elliptic problem. The benefits of the solution-adaptive moving mesh technique for the simulation of multiscale atmospheric flows are demonstrated. The developed solver is verified for two idealised flow problems with distinct levels of complexity: passive scalar advection in a prescribed deformational flow, and the life cycle of a large-scale atmospheric baroclinic wave instability showing fine-scale phenomena of fronts and internal gravity waves.

Atmospheric stability and complex terrain: comparing measurements and CFD

NASA Astrophysics Data System (ADS)

Koblitz, T.; Bechmann, A.; Berg, J.; Sogachev, A.; Sørensen, N.; Réthoré, P.-E.

2014-12-01

For wind resource assessment, the wind industry is increasingly relying on Computational Fluid Dynamics models that focus on modeling the airflow in a neutrally stratified surface layer. So far, physical processes that are specific to the atmospheric boundary layer, for example the Coriolis force, buoyancy forces and heat transport, are mostly ignored in state-of-the-art flow solvers. In order to decrease the uncertainty of wind resource assessment, the effect of thermal stratification on the atmospheric boundary layer should be included in such models. The present work focuses on non-neutral atmospheric flow over complex terrain including physical processes like stability and Coriolis force. We examine the influence of these effects on the whole atmospheric boundary layer using the DTU Wind Energy flow solver EllipSys3D. To validate the flow solver, measurements from Benakanahalli hill, a field experiment that took place in India in early 2010, are used. The experiment was specifically designed to address the combined effects of stability and Coriolis force over complex terrain, and provides a dataset to validate flow solvers. Including those effects into EllipSys3D significantly improves the predicted flow field when compared against the measurements.

Steady potential solver for unsteady aerodynamic analyses

NASA Technical Reports Server (NTRS)

Hoyniak, Dan

1994-01-01

Development of a steady flow solver for use with LINFLO was the objective of this report. The solver must be compatible with LINFLO, be composed of composite mesh, and have transonic capability. The approaches used were: (1) steady flow potential equations written in nonconservative form; (2) Newton's Method; (3) implicit, least-squares, interpolation method to obtain finite difference equations; and (4) matrix inversion routines from LINFLO. This report was given during the NASA LeRC Workshop on Forced Response in Turbomachinery in August of 1993.

Some recent applications of Navier-Stokes codes to rotorcraft

NASA Technical Reports Server (NTRS)

Mccroskey, W. J.

1992-01-01

Many operational limitations of helicopters and other rotary-wing aircraft are due to nonlinear aerodynamic phenomena incuding unsteady, three-dimensional transonic and separated flow near the surfaces and highly vortical flow in the wakes of rotating blades. Modern computational fluid dynamics (CFD) technology offers new tools to study and simulate these complex flows. However, existing Euler and Navier-Stokes codes have to be modified significantly for rotorcraft applications, and the enormous computational requirements presently limit their use in routine design applications. Nevertheless, the Euler/Navier-Stokes technology is progressing in anticipation of future supercomputers that will enable meaningful calculations to be made for complete rotorcraft configurations.

A coarse-grid projection method for accelerating incompressible flow computations

NASA Astrophysics Data System (ADS)

San, Omer; Staples, Anne E.

2013-01-01

We present a coarse-grid projection (CGP) method for accelerating incompressible flow computations, which is applicable to methods involving Poisson equations as incompressibility constraints. The CGP methodology is a modular approach that facilitates data transfer with simple interpolations and uses black-box solvers for the Poisson and advection-diffusion equations in the flow solver. After solving the Poisson equation on a coarsened grid, an interpolation scheme is used to obtain the fine data for subsequent time stepping on the full grid. A particular version of the method is applied here to the vorticity-stream function, primitive variable, and vorticity-velocity formulations of incompressible Navier-Stokes equations. We compute several benchmark flow problems on two-dimensional Cartesian and non-Cartesian grids, as well as a three-dimensional flow problem. The method is found to accelerate these computations while retaining a level of accuracy close to that of the fine resolution field, which is significantly better than the accuracy obtained for a similar computation performed solely using a coarse grid. A linear acceleration rate is obtained for all the cases we consider due to the linear-cost elliptic Poisson solver used, with reduction factors in computational time between 2 and 42. The computational savings are larger when a suboptimal Poisson solver is used. We also find that the computational savings increase with increasing distortion ratio on non-Cartesian grids, making the CGP method a useful tool for accelerating generalized curvilinear incompressible flow solvers.

Accelerated iteration schemes for transonic flow calculations using fast poisson solvers. [aerodynamics

NASA Technical Reports Server (NTRS)

Jameson, A.

1975-01-01

The use of a fast elliptic solver in combination with relaxation is presented as an effective way to accelerate the convergence of transonic flow calculations, particularly when a marching scheme can be used to treat the supersonic zone in the relaxation process.

Parallel discontinuous Galerkin FEM for computing hyperbolic conservation law on unstructured grids

NASA Astrophysics Data System (ADS)

Ma, Xinrong; Duan, Zhijian

2018-04-01

High-order resolution Discontinuous Galerkin finite element methods (DGFEM) has been known as a good method for solving Euler equations and Navier-Stokes equations on unstructured grid, but it costs too much computational resources. An efficient parallel algorithm was presented for solving the compressible Euler equations. Moreover, the multigrid strategy based on three-stage three-order TVD Runge-Kutta scheme was used in order to improve the computational efficiency of DGFEM and accelerate the convergence of the solution of unsteady compressible Euler equations. In order to make each processor maintain load balancing, the domain decomposition method was employed. Numerical experiment performed for the inviscid transonic flow fluid problems around NACA0012 airfoil and M6 wing. The results indicated that our parallel algorithm can improve acceleration and efficiency significantly, which is suitable for calculating the complex flow fluid.

Computation of viscous incompressible flows

NASA Technical Reports Server (NTRS)

Kwak, Dochan

1989-01-01

Incompressible Navier-Stokes solution methods and their applications to three-dimensional flows are discussed. A brief review of existing methods is given followed by a detailed description of recent progress on development of three-dimensional generalized flow solvers. Emphasis is placed on primitive variable formulations which are most promising and flexible for general three-dimensional computations of viscous incompressible flows. Both steady- and unsteady-solution algorithms and their salient features are discussed. Finally, examples of real world applications of these flow solvers are given.

A NURBS-enhanced finite volume solver for steady Euler equations

NASA Astrophysics Data System (ADS)

Meng, Xucheng; Hu, Guanghui

2018-04-01

In Hu and Yi (2016) [20], a non-oscillatory k-exact reconstruction method was proposed towards the high-order finite volume methods for steady Euler equations, which successfully demonstrated the high-order behavior in the simulations. However, the degeneracy of the numerical accuracy of the approximate solutions to problems with curved boundary can be observed obviously. In this paper, the issue is resolved by introducing the Non-Uniform Rational B-splines (NURBS) method, i.e., with given discrete description of the computational domain, an approximate NURBS curve is reconstructed to provide quality quadrature information along the curved boundary. The advantages of using NURBS include i). both the numerical accuracy of the approximate solutions and convergence rate of the numerical methods are improved simultaneously, and ii). the NURBS curve generation is independent of other modules of the numerical framework, which makes its application very flexible. It is also shown in the paper that by introducing more elements along the normal direction for the reconstruction patch of the boundary element, significant improvement in the convergence to steady state can be achieved. The numerical examples confirm the above features very well.

Modelling and simulation of wood chip combustion in a hot air generator system.

PubMed

Rajika, J K A T; Narayana, Mahinsasa

2016-01-01

This study focuses on modelling and simulation of horizontal moving bed/grate wood chip combustor. A standalone finite volume based 2-D steady state Euler-Euler Computational Fluid Dynamics (CFD) model was developed for packed bed combustion. Packed bed combustion of a medium scale biomass combustor, which was retrofitted from wood log to wood chip feeding for Tea drying in Sri Lanka, was evaluated by a CFD simulation study. The model was validated by the experimental results of an industrial biomass combustor for a hot air generation system in tea industry. Open-source CFD tool; OpenFOAM was used to generate CFD model source code for the packed bed combustion and simulated along with an available solver for free board region modelling in the CFD tool. Height of the packed bed is about 20 cm and biomass particles are assumed to be spherical shape with constant surface area to volume ratio. Temperature measurements of the combustor are well agreed with simulation results while gas phase compositions have discrepancies. Combustion efficiency of the validated hot air generator is around 52.2 %.

New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil

2016-04-29

We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioningmore » strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.« less

Multiphase simulation of blood flow within main thoracic arteries of 8-year-old child with coarctation of the aorta

NASA Astrophysics Data System (ADS)

Melka, Bartlomiej; Gracka, Maria; Adamczyk, Wojciech; Rojczyk, Marek; Golda, Adam; Nowak, Andrzej J.; Białecki, Ryszard A.; Ostrowski, Ziemowit

2017-08-01

In the research, a numerical Computational Fluid Dynamics (CFD) model of the pulsatile blood flow was created and analysed. A real geometry of aorta and its thoracic branches of an 8-year old patient diagnosed with a congenital heart defect - coarctation of the aorta was used. The inlet boundary condition was implemented as the User Define Function according to measured values of volumetric blood flow. The blood flow was treated as multiphase using Euler-Euler approach. Plasma was set as the primary and dominant fluid phase, with the volume fraction of 0.585. The morphological elements (RBC and WBC) were set as dispersed phases being the remaining volume fraction.

LSPRAY-III: A Lagrangian Spray Module

NASA Technical Reports Server (NTRS)

Raju, M. S.

2008-01-01

LSPRAY-III is a Lagrangian spray solver developed for application with parallel computing and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type for the gas flow grid representation. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray because of its importance in aerospace application. The manual provides the user with an understanding of various models involved in the spray formulation, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers. With the development of LSPRAY-III, we have advanced the state-of-the-art in spray computations in several important ways.

LSPRAY-II: A Lagrangian Spray Module

NASA Technical Reports Server (NTRS)

Raju, M. S.

2004-01-01

LSPRAY-II is a Lagrangian spray solver developed for application with parallel computing and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type for the gas flow grid representation. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray because of its importance in aerospace application. The manual provides the user with an understanding of various models involved in the spray formulation, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers. With the development of LSPRAY-II, we have advanced the state-of-the-art in spray computations in several important ways.

Efficient solutions to the Euler equations for supersonic flow with embedded subsonic regions

NASA Technical Reports Server (NTRS)

Walters, Robert W.; Dwoyer, Douglas L.

1987-01-01

A line Gauss-Seidel (LGS) relaxation algorithm in conjunction with a one-parameter family of upwind discretizations of the Euler equations in two dimensions is described. Convergence of the basic algorithm to the steady state is quadratic for fully supersonic flows and is linear for other flows. This is in contrast to the block alternating direction implicit methods (either central or upwind differenced) and the upwind biased relaxation schemes, all of which converge linearly, independent of the flow regime. Moreover, the algorithm presented herein is easily coupled with methods to detect regions of subsonic flow embedded in supersonic flow. This allows marching by lines in the supersonic regions, converging each line quadratically, and iterating in the subsonic regions, and yields a very efficient iteration strategy. Numerical results are presented for two-dimensional supersonic and transonic flows containing oblique and normal shock waves which confirm the efficiency of the iteration strategy.

Dynamic CFD Simulations of the Supersonic Inflatable Aerodynamic Decelerator (SIAD) Ballistic Range Tests

NASA Technical Reports Server (NTRS)

Brock, Joseph M; Stern, Eric

2016-01-01

Dynamic CFD simulations of the SIAD ballistic test model were performed using US3D flow solver. Motivation for performing these simulations is for the purpose of validation and verification of the US3D flow solver as a viable computational tool for predicting dynamic coefficients.

Airfoil Design Using a Coupled Euler and Integral Boundary Layer Method with Adjoint Based Sensitivities

NASA Technical Reports Server (NTRS)

Edwards, S.; Reuther, J.; Chattot, J. J.

1997-01-01

The objective of this paper is to present a control theory approach for the design of airfoils in the presence of viscous compressible flows. A coupled system of the integral boundary layer and the Euler equations is solved to provide rapid flow simulations. An adjunct approach consistent with the complete coupled state equations is employed to obtain the sensitivities needed to drive a numerical optimization algorithm. Design to target pressure distribution is demonstrated on an RAE 2822 airfoil at transonic speed.

Interactive boundary-layer calculations of a transonic wing flow

NASA Technical Reports Server (NTRS)

Kaups, Kalle; Cebeci, Tuncer; Mehta, Unmeel

1989-01-01

Results obtained from iterative solutions of inviscid and boundary-layer equations are presented and compared with experimental values. The calculated results were obtained with an Euler code and a transonic potential code in order to furnish solutions for the inviscid flow; they were interacted with solutions of two-dimensional boundary-layer equations having a strip-theory approximation. Euler code results are found to be in better agreement with the experimental data than with the full potential code, especially in the presence of shock waves, (with the sole exception of the near-tip region).

Simulation of Unsteady Flows Using an Unstructured Navier-Stokes Solver on Moving and Stationary Grids

NASA Technical Reports Server (NTRS)

Biedron, Robert T.; Vatsa, Veer N.; Atkins, Harold L.

2005-01-01

We apply an unsteady Reynolds-averaged Navier-Stokes (URANS) solver for unstructured grids to unsteady flows on moving and stationary grids. Example problems considered are relevant to active flow control and stability and control. Computational results are presented using the Spalart-Allmaras turbulence model and are compared to experimental data. The effect of grid and time-step refinement are examined.

MODFLOW-NWT, A Newton formulation for MODFLOW-2005

USGS Publications Warehouse

Niswonger, Richard G.; Panday, Sorab; Ibaraki, Motomu

2011-01-01

This report documents a Newton formulation of MODFLOW-2005, called MODFLOW-NWT. MODFLOW-NWT is a standalone program that is intended for solving problems involving drying and rewetting nonlinearities of the unconfined groundwater-flow equation. MODFLOW-NWT must be used with the Upstream-Weighting (UPW) Package for calculating intercell conductances in a different manner than is done in the Block-Centered Flow (BCF), Layer Property Flow (LPF), or Hydrogeologic-Unit Flow (HUF; Anderman and Hill, 2000) Packages. The UPW Package treats nonlinearities of cell drying and rewetting by use of a continuous function of groundwater head, rather than the discrete approach of drying and rewetting that is used by the BCF, LPF, and HUF Packages. This further enables application of the Newton formulation for unconfined groundwater-flow problems because conductance derivatives required by the Newton method are smooth over the full range of head for a model cell. The NWT linearization approach generates an asymmetric matrix, which is different from the standard MODFLOW formulation that generates a symmetric matrix. Because all linear solvers presently available for use with MODFLOW-2005 solve only symmetric matrices, MODFLOW-NWT includes two previously developed asymmetric matrix-solver options. The matrix-solver options include a generalized-minimum-residual (GMRES) Solver and an Orthomin / stabilized conjugate-gradient (CGSTAB) Solver. The GMRES Solver is documented in a previously published report, such that only a brief description and input instructions are provided in this report. However, the CGSTAB Solver (called XMD) is documented in this report. Flow-property input for the UPW Package is designed based on the LPF Package and material-property input is identical to that for the LPF Package except that the rewetting and vertical-conductance correction options of the LPF Package are not available with the UPW Package. Input files constructed for the LPF Package can be used with slight modification as input for the UPW Package. This report presents the theory and methods used by MODFLOW-NWT, including the UPW Package. Additionally, this report provides comparisons of the new methodology to analytical solutions of groundwater flow and to standard MODFLOW-2005 results by use of an unconfined aquifer MODFLOW example problem. The standard MODFLOW-2005 simulation uses the LPF Package with the wet/dry option active. A new example problem also is presented to demonstrate MODFLOW-NWT's ability to provide a solution for a difficult unconfined groundwater-flow problem.

Vanishing Viscosity Approach to the Compressible Euler Equations for Transonic Nozzle and Spherically Symmetric Flows

NASA Astrophysics Data System (ADS)

Chen, Gui-Qiang G.; Schrecker, Matthew R. I.

2018-04-01

We are concerned with globally defined entropy solutions to the Euler equations for compressible fluid flows in transonic nozzles with general cross-sectional areas. Such nozzles include the de Laval nozzles and other more general nozzles whose cross-sectional area functions are allowed at the nozzle ends to be either zero (closed ends) or infinity (unbounded ends). To achieve this, in this paper, we develop a vanishing viscosity method to construct globally defined approximate solutions and then establish essential uniform estimates in weighted L p norms for the whole range of physical adiabatic exponents γ\\in (1, ∞) , so that the viscosity approximate solutions satisfy the general L p compensated compactness framework. The viscosity method is designed to incorporate artificial viscosity terms with the natural Dirichlet boundary conditions to ensure the uniform estimates. Then such estimates lead to both the convergence of the approximate solutions and the existence theory of globally defined finite-energy entropy solutions to the Euler equations for transonic flows that may have different end-states in the class of nozzles with general cross-sectional areas for all γ\\in (1, ∞) . The approach and techniques developed here apply to other problems with similar difficulties. In particular, we successfully apply them to construct globally defined spherically symmetric entropy solutions to the Euler equations for all γ\\in (1, ∞).

Navy Enhanced Sierra Mechanics (NESM): Toolbox for predicting Navy shock and damage

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moyer, Thomas; Stergiou, Jonathan; Reese, Garth

Here, the US Navy is developing a new suite of computational mechanics tools (Navy Enhanced Sierra Mechanics) for the prediction of ship response, damage, and shock environments transmitted to vital systems during threat weapon encounters. NESM includes fully coupled Euler-Lagrange solvers tailored to ship shock/damage predictions. NESM is optimized to support high-performance computing architectures, providing the physics-based ship response/threat weapon damage predictions needed to support the design and assessment of highly survivable ships. NESM is being employed to support current Navy ship design and acquisition programs while being further developed for future Navy fleet needs.

Comparison of measured and computed pitot pressures in a leading edge vortex from a delta wing

NASA Technical Reports Server (NTRS)

Murman, Earll M.; Powell, Kenneth G.

1987-01-01

Calculations are presented for a 75-deg swept flat plate wing tested at a freestream Mach number of 1.95 and 10 degrees angle of attack. Good agreement is found between computational data and previous experimental pitot pressure measurements in the core of the vortex, suggesting that the total pressure losses predicted by the Euler equation solvers are not errors, but realistic predictions. Data suggest that the magnitude of the total pressure loss is related to the circumferential velocity field through the vortex, and that it increases with angle of attack and varies with Mach number and sweep angle.

Navy Enhanced Sierra Mechanics (NESM): Toolbox for predicting Navy shock and damage

DOE PAGES

Moyer, Thomas; Stergiou, Jonathan; Reese, Garth; ...

2016-05-25

Here, the US Navy is developing a new suite of computational mechanics tools (Navy Enhanced Sierra Mechanics) for the prediction of ship response, damage, and shock environments transmitted to vital systems during threat weapon encounters. NESM includes fully coupled Euler-Lagrange solvers tailored to ship shock/damage predictions. NESM is optimized to support high-performance computing architectures, providing the physics-based ship response/threat weapon damage predictions needed to support the design and assessment of highly survivable ships. NESM is being employed to support current Navy ship design and acquisition programs while being further developed for future Navy fleet needs.

Flow analysis for the nacelle of an advanced ducted propeller at high angle-of-attack and at cruise with boundary layer control

NASA Technical Reports Server (NTRS)

Hwang, D. P.; Boldman, D. R.; Hughes, C. E.

1994-01-01

An axisymmetric panel code and a three dimensional Navier-Stokes code (used as an inviscid Euler code) were verified for low speed, high angle of attack flow conditions. A three dimensional Navier-Stokes code (used as an inviscid code), and an axisymmetric Navier-Stokes code (used as both viscous and inviscid code) were also assessed for high Mach number cruise conditions. The boundary layer calculations were made by using the results from the panel code or Euler calculation. The panel method can predict the internal surface pressure distributions very well if no shock exists. However, only Euler and Navier-Stokes calculations can provide a good prediction of the surface static pressure distribution including the pressure rise across the shock. Because of the high CPU time required for a three dimensional Navier-Stokes calculation, only the axisymmetric Navier-Stokes calculation was considered at cruise conditions. The use of suction and tangential blowing boundary layer control to eliminate the flow separation on the internal surface was demonstrated for low free stream Mach number and high angle of attack cases. The calculation also shows that transition from laminar flow to turbulent flow on the external cowl surface can be delayed by using suction boundary layer control at cruise flow conditions. The results were compared with experimental data where possible.

A level-set method for two-phase flows with moving contact line and insoluble surfactant

NASA Astrophysics Data System (ADS)

Xu, Jian-Jun; Ren, Weiqing

2014-04-01

A level-set method for two-phase flows with moving contact line and insoluble surfactant is presented. The mathematical model consists of the Navier-Stokes equation for the flow field, a convection-diffusion equation for the surfactant concentration, together with the Navier boundary condition and a condition for the dynamic contact angle derived by Ren et al. (2010) [37]. The numerical method is based on the level-set continuum surface force method for two-phase flows with surfactant developed by Xu et al. (2012) [54] with some cautious treatment for the boundary conditions. The numerical method consists of three components: a flow solver for the velocity field, a solver for the surfactant concentration, and a solver for the level-set function. In the flow solver, the surface force is dealt with using the continuum surface force model. The unbalanced Young stress at the moving contact line is incorporated into the Navier boundary condition. A convergence study of the numerical method and a parametric study are presented. The influence of surfactant on the dynamics of the moving contact line is illustrated using examples. The capability of the level-set method to handle complex geometries is demonstrated by simulating a pendant drop detaching from a wall under gravity.

EUPDF: An Eulerian-Based Monte Carlo Probability Density Function (PDF) Solver. User's Manual

NASA Technical Reports Server (NTRS)

Raju, M. S.

1998-01-01

EUPDF is an Eulerian-based Monte Carlo PDF solver developed for application with sprays, combustion, parallel computing and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and spray solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type. The manual provides the user with the coding required to couple the PDF code to any given flow code and a basic understanding of the EUPDF code structure as well as the models involved in the PDF formulation. The source code of EUPDF will be available with the release of the National Combustion Code (NCC) as a complete package.

Lattice Boltzmann Model of 3D Multiphase Flow in Artery Bifurcation Aneurysm Problem

PubMed Central

Abas, Aizat; Mokhtar, N. Hafizah; Ishak, M. H. H.; Abdullah, M. Z.; Ho Tian, Ang

2016-01-01

This paper simulates and predicts the laminar flow inside the 3D aneurysm geometry, since the hemodynamic situation in the blood vessels is difficult to determine and visualize using standard imaging techniques, for example, magnetic resonance imaging (MRI). Three different types of Lattice Boltzmann (LB) models are computed, namely, single relaxation time (SRT), multiple relaxation time (MRT), and regularized BGK models. The results obtained using these different versions of the LB-based code will then be validated with ANSYS FLUENT, a commercially available finite volume- (FV-) based CFD solver. The simulated flow profiles that include velocity, pressure, and wall shear stress (WSS) are then compared between the two solvers. The predicted outcomes show that all the LB models are comparable and in good agreement with the FVM solver for complex blood flow simulation. The findings also show minor differences in their WSS profiles. The performance of the parallel implementation for each solver is also included and discussed in this paper. In terms of parallelization, it was shown that LBM-based code performed better in terms of the computation time required. PMID:27239221

Singularities of the Euler equation and hydrodynamic stability

NASA Technical Reports Server (NTRS)

Tanveer, S.; Speziale, Charles G.

1993-01-01

Equations governing the motion of a specific class of singularities of the Euler equation in the extended complex spatial domain are derived. Under some assumptions, it is shown how this motion is dictated by the smooth part of the complex velocity at a singular point in the unphysical domain. These results are used to relate the motion of complex singularities to the stability of steady solutions of the Euler equation. A sufficient condition for instability is conjectured. Several examples are presented to demonstrate the efficacy of this sufficient condition which include the class of elliptical flows and the Kelvin-Stuart Cat's Eye.

Singularities of the Euler equation and hydrodynamic stability

NASA Technical Reports Server (NTRS)

Tanveer, S.; Speziale, Charles G.

1992-01-01

Equations governing the motion of a specific class of singularities of the Euler equation in the extended complex spatial domain are derived. Under some assumptions, it is shown how this motion is dictated by the smooth part of the complex velocity at a singular point in the unphysical domain. These results are used to relate the motion of complex singularities to the stability of steady solutions of the Euler equation. A sufficient condition for instability is conjectured. Several examples are presented to demonstrate the efficacy of this sufficient condition which include the class of elliptical flows and the Kelvin-Stuart Cat's Eye.

The effects of rotational flow, viscosity, thickness, and shape on transonic flutter dip phenomena

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Srivastava, Rakesh; Kaza, Krishna Rao V.

1988-01-01

The transonic flutter dip phenomena on thin airfoils, which are employed for propfan blades, is investigated using an integrated Euler/Navier-Stokes code and a two degrees of freedom typical section structural model. As a part of the code validation, the flutter characteristics of the NACA 64A010 airfoil are also investigated. In addition, the effects of artificial dissipation models, rotational flow, initial conditions, mean angle of attack, viscosity, airfoil thickness and shape on flutter are investigated. The results obtained with a Euler code for the NACA 64A010 airfoil are in reasonable agreement with published results obtained by using transonic small disturbance and Euler codes. The two artificial dissipation models, one based on the local pressure gradient scaled by a common factor and the other based on the local pressure gradient scaled by a spectral radius, predicted the same flutter speeds except in the recovery region for the case studied. The effects of rotational flow, initial conditions, mean angle of attack, and viscosity for the Reynold's number studied seem to be negligible or small on the minima of the flutter dip.

Euler flow predictions for an oscillating cascade using a high resolution wave-split scheme

NASA Technical Reports Server (NTRS)

Huff, Dennis L.; Swafford, Timothy W.; Reddy, T. S. R.

1991-01-01

A compressible flow code that can predict the nonlinear unsteady aerodynamics associated with transonic flows over oscillating cascades is developed and validated. The code solves the two dimensional, unsteady Euler equations using a time-marching, flux-difference splitting scheme. The unsteady pressures and forces can be determined for arbitrary input motions, although only harmonic pitching and plunging motions are addressed. The code solves the flow equations on a H-grid which is allowed to deform with the airfoil motion. Predictions are presented for both flat plate cascades and loaded airfoil cascades. Results are compared to flat plate theory and experimental data. Predictions are also presented for several oscillating cascades with strong normal shocks where the pitching amplitudes, cascade geometry and interblade phase angles are varied to investigate nonlinear behavior.

High resolution solutions of the Euler equations for vortex flows

NASA Technical Reports Server (NTRS)

Murman, E. M.; Powell, K. G.; Rizzi, A.

1985-01-01

Solutions of the Euler equations are presented for M = 1.5 flow past a 70-degree-swept delta wing. At an angle of attack of 10 degrees, strong leading-edge vortices are produced. Two computational approaches are taken, based upon fully three-dimensional and conical flow theory. Both methods utilize a finite-volume discretization solved by a pseudounsteady multistage scheme. Results from the two approaches are in good agreement. Computations have been done on a 16-million-word CYBER 205 using 196 x 56 x 96 and 128 x 128 cells for the two methods. A sizable data base is generated, and some of the practical aspects of manipulating it are mentioned. The results reveal many interesting physical features of the compressible vortical flow field and also suggest new areas needing research.

Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

This study concerns the application and solver robustness of the Newton-Krylov method in solving two-phase flow drift-flux model problems using high-order numerical schemes. In our previous studies, the Newton-Krylov method has been proven as a promising solver for two-phase flow drift-flux model problems. However, these studies were limited to use first-order numerical schemes only. Moreover, the previous approach to treating the drift-flux closure correlations was later revealed to cause deteriorated solver convergence performance, when the mesh was highly refined, and also when higher-order numerical schemes were employed. In this study, a second-order spatial discretization scheme that has been tested withmore » two-fluid two-phase flow model was extended to solve drift-flux model problems. In order to improve solver robustness, and therefore efficiency, a new approach was proposed to treating the mean drift velocity of the gas phase as a primary nonlinear variable to the equation system. With this new approach, significant improvement in solver robustness was achieved. With highly refined mesh, the proposed treatment along with the Newton-Krylov solver were extensively tested with two-phase flow problems that cover a wide range of thermal-hydraulics conditions. Satisfactory convergence performances were observed for all test cases. Numerical verification was then performed in the form of mesh convergence studies, from which expected orders of accuracy were obtained for both the first-order and the second-order spatial discretization schemes. Finally, the drift-flux model, along with numerical methods presented, were validated with three sets of flow boiling experiments that cover different flow channel geometries (round tube, rectangular tube, and rod bundle), and a wide range of test conditions (pressure, mass flux, wall heat flux, inlet subcooling and outlet void fraction).« less

Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2017-08-07

This study concerns the application and solver robustness of the Newton-Krylov method in solving two-phase flow drift-flux model problems using high-order numerical schemes. In our previous studies, the Newton-Krylov method has been proven as a promising solver for two-phase flow drift-flux model problems. However, these studies were limited to use first-order numerical schemes only. Moreover, the previous approach to treating the drift-flux closure correlations was later revealed to cause deteriorated solver convergence performance, when the mesh was highly refined, and also when higher-order numerical schemes were employed. In this study, a second-order spatial discretization scheme that has been tested withmore » two-fluid two-phase flow model was extended to solve drift-flux model problems. In order to improve solver robustness, and therefore efficiency, a new approach was proposed to treating the mean drift velocity of the gas phase as a primary nonlinear variable to the equation system. With this new approach, significant improvement in solver robustness was achieved. With highly refined mesh, the proposed treatment along with the Newton-Krylov solver were extensively tested with two-phase flow problems that cover a wide range of thermal-hydraulics conditions. Satisfactory convergence performances were observed for all test cases. Numerical verification was then performed in the form of mesh convergence studies, from which expected orders of accuracy were obtained for both the first-order and the second-order spatial discretization schemes. Finally, the drift-flux model, along with numerical methods presented, were validated with three sets of flow boiling experiments that cover different flow channel geometries (round tube, rectangular tube, and rod bundle), and a wide range of test conditions (pressure, mass flux, wall heat flux, inlet subcooling and outlet void fraction).« less

A Robust and Efficient Method for Steady State Patterns in Reaction-Diffusion Systems

PubMed Central

Lo, Wing-Cheong; Chen, Long; Wang, Ming; Nie, Qing

2012-01-01

An inhomogeneous steady state pattern of nonlinear reaction-diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding time-dependent reaction-diffusion equations using temporal schemes. Nonlinear solvers (e.g., Newton’s method) take less CPU time in direct computation for the steady state; however, their convergence is sensitive to the initial guess, often leading to divergence or convergence to spatially homogeneous solution. Systematically numerical exploration of spatial patterns of reaction-diffusion equations under different parameter regimes requires that the numerical method be efficient and robust to initial condition or initial guess, with better likelihood of convergence to an inhomogeneous pattern. Here, a new approach that combines the advantages of temporal schemes in robustness and Newton’s method in fast convergence in solving steady states of reaction-diffusion equations is proposed. In particular, an adaptive implicit Euler with inexact solver (AIIE) method is found to be much more efficient than temporal schemes and more robust in convergence than typical nonlinear solvers (e.g., Newton’s method) in finding the inhomogeneous pattern. Application of this new approach to two reaction-diffusion equations in one, two, and three spatial dimensions, along with direct comparisons to several other existing methods, demonstrates that AIIE is a more desirable method for searching inhomogeneous spatial patterns of reaction-diffusion equations in a large parameter space. PMID:22773849

High-resolution numerical approximation of traffic flow problems with variable lanes and free-flow velocities.

PubMed

Zhang, Peng; Liu, Ru-Xun; Wong, S C

2005-05-01

This paper develops macroscopic traffic flow models for a highway section with variable lanes and free-flow velocities, that involve spatially varying flux functions. To address this complex physical property, we develop a Riemann solver that derives the exact flux values at the interface of the Riemann problem. Based on this solver, we formulate Godunov-type numerical schemes to solve the traffic flow models. Numerical examples that simulate the traffic flow around a bottleneck that arises from a drop in traffic capacity on the highway section are given to illustrate the efficiency of these schemes.

A note on singularities of the 3-D Euler equation

NASA Technical Reports Server (NTRS)

Tanveer, S.

1994-01-01

In this paper, we consider analytic initial conditions with finite energy, whose complex spatial continuation is a superposition of a smooth background flow and a singular field. Through explicit calculation in the complex plane, we show that under some assumptions, the solution to the 3-D Euler equation ceases to be analytic in the real domain in finite time.

A multigrid LU-SSOR scheme for approximate Newton iteration applied to the Euler equations

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan; Jameson, Antony

1986-01-01

A new efficient relaxation scheme in conjunction with a multigrid method is developed for the Euler equations. The LU SSOR scheme is based on a central difference scheme and does not need flux splitting for Newton iteration. Application to transonic flow shows that the new method surpasses the performance of the LU implicit scheme.

A hybrid approach for nonlinear computational aeroacoustics predictions

NASA Astrophysics Data System (ADS)

Sassanis, Vasileios; Sescu, Adrian; Collins, Eric M.; Harris, Robert E.; Luke, Edward A.

2017-01-01

In many aeroacoustics applications involving nonlinear waves and obstructions in the far-field, approaches based on the classical acoustic analogy theory or the linearised Euler equations are unable to fully characterise the acoustic field. Therefore, computational aeroacoustics hybrid methods that incorporate nonlinear wave propagation have to be constructed. In this study, a hybrid approach coupling Navier-Stokes equations in the acoustic source region with nonlinear Euler equations in the acoustic propagation region is introduced and tested. The full Navier-Stokes equations are solved in the source region to identify the acoustic sources. The flow variables of interest are then transferred from the source region to the acoustic propagation region, where the full nonlinear Euler equations with source terms are solved. The transition between the two regions is made through a buffer zone where the flow variables are penalised via a source term added to the Euler equations. Tests were conducted on simple acoustic and vorticity disturbances, two-dimensional jets (Mach 0.9 and 2), and a three-dimensional jet (Mach 1.5), impinging on a wall. The method is proven to be effective and accurate in predicting sound pressure levels associated with the propagation of linear and nonlinear waves in the near- and far-field regions.

Fluid-structure interaction involving large deformations: 3D simulations and applications to biological systems

NASA Astrophysics Data System (ADS)

Tian, Fang-Bao; Dai, Hu; Luo, Haoxiang; Doyle, James F.; Rousseau, Bernard

2014-02-01

Three-dimensional fluid-structure interaction (FSI) involving large deformations of flexible bodies is common in biological systems, but accurate and efficient numerical approaches for modeling such systems are still scarce. In this work, we report a successful case of combining an existing immersed-boundary flow solver with a nonlinear finite-element solid-mechanics solver specifically for three-dimensional FSI simulations. This method represents a significant enhancement from the similar methods that are previously available. Based on the Cartesian grid, the viscous incompressible flow solver can handle boundaries of large displacements with simple mesh generation. The solid-mechanics solver has separate subroutines for analyzing general three-dimensional bodies and thin-walled structures composed of frames, membranes, and plates. Both geometric nonlinearity associated with large displacements and material nonlinearity associated with large strains are incorporated in the solver. The FSI is achieved through a strong coupling and partitioned approach. We perform several validation cases, and the results may be used to expand the currently limited database of FSI benchmark study. Finally, we demonstrate the versatility of the present method by applying it to the aerodynamics of elastic wings of insects and the flow-induced vocal fold vibration.

Fluid–structure interaction involving large deformations: 3D simulations and applications to biological systems

PubMed Central

Tian, Fang-Bao; Dai, Hu; Luo, Haoxiang; Doyle, James F.; Rousseau, Bernard

2013-01-01

Three-dimensional fluid–structure interaction (FSI) involving large deformations of flexible bodies is common in biological systems, but accurate and efficient numerical approaches for modeling such systems are still scarce. In this work, we report a successful case of combining an existing immersed-boundary flow solver with a nonlinear finite-element solid-mechanics solver specifically for three-dimensional FSI simulations. This method represents a significant enhancement from the similar methods that are previously available. Based on the Cartesian grid, the viscous incompressible flow solver can handle boundaries of large displacements with simple mesh generation. The solid-mechanics solver has separate subroutines for analyzing general three-dimensional bodies and thin-walled structures composed of frames, membranes, and plates. Both geometric nonlinearity associated with large displacements and material nonlinearity associated with large strains are incorporated in the solver. The FSI is achieved through a strong coupling and partitioned approach. We perform several validation cases, and the results may be used to expand the currently limited database of FSI benchmark study. Finally, we demonstrate the versatility of the present method by applying it to the aerodynamics of elastic wings of insects and the flow-induced vocal fold vibration. PMID:24415796

Application of a compressible flow solver and barotropic cavitation model for the evaluation of the suction head in a low specific speed centrifugal pump impeller channel

NASA Astrophysics Data System (ADS)

Limbach, P.; Müller, T.; Skoda, R.

2015-12-01

Commonly, for the simulation of cavitation in centrifugal pumps incompressible flow solvers with VOF kind cavitation models are applied. Since the source/sink terms of the void fraction transport equation are based on simplified bubble dynamics, empirical parameters may need to be adjusted to the particular pump operating point. In the present study a barotropic cavitation model, which is based solely on thermodynamic fluid properties and does not include any empirical parameters, is applied on a single flow channel of a pump impeller in combination with a time-explicit viscous compressible flow solver. The suction head curves (head drop) are compared to the results of an incompressible implicit standard industrial CFD tool and are predicted qualitatively correct by the barotropic model.

USM3D Unstructured Grid Solutions for CAWAPI at NASA LaRC

NASA Technical Reports Server (NTRS)

Lamar, John E.; Abdol-Hamid, Khaled S.

2007-01-01

In support the Cranked Arrow Wing Aerodynamic Project International (CAWAPI) to improve the Technology Readiness Level of flow solvers by comparing results with measured F-16XL-1 flight data, NASA Langley employed the TetrUSS unstructured grid solver, USM3D, to obtain solutions for all seven flight conditions of interest. A newly available solver version that incorporates a number of turbulence models, including the two-equation linear and non-linear k-epsilon, was used in this study. As a first test, a choice was made to utilize only a single grid resolution with the solver for the simulation of the different flight conditions. Comparisons are presented with three turbulence models in USM3D, flight data for surface pressure, boundary-layer profiles, and skin-friction results, as well as limited predictions from other solvers. A result of these comparisons is that the USM3D solver can be used in an engineering environment to predict flow physics on a complex configuration at flight Reynolds numbers with a two-equation linear k-epsilon turbulence model.

Computational methods for vortex dominated compressible flows

NASA Technical Reports Server (NTRS)

Murman, Earll M.

1987-01-01

The principal objectives were to: understand the mechanisms by which Euler equation computations model leading edge vortex flows; understand the vortical and shock wave structures that may exist for different wing shapes, angles of incidence, and Mach numbers; and compare calculations with experiments in order to ascertain the limitations and advantages of Euler equation models. The initial approach utilized the cell centered finite volume Jameson scheme. The final calculation utilized a cell vertex finite volume method on an unstructured grid. Both methods used Runge-Kutta four stage schemes for integrating the equations. The principal findings are briefly summarized.

Voidage correction algorithm for unresolved Euler-Lagrange simulations

NASA Astrophysics Data System (ADS)

Askarishahi, Maryam; Salehi, Mohammad-Sadegh; Radl, Stefan

2018-04-01

The effect of grid coarsening on the predicted total drag force and heat exchange rate in dense gas-particle flows is investigated using Euler-Lagrange (EL) approach. We demonstrate that grid coarsening may reduce the predicted total drag force and exchange rate. Surprisingly, exchange coefficients predicted by the EL approach deviate more significantly from the exact value compared to results of Euler-Euler (EE)-based calculations. The voidage gradient is identified as the root cause of this peculiar behavior. Consequently, we propose a correction algorithm based on a sigmoidal function to predict the voidage experienced by individual particles. Our correction algorithm can significantly improve the prediction of exchange coefficients in EL models, which is tested for simulations involving Euler grid cell sizes between 2d_p and 12d_p . It is most relevant in simulations of dense polydisperse particle suspensions featuring steep voidage profiles. For these suspensions, classical approaches may result in an error of the total exchange rate of up to 30%.

Modeling of heavy-gas effects on airfoil flows

NASA Technical Reports Server (NTRS)

Drela, Mark

1992-01-01

Thermodynamic models were constructed for a calorically imperfect gas and for a non-ideal gas. These were incorporated into a quasi one dimensional flow solver to develop an understanding of the differences in flow behavior between the new models and the perfect gas model. The models were also incorporated into a two dimensional flow solver to investigate their effects on transonic airfoil flows. Specifically, the calculations simulated airfoil testing in a proposed high Reynolds number heavy gas test facility. The results indicate that the non-idealities caused significant differences in the flow field, but that matching of an appropriate non-dimensional parameter led to flows similar to those in air.

Benchmarking Defmod, an open source FEM code for modeling episodic fault rupture

NASA Astrophysics Data System (ADS)

Meng, Chunfang

2017-03-01

We present Defmod, an open source (linear) finite element code that enables us to efficiently model the crustal deformation due to (quasi-)static and dynamic loadings, poroelastic flow, viscoelastic flow and frictional fault slip. Ali (2015) provides the original code introducing an implicit solver for (quasi-)static problem, and an explicit solver for dynamic problem. The fault constraint is implemented via Lagrange Multiplier. Meng (2015) combines these two solvers into a hybrid solver that uses failure criteria and friction laws to adaptively switch between the (quasi-)static state and dynamic state. The code is capable of modeling episodic fault rupture driven by quasi-static loadings, e.g. due to reservoir fluid withdraw or injection. Here, we focus on benchmarking the Defmod results against some establish results.

Shock-driven fluid-structure interaction for civil design

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wood, Stephen L; Deiterding, Ralf

The multiphysics fluid-structure interaction simulation of shock-loaded structures requires the dynamic coupling of a shock-capturing flow solver to a solid mechanics solver for large deformations. The Virtual Test Facility combines a Cartesian embedded boundary approach with dynamic mesh adaptation in a generic software framework of flow solvers using hydrodynamic finite volume upwind schemes that are coupled to various explicit finite element solid dynamics solvers (Deiterding et al., 2006). This paper gives a brief overview of the computational approach and presents first simulations that utilize the general purpose solid dynamics code DYNA3D for complex 3D structures of interest in civil engineering.more » Results from simulations of a reinforced column, highway bridge, multistory building, and nuclear reactor building are presented.« less

An adaptive discontinuous Galerkin solver for aerodynamic flows

NASA Astrophysics Data System (ADS)

Burgess, Nicholas K.

This work considers the accuracy, efficiency, and robustness of an unstructured high-order accurate discontinuous Galerkin (DG) solver for computational fluid dynamics (CFD). Recently, there has been a drive to reduce the discretization error of CFD simulations using high-order methods on unstructured grids. However, high-order methods are often criticized for lacking robustness and having high computational cost. The goal of this work is to investigate methods that enhance the robustness of high-order discontinuous Galerkin (DG) methods on unstructured meshes, while maintaining low computational cost and high accuracy of the numerical solutions. This work investigates robustness enhancement of high-order methods by examining effective non-linear solvers, shock capturing methods, turbulence model discretizations and adaptive refinement techniques. The goal is to develop an all encompassing solver that can simulate a large range of physical phenomena, where all aspects of the solver work together to achieve a robust, efficient and accurate solution strategy. The components and framework for a robust high-order accurate solver that is capable of solving viscous, Reynolds Averaged Navier-Stokes (RANS) and shocked flows is presented. In particular, this work discusses robust discretizations of the turbulence model equation used to close the RANS equations, as well as stable shock capturing strategies that are applicable across a wide range of discretization orders and applicable to very strong shock waves. Furthermore, refinement techniques are considered as both efficiency and robustness enhancement strategies. Additionally, efficient non-linear solvers based on multigrid and Krylov subspace methods are presented. The accuracy, efficiency, and robustness of the solver is demonstrated using a variety of challenging aerodynamic test problems, which include turbulent high-lift and viscous hypersonic flows. Adaptive mesh refinement was found to play a critical role in obtaining a robust and efficient high-order accurate flow solver. A goal-oriented error estimation technique has been developed to estimate the discretization error of simulation outputs. For high-order discretizations, it is shown that functional output error super-convergence can be obtained, provided the discretization satisfies a property known as dual consistency. The dual consistency of the DG methods developed in this work is shown via mathematical analysis and numerical experimentation. Goal-oriented error estimation is also used to drive an hp-adaptive mesh refinement strategy, where a combination of mesh or h-refinement, and order or p-enrichment, is employed based on the smoothness of the solution. The results demonstrate that the combination of goal-oriented error estimation and hp-adaptation yield superior accuracy, as well as enhanced robustness and efficiency for a variety of aerodynamic flows including flows with strong shock waves. This work demonstrates that DG discretizations can be the basis of an accurate, efficient, and robust CFD solver. Furthermore, enhancing the robustness of DG methods does not adversely impact the accuracy or efficiency of the solver for challenging and complex flow problems. In particular, when considering the computation of shocked flows, this work demonstrates that the available shock capturing techniques are sufficiently accurate and robust, particularly when used in conjunction with adaptive mesh refinement . This work also demonstrates that robust solutions of the Reynolds Averaged Navier-Stokes (RANS) and turbulence model equations can be obtained for complex and challenging aerodynamic flows. In this context, the most robust strategy was determined to be a low-order turbulence model discretization coupled to a high-order discretization of the RANS equations. Although RANS solutions using high-order accurate discretizations of the turbulence model were obtained, the behavior of current-day RANS turbulence models discretized to high-order was found to be problematic, leading to solver robustness issues. This suggests that future work is warranted in the area of turbulence model formulation for use with high-order discretizations. Alternately, the use of Large-Eddy Simulation (LES) subgrid scale models with high-order DG methods offers the potential to leverage the high accuracy of these methods for very high fidelity turbulent simulations. This thesis has developed the algorithmic improvements that will lay the foundation for the development of a three-dimensional high-order flow solution strategy that can be used as the basis for future LES simulations.

An efficient iteration strategy for the solution of the Euler equations

NASA Technical Reports Server (NTRS)

Walters, R. W.; Dwoyer, D. L.

1985-01-01

A line Gauss-Seidel (LGS) relaxation algorithm in conjunction with a one-parameter family of upwind discretizations of the Euler equations in two-dimensions is described. The basic algorithm has the property that convergence to the steady-state is quadratic for fully supersonic flows and linear otherwise. This is in contrast to the block ADI methods (either central or upwind differenced) and the upwind biased relaxation schemes, all of which converge linearly, independent of the flow regime. Moreover, the algorithm presented here is easily enhanced to detect regions of subsonic flow embedded in supersonic flow. This allows marching by lines in the supersonic regions, converging each line quadratically, and iterating in the subsonic regions, thus yielding a very efficient iteration strategy. Numerical results are presented for two-dimensional supersonic and transonic flows containing both oblique and normal shock waves which confirm the efficiency of the iteration strategy.

Computation of Large-Scale Structure Jet Noise Sources With Weak Nonlinear Effects Using Linear Euler

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Hixon, Ray; Mankbadi, Reda R.

2003-01-01

An approximate technique is presented for the prediction of the large-scale turbulent structure sound source in a supersonic jet. A linearized Euler equations code is used to solve for the flow disturbances within and near a jet with a given mean flow. Assuming a normal mode composition for the wave-like disturbances, the linear radial profiles are used in an integration of the Navier-Stokes equations. This results in a set of ordinary differential equations representing the weakly nonlinear self-interactions of the modes along with their interaction with the mean flow. Solutions are then used to correct the amplitude of the disturbances that represent the source of large-scale turbulent structure sound in the jet.

A finite element approach for solution of the 3D Euler equations

NASA Technical Reports Server (NTRS)

Thornton, E. A.; Ramakrishnan, R.; Dechaumphai, P.

1986-01-01

Prediction of thermal deformations and stresses has prime importance in the design of the next generation of high speed flight vehicles. Aerothermal load computations for complex three-dimensional shapes necessitate development of procedures to solve the full Navier-Stokes equations. This paper details the development of a three-dimensional inviscid flow approach which can be extended for three-dimensional viscous flows. A finite element formulation, based on a Taylor series expansion in time, is employed to solve the compressible Euler equations. Model generation and results display are done using a commercially available program, PATRAN, and vectorizing strategies are incorporated to ensure computational efficiency. Sample problems are presented to demonstrate the validity of the approach for analyzing high speed compressible flows.

A GPU-based incompressible Navier-Stokes solver on moving overset grids

NASA Astrophysics Data System (ADS)

Chandar, Dominic D. J.; Sitaraman, Jayanarayanan; Mavriplis, Dimitri J.

2013-07-01

In pursuit of obtaining high fidelity solutions to the fluid flow equations in a short span of time, graphics processing units (GPUs) which were originally intended for gaming applications are currently being used to accelerate computational fluid dynamics (CFD) codes. With a high peak throughput of about 1 TFLOPS on a PC, GPUs seem to be favourable for many high-resolution computations. One such computation that involves a lot of number crunching is computing time accurate flow solutions past moving bodies. The aim of the present paper is thus to discuss the development of a flow solver on unstructured and overset grids and its implementation on GPUs. In its present form, the flow solver solves the incompressible fluid flow equations on unstructured/hybrid/overset grids using a fully implicit projection method. The resulting discretised equations are solved using a matrix-free Krylov solver using several GPU kernels such as gradient, Laplacian and reduction. Some of the simple arithmetic vector calculations are implemented using the CU++: An Object Oriented Framework for Computational Fluid Dynamics Applications using Graphics Processing Units, Journal of Supercomputing, 2013, doi:10.1007/s11227-013-0985-9 approach where GPU kernels are automatically generated at compile time. Results are presented for two- and three-dimensional computations on static and moving grids.

Comparing Split and Unsplit Numerical Methods for Simulating Low and High Mach Number Turbulent Flows in Xrage

NASA Astrophysics Data System (ADS)

Saenz, Juan; Grinstein, Fernando; Dolence, Joshua; Rauenzahn, Rick; Masser, Thomas; Francois, Marianne; LANL Team

2017-11-01

We report progress in evaluating an unsplit hydrodynamic solver being implemented in the radiation adaptive grid Eulerian (xRAGE) code, and compare to a split scheme. xRage is a Eulerian hydrodynamics code used for implicit large eddy simulations (ILES) of multi-material, multi-physics flows where low and high Mach number (Ma) processes and instabilities interact and co-exist. The hydrodynamic solver in xRAGE uses a directionally split, second order Godunov, finite volume (FV) scheme. However, a standard, unsplit, Godunov-type FV scheme with 2nd and 3rd order reconstruction options, low Ma correction and a variety of Riemann solvers has recently become available. To evaluate the hydrodynamic solvers for turbulent low Ma flows, we use simulations of the Taylor Green Vortex (TGV), where there is a transition to turbulence via vortex stretching and production of small-scale eddies. We also simulate a high-low Ma shock-tube flow, where a shock passing over a perturbed surface generates a baroclinic Richtmyer-Meshkov instability (RMI); after the shock has passed, the turbulence in the accelerated interface region resembles Rayleigh Taylor (RT) instability. We compare turbulence spectra and decay in simulated TGV flows, and we present progress in simulating the high-low Ma RMI-RT flow. LANL is operated by LANS LLC for the U.S. DOE NNSA under Contract No. DE-AC52-06NA25396.

A three-dimensional structured/unstructured hybrid Navier-Stokes method for turbine blade rows

NASA Technical Reports Server (NTRS)

Tsung, F.-L.; Loellbach, J.; Kwon, O.; Hah, C.

1994-01-01

A three-dimensional viscous structured/unstructured hybrid scheme has been developed for numerical computation of high Reynolds number turbomachinery flows. The procedure allows an efficient structured solver to be employed in the densely clustered, high aspect-ratio grid around the viscous regions near solid surfaces, while employing an unstructured solver elsewhere in the flow domain to add flexibility in mesh generation. Test results for an inviscid flow over an external transonic wing and a Navier-Stokes flow for an internal annular cascade are presented.

Aeroacoustic simulation of a linear cascade by a prefactored compact scheme

NASA Astrophysics Data System (ADS)

Ghillani, Pietro

This work documents the development of a three-dimensional high-order prefactored compact finite-difference solver for computational aeroacoustics (CAA) based on the inviscid Euler equations. This time explicit scheme is applied to representative problems of sound generation by flow interacting with solid boundaries. Four aeroacoustic problems are explored and the results validated against available reference analytical solution. Selected mesh convergence studies are conducted to determine the effective order of accuracy of the complete scheme. The first test case simulates the noise emitted by a still cylinder in an oscillating field. It provides a simple validation for the CAA-compatible solid wall condition used in the remainder of the work. The following test cases are increasingly complex versions of the turbomachinery rotor-stator interaction problem taken from NASA CAA workshops. In all the cases the results are compared against the available literature. The numerical method features some appreciable contributions to computational aeroacoustics. A reduced data exchange technique for parallel computations is implemented, which requires the exchange of just two values for each boundary node, independently of the size of the zone overlap. A modified version of the non-reflecting buffer layer by Chen is used to allow aerodynamic perturbations at the through flow boundaries. The Giles subsonic boundary conditions are extended to three-dimensional curvilinear coordinates. These advances have enabled to resolve the aerodynamic noise generation and near-field propagation on a representative cascade geometry with a time-marching scheme, with accuracy similar to spectral methods..

The coupling of fluids, dynamics, and controls on advanced architecture computers

NASA Technical Reports Server (NTRS)

Atwood, Christopher

1995-01-01

This grant provided for the demonstration of coupled controls, body dynamics, and fluids computations in a workstation cluster environment; and an investigation of the impact of peer-peer communication on flow solver performance and robustness. The findings of these investigations were documented in the conference articles.The attached publication, 'Towards Distributed Fluids/Controls Simulations', documents the solution and scaling of the coupled Navier-Stokes, Euler rigid-body dynamics, and state feedback control equations for a two-dimensional canard-wing. The poor scaling shown was due to serialized grid connectivity computation and Ethernet bandwidth limits. The scaling of a peer-to-peer communication flow code on an IBM SP-2 was also shown. The scaling of the code on the switched fabric-linked nodes was good, with a 2.4 percent loss due to communication of intergrid boundary point information. The code performance on 30 worker nodes was 1.7 (mu)s/point/iteration, or a factor of three over a Cray C-90 head. The attached paper, 'Nonlinear Fluid Computations in a Distributed Environment', documents the effect of several computational rate enhancing methods on convergence. For the cases shown, the highest throughput was achieved using boundary updates at each step, with the manager process performing communication tasks only. Constrained domain decomposition of the implicit fluid equations did not degrade the convergence rate or final solution. The scaling of a coupled body/fluid dynamics problem on an Ethernet-linked cluster was also shown.

A Multi-Level Parallelization Concept for High-Fidelity Multi-Block Solvers

NASA Technical Reports Server (NTRS)

Hatay, Ferhat F.; Jespersen, Dennis C.; Guruswamy, Guru P.; Rizk, Yehia M.; Byun, Chansup; Gee, Ken; VanDalsem, William R. (Technical Monitor)

1997-01-01

The integration of high-fidelity Computational Fluid Dynamics (CFD) analysis tools with the industrial design process benefits greatly from the robust implementations that are transportable across a wide range of computer architectures. In the present work, a hybrid domain-decomposition and parallelization concept was developed and implemented into the widely-used NASA multi-block Computational Fluid Dynamics (CFD) packages implemented in ENSAERO and OVERFLOW. The new parallel solver concept, PENS (Parallel Euler Navier-Stokes Solver), employs both fine and coarse granularity in data partitioning as well as data coalescing to obtain the desired load-balance characteristics on the available computer platforms. This multi-level parallelism implementation itself introduces no changes to the numerical results, hence the original fidelity of the packages are identically preserved. The present implementation uses the Message Passing Interface (MPI) library for interprocessor message passing and memory accessing. By choosing an appropriate combination of the available partitioning and coalescing capabilities only during the execution stage, the PENS solver becomes adaptable to different computer architectures from shared-memory to distributed-memory platforms with varying degrees of parallelism. The PENS implementation on the IBM SP2 distributed memory environment at the NASA Ames Research Center obtains 85 percent scalable parallel performance using fine-grain partitioning of single-block CFD domains using up to 128 wide computational nodes. Multi-block CFD simulations of complete aircraft simulations achieve 75 percent perfect load-balanced executions using data coalescing and the two levels of parallelism. SGI PowerChallenge, SGI Origin 2000, and a cluster of workstations are the other platforms where the robustness of the implementation is tested. The performance behavior on the other computer platforms with a variety of realistic problems will be included as this on-going study progresses.

Comparative Study of Advanced Turbulence Models for Turbomachinery

NASA Technical Reports Server (NTRS)

Hadid, Ali H.; Sindir, Munir M.

1996-01-01

A computational study has been undertaken to study the performance of advanced phenomenological turbulence models coded in a modular form to describe incompressible turbulent flow behavior in two dimensional/axisymmetric and three dimensional complex geometry. The models include a variety of two equation models (single and multi-scale k-epsilon models with different near wall treatments) and second moment algebraic and full Reynolds stress closure models. These models were systematically assessed to evaluate their performance in complex flows with rotation, curvature and separation. The models are coded as self contained modules that can be interfaced with a number of flow solvers. These modules are stand alone satellite programs that come with their own formulation, finite-volume discretization scheme, solver and boundary condition implementation. They will take as input (from any generic Navier-Stokes solver) the velocity field, grid (structured H-type grid) and computational domain specification (boundary conditions), and will deliver, depending on the model used, turbulent viscosity, or the components of the Reynolds stress tensor. There are separate 2D/axisymmetric and/or 3D decks for each module considered. The modules are tested using Rocketdyn's proprietary code REACT. The code utilizes an efficient solution procedure to solve Navier-Stokes equations in a non-orthogonal body-fitted coordinate system. The differential equations are discretized over a finite-volume grid using a non-staggered variable arrangement and an efficient solution procedure based on the SIMPLE algorithm for the velocity-pressure coupling is used. The modules developed have been interfaced and tested using finite-volume, pressure-correction CFD solvers which are widely used in the CFD community. Other solvers can also be used to test these modules since they are independently structured with their own discretization scheme and solver methodology. Many of these modules have been independently tested by Professor C.P. Chen and his group at the University of Alabama at Huntsville (UAH) by interfacing them with own flow solver (MAST).

Performance of uncertainty quantification methodologies and linear solvers in cardiovascular simulations

NASA Astrophysics Data System (ADS)

Seo, Jongmin; Schiavazzi, Daniele; Marsden, Alison

2017-11-01

Cardiovascular simulations are increasingly used in clinical decision making, surgical planning, and disease diagnostics. Patient-specific modeling and simulation typically proceeds through a pipeline from anatomic model construction using medical image data to blood flow simulation and analysis. To provide confidence intervals on simulation predictions, we use an uncertainty quantification (UQ) framework to analyze the effects of numerous uncertainties that stem from clinical data acquisition, modeling, material properties, and boundary condition selection. However, UQ poses a computational challenge requiring multiple evaluations of the Navier-Stokes equations in complex 3-D models. To achieve efficiency in UQ problems with many function evaluations, we implement and compare a range of iterative linear solver and preconditioning techniques in our flow solver. We then discuss applications to patient-specific cardiovascular simulation and how the problem/boundary condition formulation in the solver affects the selection of the most efficient linear solver. Finally, we discuss performance improvements in the context of uncertainty propagation. Support from National Institute of Health (R01 EB018302) is greatly appreciated.

A new solver for granular avalanche simulation: Indoor experiment verification and field scale case study

NASA Astrophysics Data System (ADS)

Wang, XiaoLiang; Li, JiaChun

2017-12-01

A new solver based on the high-resolution scheme with novel treatments of source terms and interface capture for the Savage-Hutter model is developed to simulate granular avalanche flows. The capability to simulate flow spread and deposit processes is verified through indoor experiments of a two-dimensional granular avalanche. Parameter studies show that reduction in bed friction enhances runout efficiency, and that lower earth pressure restraints enlarge the deposit spread. The April 9, 2000, Yigong avalanche in Tibet, China, is simulated as a case study by this new solver. The predicted results, including evolution process, deposit spread, and hazard impacts, generally agree with site observations. It is concluded that the new solver for the Savage-Hutter equation provides a comprehensive software platform for granular avalanche simulation at both experimental and field scales. In particular, the solver can be a valuable tool for providing necessary information for hazard forecasts, disaster mitigation, and countermeasure decisions in mountainous areas.

SediFoam: A general-purpose, open-source CFD-DEM solver for particle-laden flow with emphasis on sediment transport

NASA Astrophysics Data System (ADS)

Sun, Rui; Xiao, Heng

2016-04-01

With the growth of available computational resource, CFD-DEM (computational fluid dynamics-discrete element method) becomes an increasingly promising and feasible approach for the study of sediment transport. Several existing CFD-DEM solvers are applied in chemical engineering and mining industry. However, a robust CFD-DEM solver for the simulation of sediment transport is still desirable. In this work, the development of a three-dimensional, massively parallel, and open-source CFD-DEM solver SediFoam is detailed. This solver is built based on open-source solvers OpenFOAM and LAMMPS. OpenFOAM is a CFD toolbox that can perform three-dimensional fluid flow simulations on unstructured meshes; LAMMPS is a massively parallel DEM solver for molecular dynamics. Several validation tests of SediFoam are performed using cases of a wide range of complexities. The results obtained in the present simulations are consistent with those in the literature, which demonstrates the capability of SediFoam for sediment transport applications. In addition to the validation test, the parallel efficiency of SediFoam is studied to test the performance of the code for large-scale and complex simulations. The parallel efficiency tests show that the scalability of SediFoam is satisfactory in the simulations using up to O(107) particles.

A coarse-grid projection method for accelerating incompressible flow computations

NASA Astrophysics Data System (ADS)

San, Omer; Staples, Anne

2011-11-01

We present a coarse-grid projection (CGP) algorithm for accelerating incompressible flow computations, which is applicable to methods involving Poisson equations as incompressibility constraints. CGP methodology is a modular approach that facilitates data transfer with simple interpolations and uses black-box solvers for the Poisson and advection-diffusion equations in the flow solver. Here, we investigate a particular CGP method for the vorticity-stream function formulation that uses the full weighting operation for mapping from fine to coarse grids, the third-order Runge-Kutta method for time stepping, and finite differences for the spatial discretization. After solving the Poisson equation on a coarsened grid, bilinear interpolation is used to obtain the fine data for consequent time stepping on the full grid. We compute several benchmark flows: the Taylor-Green vortex, a vortex pair merging, a double shear layer, decaying turbulence and the Taylor-Green vortex on a distorted grid. In all cases we use either FFT-based or V-cycle multigrid linear-cost Poisson solvers. Reducing the number of degrees of freedom of the Poisson solver by powers of two accelerates these computations while, for the first level of coarsening, retaining the same level of accuracy in the fine resolution vorticity field.

Numerical Simulations for Landing Gear Noise Generation and Radiation

NASA Technical Reports Server (NTRS)

Morris, Philip J.; Long, Lyle N.

2002-01-01

Aerodynamic noise from a landing gear in a uniform flow is computed using the Ffowcs Williams -Hawkings (FW-H) equation. The time accurate flow data on the surface is obtained using a finite volume flow solver on an unstructured and. The Ffowcs Williams-Hawkings equation is solved using surface integrals over the landing gear surface and over a permeable surface away from the landing gear. Two geometric configurations are tested in order to assess the impact of two lateral struts on the sound level and directivity in the far-field. Predictions from the Ffowcs Williams-Hawkings code are compared with direct calculations by the flow solver at several observer locations inside the computational domain. The permeable Ffowcs Williams-Hawkings surface predictions match those of the flow solver in the near-field. Far-field noise calculations coincide for both integration surfaces. The increase in drag observed between the two landing gear configurations is reflected in the sound pressure level and directivity mainly in the streamwise direction.

Application of a Modular Particle-Continuum Method to Partially Rarefied, Hypersonic Flow

NASA Astrophysics Data System (ADS)

Deschenes, Timothy R.; Boyd, Iain D.

2011-05-01

The Modular Particle-Continuum (MPC) method is used to simulate partially-rarefied, hypersonic flow over a sting-mounted planetary probe configuration. This hybrid method uses computational fluid dynamics (CFD) to solve the Navier-Stokes equations in regions that are continuum, while using direct simulation Monte Carlo (DSMC) in portions of the flow that are rarefied. The MPC method uses state-based coupling to pass information between the two flow solvers and decouples both time-step and mesh densities required by each solver. It is parallelized for distributed memory systems using dynamic domain decomposition and internal energy modes can be consistently modeled to be out of equilibrium with the translational mode in both solvers. The MPC results are compared to both full DSMC and CFD predictions and available experimental measurements. By using DSMC in only regions where the flow is nonequilibrium, the MPC method is able to reproduce full DSMC results down to the level of velocity and rotational energy probability density functions while requiring a fraction of the computational time.

An implicit higher-order spatially accurate scheme for solving time dependent flows on unstructured meshes

NASA Astrophysics Data System (ADS)

Tomaro, Robert F.

1998-07-01

The present research is aimed at developing a higher-order, spatially accurate scheme for both steady and unsteady flow simulations using unstructured meshes. The resulting scheme must work on a variety of general problems to ensure the creation of a flexible, reliable and accurate aerodynamic analysis tool. To calculate the flow around complex configurations, unstructured grids and the associated flow solvers have been developed. Efficient simulations require the minimum use of computer memory and computational times. Unstructured flow solvers typically require more computer memory than a structured flow solver due to the indirect addressing of the cells. The approach taken in the present research was to modify an existing three-dimensional unstructured flow solver to first decrease the computational time required for a solution and then to increase the spatial accuracy. The terms required to simulate flow involving non-stationary grids were also implemented. First, an implicit solution algorithm was implemented to replace the existing explicit procedure. Several test cases, including internal and external, inviscid and viscous, two-dimensional, three-dimensional and axi-symmetric problems, were simulated for comparison between the explicit and implicit solution procedures. The increased efficiency and robustness of modified code due to the implicit algorithm was demonstrated. Two unsteady test cases, a plunging airfoil and a wing undergoing bending and torsion, were simulated using the implicit algorithm modified to include the terms required for a moving and/or deforming grid. Secondly, a higher than second-order spatially accurate scheme was developed and implemented into the baseline code. Third- and fourth-order spatially accurate schemes were implemented and tested. The original dissipation was modified to include higher-order terms and modified near shock waves to limit pre- and post-shock oscillations. The unsteady cases were repeated using the higher-order spatially accurate code. The new solutions were compared with those obtained using the second-order spatially accurate scheme. Finally, the increased efficiency of using an implicit solution algorithm in a production Computational Fluid Dynamics flow solver was demonstrated for steady and unsteady flows. A third- and fourth-order spatially accurate scheme has been implemented creating a basis for a state-of-the-art aerodynamic analysis tool.

Reprint of Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

NASA Astrophysics Data System (ADS)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-04-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

NASA Astrophysics Data System (ADS)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-03-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

The unstaggered extension to GFDL's FV3 dynamical core on the cubed-sphere

NASA Astrophysics Data System (ADS)

Chen, X.; Lin, S. J.; Harris, L.

2017-12-01

Finite-volume schemes have become popular for atmospheric transport since they provide intrinsic mass conservation to constituent species. Many CFD codes use unstaggered discretizations for finite volume methods with an approximate Riemann solver. However, this approach is inefficient for geophysical flows due to the complexity of the Riemann solver. We introduce a Low Mach number Approximate Riemann Solver (LMARS) simplified using assumptions appropriate for atmospheric flows: the wind speed is much slower than the sound speed, weak discontinuities, and locally uniform sound wave velocity. LMARS makes possible a Riemann-solver-based dynamical core comparable in computational efficiency to many current dynamical cores. We will present a 3D finite-volume dynamical core using LMARS in a cubed-sphere geometry with a vertically Lagrangian discretization. Results from standard idealized test cases will be discussed.

TOUGH3: A new efficient version of the TOUGH suite of multiphase flow and transport simulators

NASA Astrophysics Data System (ADS)

Jung, Yoojin; Pau, George Shu Heng; Finsterle, Stefan; Pollyea, Ryan M.

2017-11-01

The TOUGH suite of nonisothermal multiphase flow and transport simulators has been updated by various developers over many years to address a vast range of challenging subsurface problems. The increasing complexity of the simulated processes as well as the growing size of model domains that need to be handled call for an improvement in the simulator's computational robustness and efficiency. Moreover, modifications have been frequently introduced independently, resulting in multiple versions of TOUGH that (1) led to inconsistencies in feature implementation and usage, (2) made code maintenance and development inefficient, and (3) caused confusion to users and developers. TOUGH3-a new base version of TOUGH-addresses these issues. It consolidates both the serial (TOUGH2 V2.1) and parallel (TOUGH2-MP V2.0) implementations, enabling simulations to be performed on desktop computers and supercomputers using a single code. New PETSc parallel linear solvers are added to the existing serial solvers of TOUGH2 and the Aztec solver used in TOUGH2-MP. The PETSc solvers generally perform better than the Aztec solvers in parallel and the internal TOUGH3 linear solver in serial. TOUGH3 also incorporates many new features, addresses bugs, and improves the flexibility of data handling. Due to the improved capabilities and usability, TOUGH3 is more robust and efficient for solving tough and computationally demanding problems in diverse scientific and practical applications related to subsurface flow modeling.

An unstructured shock-fitting solver for hypersonic plasma flows in chemical non-equilibrium

NASA Astrophysics Data System (ADS)

Pepe, R.; Bonfiglioli, A.; D'Angola, A.; Colonna, G.; Paciorri, R.

2015-11-01

A CFD solver, using Residual Distribution Schemes on unstructured grids, has been extended to deal with inviscid chemical non-equilibrium flows. The conservative equations have been coupled with a kinetic model for argon plasma which includes the argon metastable state as independent species, taking into account electron-atom and atom-atom processes. Results in the case of an hypersonic flow around an infinite cylinder, obtained by using both shock-capturing and shock-fitting approaches, show higher accuracy of the shock-fitting approach.

Adaptive Discontinuous Evolution Galerkin Method for Dry Atmospheric Flow

DTIC Science & Technology

2013-04-02

standard one-dimensional approximate Riemann solver used for the flux integration demonstrate better stability, accuracy as well as reliability of the...discontinuous evolution Galerkin method for dry atmospheric convection. Comparisons with the standard one-dimensional approximate Riemann solver used...instead of a standard one- dimensional approximate Riemann solver , the flux integration within the discontinuous Galerkin method is now realized by

Methods for Solving Gas Damping Problems in Perforated Microstructures Using a 2D Finite-Element Solver

PubMed Central

Veijola, Timo; Råback, Peter

2007-01-01

We present a straightforward method to solve gas damping problems for perforated structures in two dimensions (2D) utilising a Perforation Profile Reynolds (PPR) solver. The PPR equation is an extended Reynolds equation that includes additional terms modelling the leakage flow through the perforations, and variable diffusivity and compressibility profiles. The solution method consists of two phases: 1) determination of the specific admittance profile and relative diffusivity (and relative compressibility) profiles due to the perforation, and 2) solution of the PPR equation with a FEM solver in 2D. Rarefied gas corrections in the slip-flow region are also included. Analytic profiles for circular and square holes with slip conditions are presented in the paper. To verify the method, square perforated dampers with 16–64 holes were simulated with a three-dimensional (3D) Navier-Stokes solver, a homogenised extended Reynolds solver, and a 2D PPR solver. Cases for both translational (in normal to the surfaces) and torsional motion were simulated. The presented method extends the region of accurate simulation of perforated structures to cases where the homogenisation method is inaccurate and the full 3D Navier-Stokes simulation is too time-consuming.

LAVA Simulations for the 3rd AIAA CFD High Lift Prediction Workshop with Body Fitted Grids

NASA Technical Reports Server (NTRS)

Jensen, James C.; Stich, Gerrit-Daniel; Housman, Jeffrey A.; Denison, Marie; Kiris, Cetin C.

2018-01-01

In response to the 3rd AIAA CFD High Lift Prediction Workshop, the workshop cases were analyzed using Reynolds-averaged Navier-Stokes flow solvers within the Launch Ascent and Vehicle Aerodynamics (LAVA) solver framework. For the workshop cases the advantages and limitations of both overset-structured an unstructured polyhedral meshes were assessed. The workshop included 3 cases: a 2D airfoil validation case, a mesh convergence study using the High Lift Common Research Model, and a nacelle/pylon integration study using the JAXA (Japan Aerospace Exploration Agency) Standard Model. The 2D airfoil case from the workshop is used to verify the implementation of the Spalart-Allmaras turbulence model along with some of its variants within the solver. The High Lift Common Research Model case is used to assess solver performance and accuracy at varying mesh resolutions, as well as identify the minimum mesh fidelity required for LAVA on this class of problem. The JAXA Standard Model case is used to assess the solver's sensitivity to the turbulence model and to compare the structured and unstructured mesh paradigms. These workshop cases have helped establish best practices for high lift flow configurations for the LAVA solver.

An evaluation of three two-dimensional computational fluid dynamics codes including low Reynolds numbers and transonic Mach numbers

NASA Technical Reports Server (NTRS)

Hicks, Raymond M.; Cliff, Susan E.

1991-01-01

Full-potential, Euler, and Navier-Stokes computational fluid dynamics (CFD) codes were evaluated for use in analyzing the flow field about airfoils sections operating at Mach numbers from 0.20 to 0.60 and Reynolds numbers from 500,000 to 2,000,000. The potential code (LBAUER) includes weakly coupled integral boundary layer equations for laminar and turbulent flow with simple transition and separation models. The Navier-Stokes code (ARC2D) uses the thin-layer formulation of the Reynolds-averaged equations with an algebraic turbulence model. The Euler code (ISES) includes strongly coupled integral boundary layer equations and advanced transition and separation calculations with the capability to model laminar separation bubbles and limited zones of turbulent separation. The best experiment/CFD correlation was obtained with the Euler code because its boundary layer equations model the physics of the flow better than the other two codes. An unusual reversal of boundary layer separation with increasing angle of attack, following initial shock formation on the upper surface of the airfoil, was found in the experiment data. This phenomenon was not predicted by the CFD codes evaluated.

Euler equation existence, non-uniqueness and mesh converged statistics

PubMed Central

Glimm, James; Sharp, David H.; Lim, Hyunkyung; Kaufman, Ryan; Hu, Wenlin

2015-01-01

We review existence and non-uniqueness results for the Euler equation of fluid flow. These results are placed in the context of physical models and their solutions. Non-uniqueness is in direct conflict with the purpose of practical simulations, so that a mitigating strategy, outlined here, is important. We illustrate these issues in an examination of mesh converged turbulent statistics, with comparison to laboratory experiments. PMID:26261361

Hydrodynamic Drag Reduction

DTIC Science & Technology

2015-04-01

Computational Engineering unstructured RANS/LES/DES solver , Tenasi, was used to predict drag and simulate the free surface flow around the ACV over a...using a second-order accurate Roe approximate Riemann scheme, while viscous fluxes are evaluated using a second-order directional derivative approach...Predictions of rigid body ship motions for the SI75 container ship in incident waves and methodology for a one-way coupling of the Tenasi flow solver

Prediction of unsteady transonic flow around missile configurations

NASA Technical Reports Server (NTRS)

Nixon, D.; Reisenthel, P. H.; Torres, T. O.; Klopfer, G. H.

1990-01-01

This paper describes the preliminary development of a method for predicting the unsteady transonic flow around missiles at transonic and supersonic speeds, with the final goal of developing a computer code for use in aeroelastic calculations or during maneuvers. The basic equations derived for this method are an extension of those derived by Klopfer and Nixon (1989) for steady flow and are a subset of the Euler equations. In this approach, the five Euler equations are reduced to an equation similar to the three-dimensional unsteady potential equation, and a two-dimensional Poisson equation. In addition, one of the equations in this method is almost identical to the potential equation for which there are well tested computer codes, allowing the development of a prediction method based in part on proved technology.

Transonic flow solutions using a composite velocity procedure for potential, Euler and RNS equations

NASA Technical Reports Server (NTRS)

Gordnier, R. E.; Rubin, S. G.

1986-01-01

Solutions for transonic viscous and inviscid flows using a composite velocity procedure are presented. The velocity components of the compressible flow equations are written in terms of a multiplicative composite consisting of a viscous or rotational velocity and an inviscid, irrotational, potential-like function. This provides for an efficient solution procedure that is locally representative of both asymptotic inviscid and boundary layer theories. A modified conservative form of the axial momentum equation that is required to obtain rotational solutions in the inviscid region is presented and a combined conservation/nonconservation form is applied for evaluation of the reduced Navier-Stokes (RNS), Euler and potential equations. A variety of results is presented and the effects of the approximations on entropy production, shock capturing, and viscous interaction are discussed.

A Survey of Solver-Related Geometry and Meshing Issues

NASA Technical Reports Server (NTRS)

Masters, James; Daniel, Derick; Gudenkauf, Jared; Hine, David; Sideroff, Chris

2016-01-01

There is a concern in the computational fluid dynamics community that mesh generation is a significant bottleneck in the CFD workflow. This is one of several papers that will help set the stage for a moderated panel discussion addressing this issue. Although certain general "rules of thumb" and a priori mesh metrics can be used to ensure that some base level of mesh quality is achieved, inadequate consideration is often given to the type of solver or particular flow regime on which the mesh will be utilized. This paper explores how an analyst may want to think differently about a mesh based on considerations such as if a flow is compressible vs. incompressible or hypersonic vs. subsonic or if the solver is node-centered vs. cell-centered. This paper is a high-level investigation intended to provide general insight into how considering the nature of the solver or flow when performing mesh generation has the potential to increase the accuracy and/or robustness of the solution and drive the mesh generation process to a state where it is no longer a hindrance to the analysis process.

LSPRAY-IV: A Lagrangian Spray Module

NASA Technical Reports Server (NTRS)

Raju, M. S.

2012-01-01

LSPRAY-IV is a Lagrangian spray solver developed for application with parallel computing and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type for the gas flow grid representation. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray. Some important research areas covered as a part of the code development are: (1) the extension of combined CFD/scalar-Monte- Carlo-PDF method to spray modeling, (2) the multi-component liquid spray modeling, and (3) the assessment of various atomization models used in spray calculations. The current version contains the extension to the modeling of superheated sprays. The manual provides the user with an understanding of various models involved in the spray formulation, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers.

Helicity and singular structures in fluid dynamics

PubMed Central

Moffatt, H. Keith

2014-01-01

Helicity is, like energy, a quadratic invariant of the Euler equations of ideal fluid flow, although, unlike energy, it is not sign definite. In physical terms, it represents the degree of linkage of the vortex lines of a flow, conserved when conditions are such that these vortex lines are frozen in the fluid. Some basic properties of helicity are reviewed, with particular reference to (i) its crucial role in the dynamo excitation of magnetic fields in cosmic systems; (ii) its bearing on the existence of Euler flows of arbitrarily complex streamline topology; (iii) the constraining role of the analogous magnetic helicity in the determination of stable knotted minimum-energy magnetostatic structures; and (iv) its role in depleting nonlinearity in the Navier-Stokes equations, with implications for the coherent structures and energy cascade of turbulence. In a final section, some singular phenomena in low Reynolds number flows are briefly described. PMID:24520175

Implicit flux-split schemes for the Euler equations

NASA Technical Reports Server (NTRS)

Thomas, J. L.; Walters, R. W.; Van Leer, B.

1985-01-01

Recent progress in the development of implicit algorithms for the Euler equations using the flux-vector splitting method is described. Comparisons of the relative efficiency of relaxation and spatially-split approximately factored methods on a vector processor for two-dimensional flows are made. For transonic flows, the higher convergence rate per iteration of the Gauss-Seidel relaxation algorithms, which are only partially vectorizable, is amply compensated for by the faster computational rate per iteration of the approximately factored algorithm. For supersonic flows, the fully-upwind line-relaxation method is more efficient since the numerical domain of dependence is more closely matched to the physical domain of dependence. A hybrid three-dimensional algorithm using relaxation in one coordinate direction and approximate factorization in the cross-flow plane is developed and applied to a forebody shape at supersonic speeds and a swept, tapered wing at transonic speeds.

Simulation of violent free surface flow by AMR method

NASA Astrophysics Data System (ADS)

Hu, Changhong; Liu, Cheng

2018-05-01

A novel CFD approach based on adaptive mesh refinement (AMR) technique is being developed for numerical simulation of violent free surface flows. CIP method is applied to the flow solver and tangent of hyperbola for interface capturing with slope weighting (THINC/SW) scheme is implemented as the free surface capturing scheme. The PETSc library is adopted to solve the linear system. The linear solver is redesigned and modified to satisfy the requirement of the AMR mesh topology. In this paper, our CFD method is outlined and newly obtained results on numerical simulation of violent free surface flows are presented.

A Parallel Cartesian Approach for External Aerodynamics of Vehicles with Complex Geometry

NASA Technical Reports Server (NTRS)

Aftosmis, M. J.; Berger, M. J.; Adomavicius, G.

2001-01-01

This workshop paper presents the current status in the development of a new approach for the solution of the Euler equations on Cartesian meshes with embedded boundaries in three dimensions on distributed and shared memory architectures. The approach uses adaptively refined Cartesian hexahedra to fill the computational domain. Where these cells intersect the geometry, they are cut by the boundary into arbitrarily shaped polyhedra which receive special treatment by the solver. The presentation documents a newly developed multilevel upwind solver based on a flexible domain-decomposition strategy. One novel aspect of the work is its use of space-filling curves (SFC) for memory efficient on-the-fly parallelization, dynamic re-partitioning and automatic coarse mesh generation. Within each subdomain the approach employs a variety reordering techniques so that relevant data are on the same page in memory permitting high-performance on cache-based processors. Details of the on-the-fly SFC based partitioning are presented as are construction rules for the automatic coarse mesh generation. After describing the approach, the paper uses model problems and 3- D configurations to both verify and validate the solver. The model problems demonstrate that second-order accuracy is maintained despite the presence of the irregular cut-cells in the mesh. In addition, it examines both parallel efficiency and convergence behavior. These investigations demonstrate a parallel speed-up in excess of 28 on 32 processors of an SGI Origin 2000 system and confirm that mesh partitioning has no effect on convergence behavior.

Computational Fluid Dynamics Analysis Success Stories of X-Plane Design to Flight Test

NASA Technical Reports Server (NTRS)

Cosentino, Gary B.

2008-01-01

Examples of the design and flight test of three true X-planes are described, particularly X-plane design techniques that relied heavily on computational fluid dynamics(CFD) analysis. Three examples are presented: the X-36 Tailless Fighter Agility Research Aircraft, the X-45A Unmanned Combat Air Vehicle, and the X-48B Blended Wing Body Demonstrator Aircraft. An overview is presented of the uses of CFD analysis, comparison and contrast with wind tunnel testing, and information derived from CFD analysis that directly related to successful flight test. Lessons learned on the proper and improper application of CFD analysis are presented. Highlights of the flight-test results of the three example X-planes are presented. This report discusses developing an aircraft shape from early concept and three-dimensional modeling through CFD analysis, wind tunnel testing, further refined CFD analysis, and, finally, flight. An overview of the areas in which CFD analysis does and does not perform well during this process is presented. How wind tunnel testing complements, calibrates, and verifies CFD analysis is discussed. Lessons learned revealing circumstances under which CFD analysis results can be misleading are given. Strengths and weaknesses of the various flow solvers, including panel methods, Euler, and Navier-Stokes techniques, are discussed.

Application of an Upwind High Resolution Finite-Differencing Scheme and Multigrid Method in Steady-State Incompressible Flow Simulations

NASA Technical Reports Server (NTRS)

Yang, Cheng I.; Guo, Yan-Hu; Liu, C.- H.

1996-01-01

The analysis and design of a submarine propulsor requires the ability to predict the characteristics of both laminar and turbulent flows to a higher degree of accuracy. This report presents results of certain benchmark computations based on an upwind, high-resolution, finite-differencing Navier-Stokes solver. The purpose of the computations is to evaluate the ability, the accuracy and the performance of the solver in the simulation of detailed features of viscous flows. Features of interest include flow separation and reattachment, surface pressure and skin friction distributions. Those features are particularly relevant to the propulsor analysis. Test cases with a wide range of Reynolds numbers are selected; therefore, the effects of the convective and the diffusive terms of the solver can be evaluated separately. Test cases include flows over bluff bodies, such as circular cylinders and spheres, at various low Reynolds numbers, flows over a flat plate with and without turbulence effects, and turbulent flows over axisymmetric bodies with and without propulsor effects. Finally, to enhance the iterative solution procedure, a full approximation scheme V-cycle multigrid method is implemented. Preliminary results indicate that the method significantly reduces the computational effort.

A multi-scale network method for two-phase flow in porous media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khayrat, Karim, E-mail: khayratk@ifd.mavt.ethz.ch; Jenny, Patrick

Pore-network models of porous media are useful in the study of pore-scale flow in porous media. In order to extract macroscopic properties from flow simulations in pore-networks, it is crucial the networks are large enough to be considered representative elementary volumes. However, existing two-phase network flow solvers are limited to relatively small domains. For this purpose, a multi-scale pore-network (MSPN) method, which takes into account flow-rate effects and can simulate larger domains compared to existing methods, was developed. In our solution algorithm, a large pore network is partitioned into several smaller sub-networks. The algorithm to advance the fluid interfaces withinmore » each subnetwork consists of three steps. First, a global pressure problem on the network is solved approximately using the multiscale finite volume (MSFV) method. Next, the fluxes across the subnetworks are computed. Lastly, using fluxes as boundary conditions, a dynamic two-phase flow solver is used to advance the solution in time. Simulation results of drainage scenarios at different capillary numbers and unfavourable viscosity ratios are presented and used to validate the MSPN method against solutions obtained by an existing dynamic network flow solver.« less

An implicit numerical scheme for the simulation of internal viscous flows on unstructured grids

NASA Technical Reports Server (NTRS)

Jorgenson, Philip C. E.; Pletcher, Richard H.

1994-01-01

The Navier-Stokes equations are solved numerically for two-dimensional steady viscous laminar flows. The grids are generated based on the method of Delaunay triangulation. A finite-volume approach is used to discretize the conservation law form of the compressible flow equations written in terms of primitive variables. A preconditioning matrix is added to the equations so that low Mach number flows can be solved economically. The equations are time marched using either an implicit Gauss-Seidel iterative procedure or a solver based on a conjugate gradient like method. A four color scheme is employed to vectorize the block Gauss-Seidel relaxation procedure. This increases the memory requirements minimally and decreases the computer time spent solving the resulting system of equations substantially. A factor of 7.6 speed up in the matrix solver is typical for the viscous equations. Numerical results are obtained for inviscid flow over a bump in a channel at subsonic and transonic conditions for validation with structured solvers. Viscous results are computed for developing flow in a channel, a symmetric sudden expansion, periodic tandem cylinders in a cross-flow, and a four-port valve. Comparisons are made with available results obtained by other investigators.

Gpu Implementation of a Viscous Flow Solver on Unstructured Grids

NASA Astrophysics Data System (ADS)

Xu, Tianhao; Chen, Long

2016-06-01

Graphics processing units have gained popularities in scientific computing over past several years due to their outstanding parallel computing capability. Computational fluid dynamics applications involve large amounts of calculations, therefore a latest GPU card is preferable of which the peak computing performance and memory bandwidth are much better than a contemporary high-end CPU. We herein focus on the detailed implementation of our GPU targeting Reynolds-averaged Navier-Stokes equations solver based on finite-volume method. The solver employs a vertex-centered scheme on unstructured grids for the sake of being capable of handling complex topologies. Multiple optimizations are carried out to improve the memory accessing performance and kernel utilization. Both steady and unsteady flow simulation cases are carried out using explicit Runge-Kutta scheme. The solver with GPU acceleration in this paper is demonstrated to have competitive advantages over the CPU targeting one.

A Parallel Multigrid Solver for Viscous Flows on Anisotropic Structured Grids

NASA Technical Reports Server (NTRS)

Prieto, Manuel; Montero, Ruben S.; Llorente, Ignacio M.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

This paper presents an efficient parallel multigrid solver for speeding up the computation of a 3-D model that treats the flow of a viscous fluid over a flat plate. The main interest of this simulation lies in exhibiting some basic difficulties that prevent optimal multigrid efficiencies from being achieved. As the computing platform, we have used Coral, a Beowulf-class system based on Intel Pentium processors and equipped with GigaNet cLAN and switched Fast Ethernet networks. Our study not only examines the scalability of the solver but also includes a performance evaluation of Coral where the investigated solver has been used to compare several of its design choices, namely, the interconnection network (GigaNet versus switched Fast-Ethernet) and the node configuration (dual nodes versus single nodes). As a reference, the performance results have been compared with those obtained with the NAS-MG benchmark.

Evaluating the performance of the two-phase flow solver interFoam

NASA Astrophysics Data System (ADS)

Deshpande, Suraj S.; Anumolu, Lakshman; Trujillo, Mario F.

2012-01-01

The performance of the open source multiphase flow solver, interFoam, is evaluated in this work. The solver is based on a modified volume of fluid (VoF) approach, which incorporates an interfacial compression flux term to mitigate the effects of numerical smearing of the interface. It forms a part of the C + + libraries and utilities of OpenFOAM and is gaining popularity in the multiphase flow research community. However, to the best of our knowledge, the evaluation of this solver is confined to the validation tests of specific interest to the users of the code and the extent of its applicability to a wide range of multiphase flow situations remains to be explored. In this work, we have performed a thorough investigation of the solver performance using a variety of verification and validation test cases, which include (i) verification tests for pure advection (kinematics), (ii) dynamics in the high Weber number limit and (iii) dynamics of surface tension-dominated flows. With respect to (i), the kinematics tests show that the performance of interFoam is generally comparable with the recent algebraic VoF algorithms; however, it is noticeably worse than the geometric reconstruction schemes. For (ii), the simulations of inertia-dominated flows with large density ratios {\\sim }\\mathscr {O}(10^3) yielded excellent agreement with analytical and experimental results. In regime (iii), where surface tension is important, consistency of pressure-surface tension formulation and accuracy of curvature are important, as established by Francois et al (2006 J. Comput. Phys. 213 141-73). Several verification tests were performed along these lines and the main findings are: (a) the algorithm of interFoam ensures a consistent formulation of pressure and surface tension; (b) the curvatures computed by the solver converge to a value slightly (10%) different from the analytical value and a scope for improvement exists in this respect. To reduce the disruptive effects of spurious currents, we followed the analysis of Galusinski and Vigneaux (2008 J. Comput. Phys. 227 6140-64) and arrived at the following criterion for stable capillary simulations for interFoam: \\Delta t\\leqslant \\max (10\\tau _\\mu , 0.1\\tau _\\rho) where \\tau _\\mu =\\mu \\Delta x/\\sigma ,~ {and}~\\tau _\\rho =\\sqrt {\\rho \\Delta x^3/\\sigma } . Finally, some capillary flows relevant to atomization were simulated, resulting in good agreement with the results from the literature.

The Thin Oil Film Equation

NASA Technical Reports Server (NTRS)

Brown, James L.; Naughton, Jonathan W.

1999-01-01

A thin film of oil on a surface responds primarily to the wall shear stress generated on that surface by a three-dimensional flow. The oil film is also subject to wall pressure gradients, surface tension effects and gravity. The partial differential equation governing the oil film flow is shown to be related to Burgers' equation. Analytical and numerical methods for solving the thin oil film equation are presented. A direct numerical solver is developed where the wall shear stress variation on the surface is known and which solves for the oil film thickness spatial and time variation on the surface. An inverse numerical solver is also developed where the oil film thickness spatial variation over the surface at two discrete times is known and which solves for the wall shear stress variation over the test surface. A One-Time-Level inverse solver is also demonstrated. The inverse numerical solver provides a mathematically rigorous basis for an improved form of a wall shear stress instrument suitable for application to complex three-dimensional flows. To demonstrate the complexity of flows for which these oil film methods are now suitable, extensive examination is accomplished for these analytical and numerical methods as applied to a thin oil film in the vicinity of a three-dimensional saddle of separation.

On the Solution of the Three-Dimensional Flowfield About a Flow-Through Nacelle. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Compton, William Bernard

1985-01-01

The solution of the three dimensional flow field for a flow through nacelle was studied. Both inviscid and viscous inviscid interacting solutions were examined. Inviscid solutions were obtained with two different computational procedures for solving the three dimensional Euler equations. The first procedure employs an alternating direction implicit numerical algorithm, and required the development of a complete computational model for the nacelle problem. The second computational technique employs a fourth order Runge-Kutta numerical algorithm which was modified to fit the nacelle problem. Viscous effects on the flow field were evaluated with a viscous inviscid interacting computational model. This model was constructed by coupling the explicit Euler solution procedure with a flag entrainment boundary layer solution procedure in a global iteration scheme. The computational techniques were used to compute the flow field for a long duct turbofan engine nacelle at free stream Mach numbers of 0.80 and 0.94 and angles of attack of 0 and 4 deg.

Fast preconditioned multigrid solution of the Euler and Navier-Stokes equations for steady, compressible flows

NASA Astrophysics Data System (ADS)

Caughey, David A.; Jameson, Antony

2003-10-01

New versions of implicit algorithms are developed for the efficient solution of the Euler and Navier-Stokes equations of compressible flow. The methods are based on a preconditioned, lower-upper (LU) implementation of a non-linear, symmetric Gauss-Seidel (SGS) algorithm for use as a smoothing algorithm in a multigrid method. Previously, this method had been implemented for flows in quasi-one-dimensional ducts and for two-dimensional flows past airfoils on boundary-conforming O-type grids for a variety of symmetric limited positive (SLIP) spatial approximations, including the scalar dissipation and convective upwind split pressure (CUSP) schemes. Here results are presented for both inviscid and viscous (laminar) flows past airfoils on boundary-conforming C-type grids. The method is significantly faster than earlier explicit or implicit methods for inviscid problems, allowing solution of these problems to the level of truncation error in three to five multigrid cycles. Viscous solutions still require as many as twenty multigrid cycles.

Investigation of instabilities affecting detonations: Improving the resolution using block-structured adaptive mesh refinement

NASA Astrophysics Data System (ADS)

Ravindran, Prashaanth

The unstable nature of detonation waves is a result of the critical relationship between the hydrodynamic shock and the chemical reactions sustaining the shock. A perturbative analysis of the critical point is quite challenging due to the multiple spatio-temporal scales involved along with the non-linear nature of the shock-reaction mechanism. The author's research attempts to provide detailed resolution of the instabilities at the shock front. Another key aspect of the present research is to develop an understanding of the causality between the non-linear dynamics of the front and the eventual breakdown of the sub-structures. An accurate numerical simulation of detonation waves requires a very efficient solution of the Euler equations in conservation form with detailed, non-equilibrium chemistry. The difference in the flow and reaction length scales results in very stiff source terms, requiring the problem to be solved with adaptive mesh refinement. For this purpose, Berger-Colella's block-structured adaptive mesh refinement (AMR) strategy has been developed and applied to time-explicit finite volume methods. The block-structured technique uses a hierarchy of parent-child sub-grids, integrated recursively over time. One novel approach to partition the problem within a large supercomputer was the use of modified Peano-Hilbert space filling curves. The AMR framework was merged with CLAWPACK, a package providing finite volume numerical methods tailored for wave-propagation problems. The stiffness problem is bypassed by using a 1st order Godunov or a 2nd order Strang splitting technique, where the flow variables and source terms are integrated independently. A linearly explicit fourth-order Runge-Kutta integrator is used for the flow, and an ODE solver was used to overcome the numerical stiffness. Second-order spatial resolution is obtained by using a second-order Roe-HLL scheme with the inclusion of numerical viscosity to stabilize the solution near the discontinuity. The scheme is made monotonic by coupling the van Albada limiter with the higher order MUSCL-Hancock extrapolation to the primitive variables of the Euler equations. Simulations using simplified single-step and detailed chemical kinetics have been provided. In detonations with simplified chemistry, the one-dimensional longitudinal instabilities have been simulated, and a mechanism forcing the collapse of the period-doubling modes was identified. The transverse instabilities were simulated for a 2D detonation, and the corresponding transverse wave was shown to be unstable with a periodic normal mode. Also, a Floquet analysis was carried out with the three-dimensional inviscid Euler equations for a longitudinally stable case. Using domain decomposition to identify the global eigenfunctions corresponding to the two least stable eigenvalues, it was found that the bifurcation of limit cycles in three dimensions follows a period doubling process similar to that proven to occur in one dimension and it is because of transverse instabilities. For detonations with detailed chemistry, the one dimensional simulations for two cases were presented and validated with experimental results. The 2D simulation shows the re-initiation of the triple point leading to the formation of cellular structure of the detonation wave. Some of the important features in the front were identified and explained.

Comparison of an algebraic multigrid algorithm to two iterative solvers used for modeling ground water flow and transport

USGS Publications Warehouse

Detwiler, R.L.; Mehl, S.; Rajaram, H.; Cheung, W.W.

2002-01-01

Numerical solution of large-scale ground water flow and transport problems is often constrained by the convergence behavior of the iterative solvers used to solve the resulting systems of equations. We demonstrate the ability of an algebraic multigrid algorithm (AMG) to efficiently solve the large, sparse systems of equations that result from computational models of ground water flow and transport in large and complex domains. Unlike geometric multigrid methods, this algorithm is applicable to problems in complex flow geometries, such as those encountered in pore-scale modeling of two-phase flow and transport. We integrated AMG into MODFLOW 2000 to compare two- and three-dimensional flow simulations using AMG to simulations using PCG2, a preconditioned conjugate gradient solver that uses the modified incomplete Cholesky preconditioner and is included with MODFLOW 2000. CPU times required for convergence with AMG were up to 140 times faster than those for PCG2. The cost of this increased speed was up to a nine-fold increase in required random access memory (RAM) for the three-dimensional problems and up to a four-fold increase in required RAM for the two-dimensional problems. We also compared two-dimensional numerical simulations of steady-state transport using AMG and the generalized minimum residual method with an incomplete LU-decomposition preconditioner. For these transport simulations, AMG yielded increased speeds of up to 17 times with only a 20% increase in required RAM. The ability of AMG to solve flow and transport problems in large, complex flow systems and its ready availability make it an ideal solver for use in both field-scale and pore-scale modeling.

Progress Toward Overset-Grid Moving Body Capability for USM3D Unstructured Flow Solver

NASA Technical Reports Server (NTRS)

Pandyna, Mohagna J.; Frink, Neal T.; Noack, Ralph W.

2005-01-01

A static and dynamic Chimera overset-grid capability is added to an established NASA tetrahedral unstructured parallel Navier-Stokes flow solver, USM3D. Modifications to the solver primarily consist of a few strategic calls to the Donor interpolation Receptor Transaction library (DiRTlib) to facilitate communication of solution information between various grids. The assembly of multiple overlapping grids into a single-zone composite grid is performed by the Structured, Unstructured and Generalized Grid AssembleR (SUGGAR) code. Several test cases are presented to verify the implementation, assess overset-grid solution accuracy and convergence relative to single-grid solutions, and demonstrate the prescribed relative grid motion capability.

Fast immersed interface Poisson solver for 3D unbounded problems around arbitrary geometries

NASA Astrophysics Data System (ADS)

Gillis, T.; Winckelmans, G.; Chatelain, P.

2018-02-01

We present a fast and efficient Fourier-based solver for the Poisson problem around an arbitrary geometry in an unbounded 3D domain. This solver merges two rewarding approaches, the lattice Green's function method and the immersed interface method, using the Sherman-Morrison-Woodbury decomposition formula. The method is intended to be second order up to the boundary. This is verified on two potential flow benchmarks. We also further analyse the iterative process and the convergence behavior of the proposed algorithm. The method is applicable to a wide range of problems involving a Poisson equation around inner bodies, which goes well beyond the present validation on potential flows.

Adding Complex Terrain and Stable Atmospheric Condition Capability to the Simulator for On/Offshore Wind Farm Applications (SOWFA) (Presentation)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Churchfield, M. J.

This presentation describes changes made to NREL's OpenFOAM-based wind plant aerodynamics solver so that it can compute the stably stratified atmospheric boundary layer and flow over terrain. Background about the flow solver, the Simulator for Off/Onshore Wind Farm Applications (SOWFA) is given, followed by details of the stable stratification/complex terrain modifications to SOWFA, along with some preliminary results calculations of a stable atmospheric boundary layer and flow over a simple set of hills.

Transonic Drag Prediction on a DLR-F6 Transport Configuration Using Unstructured Grid Solvers

NASA Technical Reports Server (NTRS)

Lee-Rausch, E. M.; Frink, N. T.; Mavriplis, D. J.; Rausch, R. D.; Milholen, W. E.

2004-01-01

A second international AIAA Drag Prediction Workshop (DPW-II) was organized and held in Orlando Florida on June 21-22, 2003. The primary purpose was to inves- tigate the code-to-code uncertainty. address the sensitivity of the drag prediction to grid size and quantify the uncertainty in predicting nacelle/pylon drag increments at a transonic cruise condition. This paper presents an in-depth analysis of the DPW-II computational results from three state-of-the-art unstructured grid Navier-Stokes flow solvers exercised on similar families of tetrahedral grids. The flow solvers are USM3D - a tetrahedral cell-centered upwind solver. FUN3D - a tetrahedral node-centered upwind solver, and NSU3D - a general element node-centered central-differenced solver. For the wingbody, the total drag predicted for a constant-lift transonic cruise condition showed a decrease in code-to-code variation with grid refinement as expected. For the same flight condition, the wing/body/nacelle/pylon total drag and the nacelle/pylon drag increment predicted showed an increase in code-to-code variation with grid refinement. Although the range in total drag for the wingbody fine grids was only 5 counts, a code-to-code comparison of surface pressures and surface restricted streamlines indicated that the three solvers were not all converging to the same flow solutions- different shock locations and separation patterns were evident. Similarly, the wing/body/nacelle/pylon solutions did not appear to be converging to the same flow solutions. Overall, grid refinement did not consistently improve the correlation with experimental data for either the wingbody or the wing/body/nacelle pylon configuration. Although the absolute values of total drag predicted by two of the solvers for the medium and fine grids did not compare well with the experiment, the incremental drag predictions were within plus or minus 3 counts of the experimental data. The correlation with experimental incremental drag was not significantly changed by specifying transition. Although the sources of code-to-code variation in force and moment predictions for the three unstructured grid codes have not yet been identified, the current study reinforces the necessity of applying multiple codes to the same application to assess uncertainty.

Parameter Optimization for Turbulent Reacting Flows Using Adjoints

NASA Astrophysics Data System (ADS)

Lapointe, Caelan; Hamlington, Peter E.

2017-11-01

The formulation of a new adjoint solver for topology optimization of turbulent reacting flows is presented. This solver provides novel configurations (e.g., geometries and operating conditions) based on desired system outcomes (i.e., objective functions) for complex reacting flow problems of practical interest. For many such problems, it would be desirable to know optimal values of design parameters (e.g., physical dimensions, fuel-oxidizer ratios, and inflow-outflow conditions) prior to real-world manufacture and testing, which can be expensive, time-consuming, and dangerous. However, computational optimization of these problems is made difficult by the complexity of most reacting flows, necessitating the use of gradient-based optimization techniques in order to explore a wide design space at manageable computational cost. The adjoint method is an attractive way to obtain the required gradients, because the cost of the method is determined by the dimension of the objective function rather than the size of the design space. Here, the formulation of a novel solver is outlined that enables gradient-based parameter optimization of turbulent reacting flows using the discrete adjoint method. Initial results and an outlook for future research directions are provided.

Ames Optimized TCA Configuration

NASA Technical Reports Server (NTRS)

Cliff, Susan E.; Reuther, James J.; Hicks, Raymond M.

1999-01-01

Configuration design at Ames was carried out with the SYN87-SB (single block) Euler code using a 193 x 49 x 65 C-H grid. The Euler solver is coupled to the constrained (NPSOL) and the unconstrained (QNMDIF) optimization packages. Since the single block grid is able to model only wing-body configurations, the nacelle/diverter effects were included in the optimization process by SYN87's option to superimpose the nacelle/diverter interference pressures on the wing. These interference pressures were calculated using the AIRPLANE code. AIRPLANE is an Euler solver that uses a unstructured tetrahedral mesh and is capable of computations about arbitrary complete configurations. In addition, the buoyancy effects of the nacelle/diverters were also included in the design process by imposing the pressure field obtained during the design process onto the triangulated surfaces of the nacelle/diverter mesh generated by AIRPLANE. The interference pressures and nacelle buoyancy effects are added to the final forces after each flow field calculation. Full details of the (recently enhanced) ghost nacelle capability are given in a related talk. The pseudo nacelle corrections were greatly improved during this design cycle. During the Ref H and Cycle 1 design activities, the nacelles were only translated and pitched. In the cycle 2 design effort the nacelles can translate vertically, and pitch to accommodate the changes in the lower surface geometry. The diverter heights (between their leading and trailing edges) were modified during design as the shape of the lower wing changed, with the drag of the diverter changing accordingly. Both adjoint and finite difference gradients were used during optimization. The adjoint-based gradients were found to give good direction in the design space for configurations near the starting point, but as the design approached a minimum, the finite difference gradients were found to be more accurate. Use of finite difference gradients was limited by the CPU time limit available on the Cray machines. A typical optimization run using finite difference gradients can use only 30 to 40 design variables and one optimization iteration within the 8 hour queue limit for the chosen grid size and convergence level. The efficiency afforded by the adjoint method allowed for 50-120 design variables and 5-10 optimization iterations in the 8 hour queue. Geometric perturbations to the wing and fuselage were made using the Hicks/Henne (HH) shape functions. The HH functions were distributed uniformly along the chords of the wing defining sections and lofted linearly. During single-surface design, constraints on thickness and volume at selected wing stations were imposed. Both fuselage camber and cross-sectional area distributions were permitted to change during design. The major disadvantage to the use of these functions is the inherent surface waviness produced by repeated use of such functions. Many smoothing operations were required following optimization runs to produce a configuration with reasonable smoothness. Wagner functions were also used on the wing sections but were never used on the fuselage. The Wagner functions are a family of increasingly oscillatory functions that have also been used extensively in airfoil design. The leading and trailing edge regions of the wing were designed by use of polynomial and monomial functions respectively. Twist was attempted but was abandoned because of little performance improvement available from changing the baseline twist.

An entropy correction method for unsteady full potential flows with strong shocks

NASA Technical Reports Server (NTRS)

Whitlow, W., Jr.; Hafez, M. M.; Osher, S. J.

1986-01-01

An entropy correction method for the unsteady full potential equation is presented. The unsteady potential equation is modified to account for entropy jumps across shock waves. The conservative form of the modified equation is solved in generalized coordinates using an implicit, approximate factorization method. A flux-biasing differencing method, which generates the proper amounts of artificial viscosity in supersonic regions, is used to discretize the flow equations in space. Comparisons between the present method and solutions of the Euler equations and between the present method and experimental data are presented. The comparisons show that the present method more accurately models solutions of the Euler equations and experiment than does the isentropic potential formulation.

Droplets size evolution of dispersion in a stirred tank

NASA Astrophysics Data System (ADS)

Kysela, Bohus; Konfrst, Jiri; Chara, Zdenek; Sulc, Radek; Jasikova, Darina

2018-06-01

Dispersion of two immiscible liquids is commonly used in chemical industry as wall as in metallurgical industry e. g. extraction process. The governing property is droplet size distribution. The droplet sizes are given by the physical properties of both liquids and flow properties inside a stirred tank. The first investigation stage is focused on in-situ droplet size measurement using image analysis and optimizing of the evaluation method to achieve maximal result reproducibility. The obtained experimental results are compared with multiphase flow simulation based on Euler-Euler approach combined with PBM (Population Balance Modelling). The population balance model was, in that specific case, simplified with assumption of pure breakage of droplets.

A CFD Heterogeneous Parallel Solver Based on Collaborating CPU and GPU

NASA Astrophysics Data System (ADS)

Lai, Jianqi; Tian, Zhengyu; Li, Hua; Pan, Sha

2018-03-01

Since Graphic Processing Unit (GPU) has a strong ability of floating-point computation and memory bandwidth for data parallelism, it has been widely used in the areas of common computing such as molecular dynamics (MD), computational fluid dynamics (CFD) and so on. The emergence of compute unified device architecture (CUDA), which reduces the complexity of compiling program, brings the great opportunities to CFD. There are three different modes for parallel solution of NS equations: parallel solver based on CPU, parallel solver based on GPU and heterogeneous parallel solver based on collaborating CPU and GPU. As we can see, GPUs are relatively rich in compute capacity but poor in memory capacity and the CPUs do the opposite. We need to make full use of the GPUs and CPUs, so a CFD heterogeneous parallel solver based on collaborating CPU and GPU has been established. Three cases are presented to analyse the solver’s computational accuracy and heterogeneous parallel efficiency. The numerical results agree well with experiment results, which demonstrate that the heterogeneous parallel solver has high computational precision. The speedup on a single GPU is more than 40 for laminar flow, it decreases for turbulent flow, but it still can reach more than 20. What’s more, the speedup increases as the grid size becomes larger.

Moving Computational Domain Method and Its Application to Flow Around a High-Speed Car Passing Through a Hairpin Curve

NASA Astrophysics Data System (ADS)

Watanabe, Koji; Matsuno, Kenichi

This paper presents a new method for simulating flows driven by a body traveling with neither restriction on motion nor a limit of a region size. In the present method named 'Moving Computational Domain Method', the whole of the computational domain including bodies inside moves in the physical space without the limit of region size. Since the whole of the grid of the computational domain moves according to the movement of the body, a flow solver of the method has to be constructed on the moving grid system and it is important for the flow solver to satisfy physical and geometric conservation laws simultaneously on moving grid. For this issue, the Moving-Grid Finite-Volume Method is employed as the flow solver. The present Moving Computational Domain Method makes it possible to simulate flow driven by any kind of motion of the body in any size of the region with satisfying physical and geometric conservation laws simultaneously. In this paper, the method is applied to the flow around a high-speed car passing through a hairpin curve. The distinctive flow field driven by the car at the hairpin curve has been demonstrated in detail. The results show the promising feature of the method.

Parallel Execution of Functional Mock-up Units in Buildings Modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ozmen, Ozgur; Nutaro, James J.; New, Joshua Ryan

2016-06-30

A Functional Mock-up Interface (FMI) defines a standardized interface to be used in computer simulations to develop complex cyber-physical systems. FMI implementation by a software modeling tool enables the creation of a simulation model that can be interconnected, or the creation of a software library called a Functional Mock-up Unit (FMU). This report describes an FMU wrapper implementation that imports FMUs into a C++ environment and uses an Euler solver that executes FMUs in parallel using Open Multi-Processing (OpenMP). The purpose of this report is to elucidate the runtime performance of the solver when a multi-component system is imported asmore » a single FMU (for the whole system) or as multiple FMUs (for different groups of components as sub-systems). This performance comparison is conducted using two test cases: (1) a simple, multi-tank problem; and (2) a more realistic use case based on the Modelica Buildings Library. In both test cases, the performance gains are promising when each FMU consists of a large number of states and state events that are wrapped in a single FMU. Load balancing is demonstrated to be a critical factor in speeding up parallel execution of multiple FMUs.« less

Validation of High-Fidelity CFD/CAA Framework for Launch Vehicle Acoustic Environment Simulation against Scale Model Test Data

NASA Technical Reports Server (NTRS)

Liever, Peter A.; West, Jeffrey S.

2016-01-01

A hybrid Computational Fluid Dynamics and Computational Aero-Acoustics (CFD/CAA) modeling framework has been developed for launch vehicle liftoff acoustic environment predictions. The framework couples the existing highly-scalable NASA production CFD code, Loci/CHEM, with a high-order accurate discontinuous Galerkin solver developed in the same production framework, Loci/THRUST, to accurately resolve and propagate acoustic physics across the entire launch environment. Time-accurate, Hybrid RANS/LES CFD modeling is applied for predicting the acoustic generation physics at the plume source, and a high-order accurate unstructured discontinuous Galerkin (DG) method is employed to propagate acoustic waves away from the source across large distances using high-order accurate schemes. The DG solver is capable of solving 2nd, 3rd, and 4th order Euler solutions for non-linear, conservative acoustic field propagation. Initial application testing and validation has been carried out against high resolution acoustic data from the Ares Scale Model Acoustic Test (ASMAT) series to evaluate the capabilities and production readiness of the CFD/CAA system to resolve the observed spectrum of acoustic frequency content. This paper presents results from this validation and outlines efforts to mature and improve the computational simulation framework.

Examination of Wave Speed in Rotating Detonation Engines Using Simplified Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Paxson, Daniel E.

2018-01-01

A simplified, two-dimensional, computational fluid dynamic (CFD) simulation, with a reactive Euler solver is used to examine possible causes for the low detonation wave propagation speeds that are consistently observed in air breathing rotating detonation engine (RDE) experiments. Intense, small-scale turbulence is proposed as the primary mechanism. While the solver cannot model this turbulence, it can be used to examine the most likely, and profound effect of turbulence. That is a substantial enlargement of the reaction zone, or equivalently, an effective reduction in the chemical reaction rate. It is demonstrated that in the unique flowfield of the RDE, a reduction in reaction rate leads to a reduction in the detonation speed. A subsequent test of reduced reaction rate in a purely one-dimensional pulsed detonation engine (PDE) flowfield yields no reduction in wave speed. The reasons for this are explained. The impact of reduced wave speed on RDE performance is then examined, and found to be minimal. Two other potential mechanisms are briefly examined. These are heat transfer, and reactive mixture non-uniformity. In the context of the simulation used for this study, both mechanisms are shown to have negligible effect on either wave speed or performance.

Assessing uncertainty in the turbulent upper-ocean mixed layer using an unstructured finite-element solver

NASA Astrophysics Data System (ADS)

Pacheco, Luz; Smith, Katherine; Hamlington, Peter; Niemeyer, Kyle

2017-11-01

Vertical transport flux in the ocean upper mixed layer has recently been attributed to submesoscale currents, which occur at scales on the order of kilometers in the horizontal direction. These phenomena, which include fronts and mixed-layer instabilities, have been of particular interest due to the effect of turbulent mixing on nutrient transport, facilitating phytoplankton blooms. We study these phenomena using a non-hydrostatic, large eddy simulation for submesoscale currents in the ocean, developed using the extensible, open-source finite element platform FEniCs. Our model solves the standard Boussinesq Euler equations in variational form using the finite element method. FEniCs enables the use of parallel computing on modern systems for efficient computing time, and is suitable for unstructured grids where irregular topography can be considered in the future. The solver will be verified against the well-established NCAR-LES model and validated against observational data. For the verification with NCAR-LES, the velocity, pressure, and buoyancy fields are compared through a surface-wind-driven, open-ocean case. We use this model to study the impacts of uncertainties in the model parameters, such as near-surface buoyancy flux and secondary circulation, and discuss implications.

''A Parallel Adaptive Simulation Tool for Two Phase Steady State Reacting Flows in Industrial Boilers and Furnaces''

DOE Office of Scientific and Technical Information (OSTI.GOV)

Michael J. Bockelie

2002-01-04

This DOE SBIR Phase II final report summarizes research that has been performed to develop a parallel adaptive tool for modeling steady, two phase turbulent reacting flow. The target applications for the new tool are full scale, fossil-fuel fired boilers and furnaces such as those used in the electric utility industry, chemical process industry and mineral/metal process industry. The type of analyses to be performed on these systems are engineering calculations to evaluate the impact on overall furnace performance due to operational, process or equipment changes. To develop a Computational Fluid Dynamics (CFD) model of an industrial scale furnace requiresmore » a carefully designed grid that will capture all of the large and small scale features of the flowfield. Industrial systems are quite large, usually measured in tens of feet, but contain numerous burners, air injection ports, flames and localized behavior with dimensions that are measured in inches or fractions of inches. To create an accurate computational model of such systems requires capturing length scales within the flow field that span several orders of magnitude. In addition, to create an industrially useful model, the grid can not contain too many grid points - the model must be able to execute on an inexpensive desktop PC in a matter of days. An adaptive mesh provides a convenient means to create a grid that can capture both fine flow field detail within a very large domain with a ''reasonable'' number of grid points. However, the use of an adaptive mesh requires the development of a new flow solver. To create the new simulation tool, we have combined existing reacting CFD modeling software with new software based on emerging block structured Adaptive Mesh Refinement (AMR) technologies developed at Lawrence Berkeley National Laboratory (LBNL). Specifically, we combined: -physical models, modeling expertise, and software from existing combustion simulation codes used by Reaction Engineering International; -mesh adaption, data management, and parallelization software and technology being developed by users of the BoxLib library at LBNL; and -solution methods for problems formulated on block structured grids that were being developed in collaboration with technical staff members at the University of Utah Center for High Performance Computing (CHPC) and at LBNL. The combustion modeling software used by Reaction Engineering International represents an investment of over fifty man-years of development, conducted over a period of twenty years. Thus, it was impractical to achieve our objective by starting from scratch. The research program resulted in an adaptive grid, reacting CFD flow solver that can be used only on limited problems. In current form the code is appropriate for use on academic problems with simplified geometries. The new solver is not sufficiently robust or sufficiently general to be used in a ''production mode'' for industrial applications. The principle difficulty lies with the multi-level solver technology. The use of multi-level solvers on adaptive grids with embedded boundaries is not yet a mature field and there are many issues that remain to be resolved. From the lessons learned in this SBIR program, we have started work on a new flow solver with an AMR capability. The new code is based on a conventional cell-by-cell mesh refinement strategy used in unstructured grid solvers that employ hexahedral cells. The new solver employs several of the concepts and solution strategies developed within this research program. The formulation of the composite grid problem for the new solver has been designed to avoid the embedded boundary complications encountered in this SBIR project. This follow-on effort will result in a reacting flow CFD solver with localized mesh capability that can be used to perform engineering calculations on industrial problems in a production mode.« less

Verification of ANSYS Fluent and OpenFOAM CFD platforms for prediction of impact flow

NASA Astrophysics Data System (ADS)

Tisovská, Petra; Peukert, Pavel; Kolář, Jan

The main goal of the article is a verification of the heat transfer coefficient numerically predicted by two CDF platforms - ANSYS-Fluent and OpenFOAM on the problem of impact flows oncoming from 2D nozzle. Various mesh parameters and solver settings were tested under several boundary conditions and compared to known experimental results. The best solver setting, suitable for further optimization of more complex geometry is evaluated.

Development of a steady potential solver for use with linearized, unsteady aerodynamic analyses

NASA Technical Reports Server (NTRS)

Hoyniak, Daniel; Verdon, Joseph M.

1991-01-01

A full potential steady flow solver (SFLOW) developed explicitly for use with an inviscid unsteady aerodynamic analysis (LINFLO) is described. The steady solver uses the nonconservative form of the nonlinear potential flow equations together with an implicit, least squares, finite difference approximation to solve for the steady flow field. The difference equations were developed on a composite mesh which consists of a C grid embedded in a rectilinear (H grid) cascade mesh. The composite mesh is capable of resolving blade to blade and far field phenomena on the H grid, while accurately resolving local phenomena on the C grid. The resulting system of algebraic equations is arranged in matrix form using a sparse matrix package and solved by Newton's method. Steady and unsteady results are presented for two cascade configurations: a high speed compressor and a turbine with high exit Mach number.

National Combustion Code: Parallel Implementation and Performance

NASA Technical Reports Server (NTRS)

Quealy, A.; Ryder, R.; Norris, A.; Liu, N.-S.

2000-01-01

The National Combustion Code (NCC) is being developed by an industry-government team for the design and analysis of combustion systems. CORSAIR-CCD is the current baseline reacting flow solver for NCC. This is a parallel, unstructured grid code which uses a distributed memory, message passing model for its parallel implementation. The focus of the present effort has been to improve the performance of the NCC flow solver to meet combustor designer requirements for model accuracy and analysis turnaround time. Improving the performance of this code contributes significantly to the overall reduction in time and cost of the combustor design cycle. This paper describes the parallel implementation of the NCC flow solver and summarizes its current parallel performance on an SGI Origin 2000. Earlier parallel performance results on an IBM SP-2 are also included. The performance improvements which have enabled a turnaround of less than 15 hours for a 1.3 million element fully reacting combustion simulation are described.

The Overgrid Interface for Computational Simulations on Overset Grids

NASA Technical Reports Server (NTRS)

Chan, William M.; Kwak, Dochan (Technical Monitor)

2002-01-01

Computational simulations using overset grids typically involve multiple steps and a variety of software modules. A graphical interface called OVERGRID has been specially designed for such purposes. Data required and created by the different steps include geometry, grids, domain connectivity information and flow solver input parameters. The interface provides a unified environment for the visualization, processing, generation and diagnosis of such data. General modules are available for the manipulation of structured grids and unstructured surface triangulations. Modules more specific for the overset approach include surface curve generators, hyperbolic and algebraic surface grid generators, a hyperbolic volume grid generator, Cartesian box grid generators, and domain connectivity: pre-processing tools. An interface provides automatic selection and viewing of flow solver boundary conditions, and various other flow solver inputs. For problems involving multiple components in relative motion, a module is available to build the component/grid relationships and to prescribe and animate the dynamics of the different components.

A matrix-form GSM-CFD solver for incompressible fluids and its application to hemodynamics

NASA Astrophysics Data System (ADS)

Yao, Jianyao; Liu, G. R.

2014-10-01

A GSM-CFD solver for incompressible flows is developed based on the gradient smoothing method (GSM). A matrix-form algorithm and corresponding data structure for GSM are devised to efficiently approximate the spatial gradients of field variables using the gradient smoothing operation. The calculated gradient values on various test fields show that the proposed GSM is capable of exactly reproducing linear field and of second order accuracy on all kinds of meshes. It is found that the GSM is much more robust to mesh deformation and therefore more suitable for problems with complicated geometries. Integrated with the artificial compressibility approach, the GSM is extended to solve the incompressible flows. As an example, the flow simulation of carotid bifurcation is carried out to show the effectiveness of the proposed GSM-CFD solver. The blood is modeled as incompressible Newtonian fluid and the vessel is treated as rigid wall in this paper.

Incompressible viscous flow simulations of the NFAC wind tunnel

NASA Technical Reports Server (NTRS)

Champney, Joelle Milene

1986-01-01

The capabilities of an existing 3-D incompressible Navier-Stokes flow solver, INS3D, are extended and improved to solve turbulent flows through the incorporation of zero- and two-equation turbulence models. The two-equation model equations are solved in their high Reynolds number form and utilize wall functions in the treatment of solid wall boundary conditions. The implicit approximate factorization scheme is modified to improve the stability of the two-equation solver. Applications to the 3-D viscous flow inside the 80 by 120 feet open return wind tunnel of the National Full Scale Aerodynamics Complex (NFAC) are discussed and described.

A Comparison of Three Navier-Stokes Solvers for Exhaust Nozzle Flowfields

NASA Technical Reports Server (NTRS)

Georgiadis, Nicholas J.; Yoder, Dennis A.; Debonis, James R.

1999-01-01

A comparison of the NPARC, PAB, and WIND (previously known as NASTD) Navier-Stokes solvers is made for two flow cases with turbulent mixing as the dominant flow characteristic, a two-dimensional ejector nozzle and a Mach 1.5 elliptic jet. The objective of the work is to determine if comparable predictions of nozzle flows can be obtained from different Navier-Stokes codes employed in a multiple site research program. A single computational grid was constructed for each of the two flows and used for all of the Navier-Stokes solvers. In addition, similar k-e based turbulence models were employed in each code, and boundary conditions were specified as similarly as possible across the codes. Comparisons of mass flow rates, velocity profiles, and turbulence model quantities are made between the computations and experimental data. The computational cost of obtaining converged solutions with each of the codes is also documented. Results indicate that all of the codes provided similar predictions for the two nozzle flows. Agreement of the Navier-Stokes calculations with experimental data was good for the ejector nozzle. However, for the Mach 1.5 elliptic jet, the calculations were unable to accurately capture the development of the three dimensional elliptic mixing layer.

Evaluation of the Performance of the Hybrid Lattice Boltzmann Based Numerical Flux

NASA Astrophysics Data System (ADS)

Zheng, H. W.; Shu, C.

2016-06-01

It is well known that the numerical scheme is a key factor to the stability and accuracy of a Navier-Stokes solver. Recently, a new hybrid lattice Boltzmann numerical flux (HLBFS) is developed by Shu's group. It combines two different LBFS schemes by a switch function. It solves the Boltzmann equation instead of the Euler equation. In this article, the main object is to evaluate the ability of this HLBFS scheme by our in-house cell centered hybrid mesh based Navier-Stokes code. Its performance is examined by several widely-used bench-mark test cases. The comparisons on results between calculation and experiment are conducted. They show that the scheme can capture the shock wave as well as the resolving of boundary layer.

Application of advanced grid generation techniques for flow field computations about complex configurations

NASA Technical Reports Server (NTRS)

Kathong, Monchai; Tiwari, Surendra N.

1988-01-01

In the computation of flowfields about complex configurations, it is very difficult to construct a boundary-fitted coordinate system. An alternative approach is to use several grids at once, each of which is generated independently. This procedure is called the multiple grids or zonal grids approach; its applications are investigated. The method conservative providing conservation of fluxes at grid interfaces. The Euler equations are solved numerically on such grids for various configurations. The numerical scheme used is the finite-volume technique with a three-stage Runge-Kutta time integration. The code is vectorized and programmed to run on the CDC VPS-32 computer. Steady state solutions of the Euler equations are presented and discussed. The solutions include: low speed flow over a sphere, high speed flow over a slender body, supersonic flow through a duct, and supersonic internal/external flow interaction for an aircraft configuration at various angles of attack. The results demonstrate that the multiple grids approach along with the conservative interfacing is capable of computing the flows about the complex configurations where the use of a single grid system is not possible.

A grid generation and flow solution method for the Euler equations on unstructured grids

NASA Astrophysics Data System (ADS)

Anderson, W. Kyle

1994-01-01

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme utilizes Delaunay triangulation and self-generates the field points for the mesh based on cell aspect ratios and allows for clustering near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss Seidel procedure which is completely vectorizable. In addition, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for a National Advisory Committee for Aeronautics (NACA) 0012 airfoil as well as a two-element configuration. Flow solution results are shown for two-dimensional flow over the NACA 0012 airfoil and for a two-element configuration in which the solution has been obtained through an adaptation procedure and compared to an exact solution. Preliminary three-dimensional results are also shown in which subsonic flow over a business jet is computed.

Least-Squares Spectral Element Solutions to the CAA Workshop Benchmark Problems

NASA Technical Reports Server (NTRS)

Lin, Wen H.; Chan, Daniel C.

1997-01-01

This paper presents computed results for some of the CAA benchmark problems via the acoustic solver developed at Rocketdyne CFD Technology Center under the corporate agreement between Boeing North American, Inc. and NASA for the Aerospace Industry Technology Program. The calculations are considered as benchmark testing of the functionality, accuracy, and performance of the solver. Results of these computations demonstrate that the solver is capable of solving the propagation of aeroacoustic signals. Testing of sound generation and on more realistic problems is now pursued for the industrial applications of this solver. Numerical calculations were performed for the second problem of Category 1 of the current workshop problems for an acoustic pulse scattered from a rigid circular cylinder, and for two of the first CAA workshop problems, i. e., the first problem of Category 1 for the propagation of a linear wave and the first problem of Category 4 for an acoustic pulse reflected from a rigid wall in a uniform flow of Mach 0.5. The aim for including the last two problems in this workshop is to test the effectiveness of some boundary conditions set up in the solver. Numerical results of the last two benchmark problems have been compared with their corresponding exact solutions and the comparisons are excellent. This demonstrates the high fidelity of the solver in handling wave propagation problems. This feature lends the method quite attractive in developing a computational acoustic solver for calculating the aero/hydrodynamic noise in a violent flow environment.

A Constructive Approach to Regularity of Lagrangian Trajectories for Incompressible Euler Flow in a Bounded Domain

NASA Astrophysics Data System (ADS)

Besse, Nicolas; Frisch, Uriel

2017-04-01

The 3D incompressible Euler equations are an important research topic in the mathematical study of fluid dynamics. Not only is the global regularity for smooth initial data an open issue, but the behaviour may also depend on the presence or absence of boundaries. For a good understanding, it is crucial to carry out, besides mathematical studies, high-accuracy and well-resolved numerical exploration. Such studies can be very demanding in computational resources, but recently it has been shown that very substantial gains can be achieved first, by using Cauchy's Lagrangian formulation of the Euler equations and second, by taking advantage of analyticity results of the Lagrangian trajectories for flows whose initial vorticity is Hölder-continuous. The latter has been known for about 20 years (Serfati in J Math Pures Appl 74:95-104, 1995), but the combination of the two, which makes use of recursion relations among time-Taylor coefficients to obtain constructively the time-Taylor series of the Lagrangian map, has been achieved only recently (Frisch and Zheligovsky in Commun Math Phys 326:499-505, 2014; Podvigina et al. in J Comput Phys 306:320-342, 2016 and references therein). Here we extend this methodology to incompressible Euler flow in an impermeable bounded domain whose boundary may be either analytic or have a regularity between indefinite differentiability and analyticity. Non-constructive regularity results for these cases have already been obtained by Glass et al. (Ann Sci Éc Norm Sup 45:1-51, 2012). Using the invariance of the boundary under the Lagrangian flow, we establish novel recursion relations that include contributions from the boundary. This leads to a constructive proof of time-analyticity of the Lagrangian trajectories with analytic boundaries, which can then be used subsequently for the design of a very high-order Cauchy-Lagrangian method.

Flow prediction for propfan engine installation effects on transport aircraft at transonic speeds

NASA Technical Reports Server (NTRS)

Samant, S. S.; Yu, N. J.

1986-01-01

An Euler-based method for aerodynamic analysis of turboprop transport aircraft at transonic speeds has been developed. In this method, inviscid Euler equations are solved over surface-fitted grids constructed about aircraft configurations. Propeller effects are simulated by specifying sources of momentum and energy on an actuator disc located in place of the propeller. A stripwise boundary layer procedure is included to account for the viscous effects. A preliminary version of an approach to embed the exhaust plume within the global Euler solution has also been developed for more accurate treatment of the exhaust flow. The resulting system of programs is capable of handling wing-body-nacelle-propeller configurations. The propeller disks may be tractors or pushers and may represent single or counterrotation propellers. Results from analyses of three test cases of interest (a wing alone, a wing-body-nacelle model, and a wing-nacelle-endplate model) are presented. A user's manual for executing the system of computer programs with formats of various input files, sample job decks, and sample input files is provided in appendices.

On the stability analysis of approximate factorization methods for 3D Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Demuren, A. O.; Ibraheem, S. O.

1993-01-01

The convergence characteristics of various approximate factorizations for the 3D Euler and Navier-Stokes equations are examined using the von-Neumann stability analysis method. Three upwind-difference based factorizations and several central-difference based factorizations are considered for the Euler equations. In the upwind factorizations both the flux-vector splitting methods of Steger and Warming and van Leer are considered. Analysis of the Navier-Stokes equations is performed only on the Beam and Warming central-difference scheme. The range of CFL numbers over which each factorization is stable is presented for one-, two-, and three-dimensional flow. Also presented for each factorization is the CFL number at which the maximum eigenvalue is minimized, for all Fourier components, as well as for the high frequency range only. The latter is useful for predicting the effectiveness of multigrid procedures with these schemes as smoothers. Further, local mode analysis is performed to test the suitability of using a uniform flow field in the stability analysis. Some inconsistencies in the results from previous analyses are resolved.

Restricted Euler dynamics along trajectories of small inertial particles in turbulence

NASA Astrophysics Data System (ADS)

Johnson, Perry; Meneveau, Charles

2016-11-01

The fate of small particles in turbulent flows depends strongly on the surrounding fluid's velocity gradient properties such as rotation and strain-rates. For non-inertial (fluid) particles, the Restricted Euler model provides a simple, low-dimensional dynamical system representation of Lagrangian evolution of velocity gradients in fluid turbulence, at least for short times. Here we derive a new restricted Euler dynamical system for the velocity gradient evolution of inertial particles such as solid particles in a gas or droplets and bubbles in turbulent liquid flows. The model is derived in the limit of small (sub Kolmogorov scale) particles and low Stokes number. The system exhibits interesting fixed points, stability and invariant properties. Comparisons with data from Direct Numerical Simulations show that the model predicts realistic trends such as the tendency of increased straining over rotation along heavy particle trajectories and, for light particles such as bubbles, the tendency of severely reduced self-stretching of strain-rate. Supported by a National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1232825 and by a Grant from The Gulf of Mexico Research Initiative.

Stabilizing the long-time behavior of the forced Navier-Stokes and damped Euler systems by large mean flow

NASA Astrophysics Data System (ADS)

Cyranka, Jacek; Mucha, Piotr B.; Titi, Edriss S.; Zgliczyński, Piotr

2018-04-01

The paper studies the issue of stability of solutions to the forced Navier-Stokes and damped Euler systems in periodic boxes. It is shown that for large, but fixed, Grashoff (Reynolds) number the turbulent behavior of all Leray-Hopf weak solutions of the three-dimensional Navier-Stokes equations, in periodic box, is suppressed, when viewed in the right frame of reference, by large enough average flow of the initial data; a phenomenon that is similar in spirit to the Landau damping. Specifically, we consider an initial data which have large enough spatial average, then by means of the Galilean transformation, and thanks to the periodic boundary conditions, the large time independent forcing term changes into a highly oscillatory force; which then allows us to employ some averaging principles to establish our result. Moreover, we also show that under the action of fast oscillatory-in-time external forces all two-dimensional regular solutions of the Navier-Stokes and the damped Euler equations converge to a unique time-periodic solution.

Conjugate Analysis of Two-Dimensional Ablation and Pyrolysis in Rocket Nozzles

NASA Astrophysics Data System (ADS)

Cross, Peter G.

The development of a methodology and computational framework for performing conjugate analyses of transient, two-dimensional ablation of pyrolyzing materials in rocket nozzle applications is presented. This new engineering methodology comprehensively incorporates fluid-thermal-chemical processes relevant to nozzles and other high temperature components, making it possible, for the first time, to rigorously capture the strong interactions and interdependencies that exist between the reacting flowfield and the ablating material. By basing thermal protection system engineering more firmly on first principles, improved analysis accuracy can be achieved. The computational framework developed in this work couples a multi-species, reacting flow solver to a two-dimensional material response solver. New capabilities are added to the flow solver in order to be able to model unique aspects of the flow through solid rocket nozzles. The material response solver is also enhanced with new features that enable full modeling of pyrolyzing, anisotropic materials with a true two-dimensional treatment of the porous flow of the pyrolysis gases. Verification and validation studies demonstrating correct implementation of these new models in the flow and material response solvers are also presented. Five different treatments of the surface energy balance at the ablating wall, with increasing levels of fidelity, are investigated. The Integrated Equilibrium Surface Chemistry (IESC) treatment computes the surface energy balance and recession rate directly from the diffusive fluxes at the ablating wall, without making transport coefficient or unity Lewis number assumptions, or requiring pre-computed surface thermochemistry tables. This method provides the highest level of fidelity, and can inherently account for the effects that recession, wall temperature, blowing, and the presence of ablation product species in the boundary layer have on the flowfield and ablation response. Multiple decoupled and conjugate ablation analysis studies for the HIPPO nozzle test case are presented. Results from decoupled simulations show sensitivity to the wall temperature profile used within the flow solver, indicating the need for conjugate analyses. Conjugate simulations show that the thermal response of the nozzle is relatively insensitive to the choice of the surface energy balance treatment. However, the surface energy balance treatment is found to strongly affect the surface recession predictions. Out of all the methods considered, the IESC treatment produces surface recession predictions with the best agreement to experimental data. These results show that the increased fidelity provided by the proposed conjugate ablation modeling methodology produces improved analysis accuracy, as desired.

CFD Analysis of Thermal Control System Using NX Thermal and Flow

NASA Technical Reports Server (NTRS)

Fortier, C. R.; Harris, M. F. (Editor); McConnell, S. (Editor)

2014-01-01

The Thermal Control Subsystem (TCS) is a key part of the Advanced Plant Habitat (APH) for the International Space Station (ISS). The purpose of this subsystem is to provide thermal control, mainly cooling, to the other APH subsystems. One of these subsystems, the Environmental Control Subsystem (ECS), controls the temperature and humidity of the growth chamber (GC) air to optimize the growth of plants in the habitat. The TCS provides thermal control to the ECS with three cold plates, which use Thermoelectric Coolers (TECs) to heat or cool water as needed to control the air temperature in the ECS system. In order to optimize the TCS design, pressure drop and heat transfer analyses were needed. The analysis for this system was performed in Siemens NX Thermal/Flow software (Version 8.5). NX Thermal/Flow has the ability to perform 1D or 3D flow solutions. The 1D flow solver can be used to represent simple geometries, such as pipes and tubes. The 1D flow method also has the ability to simulate either fluid only or fluid and wall regions. The 3D flow solver is similar to other Computational Fluid Dynamic (CFD) software. TCS performance was analyzed using both the 1D and 3D solvers. Each method produced different results, which will be evaluated and discussed.

LSPRAY-V: A Lagrangian Spray Module

NASA Technical Reports Server (NTRS)

Raju, M. S.

2015-01-01

LSPRAY-V is a Lagrangian spray solver developed for application with unstructured grids and massively parallel computers. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray encountered over a wide range of operating conditions in modern aircraft engine development. It could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The manual provides the user with an understanding of various models involved in the spray formulation, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers. With the development of LSPRAY-V, we have advanced the state-of-the-art in spray computations in several important ways.

Parallel Three-Dimensional Computation of Fluid Dynamics and Fluid-Structure Interactions of Ram-Air Parachutes

NASA Technical Reports Server (NTRS)

Tezduyar, Tayfun E.

1998-01-01

This is a final report as far as our work at University of Minnesota is concerned. The report describes our research progress and accomplishments in development of high performance computing methods and tools for 3D finite element computation of aerodynamic characteristics and fluid-structure interactions (FSI) arising in airdrop systems, namely ram-air parachutes and round parachutes. This class of simulations involves complex geometries, flexible structural components, deforming fluid domains, and unsteady flow patterns. The key components of our simulation toolkit are a stabilized finite element flow solver, a nonlinear structural dynamics solver, an automatic mesh moving scheme, and an interface between the fluid and structural solvers; all of these have been developed within a parallel message-passing paradigm.

References and benchmarks for pore-scale flow simulated using micro-CT images of porous media and digital rocks

NASA Astrophysics Data System (ADS)

Saxena, Nishank; Hofmann, Ronny; Alpak, Faruk O.; Berg, Steffen; Dietderich, Jesse; Agarwal, Umang; Tandon, Kunj; Hunter, Sander; Freeman, Justin; Wilson, Ove Bjorn

2017-11-01

We generate a novel reference dataset to quantify the impact of numerical solvers, boundary conditions, and simulation platforms. We consider a variety of microstructures ranging from idealized pipes to digital rocks. Pore throats of the digital rocks considered are large enough to be well resolved with state-of-the-art micro-computerized tomography technology. Permeability is computed using multiple numerical engines, 12 in total, including, Lattice-Boltzmann, computational fluid dynamics, voxel based, fast semi-analytical, and known empirical models. Thus, we provide a measure of uncertainty associated with flow computations of digital media. Moreover, the reference and standards dataset generated is the first of its kind and can be used to test and improve new fluid flow algorithms. We find that there is an overall good agreement between solvers for idealized cross-section shape pipes. As expected, the disagreement increases with increase in complexity of the pore space. Numerical solutions for pipes with sinusoidal variation of cross section show larger variability compared to pipes of constant cross-section shapes. We notice relatively larger variability in computed permeability of digital rocks with coefficient of variation (of up to 25%) in computed values between various solvers. Still, these differences are small given other subsurface uncertainties. The observed differences between solvers can be attributed to several causes including, differences in boundary conditions, numerical convergence criteria, and parameterization of fundamental physics equations. Solvers that perform additional meshing of irregular pore shapes require an additional step in practical workflows which involves skill and can introduce further uncertainty. Computation times for digital rocks vary from minutes to several days depending on the algorithm and available computational resources. We find that more stringent convergence criteria can improve solver accuracy but at the expense of longer computation time.

Local invariants in non-ideal flows of neutral fluids and two-fluid plasmas

NASA Astrophysics Data System (ADS)

Zhu, Jian-Zhou

2018-03-01

The main objective is the locally invariant geometric object of any (magneto-)fluid dynamics with forcing and damping (nonideal), while more attention is paid to the untouched dynamical properties of two-fluid fashion. Specifically, local structures, beyond the well-known "frozen-in" to the barotropic flows of the generalized vorticities, of the two-fluid model of plasma flows are presented. More general non-barotropic situations are also considered. A modified Euler equation [T. Tao, "Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation," Ann. PDE 2, 9 (2016)] is also accordingly analyzed and remarked from the angle of view of the two-fluid model, with emphasis on the local structures. The local constraints of high-order differential forms such as helicity, among others, find simple formulation for possible practices in modeling the dynamics. Thus, the Cauchy invariants equation [N. Besse and U. Frisch, "Geometric formulation of the Cauchy invariants for incompressible Euler flow in flat and curved spaces," J. Fluid Mech. 825, 412 (2017)] may be enabled to find applications in non-ideal flows. Some formal examples are offered to demonstrate the calculations, and particularly interestingly the two-dimensional-three-component (2D3C) or the 2D passive scalar problem presents that a locally invariant Θ = 2θζ, with θ and ζ being, respectively, the scalar value of the "vertical velocity" (or the passive scalar) and the "vertical vorticity," may be used as if it were the spatial density of the globally invariant helicity, providing a Lagrangian prescription to control the latter in some situations of studying its physical effects in rapidly rotating flows (ubiquitous in atmosphere of astrophysical objects) with marked 2D3C vortical modes or in purely 2D passive scalars.

High-Fidelity Thermal Radiation Models and Measurements for High-Pressure Reacting Laminar and Turbulent Flows

DTIC Science & Technology

2013-06-26

flow code used ( OpenFOAM ) to include differential diffusion and cell-based stochastic RTE solvers. The models were validated by simulation of laminar...wavenumber selection is improved about by a factor of 10. (5) OpenFOAM Improvements for Laminar Flames A laminar-diffusion combustion solver, taking into...account the effects of differential diffusion, was developed within the open source CFD package OpenFOAM [18]. In addition, OpenFOAM was augmented to take

Transonic Drag Prediction Using an Unstructured Multigrid Solver

NASA Technical Reports Server (NTRS)

Mavriplis, D. J.; Levy, David W.

2001-01-01

This paper summarizes the results obtained with the NSU-3D unstructured multigrid solver for the AIAA Drag Prediction Workshop held in Anaheim, CA, June 2001. The test case for the workshop consists of a wing-body configuration at transonic flow conditions. Flow analyses for a complete test matrix of lift coefficient values and Mach numbers at a constant Reynolds number are performed, thus producing a set of drag polars and drag rise curves which are compared with experimental data. Results were obtained independently by both authors using an identical baseline grid and different refined grids. Most cases were run in parallel on commodity cluster-type machines while the largest cases were run on an SGI Origin machine using 128 processors. The objective of this paper is to study the accuracy of the subject unstructured grid solver for predicting drag in the transonic cruise regime, to assess the efficiency of the method in terms of convergence, cpu time, and memory, and to determine the effects of grid resolution on this predictive ability and its computational efficiency. A good predictive ability is demonstrated over a wide range of conditions, although accuracy was found to degrade for cases at higher Mach numbers and lift values where increasing amounts of flow separation occur. The ability to rapidly compute large numbers of cases at varying flow conditions using an unstructured solver on inexpensive clusters of commodity computers is also demonstrated.

Visualization of Unsteady Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Haimes, Robert

1997-01-01

The current compute environment that most researchers are using for the calculation of 3D unsteady Computational Fluid Dynamic (CFD) results is a super-computer class machine. The Massively Parallel Processors (MPP's) such as the 160 node IBM SP2 at NAS and clusters of workstations acting as a single MPP (like NAS's SGI Power-Challenge array and the J90 cluster) provide the required computation bandwidth for CFD calculations of transient problems. If we follow the traditional computational analysis steps for CFD (and we wish to construct an interactive visualizer) we need to be aware of the following: (1) Disk space requirements. A single snap-shot must contain at least the values (primitive variables) stored at the appropriate locations within the mesh. For most simple 3D Euler solvers that means 5 floating point words. Navier-Stokes solutions with turbulence models may contain 7 state-variables. (2) Disk speed vs. Computational speeds. The time required to read the complete solution of a saved time frame from disk is now longer than the compute time for a set number of iterations from an explicit solver. Depending, on the hardware and solver an iteration of an implicit code may also take less time than reading the solution from disk. If one examines the performance improvements in the last decade or two, it is easy to see that depending on disk performance (vs. CPU improvement) may not be the best method for enhancing interactivity. (3) Cluster and Parallel Machine I/O problems. Disk access time is much worse within current parallel machines and cluster of workstations that are acting in concert to solve a single problem. In this case we are not trying to read the volume of data, but are running the solver and the solver outputs the solution. These traditional network interfaces must be used for the file system. (4) Numerics of particle traces. Most visualization tools can work upon a single snap shot of the data but some visualization tools for transient problems require dealing with time.

Accurate upwind methods for the Euler equations

NASA Technical Reports Server (NTRS)

Huynh, Hung T.

1993-01-01

A new class of piecewise linear methods for the numerical solution of the one-dimensional Euler equations of gas dynamics is presented. These methods are uniformly second-order accurate, and can be considered as extensions of Godunov's scheme. With an appropriate definition of monotonicity preservation for the case of linear convection, it can be shown that they preserve monotonicity. Similar to Van Leer's MUSCL scheme, they consist of two key steps: a reconstruction step followed by an upwind step. For the reconstruction step, a monotonicity constraint that preserves uniform second-order accuracy is introduced. Computational efficiency is enhanced by devising a criterion that detects the 'smooth' part of the data where the constraint is redundant. The concept and coding of the constraint are simplified by the use of the median function. A slope steepening technique, which has no effect at smooth regions and can resolve a contact discontinuity in four cells, is described. As for the upwind step, existing and new methods are applied in a manner slightly different from those in the literature. These methods are derived by approximating the Euler equations via linearization and diagonalization. At a 'smooth' interface, Harten, Lax, and Van Leer's one intermediate state model is employed. A modification for this model that can resolve contact discontinuities is presented. Near a discontinuity, either this modified model or a more accurate one, namely, Roe's flux-difference splitting. is used. The current presentation of Roe's method, via the conceptually simple flux-vector splitting, not only establishes a connection between the two splittings, but also leads to an admissibility correction with no conditional statement, and an efficient approximation to Osher's approximate Riemann solver. These reconstruction and upwind steps result in schemes that are uniformly second-order accurate and economical at smooth regions, and yield high resolution at discontinuities.

LSPRAY: Lagrangian Spray Solver for Applications With Parallel Computing and Unstructured Gas-Phase Flow Solvers

NASA Technical Reports Server (NTRS)

Raju, Manthena S.

1998-01-01

Sprays occur in a wide variety of industrial and power applications and in the processing of materials. A liquid spray is a phase flow with a gas as the continuous phase and a liquid as the dispersed phase (in the form of droplets or ligaments). Interactions between the two phases, which are coupled through exchanges of mass, momentum, and energy, can occur in different ways at different times and locations involving various thermal, mass, and fluid dynamic factors. An understanding of the flow, combustion, and thermal properties of a rapidly vaporizing spray requires careful modeling of the rate-controlling processes associated with the spray's turbulent transport, mixing, chemical kinetics, evaporation, and spreading rates, as well as other phenomena. In an attempt to advance the state-of-the-art in multidimensional numerical methods, we at the NASA Lewis Research Center extended our previous work on sprays to unstructured grids and parallel computing. LSPRAY, which was developed by M.S. Raju of Nyma, Inc., is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo probability density function (PDF) solver. The LSPRAY solver accommodates the use of an unstructured mesh with mixed triangular, quadrilateral, and/or tetrahedral elements in the gas-phase solvers. It is used specifically for fuel sprays within gas turbine combustors, but it has many other uses. The spray model used in LSPRAY provided favorable results when applied to stratified-charge rotary combustion (Wankel) engines and several other confined and unconfined spray flames. The source code will be available with the National Combustion Code (NCC) as a complete package.

A comparative study of computational solutions to flow over a backward-facing step

NASA Technical Reports Server (NTRS)

Mizukami, M.; Georgiadis, N. J.; Cannon, M. R.

1993-01-01

A comparative study was conducted for computational fluid dynamic solutions to flow over a backward-facing step. This flow is a benchmark problem, with a simple geometry, but involves complicated flow physics such as free shear layers, reattaching flow, recirculation, and high turbulence intensities. Three Reynolds-averaged Navier-Stokes flow solvers with k-epsilon turbulence models were used, each using a different solution algorithm: finite difference, finite element, and hybrid finite element - finite difference. Comparisons were made with existing experimental data. Results showed that velocity profiles and reattachment lengths were predicted reasonably well by all three methods, while the skin friction coefficients were more difficult to predict accurately. It was noted that, in general, selecting an appropriate solver for each problem to be considered is important.

Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction

NASA Technical Reports Server (NTRS)

Barth, Timothy J.; Frederickson, Paul O.

1990-01-01

High order accurate finite-volume schemes for solving the Euler equations of gasdynamics are developed. Central to the development of these methods are the construction of a k-exact reconstruction operator given cell-averaged quantities and the use of high order flux quadrature formulas. General polygonal control volumes (with curved boundary edges) are considered. The formulations presented make no explicit assumption as to complexity or convexity of control volumes. Numerical examples are presented for Ringleb flow to validate the methodology.

Modeling hemodynamics in intracranial aneurysms: Comparing accuracy of CFD solvers based on finite element and finite volume schemes.

PubMed

Botti, Lorenzo; Paliwal, Nikhil; Conti, Pierangelo; Antiga, Luca; Meng, Hui

2018-06-01

Image-based computational fluid dynamics (CFD) has shown potential to aid in the clinical management of intracranial aneurysms (IAs) but its adoption in the clinical practice has been missing, partially due to lack of accuracy assessment and sensitivity analysis. To numerically solve the flow-governing equations CFD solvers generally rely on two spatial discretization schemes: Finite Volume (FV) and Finite Element (FE). Since increasingly accurate numerical solutions are obtained by different means, accuracies and computational costs of FV and FE formulations cannot be compared directly. To this end, in this study we benchmark two representative CFD solvers in simulating flow in a patient-specific IA model: (1) ANSYS Fluent, a commercial FV-based solver and (2) VMTKLab multidGetto, a discontinuous Galerkin (dG) FE-based solver. The FV solver's accuracy is improved by increasing the spatial mesh resolution (134k, 1.1m, 8.6m and 68.5m tetrahedral element meshes). The dGFE solver accuracy is increased by increasing the degree of polynomials (first, second, third and fourth degree) on the base 134k tetrahedral element mesh. Solutions from best FV and dGFE approximations are used as baseline for error quantification. On average, velocity errors for second-best approximations are approximately 1cm/s for a [0,125]cm/s velocity magnitude field. Results show that high-order dGFE provide better accuracy per degree of freedom but worse accuracy per Jacobian non-zero entry as compared to FV. Cross-comparison of velocity errors demonstrates asymptotic convergence of both solvers to the same numerical solution. Nevertheless, the discrepancy between under-resolved velocity fields suggests that mesh independence is reached following different paths. This article is protected by copyright. All rights reserved.

Evaluation of the Lattice-Boltzmann Equation Solver PowerFLOW for Aerodynamic Applications

NASA Technical Reports Server (NTRS)

Lockard, David P.; Luo, Li-Shi; Singer, Bart A.; Bushnell, Dennis M. (Technical Monitor)

2000-01-01

A careful comparison of the performance of a commercially available Lattice-Boltzmann Equation solver (Power-FLOW) was made with a conventional, block-structured computational fluid-dynamics code (CFL3D) for the flow over a two-dimensional NACA-0012 airfoil. The results suggest that the version of PowerFLOW used in the investigation produced solutions with large errors in the computed flow field; these errors are attributed to inadequate resolution of the boundary layer for reasons related to grid resolution and primitive turbulence modeling. The requirement of square grid cells in the PowerFLOW calculations limited the number of points that could be used to span the boundary layer on the wing and still keep the computation size small enough to fit on the available computers. Although not discussed in detail, disappointing results were also obtained with PowerFLOW for a cavity flow and for the flow around a generic helicopter configuration.

A multigrid nonoscillatory method for computing high speed flows

NASA Technical Reports Server (NTRS)

Li, C. P.; Shieh, T. H.

1993-01-01

A multigrid method using different smoothers has been developed to solve the Euler equations discretized by a nonoscillatory scheme up to fourth order accuracy. The best smoothing property is provided by a five-stage Runge-Kutta technique with optimized coefficients, yet the most efficient smoother is a backward Euler technique in factored and diagonalized form. The singlegrid solution for a hypersonic, viscous conic flow is in excellent agreement with the solution obtained by the third order MUSCL and Roe's method. Mach 8 inviscid flow computations for a complete entry probe have shown that the accuracy is at least as good as the symmetric TVD scheme of Yee and Harten. The implicit multigrid method is four times more efficient than the explicit multigrid technique and 3.5 times faster than the single-grid implicit technique. For a Mach 8.7 inviscid flow over a blunt delta wing at 30 deg incidence, the CPU reduction factor from the three-level multigrid computation is 2.2 on a grid of 37 x 41 x 73 nodes.

On buffer layers as non-reflecting computational boundaries

NASA Technical Reports Server (NTRS)

Hayder, M. Ehtesham; Turkel, Eli L.

1996-01-01

We examine an absorbing buffer layer technique for use as a non-reflecting boundary condition in the numerical simulation of flows. One such formulation was by Ta'asan and Nark for the linearized Euler equations. They modified the flow inside the buffer zone to artificially make it supersonic in the layer. We examine how this approach can be extended to the nonlinear Euler equations. We consider both a conservative and a non-conservative form modifying the governing equations in the buffer layer. We compare this with the case that the governing equations in the layer are the same as in the interior domain. We test the effectiveness of these buffer layers by a simulation of an excited axisymmetric jet based on a nonlinear compressible Navier-Stokes equations.

Existence of the passage to the limit of an inviscid fluid.

PubMed

Goldobin, Denis S

2017-11-24

In the dynamics of a viscous fluid, the case of vanishing kinematic viscosity is actually equivalent to the Reynolds number tending to infinity. Hence, in the limit of vanishing viscosity the fluid flow is essentially turbulent. On the other hand, the Euler equation, which is conventionally adopted for the description of the flow of an inviscid fluid, does not possess proper turbulent behaviour. This raises the question of the existence of the passage to the limit of an inviscid fluid for real low-viscosity fluids. To address this question, one should employ the theory of turbulent boundary layer near an inflexible boundary (e.g., rigid wall). On the basis of this theory, one can see how the solutions to the Euler equation become relevant for the description of the flow of low-viscosity fluids, and obtain the small parameter quantifying accuracy of this description for real fluids.

Supersonic wing and wing-body shape optimization using an adjoint formulation

NASA Technical Reports Server (NTRS)

Reuther, James; Jameson, Antony

1995-01-01

This paper describes the implementation of optimization techniques based on control theory for wing and wing-body design of supersonic configurations. The work represents an extension of our earlier research in which control theory is used to devise a design procedure that significantly reduces the computational cost by employing an adjoint equation. In previous studies it was shown that control theory could be used toeviseransonic design methods for airfoils and wings in which the shape and the surrounding body-fitted mesh are both generated analytically, and the control is the mapping function. The method has also been implemented for both transonic potential flows and transonic flows governed by the Euler equations using an alternative formulation which employs numerically generated grids, so that it can treat more general configurations. Here results are presented for three-dimensional design cases subject to supersonic flows governed by the Euler equation.

Second-Moment RANS Model Verification and Validation Using the Turbulence Modeling Resource Website (Invited)

NASA Technical Reports Server (NTRS)

Eisfeld, Bernhard; Rumsey, Chris; Togiti, Vamshi

2015-01-01

The implementation of the SSG/LRR-omega differential Reynolds stress model into the NASA flow solvers CFL3D and FUN3D and the DLR flow solver TAU is verified by studying the grid convergence of the solution of three different test cases from the Turbulence Modeling Resource Website. The model's predictive capabilities are assessed based on four basic and four extended validation cases also provided on this website, involving attached and separated boundary layer flows, effects of streamline curvature and secondary flow. Simulation results are compared against experimental data and predictions by the eddy-viscosity models of Spalart-Allmaras (SA) and Menter's Shear Stress Transport (SST).

A Three-Dimensional Linearized Unsteady Euler Analysis for Turbomachinery Blade Rows

NASA Technical Reports Server (NTRS)

Montgomery, Matthew D.; Verdon, Joseph M.

1997-01-01

A three-dimensional, linearized, Euler analysis is being developed to provide an efficient unsteady aerodynamic analysis that can be used to predict the aeroelastic and aeroacoustic responses of axial-flow turbo-machinery blading.The field equations and boundary conditions needed to describe nonlinear and linearized inviscid unsteady flows through a blade row operating within a cylindrical annular duct are presented. A numerical model for linearized inviscid unsteady flows, which couples a near-field, implicit, wave-split, finite volume analysis to a far-field eigenanalysis, is also described. The linearized aerodynamic and numerical models have been implemented into a three-dimensional linearized unsteady flow code, called LINFLUX. This code has been applied to selected, benchmark, unsteady, subsonic flows to establish its accuracy and to demonstrate its current capabilities. The unsteady flows considered, have been chosen to allow convenient comparisons between the LINFLUX results and those of well-known, two-dimensional, unsteady flow codes. Detailed numerical results for a helical fan and a three-dimensional version of the 10th Standard Cascade indicate that important progress has been made towards the development of a reliable and useful, three-dimensional, prediction capability that can be used in aeroelastic and aeroacoustic design studies.

Development of new vibration energy flow analysis software and its applications to vehicle systems

NASA Astrophysics Data System (ADS)

Kim, D.-J.; Hong, S.-Y.; Park, Y.-H.

2005-09-01

The Energy flow analysis (EFA) offers very promising results in predicting the noise and vibration responses of system structures in medium-to-high frequency ranges. We have developed the Energy flow finite element method (EFFEM) based software, EFADSC++ R4, for the vibration analysis. The software can analyze the system structures composed of beam, plate, spring-damper, rigid body elements and many other components developed, and has many useful functions in analysis. For convenient use of the software, the main functions of the whole software are modularized into translator, model-converter, and solver. The translator module makes it possible to use finite element (FE) model for the vibration analysis. The model-converter module changes FE model into energy flow finite element (EFFE) model, and generates joint elements to cover the vibrational attenuation in the complex structures composed of various elements and can solve the joint element equations by using the wave tra! nsmission approach very quickly. The solver module supports the various direct and iterative solvers for multi-DOF structures. The predictions of vibration for real vehicles by using the developed software were performed successfully.

Eddylicious: A Python package for turbulent inflow generation

NASA Astrophysics Data System (ADS)

Mukha, Timofey; Liefvendahl, Mattias

2018-01-01

A Python package for generating inflow for scale-resolving computer simulations of turbulent flow is presented. The purpose of the package is to unite existing inflow generation methods in a single code-base and make them accessible to users of various Computational Fluid Dynamics (CFD) solvers. The currently existing functionality consists of an accurate inflow generation method suitable for flows with a turbulent boundary layer inflow and input/output routines for coupling with the open-source CFD solver OpenFOAM.

Development of upwind schemes for the Euler equations

NASA Technical Reports Server (NTRS)

Chakravarthy, Sukumar R.

1987-01-01

Described are many algorithmic and computational aspects of upwind schemes and their second-order accurate formulations based on Total-Variation-Diminishing (TVD) approaches. An operational unification of the underlying first-order scheme is first presented encompassing Godunov's, Roe's, Osher's, and Split-Flux methods. For higher order versions, the preprocessing and postprocessing approaches to constructing TVD discretizations are considered. TVD formulations can be used to construct relaxation methods for unfactored implicit upwind schemes, which in turn can be exploited to construct space-marching procedures for even the unsteady Euler equations. A major part of the report describes time- and space-marching procedures for solving the Euler equations in 2-D, 3-D, Cartesian, and curvilinear coordinates. Along with many illustrative examples, several results of efficient computations on 3-D supersonic flows with subsonic pockets are presented.

An accuracy assessment of Cartesian-mesh approaches for the Euler equations

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1995-01-01

A critical assessment of the accuracy of Cartesian-mesh approaches for steady, transonic solutions of the Euler equations of gas dynamics is made. An exact solution of the Euler equations (Ringleb's flow) is used not only to infer the order of the truncation error of the Cartesian-mesh approaches, but also to compare the magnitude of the discrete error directly to that obtained with a structured mesh approach. Uniformly and adaptively refined solutions using a Cartesian-mesh approach are obtained and compared to each other and to uniformly refined structured mesh results. The effect of cell merging is investigated as well as the use of two different K-exact reconstruction procedures. The solution methodology of the schemes is explained and tabulated results are presented to compare the solution accuracies.

Calculations of steady and transient channel flows with a time-accurate L-U factorization scheme

NASA Technical Reports Server (NTRS)

Kim, S.-W.

1991-01-01

Calculations of steady and unsteady, transonic, turbulent channel flows with a time accurate, lower-upper (L-U) factorization scheme are presented. The L-U factorization scheme is formally second-order accurate in time and space, and it is an extension of the steady state flow solver (RPLUS) used extensively to solve compressible flows. A time discretization method and the implementation of a consistent boundary condition specific to the L-U factorization scheme are also presented. The turbulence is described by the Baldwin-Lomax algebraic turbulence model. The present L-U scheme yields stable numerical results with the use of much smaller artificial dissipations than those used in the previous steady flow solver for steady and unsteady channel flows. The capability to solve time dependent flows is shown by solving very weakly excited and strongly excited, forced oscillatory, channel flows.

Effect of helicity on the correlation time of large scales in turbulent flows

NASA Astrophysics Data System (ADS)

Cameron, Alexandre; Alexakis, Alexandros; Brachet, Marc-Étienne

2017-11-01

Solutions of the forced Navier-Stokes equation have been conjectured to thermalize at scales larger than the forcing scale, similar to an absolute equilibrium obtained for the spectrally truncated Euler equation. Using direct numeric simulations of Taylor-Green flows and general-periodic helical flows, we present results on the probability density function, energy spectrum, autocorrelation function, and correlation time that compare the two systems. In the case of highly helical flows, we derive an analytic expression describing the correlation time for the absolute equilibrium of helical flows that is different from the E-1 /2k-1 scaling law of weakly helical flows. This model predicts a new helicity-based scaling law for the correlation time as τ (k ) ˜H-1 /2k-1 /2 . This scaling law is verified in simulations of the truncated Euler equation. In simulations of the Navier-Stokes equations the large-scale modes of forced Taylor-Green symmetric flows (with zero total helicity and large separation of scales) follow the same properties as absolute equilibrium including a τ (k ) ˜E-1 /2k-1 scaling for the correlation time. General-periodic helical flows also show similarities between the two systems; however, the largest scales of the forced flows deviate from the absolute equilibrium solutions.

Development of an Unstructured Mesh Code for Flows About Complete Vehicles

NASA Technical Reports Server (NTRS)

Peraire, Jaime; Gupta, K. K. (Technical Monitor)

2001-01-01

This report describes the research work undertaken at the Massachusetts Institute of Technology, under NASA Research Grant NAG4-157. The aim of this research is to identify effective algorithms and methodologies for the efficient and routine solution of flow simulations about complete vehicle configurations. For over ten years we have received support from NASA to develop unstructured mesh methods for Computational Fluid Dynamics. As a result of this effort a methodology based on the use of unstructured adapted meshes of tetrahedra and finite volume flow solvers has been developed. A number of gridding algorithms, flow solvers, and adaptive strategies have been proposed. The most successful algorithms developed from the basis of the unstructured mesh system FELISA. The FELISA system has been extensively for the analysis of transonic and hypersonic flows about complete vehicle configurations. The system is highly automatic and allows for the routine aerodynamic analysis of complex configurations starting from CAD data. The code has been parallelized and utilizes efficient solution algorithms. For hypersonic flows, a version of the code which incorporates real gas effects, has been produced. The FELISA system is also a component of the STARS aeroservoelastic system developed at NASA Dryden. One of the latest developments before the start of this grant was to extend the system to include viscous effects. This required the development of viscous generators, capable of generating the anisotropic grids required to represent boundary layers, and viscous flow solvers. We show some sample hypersonic viscous computations using the developed viscous generators and solvers. Although this initial results were encouraging it became apparent that in order to develop a fully functional capability for viscous flows, several advances in solution accuracy, robustness and efficiency were required. In this grant we set out to investigate some novel methodologies that could lead to the required improvements. In particular we focused on two fronts: (1) finite element methods and (2) iterative algebraic multigrid solution techniques.

Unsteady, Cooled Turbine Simulation Using a PC-Linux Analysis System

NASA Technical Reports Server (NTRS)

List, Michael G.; Turner, Mark G.; Chen, Jen-Pimg; Remotigue, Michael G.; Veres, Joseph P.

2004-01-01

The fist stage of the high-pressure turbine (HPT) of the GE90 engine was simulated with a three-dimensional unsteady Navier-Sokes solver, MSU Turbo, which uses source terms to simulate the cooling flows. In addition to the solver, its pre-processor, GUMBO, and a post-processing and visualization tool, Turbomachinery Visual3 (TV3) were run in a Linux environment to carry out the simulation and analysis. The solver was run both with and without cooling. The introduction of cooling flow on the blade surfaces, case, and hub and its effects on both rotor-vane interaction as well the effects on the blades themselves were the principle motivations for this study. The studies of the cooling flow show the large amount of unsteadiness in the turbine and the corresponding hot streak migration phenomenon. This research on the GE90 turbomachinery has also led to a procedure for running unsteady, cooled turbine analysis on commodity PC's running the Linux operating system.

Nonlinear vocal fold dynamics resulting from asymmetric fluid loading on a two-mass model of speech

NASA Astrophysics Data System (ADS)

Erath, Byron D.; Zañartu, Matías; Peterson, Sean D.; Plesniak, Michael W.

2011-09-01

Nonlinear vocal fold dynamics arising from asymmetric flow formations within the glottis are investigated using a two-mass model of speech with asymmetric vocal fold tensioning, representative of unilateral vocal fold paralysis. A refined theoretical boundary-layer flow solver is implemented to compute the intraglottal pressures, providing a more realistic description of the flow than the standard one-dimensional, inviscid Bernoulli flow solution. Vocal fold dynamics are investigated for subglottal pressures of 0.6 < ps < 1.5 kPa and tension asymmetries of 0.5 < Q < 0.8. As tension asymmetries become pronounced the asymmetric flow incites nonlinear behavior in the vocal fold dynamics at subglottal pressures that are associated with normal speech, behavior that is not captured with standard Bernoulli flow solvers. Regions of bifurcation, coexistence of solutions, and chaos are identified.

Method and apparatus for automatically generating airfoil performance tables

NASA Technical Reports Server (NTRS)

van Dam, Cornelis P. (Inventor); Mayda, Edward A. (Inventor); Strawn, Roger Clayton (Inventor)

2006-01-01

One embodiment of the present invention provides a system that facilitates automatically generating a performance table for an object, wherein the object is subject to fluid flow. The system operates by first receiving a description of the object and testing parameters for the object. The system executes a flow solver using the testing parameters and the description of the object to produce an output. Next, the system determines if the output of the flow solver indicates negative density or pressure. If not, the system analyzes the output to determine if the output is converging. If converging, the system writes the output to the performance table for the object.

Breakdown of the conservative potential equation

NASA Technical Reports Server (NTRS)

Salas, M. D.; Gumbert, C. R.

1986-01-01

The conservative full-potential equation is used to study transonic flow over five airfoil sections. The results of the study indicate that once shock are present in the flow, the qualitative approximation is different from that observed with the Euler equations. The difference in behavior of the potential eventually leads to multiple solutions.

Navier-Stokes analysis of an oxidizer turbine blade with tip clearance

NASA Technical Reports Server (NTRS)

Gibeling, Howard J.; Sabnis, Jayant S.

1992-01-01

The Gas Generator Oxidizer Turbine (GGOT) Blade is being analyzed by various investigators under the NASA MSFC sponsored Turbine Stage Technology Team design effort. The present work concentrates on the tip clearance region flow and associated losses; however, flow details for the passage region are also obtained in the simulations. The present calculations simulate the rotor blade row in a rotating reference frame with the appropriate coriolis and centrifugal acceleration terms included in the momentum equation. The upstream computational boundary is located about one axial chord from the blade leading edge. The boundary conditions at this location were determined by using a Euler analysis without the vanes to obtain approximately the same flow profiles at the rotor as were obtained with the Euler stage analysis including the vanes. Inflow boundary layer profiles are then constructed assuming the skin friction coefficient at both the hub and the casing. The downstream computational boundary is located about one axial chord from the blade trailing edge, and the circumferentially averaged static pressure at this location was also obtained from the Euler analysis. Results were obtained for the 3-D baseline GGOT geometry at the full scale design Reynolds number. Details of the clearance region flow behavior and blade pressure distributions were computed. The spanwise variation in blade loading distributions are shown, and circumferentially averaged spanwise distributions of total pressure, total temperature, Mach number, and flow angle are shown at several axial stations. The spanwise variation of relative total pressure loss shows a region of high loss in the region near the casing. Particle traces in the near tip region show vortical behavior of the fluid which passes through the clearance region and exits at the downstream edge of the gap.

A Three-Dimensional Linearized Unsteady Euler Analysis for Turbomachinery Blade Rows

NASA Technical Reports Server (NTRS)

Montgomery, Matthew D.; Verdon, Joseph M.

1996-01-01

A three-dimensional, linearized, Euler analysis is being developed to provide an efficient unsteady aerodynamic analysis that can be used to predict the aeroelastic and aeroacoustic response characteristics of axial-flow turbomachinery blading. The field equations and boundary conditions needed to describe nonlinear and linearized inviscid unsteady flows through a blade row operating within a cylindrical annular duct are presented. In addition, a numerical model for linearized inviscid unsteady flow, which is based upon an existing nonlinear, implicit, wave-split, finite volume analysis, is described. These aerodynamic and numerical models have been implemented into an unsteady flow code, called LINFLUX. A preliminary version of the LINFLUX code is applied herein to selected, benchmark three-dimensional, subsonic, unsteady flows, to illustrate its current capabilities and to uncover existing problems and deficiencies. The numerical results indicate that good progress has been made toward developing a reliable and useful three-dimensional prediction capability. However, some problems, associated with the implementation of an unsteady displacement field and numerical errors near solid boundaries, still exist. Also, accurate far-field conditions must be incorporated into the FINFLUX analysis, so that this analysis can be applied to unsteady flows driven be external aerodynamic excitations.

Multifidelity Analysis and Optimization for Supersonic Design

NASA Technical Reports Server (NTRS)

Kroo, Ilan; Willcox, Karen; March, Andrew; Haas, Alex; Rajnarayan, Dev; Kays, Cory

2010-01-01

Supersonic aircraft design is a computationally expensive optimization problem and multifidelity approaches over a significant opportunity to reduce design time and computational cost. This report presents tools developed to improve supersonic aircraft design capabilities including: aerodynamic tools for supersonic aircraft configurations; a systematic way to manage model uncertainty; and multifidelity model management concepts that incorporate uncertainty. The aerodynamic analysis tools developed are appropriate for use in a multifidelity optimization framework, and include four analysis routines to estimate the lift and drag of a supersonic airfoil, a multifidelity supersonic drag code that estimates the drag of aircraft configurations with three different methods: an area rule method, a panel method, and an Euler solver. In addition, five multifidelity optimization methods are developed, which include local and global methods as well as gradient-based and gradient-free techniques.

Thermodynamical effects and high resolution methods for compressible fluid flows

NASA Astrophysics Data System (ADS)

Li, Jiequan; Wang, Yue

2017-08-01

One of the fundamental differences of compressible fluid flows from incompressible fluid flows is the involvement of thermodynamics. This difference should be manifested in the design of numerical schemes. Unfortunately, the role of entropy, expressing irreversibility, is often neglected even though the entropy inequality, as a conceptual derivative, is verified for some first order schemes. In this paper, we refine the GRP solver to illustrate how the thermodynamical variation is integrated into the design of high resolution methods for compressible fluid flows and demonstrate numerically the importance of thermodynamic effects in the resolution of strong waves. As a by-product, we show that the GRP solver works for generic equations of state, and is independent of technical arguments.

Reduction of numerical diffusion in three-dimensional vortical flows using a coupled Eulerian/Lagrangian solution procedure

NASA Technical Reports Server (NTRS)

Felici, Helene M.; Drela, Mark

1993-01-01

A new approach based on the coupling of an Eulerian and a Lagrangian solver, aimed at reducing the numerical diffusion errors of standard Eulerian time-marching finite-volume solvers, is presented. The approach is applied to the computation of the secondary flow in two bent pipes and the flow around a 3D wing. Using convective point markers the Lagrangian approach provides a correction of the basic Eulerian solution. The Eulerian flow in turn integrates in time the Lagrangian state-vector. A comparison of coarse and fine grid Eulerian solutions makes it possible to identify numerical diffusion. It is shown that the Eulerian/Lagrangian approach is an effective method for reducing numerical diffusion errors.

Implementation of Advanced Two Equation Turbulence Models in the USM3D Unstructured Flow Solver

NASA Technical Reports Server (NTRS)

Wang, Qun-Zhen; Massey, Steven J.; Abdol-Hamid, Khaled S.

2000-01-01

USM3D is a widely-used unstructured flow solver for simulating inviscid and viscous flows over complex geometries. The current version (version 5.0) of USM3D, however, does not have advanced turbulence models to accurately simulate complicated flow. We have implemented two modified versions of the original Jones and Launder k-epsilon "two-equation" turbulence model and the Girimaji algebraic Reynolds stress model in USM3D. Tests have been conducted for three flat plate boundary layer cases, a RAE2822 airfoil and an ONERA M6 wing. The results are compared with those from direct numerical simulation, empirical formulae, theoretical results, and the existing Spalart-Allmaras one-equation model.

Prediction and Reduction of Noise in Pneumatic Bleed Valves

NASA Astrophysics Data System (ADS)

Taghavi Nezhad, Shervin

This study investigates numerically the fluid mechanics and acoustics of pneumatic bleed valves used in turbofan engines. The goal is to characterized the fundamental processes of noise generation and devise strategies for noise reduction. Three different methods are employed for both analysis and redesign of the bleed valve to reduce noise. The bleed valve noise problem is carefully divided into multiple smaller problems. For large separations and tonal noises, the unsteady Reynolds-Averaged Navier-Stokes (URANS) method is utilized. This method is also applied in the re-designing of the bleed valve geometry. For the bleed valve muffler, which is comprised of perforated plates and a honeycomb, a Reynolds-Averaged Navier-Stokes (RANS) method combined with a simplified acoustic analogy is used. The original muffler design is modified to improve noise attenuation. Finally, for sound scattering through perforated plates, a fully implicit linearized Euler solver is developed. The problem of sound interaction with perforated plates is studied from two perspectives. In the first study the effect of high--speed mean flow is considered and it is shown that at Strouhal numbers of around 0.2-0.25 there is an increase in transmitted incident sound. In the second part, the interaction of holes in two--dimensional perforated plates is investigated using three different configurations. The study demonstrates that the hole interaction has a significant impact on sound attenuation, especially at high frequencies.

Evaluation of a transient, simultaneous, arbitrary Lagrange-Euler based multi-physics method for simulating the mitral heart valve.

PubMed

Espino, Daniel M; Shepherd, Duncan E T; Hukins, David W L

2014-01-01

A transient multi-physics model of the mitral heart valve has been developed, which allows simultaneous calculation of fluid flow and structural deformation. A recently developed contact method has been applied to enable simulation of systole (the stage when blood pressure is elevated within the heart to pump blood to the body). The geometry was simplified to represent the mitral valve within the heart walls in two dimensions. Only the mitral valve undergoes deformation. A moving arbitrary Lagrange-Euler mesh is used to allow true fluid-structure interaction (FSI). The FSI model requires blood flow to induce valve closure by inducing strains in the region of 10-20%. Model predictions were found to be consistent with existing literature and will undergo further development.

Two-dimensional Euler and Navier-Stokes Time accurate simulations of fan rotor flows

NASA Technical Reports Server (NTRS)

Boretti, A. A.

1990-01-01

Two numerical methods are presented which describe the unsteady flow field in the blade-to-blade plane of an axial fan rotor. These methods solve the compressible, time-dependent, Euler and the compressible, turbulent, time-dependent, Navier-Stokes conservation equations for mass, momentum, and energy. The Navier-Stokes equations are written in Favre-averaged form and are closed with an approximate two-equation turbulence model with low Reynolds number and compressibility effects included. The unsteady aerodynamic component is obtained by superposing inflow or outflow unsteadiness to the steady conditions through time-dependent boundary conditions. The integration in space is performed by using a finite volume scheme, and the integration in time is performed by using k-stage Runge-Kutta schemes, k = 2,5. The numerical integration algorithm allows the reduction of the computational cost of an unsteady simulation involving high frequency disturbances in both CPU time and memory requirements. Less than 200 sec of CPU time are required to advance the Euler equations in a computational grid made up of about 2000 grid during 10,000 time steps on a CRAY Y-MP computer, with a required memory of less than 0.3 megawords.

Navier-Stokes analysis of an oxidizer turbine blade with tip clearance with and without a mini-shroud

NASA Technical Reports Server (NTRS)

Chan, Tony; Dejong, Frederik J.

1993-01-01

The Gas Generator Oxidizer Turbine (GGOT) Blade is being analyzed by various investigators under the NASA MSFC-sponsored Turbine Stage Technology Team design effort. The present work concentrates on the tip clearance region flow and associated losses; however, flow details for the passage region are also obtained in the simulations. The present calculations simulate the rotor blade row in a rotating reference frame with the appropriate coriolis and centrifugal acceleration term included in the momentum equations. The upstream computational boundary is located about one axial chord from the blade leading edge. The boundary conditions at this location have been determined by Pratt & Whitney using an Euler analysis without the vanes to obtain approximately the same flow profiles at the rotor as were obtained with the Euler stage analysis including the vanes. Inflow boundary layer profiles are then constructed assuming the skin friction coefficient at both the hub and the casing. The downstream computational boundary is located about one axial chord from the blade trailing edge, and the circumferentially averaged static pressure at this location was also obtained from the P&W Euler analysis. Results obtained for the 3-D baseline GGOT geometry at the full scale design Reynolds number show a region of high loss in the region near the casing. Particle traces in the near tip region show vortical flow behavior of the fluid which passes through the clearance region and exits at the downstream edge of the gap. In an effort to reduce clearance flow losses, the mini-shroud concept was proposed by the Pratt & Whitney design team. Calculations were performed on the GGO geometry with the mini-shroud. Results of these calculations indicate that the mini-shroud does not significantly affect the flow in the passage region, and although the tip clearance flow is different, the mini-shroud does not seem to prevent the above-mentioned vortical flow behavior. Since both flow distortion and total pressure losses are similar for both geometries, the addition of the mini-shroud does not seem to reduce the tip clearance flow effects.

Integrated multidisciplinary CAD/CAE environment for micro-electro-mechanical systems (MEMS)

NASA Astrophysics Data System (ADS)

Przekwas, Andrzej J.

1999-03-01

Computational design of MEMS involves several strongly coupled physical disciplines, including fluid mechanics, heat transfer, stress/deformation dynamics, electronics, electro/magneto statics, calorics, biochemistry and others. CFDRC is developing a new generation multi-disciplinary CAD systems for MEMS using high-fidelity field solvers on unstructured, solution-adaptive grids for a full range of disciplines. The software system, ACE + MEMS, includes all essential CAD tools; geometry/grid generation for multi- discipline, multi-equation solvers, GUI, tightly coupled configurable 3D field solvers for FVM, FEM and BEM and a 3D visualization/animation tool. The flow/heat transfer/calorics/chemistry equations are solved with unstructured adaptive FVM solver, stress/deformation are computed with a FEM STRESS solver and a FAST BEM solver is used to solve linear heat transfer, electro/magnetostatics and elastostatics equations on adaptive polygonal surface grids. Tight multidisciplinary coupling and automatic interoperability between the tools was achieved by designing a comprehensive database structure and APIs for complete model definition. The virtual model definition is implemented in data transfer facility, a publicly available tool described in this paper. The paper presents overall description of the software architecture and MEMS design flow in ACE + MEMS. It describes current status, ongoing effort and future plans for the software. The paper also discusses new concepts of mixed-level and mixed- dimensionality capability in which 1D microfluidic networks are simulated concurrently with 3D high-fidelity models of discrete components.

Unstructured Mesh Methods for the Simulation of Hypersonic Flows

NASA Technical Reports Server (NTRS)

Peraire, Jaime; Bibb, K. L. (Technical Monitor)

2001-01-01

This report describes the research work undertaken at the Massachusetts Institute of Technology. The aim of this research is to identify effective algorithms and methodologies for the efficient and routine solution of hypersonic viscous flows about re-entry vehicles. For over ten years we have received support from NASA to develop unstructured mesh methods for Computational Fluid Dynamics. As a result of this effort a methodology based on the use, of unstructured adapted meshes of tetrahedra and finite volume flow solvers has been developed. A number of gridding algorithms flow solvers, and adaptive strategies have been proposed. The most successful algorithms developed from the basis of the unstructured mesh system FELISA. The FELISA system has been extensively for the analysis of transonic and hypersonic flows about complete vehicle configurations. The system is highly automatic and allows for the routine aerodynamic analysis of complex configurations starting from CAD data. The code has been parallelized and utilizes efficient solution algorithms. For hypersonic flows, a version of the, code which incorporates real gas effects, has been produced. One of the latest developments before the start of this grant was to extend the system to include viscous effects. This required the development of viscous generators, capable of generating the anisotropic grids required to represent boundary layers, and viscous flow solvers. In figures I and 2, we show some sample hypersonic viscous computations using the developed viscous generators and solvers. Although these initial results were encouraging, it became apparent that in order to develop a fully functional capability for viscous flows, several advances in gridding, solution accuracy, robustness and efficiency were required. As part of this research we have developed: 1) automatic meshing techniques and the corresponding computer codes have been delivered to NASA and implemented into the GridEx system, 2) a finite element algorithm for the solution of the viscous compressible flow equations which can solve flows all the way down to the incompressible limit and that can use higher order (quadratic) approximations leading to highly accurate answers, and 3) and iterative algebraic multigrid solution techniques.

Euler-Lagrange CFD modelling of unconfined gas mixing in anaerobic digestion.

PubMed

Dapelo, Davide; Alberini, Federico; Bridgeman, John

2015-11-15

A novel Euler-Lagrangian (EL) computational fluid dynamics (CFD) finite volume-based model to simulate the gas mixing of sludge for anaerobic digestion is developed and described. Fluid motion is driven by momentum transfer from bubbles to liquid. Model validation is undertaken by assessing the flow field in a labscale model with particle image velocimetry (PIV). Conclusions are drawn about the upscaling and applicability of the model to full-scale problems, and recommendations are given for optimum application. Copyright © 2015 Elsevier Ltd. All rights reserved.

Validation of High-Fidelity CFD/CAA Framework for Launch Vehicle Acoustic Environment Simulation against Scale Model Test Data

NASA Technical Reports Server (NTRS)

Liever, Peter A.; West, Jeffrey S.; Harris, Robert E.

2016-01-01

A hybrid Computational Fluid Dynamics and Computational Aero-Acoustics (CFD/CAA) modeling framework has been developed for launch vehicle liftoff acoustic environment predictions. The framework couples the existing highly-scalable NASA production CFD code, Loci/CHEM, with a high-order accurate Discontinuous Galerkin solver developed in the same production framework, Loci/THRUST, to accurately resolve and propagate acoustic physics across the entire launch environment. Time-accurate, Hybrid RANS/LES CFD modeling is applied for predicting the acoustic generation physics at the plume source, and a high-order accurate unstructured mesh Discontinuous Galerkin (DG) method is employed to propagate acoustic waves away from the source across large distances using high-order accurate schemes. The DG solver is capable of solving 2nd, 3rd, and 4th order Euler solutions for non-linear, conservative acoustic field propagation. Initial application testing and validation has been carried out against high resolution acoustic data from the Ares Scale Model Acoustic Test (ASMAT) series to evaluate the capabilities and production readiness of the CFD/CAA system to resolve the observed spectrum of acoustic frequency content. This paper presents results from this validation and outlines efforts to mature and improve the computational simulation framework.