An efficient and robust algorithm for two dimensional time dependent incompressible Navier-Stokes equations: High Reynolds number flows

NASA Technical Reports Server (NTRS)

Goodrich, John W.

1991-01-01

An algorithm is presented for unsteady two-dimensional incompressible Navier-Stokes calculations. This algorithm is based on the fourth order partial differential equation for incompressible fluid flow which uses the streamfunction as the only dependent variable. The algorithm is second order accurate in both time and space. It uses a multigrid solver at each time step. It is extremely efficient with respect to the use of both CPU time and physical memory. It is extremely robust with respect to Reynolds number.

On the ejection-induced instability in Navier-Stokes solutions of unsteady separation.

PubMed

Obabko, Aleksandr V; Cassel, Kevin W

2005-05-15

Numerical solutions of the flow induced by a thick-core vortex have been obtained using the unsteady, two-dimensional Navier-Stokes equations. The presence of the vortex causes an adverse pressure gradient along the surface, which leads to unsteady separation. The calculations by Brinckman and Walker for a similar flow identify a possible instability, purported to be an inviscid Rayleigh instability, in the region where ejection of near-wall vorticity occurs during the unsteady separation process. In results for a range of Reynolds numbers in the present investigation, the oscillations are also found to occur. However, they can be eliminated with increased grid resolution. Despite this behaviour, the instability may be physical but requires a sufficient amplitude of disturbances to be realized.

A fully vectorized numerical solution of the incompressible Navier-Stokes equations. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Patel, N.

1983-01-01

A vectorizable algorithm is presented for the implicit finite difference solution of the incompressible Navier-Stokes equations in general curvilinear coordinates. The unsteady Reynolds averaged Navier-Stokes equations solved are in two dimension and non-conservative primitive variable form. A two-layer algebraic eddy viscosity turbulence model is used to incorporate the effects of turbulence. Two momentum equations and a Poisson pressure equation, which is obtained by taking the divergence of the momentum equations and satisfying the continuity equation, are solved simultaneously at each time step. An elliptic grid generation approach is used to generate a boundary conforming coordinate system about an airfoil. The governing equations are expressed in terms of the curvilinear coordinates and are solved on a uniform rectangular computational domain. A checkerboard SOR, which can effectively utilize the computer architectural concept of vector processing, is used for iterative solution of the governing equations.

A Comparison of Hybrid Reynolds Averaged Navier Stokes/Large Eddy Simulation (RANS/LES) and Unsteady RANS Predictions of Separated Flow for a Variable Speed Power Turbine Blade Operating with Low Inlet Turbulence Levels

DTIC Science & Technology

2017-10-01

Facility is a large-scale cascade that allows detailed flow field surveys and blade surface measurements.10–12 The facility has a continuous run ...structured grids at 2 flow conditions, cruise and takeoff, of the VSPT blade . Computations were run in parallel on a Department of Defense...RANS/LES) and Unsteady RANS Predictions of Separated Flow for a Variable-Speed Power- Turbine Blade Operating with Low Inlet Turbulence Levels

What Was Learned in Predicting Slender Airframe Aerodynamics with the F-16XL Aircraft

NASA Technical Reports Server (NTRS)

Rizzi, Arthur; Luckring, James M.

2016-01-01

The second Cranked-Arrow Wing Aerodynamics Project, International, coordinated project has been underway to improve high-fidelity computational-fluid-dynamics predictions of slender airframe aerodynamics. The work is focused on two flow conditions and leverages a unique flight data set obtained with the F-16XL aircraft for comparison and validation. These conditions, a low-speed high-angle-of-attack case and a transonic low-angle-of-attack case, were selected from a prior prediction campaign wherein the computational fluid dynamics failed to provide acceptable results. In revisiting these two cases, approaches for improved results include better, denser grids using more grid adaptation to local flow features as well as unsteady higher-fidelity physical modeling like hybrid Reynolds-averaged Navier-Stokes/unsteady Reynolds-averaged Navier-Stokes/large-eddy simulation methods. The work embodies predictions from multiple numerical formulations that are contributed from multiple organizations where some authors investigate other possible factors that could explain the discrepancies in agreement (e.g., effects due to deflected control surfaces during the flight tests as well as static aeroelastic deflection of the outer wing). This paper presents the synthesis of all the results and findings and draws some conclusions that lead to an improved understanding of the underlying flow physics, finally making the connections between the physics and aircraft features.

Retrospective cost adaptive Reynolds-averaged Navier-Stokes k-ω model for data-driven unsteady turbulent simulations

NASA Astrophysics Data System (ADS)

Li, Zhiyong; Hoagg, Jesse B.; Martin, Alexandre; Bailey, Sean C. C.

2018-03-01

This paper presents a data-driven computational model for simulating unsteady turbulent flows, where sparse measurement data is available. The model uses the retrospective cost adaptation (RCA) algorithm to automatically adjust the closure coefficients of the Reynolds-averaged Navier-Stokes (RANS) k- ω turbulence equations to improve agreement between the simulated flow and the measurements. The RCA-RANS k- ω model is verified for steady flow using a pipe-flow test case and for unsteady flow using a surface-mounted-cube test case. Measurements used for adaptation of the verification cases are obtained from baseline simulations with known closure coefficients. These verification test cases demonstrate that the RCA-RANS k- ω model can successfully adapt the closure coefficients to improve agreement between the simulated flow field and a set of sparse flow-field measurements. Furthermore, the RCA-RANS k- ω model improves agreement between the simulated flow and the baseline flow at locations at which measurements do not exist. The RCA-RANS k- ω model is also validated with experimental data from 2 test cases: steady pipe flow, and unsteady flow past a square cylinder. In both test cases, the adaptation improves agreement with experimental data in comparison to the results from a non-adaptive RANS k- ω model that uses the standard values of the k- ω closure coefficients. For the steady pipe flow, adaptation is driven by mean stream-wise velocity measurements at 24 locations along the pipe radius. The RCA-RANS k- ω model reduces the average velocity error at these locations by over 35%. For the unsteady flow over a square cylinder, adaptation is driven by time-varying surface pressure measurements at 2 locations on the square cylinder. The RCA-RANS k- ω model reduces the average surface-pressure error at these locations by 88.8%.

Study of Convective Flow Effects in Endwall Casing Treatments in Transonic Compressor Rotors

NASA Technical Reports Server (NTRS)

Hah, Chunill; Mueller, Martin W.; Schiffer, Heinz-Peter

2012-01-01

The unsteady convective flow effects in a transonic compressor rotor with a circumferential-groove casing treatment are investigated in this paper. Experimental results show that the circumferential-groove casing treatment increases the compressor stall margin by almost 50% for the current transonic compressor rotor. Steady flow simulation of the current casing treatment, however, yields only a 15% gain in stall margin. The flow field at near-stall operation is highly unsteady due to several self-induced flow phenomena. These include shock oscillation, vortex shedding at the trailing edge, and interaction between the passage shock and the tip clearance vortex. The primary focus of the current investigation is to assess the effects of flow unsteadiness and unsteady flow convection on the circumferential-groove casing treatment. Unsteady Reynolds-averaged Navier-Stokes (URANS) and Large Eddy Simulation (LES) techniques were applied in addition to steady Reynolds-averaged Navier-Stokes (RANS) to simulate the flow field at near-stall operation and to determine changes in stall margin. The current investigation reveals that unsteady flow effects are as important as steady flow effects on the performance of the circumferential grooves casing treatment in extending the stall margin of the current transonic compressor rotor. The primary unsteady flow mechanism is unsteady flow injection from the grooves into the main flow near the casing. Flows moving into and out of the grooves are caused due to local pressure difference near the grooves. As the pressure field becomes transient due to self-induced flow oscillation, flow injection from the grooves also becomes unsteady. The unsteady flow simulation shows that this unsteady flow injection from the grooves is substantial and contributes significantly to extending the compressor stall margin. Unsteady flows into and out of the grooves have as large a role as steady flows in the circumferential grooves. While the circumferential-groove casing treatment seems to be a steady flow device, unsteady flow effects should be included to accurately assess its performance as the flow is transient at near-stall operation.

PAB3D: Its History in the Use of Turbulence Models in the Simulation of Jet and Nozzle Flows

NASA Technical Reports Server (NTRS)

Abdol-Hamid, Khaled S.; Pao, S. Paul; Hunter, Craig A.; Deere, Karen A.; Massey, Steven J.; Elmiligui, Alaa

2006-01-01

This is a review paper for PAB3D s history in the implementation of turbulence models for simulating jet and nozzle flows. We describe different turbulence models used in the simulation of subsonic and supersonic jet and nozzle flows. The time-averaged simulations use modified linear or nonlinear two-equation models to account for supersonic flow as well as high temperature mixing. Two multiscale-type turbulence models are used for unsteady flow simulations. These models require modifications to the Reynolds Averaged Navier-Stokes (RANS) equations. The first scheme is a hybrid RANS/LES model utilizing the two-equation (k-epsilon) model with a RANS/LES transition function, dependent on grid spacing and the computed turbulence length scale. The second scheme is a modified version of the partially averaged Navier-Stokes (PANS) formulation. All of these models are implemented in the three-dimensional Navier-Stokes code PAB3D. This paper discusses computational methods, code implementation, computed results for a wide range of nozzle configurations at various operating conditions, and comparisons with available experimental data. Very good agreement is shown between the numerical solutions and available experimental data over a wide range of operating conditions.

Study of Liquid Breakup Process in Solid Rocket Motors

DTIC Science & Technology

2014-01-01

waves. The breakup level increases with the surrounding gas velocity; more liquid breakup in the nozzle throat reduces the liquid alumina droplet size...process of a liquid film that flows along the wall of a straight channel while a high-speed gas moves over it. We have used an unsteady-flow Reynolds...Averaged Navier-Stokes code (URANS) to investigate the interaction of the liquid film flow with the gas flow, and analyzed the breakup process for

Dakota Uncertainty Quantification Methods Applied to the CFD code Nek5000

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

Delchini, Marc-Olivier; Popov, Emilian L.; Pointer, William David

This report presents the state of advancement of a Nuclear Energy Advanced Modeling and Simulation (NEAMS) project to characterize the uncertainty of the computational fluid dynamics (CFD) code Nek5000 using the Dakota package for flows encountered in the nuclear engineering industry. Nek5000 is a high-order spectral element CFD code developed at Argonne National Laboratory for high-resolution spectral-filtered large eddy simulations (LESs) and unsteady Reynolds-averaged Navier-Stokes (URANS) simulations.

Preprocessor that Enables the Use of GridProTM Grids for Unsteady Reynolds-Averaged Navier-Stokes Code TURBO

NASA Technical Reports Server (NTRS)

Shyam, Vikram

2010-01-01

A preprocessor for the Computational Fluid Dynamics (CFD) code TURBO has been developed and tested. The preprocessor converts grids produced by GridPro (Program Development Company (PDC)) into a format readable by TURBO and generates the necessary input files associated with the grid. The preprocessor also generates information that enables the user to decide how to allocate the computational load in a multiple block per processor scenario.

Detached Eddy Simulation of Flap Side-Edge Flow

NASA Technical Reports Server (NTRS)

Balakrishnan, Shankar K.; Shariff, Karim R.

2016-01-01

Detached Eddy Simulation (DES) of flap side-edge flow was performed with a wing and half-span flap configuration used in previous experimental and numerical studies. The focus of the study is the unsteady flow features responsible for the production of far-field noise. The simulation was performed at a Reynolds number (based on the main wing chord) of 3.7 million. Reynolds Averaged Navier-Stokes (RANS) simulations were performed as a precursor to the DES. The results of these precursor simulations match previous experimental and RANS results closely. Although the present DES simulations have not reached statistical stationary yet, some unsteady features of the developing flap side-edge flowfield are presented. In the final paper it is expected that statistically stationary results will be presented including comparisons of surface pressure spectra with experimental data.

A Two-Stage Procedure Toward the Efficient Implementation of PANS and Other Hybrid Turbulence Models

NASA Technical Reports Server (NTRS)

Abdol-Hamid, Khaled S.; Girimaji, Sharath S.

2004-01-01

The main objective of this article is to introduce and to show the implementation of a novel two-stage procedure to efficiently estimate the level of scale resolution possible for a given flow on a given grid for Partial Averaged Navier-Stokes (PANS) and other hybrid models. It has been found that the prescribed scale resolution can play a major role in obtaining accurate flow solutions. The first step is to solve the unsteady or steady Reynolds Averaged Navier-Stokes (URANS/RANS) equations. From this preprocessing step, the turbulence length-scale field is obtained. This is then used to compute the characteristic length-scale ratio between the turbulence scale and the grid spacing. Based on this ratio, we can assess the finest scale resolution that a given grid for a given flow can support. Along with other additional criteria, we are able to analytically identify the appropriate hybrid solver resolution for different regions of the flow. This procedure removes the grid dependency issue that affects the results produced by different hybrid procedures in solving unsteady flows. The formulation, implementation methodology, and validation example are presented. We implemented this capability in a production Computational Fluid Dynamics (CFD) code, PAB3D, for the simulation of unsteady flows.

Computation of UH-60A Airloads Using CFD/CSD Coupling on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Biedron, Robert T.; Lee-Rausch, Elizabeth M.

2011-01-01

An unsteady Reynolds-averaged Navier-Stokes solver for unstructured grids is used to compute the rotor airloads on the UH-60A helicopter at high-speed and high thrust conditions. The flow solver is coupled to a rotorcraft comprehensive code in order to account for trim and aeroelastic deflections. Simulations are performed both with and without the fuselage, and the effects of grid resolution, temporal resolution and turbulence model are examined. Computed airloads are compared to flight data.

Study of Liquid Breakup Process in Solid Rocket Motor Nozzle

DTIC Science & Technology

2016-02-16

liquid film flow with the gas flow. The rate of the wave breakup was characterized by introducing Breakup-length, Ohnesorge Number (Oh) and Weber Number... liquid film that flows along the wall of a strraight test channel while a relatively higher-speed gas moves over it. We have used an unsteady-flow...Reynolds- Averaged Navier-Stokes code (URANS) to investigate the interaction of the liquid film flow with the gas flow. The rate of the wave breakup was

Prediction of asymmetric vortical flows around slender bodies using Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Liu, C. H.; Wong, Tin-Chee; Kandil, Osama A.

1992-01-01

Steady and unsteady asymmetric vortical flows around slender bodies at high angles of attack are solved using the unsteady, compressible, thin-layer Navier-Stokes equations. An implicit, upwind-biased, flux-difference splitting, finite-volume scheme is used for the numerical computations. For supersonic flows past point cones, the locally conical flow assumption have been used for efficient computational studies of this phenomenon. Asymmetric flows past a 5-deg semiapex-angle circular cone at different angles of attack, free-stream Mach numbers, and Reynolds numbers have been studied in responses to different sources of disturbances. The effects of grid fineness and computational domain size have also been investigated. Next, the responses of three-dimensional supersonic asymmetric flow around a 5-deg circular cone at different angles of attack and Reynolds numbers to short-duration sideslip disturbances are presented. The results show that flow asymmetry becomes stronger as the Reynolds number and angles of attack are increased. One of the cases of flow over a cone-cylinder configuration is validated fairly well by experimental data.

Numerical Simulation of the Flow over a Segment-Conical Body on the Basis of Reynolds Equations

NASA Astrophysics Data System (ADS)

Egorov, I. V.; Novikov, A. V.; Palchekovskaya, N. V.

2018-01-01

Numerical simulation was used to study the 3D supersonic flow over a segment-conical body similar in shape to the ExoMars space vehicle. The nonmonotone behavior of the normal force acting on the body placed in a supersonic gas flow was analyzed depending on the angle of attack. The simulation was based on the numerical solution of the unsteady Reynolds-averaged Navier-Stokes equations with a two-parameter differential turbulence model. The solution of the problem was obtained using the in-house solver HSFlow with an efficient parallel algorithm intended for multiprocessor super computers.

Large-Eddy / Reynolds-Averaged Navier-Stokes Simulations of a Dual-Mode Scramjet Combustor

NASA Technical Reports Server (NTRS)

Fulton, Jesse A.; Edwards, Jack R.; Hassan, Hassan A.; Rockwell, Robert; Goyne, Christopher; McDaniel, James; Smith, Chad; Cutler, Andrew; Johansen, Craig; Danehy, Paul M.;

Numerical solutions of the Navier-Stokes equations for the supersonic laminar flow over a two-dimensional compression corner

NASA Technical Reports Server (NTRS)

Carter, J. E.

1972-01-01

Numerical solutions have been obtained for the supersonic, laminar flow over a two-dimensional compression corner. These solutions were obtained as steady-state solutions to the unsteady Navier-Stokes equations using the finite difference method of Brailovskaya, which has second-order accuracy in the spatial coordinates. Good agreement was obtained between the computed results and wall pressure distributions measured experimentally for Mach numbers of 4 and 6.06, and respective Reynolds numbers, based on free-stream conditions and the distance from the leading edge to the corner. In those calculations, as well as in others, sufficient resolution was obtained to show the streamline pattern in the separation bubble. Upstream boundary conditions to the compression corner flow were provided by numerically solving the unsteady Navier-Stokes equations for the flat plate flow field, beginning at the leading edge. The compression corner flow field was enclosed by a computational boundary with the unknown boundary conditions supplied by extrapolation from internally computed points.

Computation of Sound Generated by Flow Over a Circular Cylinder: An Acoustic Analogy Approach

NASA Technical Reports Server (NTRS)

Brentner, Kenneth S.; Cox, Jared S.; Rumsey, Christopher L.; Younis, Bassam A.

1997-01-01

The sound generated by viscous flow past a circular cylinder is predicted via the Lighthill acoustic analogy approach. The two dimensional flow field is predicted using two unsteady Reynolds-averaged Navier-Stokes solvers. Flow field computations are made for laminar flow at three Reynolds numbers (Re = 1000, Re = 10,000, and Re = 90,000) and two different turbulent models at Re = 90,000. The unsteady surface pressures are utilized by an acoustics code that implements Farassat's formulation 1A to predict the acoustic field. The acoustic code is a 3-D code - 2-D results are found by using a long cylinder length. The 2-D predictions overpredict the acoustic amplitude; however, if correlation lengths in the range of 3 to 10 cylinder diameters are used, the predicted acoustic amplitude agrees well with experiment.

The Prediction and Analysis of Jet Flows and Scattered Turbulent Mixing Noise about Flight Vehicle Airframes

NASA Technical Reports Server (NTRS)

Miller, Steven A. E.

2014-01-01

Jet flows interacting with nearby surfaces exhibit a complex behavior in which acoustic and aerodynamic characteristics are altered. The physical understanding and prediction of these characteristics are essential to designing future low noise aircraft. A new approach is created for predicting scattered jet mixing noise that utilizes an acoustic analogy and steady Reynolds-averaged Navier-Stokes solutions. A tailored Green's function accounts for the propagation of mixing noise about the airframe and is calculated numerically using a newly developed ray tracing method. The steady aerodynamic statistics, associated unsteady sound source, and acoustic intensity are examined as jet conditions are varied about a large flat plate. A non-dimensional number is proposed to estimate the effect of the aerodynamic noise source relative to jet operating condition and airframe position.The steady Reynolds-averaged Navier-Stokes solutions, acoustic analogy, tailored Green's function, non-dimensional number, and predicted noise are validated with a wide variety of measurements. The combination of the developed theory, ray tracing method, and careful implementation in a stand-alone computer program result in an approach that is more first principles oriented than alternatives, computationally efficient, and captures the relevant physics of fluid-structure interaction.

The Prediction and Analysis of Jet Flows and Scattered Turbulent Mixing Noise About Flight Vehicle Airframes

NASA Technical Reports Server (NTRS)

Miller, Steven A.

2014-01-01

Jet flows interacting with nearby surfaces exhibit a complex behavior in which acoustic and aerodynamic characteristics are altered. The physical understanding and prediction of these characteristics are essential to designing future low noise aircraft. A new approach is created for predicting scattered jet mixing noise that utilizes an acoustic analogy and steady Reynolds-averaged Navier-Stokes solutions. A tailored Green's function accounts for the propagation of mixing noise about the air-frame and is calculated numerically using a newly developed ray tracing method. The steady aerodynamic statistics, associated unsteady sound source, and acoustic intensity are examined as jet conditions are varied about a large at plate. A non-dimensional number is proposed to estimate the effect of the aerodynamic noise source relative to jet operating condition and airframe position. The steady Reynolds-averaged Navier-Stokes solutions, acoustic analogy, tailored Green's function, non- dimensional number, and predicted noise are validated with a wide variety of measurements. The combination of the developed theory, ray tracing method, and careful implementation in a stand-alone computer program result in an approach that is more first principles oriented than alternatives, computationally efficient, and captures the relevant physics of fluid-structure interaction.

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Benson, Thomas J.; Suresh, Ambady

1990-01-01

A new computer code was developed to solve the 2-D or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating-direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 3 is the Programmer's Reference, and describes the program structure, the FORTRAN variables stored in common blocks, and the details of each subprogram.

Three-Dimensional Unsteady Separation at Low Reynolds Numbers

DTIC Science & Technology

1990-07-01

novel, robust adaptive- grid technique for incompressible flow (Shen & Reed 1990a "Shepard’s Interpolation for Solution-Adaptive Methods" submitted to...3-D adaptive- grid schemes developed for flat plate for full, unsteady, incompressible Navier Stokes. 4. 2-D and 3-D unsteady, vortex-lattice code...perforated to tailor suction through wall. Honeycomb and contractiong uide flow uniformly crons "a dn muwet a m Fiur32 c ic R n R ev lving -disc seals

Rotor cascade shape optimization with unsteady passing wakes using implicit dual time stepping method

NASA Astrophysics Data System (ADS)

Lee, Eun Seok

2000-10-01

An improved aerodynamics performance of a turbine cascade shape can be achieved by an understanding of the flow-field associated with the stator-rotor interaction. In this research, an axial gas turbine airfoil cascade shape is optimized for improved aerodynamic performance by using an unsteady Navier-Stokes solver and a parallel genetic algorithm. The objective of the research is twofold: (1) to develop a computational fluid dynamics code having faster convergence rate and unsteady flow simulation capabilities, and (2) to optimize a turbine airfoil cascade shape with unsteady passing wakes for improved aerodynamic performance. The computer code solves the Reynolds averaged Navier-Stokes equations. It is based on the explicit, finite difference, Runge-Kutta time marching scheme and the Diagonalized Alternating Direction Implicit (DADI) scheme, with the Baldwin-Lomax algebraic and k-epsilon turbulence modeling. Improvements in the code focused on the cascade shape design capability, convergence acceleration and unsteady formulation. First, the inverse shape design method was implemented in the code to provide the design capability, where a surface transpiration concept was employed as an inverse technique to modify the geometry satisfying the user specified pressure distribution on the airfoil surface. Second, an approximation storage multigrid method was implemented as an acceleration technique. Third, the preconditioning method was adopted to speed up the convergence rate in solving the low Mach number flows. Finally, the implicit dual time stepping method was incorporated in order to simulate the unsteady flow-fields. For the unsteady code validation, the Stokes's 2nd problem and the Poiseuille flow were chosen and compared with the computed results and analytic solutions. To test the code's ability to capture the natural unsteady flow phenomena, vortex shedding past a cylinder and the shock oscillation over a bicircular airfoil were simulated and compared with experiments and other research results. The rotor cascade shape optimization with unsteady passing wakes was performed to obtain an improved aerodynamic performance using the unsteady Navier-Stokes solver. Two objective functions were defined as minimization of total pressure loss and maximization of lift, while the mass flow rate was fixed. A parallel genetic algorithm was used as an optimizer and the penalty method was introduced. Each individual's objective function was computed simultaneously by using a 32 processor distributed memory computer. One optimization took about four days.

Unsteady Reynolds-averaged Navier-Stokes simulations of inlet distortion in the fan system of a gas-turbine aero-engine

NASA Astrophysics Data System (ADS)

Spotts, Nathan

As modern trends in commercial aircraft design move toward high-bypass-ratio fan systems of increasing diameter with shorter, nonaxisymmetric nacelle geometries, inlet distortion is becoming common in all operating regimes. The distortion may induce aerodynamic instabilities within the fan system, leading to catastrophic damage to fan blades, should the surge margin be exceeded. Even in the absence of system instability, the heterogeneity of the flow affects aerodynamic performance significantly. Therefore, an understanding of fan-distortion interaction is critical to aircraft engine system design. This thesis research elucidates the complex fluid dynamics and fan-distortion interaction by means of computational fluid dynamics (CFD) modeling of a complete engine fan system; including rotor, stator, spinner, nacelle and nozzle; under conditions typical of those encountered by commercial aircraft. The CFD simulations, based on a Reynolds-averaged Navier-Stokes (RANS) approach, were unsteady, three-dimensional, and of a full-annulus geometry. A thorough, systematic validation has been performed for configurations from a single passage of a rotor to a full-annulus system by comparing the predicted flow characteristics and aerodynamic performance to those found in literature. The original contributions of this research include the integration of a complete engine fan system, based on the NASA rotor 67 transonic stage and representative of the propulsion systems in commercial aircraft, and a benchmark case for unsteady RANS simulations of distorted flow in such a geometry under realistic operating conditions. This study is unique in that the complex flow dynamics, resulting from fan-distortion interaction, were illustrated in a practical geometry under realistic operating conditions. For example, the compressive stage is shown to influence upstream static pressure distributions and thus suppress separation of flow on the nacelle. Knowledge of such flow physics is valuable for engine system design.

Modeling of structural uncertainties in Reynolds-averaged Navier-Stokes closures

NASA Astrophysics Data System (ADS)

Emory, Michael; Larsson, Johan; Iaccarino, Gianluca

2013-11-01

Estimation of the uncertainty in numerical predictions by Reynolds-averaged Navier-Stokes closures is a vital step in building confidence in such predictions. An approach to model-form uncertainty quantification that does not assume the eddy-viscosity hypothesis to be exact is proposed. The methodology for estimation of uncertainty is demonstrated for plane channel flow, for a duct with secondary flows, and for the shock/boundary-layer interaction over a transonic bump.

A FEniCS-based programming framework for modeling turbulent flow by the Reynolds-averaged Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Mortensen, Mikael; Langtangen, Hans Petter; Wells, Garth N.

2011-09-01

Finding an appropriate turbulence model for a given flow case usually calls for extensive experimentation with both models and numerical solution methods. This work presents the design and implementation of a flexible, programmable software framework for assisting with numerical experiments in computational turbulence. The framework targets Reynolds-averaged Navier-Stokes models, discretized by finite element methods. The novel implementation makes use of Python and the FEniCS package, the combination of which leads to compact and reusable code, where model- and solver-specific code resemble closely the mathematical formulation of equations and algorithms. The presented ideas and programming techniques are also applicable to other fields that involve systems of nonlinear partial differential equations. We demonstrate the framework in two applications and investigate the impact of various linearizations on the convergence properties of nonlinear solvers for a Reynolds-averaged Navier-Stokes model.

Navier-Stokes solutions of unsteady separation induced by a vortex: Comparison with theory and influence of a moving wall

NASA Astrophysics Data System (ADS)

Obabko, Aleksandr Vladimirovich

Numerical solutions of the unsteady Navier-Stokes equations are considered for the flow induced by a thick-core vortex convecting along an infinite surface in a two-dimensional incompressible flow. The formulation is considered as a model problem of the dynamic-stall vortex and is relevant to other unsteady separation phenomena including vorticity ejections in juncture flows and the vorticity production mechanism in turbulent boundary-layers. Induced by an adverse streamwise pressure gradient due to the presence of the vortex above the wall, a primary recirculation region forms and evolves toward a singular solution of the unsteady non-interacting boundary-layer equations. The resulting eruptive spike provokes a small-scale viscous-inviscid interaction in the high-Reynolds-number regime. In the moderate-Reynolds-numbers regime, the growing recirculation region initiates a large-scale interaction in the form of local changes in the streamwise pressure gradient accelerating the spike formation and resulting small-scale interaction through development of a region of streamwise compression. It also was found to induce regions of streamwise expansion and "child" recirculation regions that contribute to ejections of near-wall vorticity and splitting of the "parent" region into multiple co-rotating eddies. These eddies later merge into a single amalgamated eddy that is observed to pair with the detaching vortex similar to the low-Reynolds-number regime where the large-scale interaction occurs, but there is no spike or subsequent small-scale interaction. It is also found that increasing the wall speed or vortex convection velocity toward a critical value results in solutions that are indicative of flows at lower Reynolds numbers eventually leading to suppression of unsteady separation and vortex detachment processes.

Deterministic blade row interactions in a centrifugal compressor stage

NASA Technical Reports Server (NTRS)

Kirtley, K. R.; Beach, T. A.

1991-01-01

The three-dimensional viscous flow in a low speed centrifugal compressor stage is simulated using an average passage Navier-Stokes analysis. The impeller discharge flow is of the jet/wake type with low momentum fluid in the shroud-pressure side corner coincident with the tip leakage vortex. This nonuniformity introduces periodic unsteadiness in the vane frame of reference. The effect of such deterministic unsteadiness on the time-mean is included in the analysis through the average passage stress, which allows the analysis of blade row interactions. The magnitude of the divergence of the deterministic unsteady stress is of the order of the divergence of the Reynolds stress over most of the span, from the impeller trailing edge to the vane throat. Although the potential effects on the blade trailing edge from the diffuser vane are small, strong secondary flows generated by the impeller degrade the performance of the diffuser vanes.

An Examination of Unsteady Airloads on a UH-60A Rotor: Computation Versus Measurement

NASA Technical Reports Server (NTRS)

Biedron, Robert T.; Lee-Rausch, Elizabeth

2012-01-01

An unsteady Reynolds-averaged Navier-Stokes solver for unstructured grids is used to simulate the flow over a UH-60A rotor. Traditionally, the computed pressure and shear stresses are integrated on the computational mesh at selected radial stations and compared to measured airloads. However, the corresponding integration of experimental data uses only the pressure contribution, and the set of integration points (pressure taps) is modest compared to the computational mesh resolution. This paper examines the difference between the traditional integration of computed airloads and an integration consistent with that used for the experimental data. In addition, a comparison of chordwise pressure distributions between computation and measurement is made. Examination of this unsteady pressure data provides new opportunities to understand differences between computation and flight measurement.

Numerical Simulations of Two-Phase Reacting Flow in a Single-Element Lean Direct Injection (LDI) Combustor Using NCC

NASA Technical Reports Server (NTRS)

Liu, Nan-Suey; Shih, Tsan-Hsing; Wey, C. Thomas

2011-01-01

A series of numerical simulations of Jet-A spray reacting flow in a single-element lean direct injection (LDI) combustor have been conducted by using the National Combustion Code (NCC). The simulations have been carried out using the time filtered Navier-Stokes (TFNS) approach ranging from the steady Reynolds-averaged Navier-Stokes (RANS), unsteady RANS (URANS), to the dynamic flow structure simulation (DFS). The sub-grid model employed for turbulent mixing and combustion includes the well-mixed model, the linear eddy mixing (LEM) model, and the filtered mass density function (FDF/PDF) model. The starting condition of the injected liquid spray is specified via empirical droplet size correlation, and a five-species single-step global reduced mechanism is employed for fuel chemistry. All the calculations use the same grid whose resolution is of the RANS type. Comparisons of results from various models are presented.

Time-Accurate Computations of Isolated Circular Synthetic Jets in Crossflow

NASA Technical Reports Server (NTRS)

Rumsey, C. L.; Schaeffler, N. W.; Milanovic, I. M.; Zaman, K. B. M. Q.

2007-01-01

Results from unsteady Reynolds-averaged Navier-Stokes computations are described for two different synthetic jet flows issuing into a turbulent boundary layer crossflow through a circular orifice. In one case the jet effect is mostly contained within the boundary layer, while in the other case the jet effect extends beyond the boundary layer edge. Both cases have momentum flux ratios less than 2. Several numerical parameters are investigated, and some lessons learned regarding the CFD methods for computing these types of flow fields are summarized. Results in both cases are compared to experiment.

Unsteady Flows in a Single-Stage Transonic Axial-Flow Fan Stator Row. Ph.D. Thesis - Iowa State Univ.

NASA Technical Reports Server (NTRS)

Hathaway, Michael D.

1986-01-01

Measurements of the unsteady velocity field within the stator row of a transonic axial-flow fan were acquired using a laser anemometer. Measurements were obtained on axisymmetric surfaces located at 10 and 50 percent span from the shroud, with the fan operating at maximum efficiency at design speed. The ensemble-average and variance of the measured velocities are used to identify rotor-wake-generated (deterministic) unsteadiness and turbulence, respectively. Correlations of both deterministic and turbulent velocity fluctuations provide information on the characteristics of unsteady interactions within the stator row. These correlations are derived from the Navier-Stokes equation in a manner similar to deriving the Reynolds stress terms, whereby various averaging operators are used to average the aperiodic, deterministic, and turbulent velocity fluctuations which are known to be present in multistage turbomachines. The correlations of deterministic and turbulent velocity fluctuations throughout the axial fan stator row are presented. In particular, amplification and attenuation of both types of unsteadiness are shown to occur within the stator blade passage.

A parabolic velocity-decomposition method for wind turbines

NASA Astrophysics Data System (ADS)

Mittal, Anshul; Briley, W. Roger; Sreenivas, Kidambi; Taylor, Lafayette K.

2017-02-01

An economical parabolized Navier-Stokes approximation for steady incompressible flow is combined with a compatible wind turbine model to simulate wind turbine flows, both upstream of the turbine and in downstream wake regions. The inviscid parabolizing approximation is based on a Helmholtz decomposition of the secondary velocity vector and physical order-of-magnitude estimates, rather than an axial pressure gradient approximation. The wind turbine is modeled by distributed source-term forces incorporating time-averaged aerodynamic forces generated by a blade-element momentum turbine model. A solution algorithm is given whose dependent variables are streamwise velocity, streamwise vorticity, and pressure, with secondary velocity determined by two-dimensional scalar and vector potentials. In addition to laminar and turbulent boundary-layer test cases, solutions for a streamwise vortex-convection test problem are assessed by mesh refinement and comparison with Navier-Stokes solutions using the same grid. Computed results for a single turbine and a three-turbine array are presented using the NREL offshore 5-MW baseline wind turbine. These are also compared with an unsteady Reynolds-averaged Navier-Stokes solution computed with full rotor resolution. On balance, the agreement in turbine wake predictions for these test cases is very encouraging given the substantial differences in physical modeling fidelity and computer resources required.

Partially-Averaged Navier-Stokes (PANS) approach for study of fluid flow and heat transfer characteristics in Czochralski melt

NASA Astrophysics Data System (ADS)

Verma, Sudeep; Dewan, Anupam

2018-01-01

The Partially-Averaged Navier-Stokes (PANS) approach has been applied for the first time to model turbulent flow and heat transfer in an ideal Czochralski set up with the realistic boundary conditions. This method provides variable level of resolution ranging from the Reynolds-Averaged Navier-Stokes (RANS) modelling to Direct Numerical Simulation (DNS) based on the filter control parameter. For the present case, a low-Re PANS model has been developed for Czochralski melt flow, which includes the effect of coriolis, centrifugal, buoyant and surface tension induced forces. The aim of the present study is to assess improvement in results on switching to PANS modelling from unsteady RANS (URANS) approach on the same computational mesh. The PANS computed results were found to be in good agreement with the reported experimental, DNS and Large Eddy Simulation (LES) data. A clear improvement in computational accuracy is observed in switching from the URANS approach to the PANS methodology. The computed results further improved with a reduction in the PANS filter width. Further the capability of the PANS model to capture key characteristics of the Czochralski crystal growth is also highlighted. It was observed that the PANS model was able to resolve the three-dimensional turbulent nature of the melt, characteristic flow structures arising due to flow instabilities and generation of thermal plumes and vortices in the Czochralski melt.

Active Control of Flow Separation Over an Airfoil

NASA Technical Reports Server (NTRS)

Ravindran, S. S.

1999-01-01

Designing an aircraft without conventional control surfaces is of interest to aerospace community. In this direction, smart actuator devices such as synthetic jets have been proposed to provide aircraft maneuverability instead of control surfaces. In this article, a numerical study is performed to investigate the effects of unsteady suction and blowing on airfoils. The unsteady suction and blowing is introduced at the leading edge of the airfoil in the form of tangential jet. Numerical solutions are obtained using Reynolds-Averaged viscous compressible Navier-Stokes equations. Unsteady suction and blowing is investigated as a means of separation control to obtain lift on airfoils. The effect of blowing coefficients on lift and drag is investigated. The numerical simulations are compared with experiments from the Tel-Aviv University (TAU). These results indicate that unsteady suction and blowing can be used as a means of separation control to generate lift on airfoils.

A computational study on oblique shock wave-turbulent boundary layer interaction

NASA Astrophysics Data System (ADS)

Joy, Md. Saddam Hossain; Rahman, Saeedur; Hasan, A. B. M. Toufique; Ali, M.; Mitsutake, Y.; Matsuo, S.; Setoguchi, T.

2016-07-01

A numerical computation of an oblique shock wave incident on a turbulent boundary layer was performed for free stream flow of air at M∞ = 2.0 and Re1 = 10.5×106 m-1. The oblique shock wave was generated from a 8° wedge. Reynolds averaged Navier-Stokes (RANS) simulation with k-ω SST turbulence model was first utilized for two dimensional (2D) steady case. The results were compared with the experiment at the same flow conditions. Further, to capture the unsteadiness, a 2D Large Eddy Simulation (LES) with sub-grid scale model WMLES was performed which showed the unsteady effects. The frequency of the shock oscillation was computed and was found to be comparable with that of experimental measurement.

Calculation and Correlation of the Unsteady Flowfield in a High Pressure Turbine

NASA Technical Reports Server (NTRS)

Bakhle, Milind A.; Liu, Jong S.; Panovsky, Josef; Keith, Theo G., Jr.; Mehmed, Oral

2002-01-01

Forced vibrations in turbomachinery components can cause blades to crack or fail due to high-cycle fatigue. Such forced response problems will become more pronounced in newer engines with higher pressure ratios and smaller axial gap between blade rows. An accurate numerical prediction of the unsteady aerodynamics phenomena that cause resonant forced vibrations is increasingly important to designers. Validation of the computational fluid dynamics (CFD) codes used to model the unsteady aerodynamic excitations is necessary before these codes can be used with confidence. Recently published benchmark data, including unsteady pressures and vibratory strains, for a high-pressure turbine stage makes such code validation possible. In the present work, a three dimensional, unsteady, multi blade-row, Reynolds-Averaged Navier Stokes code is applied to a turbine stage that was recently tested in a short duration test facility. Two configurations with three operating conditions corresponding to modes 2, 3, and 4 crossings on the Campbell diagram are analyzed. Unsteady pressures on the rotor surface are compared with data.

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 1: Analysis description

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Benson, Thomas J.; Suresh, Ambady

1990-01-01

A new computer code was developed to solve the two-dimensional or axisymmetric, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 1 is the Analysis Description, and describes in detail the governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models.

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 2: User's guide

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Benson, Thomas J.; Suresh, Ambady

1990-01-01

A new computer code was developed to solve the two-dimensional or axisymmetric, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 2 is the User's Guide, and describes the program's general features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Numerical Study of Outlet Boundary Conditions for Unsteady Turbulent Internal Flows Using the NCC

NASA Technical Reports Server (NTRS)

Liu, Nan-Suey; Shih, Tsan-Hsing

2009-01-01

This paper presents the results of studies on the outlet boundary conditions for turbulent internal flow simulations. Several outlet boundary conditions have been investigated by applying the National Combustion Code (NCC) to the configuration of a LM6000 single injector flame tube. First of all, very large eddy simulations (VLES) have been performed using the partially resolved numerical simulation (PRNS) approach, in which both the nonlinear and linear dynamic subscale models were employed. Secondly, unsteady Reynolds averaged Navier- Stokes (URANS) simulations have also been performed for the same configuration to investigate the effects of different outlet boundary conditions in the context of URANS. Thirdly, the possible role of the initial condition is inspected by using three different initial flow fields for both the PRNS/VLES simulation and the URANS simulation. The same grid is used for all the simulations and the number of mesh element is about 0.5 million. The main purpose of this study is to examine the long-time behavior of the solution as determined by the imposed outlet boundary conditions. For a particular simulation to be considered as successful under the given initial and boundary conditions, the solution must be sustainable in a physically meaningful manner over a sufficiently long period of time. The commonly used outlet boundary condition for steady Reynolds averaged Navier-Stokes (RANS) simulation is a fixed pressure at the outlet with all the other dependent variables being extrapolated from the interior. The results of the present study suggest that this is also workable for the URANS simulation of the LM6000 injector flame tube. However, it does not work for the PRNS/VLES simulation due to the unphysical reflections of the pressure disturbances at the outlet boundary. This undesirable situation can be practically alleviated by applying a simple unsteady convection equation for the pressure disturbances at the outlet boundary. The numerical results presented in this paper suggest that this unsteady convection of pressure disturbances at the outlet works very well for all the unsteady simulations (both PRNS/VLES and URANS) of the LM6000 single injector flame tube.

Transition to chaos in an open unforced 2D flow

NASA Technical Reports Server (NTRS)

Pulliam, Thomas H.; Vastano, John A.

1993-01-01

The present numerical study of unsteady, low Reynolds number flow past a 2D airfoil attempts to ascertain the bifurcation sequence leading from simple periodic to complex aperiodic flow with rising Reynolds number, as well as to characterize the degree of chaos present in the aperiodic flow and assess the role of numerics in the modification and control of the observed bifurcation scenario. The ARC2D Navier-Stokes code is used in an unsteady time-accurate mode for most of these computations. The system undergoes a period-doubling bifurcation to chaos as the Reynolds number is increased from 800 to 1600; its chaotic attractors are characterized by estimates of the fractal dimension and partial Liapunov exponent spectra.

Computation of oscillating airfoil flows with one- and two-equation turbulence models

NASA Technical Reports Server (NTRS)

Ekaterinaris, J. A.; Menter, F. R.

1994-01-01

The ability of one- and two-equation turbulence models to predict unsteady separated flows over airfoils is evaluated. An implicit, factorized, upwind-biased numerical scheme is used for the integration of the compressible, Reynolds-averaged Navier-Stokes equations. The turbulent eddy viscosity is obtained from the computed mean flowfield by integration of the turbulent field equations. One- and two-equation turbulence models are first tested for a separated airfoil flow at fixed angle of incidence. The same models are then applied to compute the unsteady flowfields about airfoils undergoing oscillatory motion at low subsonic Mach numbers. Experimental cases where the flow has been tripped at the leading-edge and where natural transition was allowed to occur naturally are considered. The more recently developed turbulence models capture the physics of unsteady separated flow significantly better than the standard kappa-epsilon and kappa-omega models. However, certain differences in the hysteresis effects are observed. For an untripped high-Reynolds-number flow, it was found necessary to take into account the leading-edge transitional flow region to capture the correct physical mechanism that leads to dynamic stall.

Application of thin-layer Navier-Stokes equations near maximum lift

NASA Technical Reports Server (NTRS)

Anderson, W. K.; Thomas, J. L.; Rumsey, C. L.

1984-01-01

The flowfield about a NACA 0012 airfoil at a Mach number of 0.3 and Reynolds number of 1 million is computed through an angle of attack range, up to 18 deg, corresponding to conditions up to and beyond the maximum lift coefficient. Results obtained using the compressible thin-layer Navier-Stokes equations are presented as well as results from the compressible Euler equations with and without a viscous coupling procedure. The applicability of each code is assessed and many thin-layer Navier-Stokes benchmark solutions are obtained which can be used for comparison with other codes intended for use at high angles of attack. Reasonable agreement of the Navier-Stokes code with experiment and the viscous-inviscid interaction code is obtained at moderate angles of attack. An unsteady solution is obtained with the thin-layer Navier-Stokes code at the highest angle of attack considered. The maximum lift coefficient is overpredicted, however, in comparison to experimental data, which is attributed to the presence of a laminar separation bubble near the leading edge not modeled in the computations. Two comparisons with experimental data are also presented at a higher Mach number.

Coupled CFD/CSD Analysis of an Active-Twist Rotor in a Wind Tunnel with Experimental Validation

NASA Technical Reports Server (NTRS)

Massey, Steven J.; Kreshock, Andrew R.; Sekula, Martin K.

2015-01-01

An unsteady Reynolds averaged Navier-Stokes analysis loosely coupled with a comprehensive rotorcraft code is presented for a second-generation active-twist rotor. High fidelity Navier-Stokes results for three configurations: an isolated rotor, a rotor with fuselage, and a rotor with fuselage mounted in a wind tunnel, are compared to lifting-line theory based comprehensive rotorcraft code calculations and wind tunnel data. Results indicate that CFD/CSD predictions of flapwise bending moments are in good agreement with wind tunnel measurements for configurations with a fuselage, and that modeling the wind tunnel environment does not significantly enhance computed results. Actuated rotor results for the rotor with fuselage configuration are also validated for predictions of vibratory blade loads and fixed-system vibratory loads. Varying levels of agreement with wind tunnel measurements are observed for blade vibratory loads, depending on the load component (flap, lag, or torsion) and the harmonic being examined. Predicted trends in fixed-system vibratory loads are in good agreement with wind tunnel measurements.

CFD Analysis and Design Optimization Using Parallel Computers

NASA Technical Reports Server (NTRS)

Martinelli, Luigi; Alonso, Juan Jose; Jameson, Antony; Reuther, James

1997-01-01

A versatile and efficient multi-block method is presented for the simulation of both steady and unsteady flow, as well as aerodynamic design optimization of complete aircraft configurations. The compressible Euler and Reynolds Averaged Navier-Stokes (RANS) equations are discretized using a high resolution scheme on body-fitted structured meshes. An efficient multigrid implicit scheme is implemented for time-accurate flow calculations. Optimum aerodynamic shape design is achieved at very low cost using an adjoint formulation. The method is implemented on parallel computing systems using the MPI message passing interface standard to ensure portability. The results demonstrate that, by combining highly efficient algorithms with parallel computing, it is possible to perform detailed steady and unsteady analysis as well as automatic design for complex configurations using the present generation of parallel computers.

On the solution of the unsteady Navier-Stokes equations for hypersonic flow about axially-symmetric blunt bodies

NASA Technical Reports Server (NTRS)

Warsi, Z. U. A.; Weed, R. A.; Thompson, J. F.

1980-01-01

A formulation of the complete Navier-Stokes problem for a viscous hypersonic flow in general curvilinear coordinates is presented. This formulation is applicable to both the axially symmetric and three dimensional flows past bodies of revolution. The equations for the case of zero angle of attack were solved past a circular cylinder with hemispherical caps by point SOR finite difference approximation. The free stream Mach number and the Reynolds number for the test case are respectively 22.04 and 168883. The whole algorithm is presented in detail along with the preliminary results for pressure, temperature, density and velocity distributions along the stagnation line.

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.

Large-Eddy/Reynolds-Averaged Navier-Stokes Simulation of Shock-Train Development in a Coil-Laser Diffuser

DTIC Science & Technology

2014-09-06

as the Riemann solver . The primitive-variable vector Ts kTwvupW ],,,,,,[ ω= is used in the reconstruction. The initial step in the PPM...University’s (NCSU) REACTMB flow solver is used in the present effort. REACTMB solves the Navier-Stokes equations governing a multi-component

Development of the Glenn-HT Computer Code to Enable Time-Filtered Navier-Stokes (TFNS) Simulations and Application to Film Cooling on a Flat Plate Through Long Cooling Tubes

NASA Technical Reports Server (NTRS)

Ameri, Ali; Shyam, Vikram; Rigby, David; Poinsatte, Philip; Thurman, Douglas; Steinthorsson, Erlendur

2014-01-01

Computational fluid dynamics (CFD) analysis using Reynolds-averaged Navier-Stokes (RANS) formulation for turbomachinery-related flows has enabled improved engine component designs. RANS methodology has limitations which are related to its inability to accurately describe the spectrum of flow phenomena encountered in engines. Examples of flows that are difficult to compute accurately with RANS include phenomena such as laminarturbulent transition, turbulent mixing due to mixing of streams, and separated flows. Large eddy simulation (LES) can improve accuracy but at a considerably higher cost. In recent years, hybrid schemes which take advantage of both unsteady RANS and LES have been proposed. This study investigated an alternative scheme, the time-filtered Navier-Stokes (TFNS) method applied to compressible flows. The method developed by Shih and Liu was implemented in the Glenn-HT code and applied to film cooling flows. In this report the method and its implementation is briefly described. The film effectiveness results obtained for film cooling from a row of 30 holes with a pitch of 3.0 diameters emitting air at a nominal density ratio of unity and four blowing ratios of 0.5, 1.0, 1.5 and 2.0 are shown. Flow features under those conditions are also described.

Partially-Averaged Navier Stokes Model for Turbulence: Implementation and Validation

NASA Technical Reports Server (NTRS)

Girimaji, Sharath S.; Abdol-Hamid, Khaled S.

2005-01-01

Partially-averaged Navier Stokes (PANS) is a suite of turbulence closure models of various modeled-to-resolved scale ratios ranging from Reynolds-averaged Navier Stokes (RANS) to Navier-Stokes (direct numerical simulations). The objective of PANS, like hybrid models, is to resolve large scale structures at reasonable computational expense. The modeled-to-resolved scale ratio or the level of physical resolution in PANS is quantified by two parameters: the unresolved-to-total ratios of kinetic energy (f(sub k)) and dissipation (f(sub epsilon)). The unresolved-scale stress is modeled with the Boussinesq approximation and modeled transport equations are solved for the unresolved kinetic energy and dissipation. In this paper, we first present a brief discussion of the PANS philosophy followed by a description of the implementation procedure and finally perform preliminary evaluation in benchmark problems.

Scaling Relations and Self-Similarity of 3-Dimensional Reynolds-Averaged Navier-Stokes Equations.

PubMed

Ercan, Ali; Kavvas, M Levent

2017-07-25

Scaling conditions to achieve self-similar solutions of 3-Dimensional (3D) Reynolds-Averaged Navier-Stokes Equations, as an initial and boundary value problem, are obtained by utilizing Lie Group of Point Scaling Transformations. By means of an open-source Navier-Stokes solver and the derived self-similarity conditions, we demonstrated self-similarity within the time variation of flow dynamics for a rigid-lid cavity problem under both up-scaled and down-scaled domains. The strength of the proposed approach lies in its ability to consider the underlying flow dynamics through not only from the governing equations under consideration but also from the initial and boundary conditions, hence allowing to obtain perfect self-similarity in different time and space scales. The proposed methodology can be a valuable tool in obtaining self-similar flow dynamics under preferred level of detail, which can be represented by initial and boundary value problems under specific assumptions.

An Approach to Improved Credibility of CFD Simulations for Rocket Injector Design

NASA Technical Reports Server (NTRS)

Tucker, Paul K.; Menon, Suresh; Merkle, Charles L.; Oefelein, Joseph C.; Yang, Vigor

2007-01-01

Computational fluid dynamics (CFD) has the potential to improve the historical rocket injector design process by simulating the sensitivity of performance and injector-driven thermal environments to. the details of the injector geometry and key operational parameters. Methodical verification and validation efforts on a range of coaxial injector elements have shown the current production CFD capability must be improved in order to quantitatively impact the injector design process.. This paper documents the status of an effort to understand and compare the predictive capabilities and resource requirements of a range of CFD methodologies on a set of model problem injectors. Preliminary results from a steady Reynolds-Average Navier-Stokes (RANS), an unsteady Reynolds-Average Navier Stokes (URANS) and three different Large Eddy Simulation (LES) techniques used to model a single element coaxial injector using gaseous oxygen and gaseous hydrogen propellants are presented. Initial observations are made comparing instantaneous results, corresponding time-averaged and steady-state solutions in the near -injector flow field. Significant differences in the flow fields exist, as expected, and are discussed. An important preliminary result is the identification of a fundamental mixing mechanism, accounted for by URANS and LES, but missing in the steady BANS methodology. Since propellant mixing is the core injector function, this mixing process may prove to have a profound effect on the ability to more correctly simulate injector performance and resulting thermal environments. Issues important to unifying the basis for future comparison such as solution initialization, required run time and grid resolution are addressed.

Estimating lift from unsteady wakes by using the Kutta-Joukowski theorem with vorticity-weighted wake width

NASA Astrophysics Data System (ADS)

Wang, Shizhao; He, Guowei; Liu, Tianshu

2017-11-01

The Kutta-Joukowski (KJ) theorem usually leads to puzzling results when it is applied to estimating the lift from the unsteady wakes generated by flapping wings. We investigate this problem by using a prevalent flapping rectangular wing model, where the unsteady wakes are obtained by numerically solving the Navier-Stokes equations at a low Reynolds number. It is found that neither the unsteady nor the time-averaged lift coefficient is correctly predicted when the parameters for the KJ theorem are selected according to the widely accepted ways in the literature. We propose a vorticity-weighted wake width model based on the vortex impulse theory to improve the prediction of the time-averaged lift. Furthermore, we investigate the phase difference of unsteady lift caused by the quasi-steady assumption of the application of the KJ theorem to the flapping flight and quantitatively link the phase difference to the local fluid acceleration. We show the phase difference can be corrected by using an added mass lift model. This work is helpful to clarify the error in estimating the lift of animal flight. Supported by the National Natural Science Foundation of China (No. 11672305).

Turbulence modeling for hypersonic flows

NASA Technical Reports Server (NTRS)

Marvin, J. G.; Coakley, T. J.

1989-01-01

Turbulence modeling for high speed compressible flows is described and discussed. Starting with the compressible Navier-Stokes equations, methods of statistical averaging are described by means of which the Reynolds-averaged Navier-Stokes equations are developed. Unknown averages in these equations are approximated using various closure concepts. Zero-, one-, and two-equation eddy viscosity models, algebraic stress models and Reynolds stress transport models are discussed. Computations of supersonic and hypersonic flows obtained using several of the models are discussed and compared with experimental results. Specific examples include attached boundary layer flows, shock wave boundary layer interactions and compressible shear layers. From these examples, conclusions regarding the status of modeling and recommendations for future studies are discussed.

Effects of thermal fluctuations and fluid compressibility on hydrodynamic synchronization of microrotors at finite oscillatory Reynolds number: a multiparticle collision dynamics simulation study.

PubMed

Theers, Mario; Winkler, Roland G

2014-08-28

We investigate the emergent dynamical behavior of hydrodynamically coupled microrotors by means of multiparticle collision dynamics (MPC) simulations. The two rotors are confined in a plane and move along circles driven by active forces. Comparing simulations to theoretical results based on linearized hydrodynamics, we demonstrate that time-dependent hydrodynamic interactions lead to synchronization of the rotational motion. Thermal noise implies large fluctuations of the phase-angle difference between the rotors, but synchronization prevails and the ensemble-averaged time dependence of the phase-angle difference agrees well with analytical predictions. Moreover, we demonstrate that compressibility effects lead to longer synchronization times. In addition, the relevance of the inertia terms of the Navier-Stokes equation are discussed, specifically the linear unsteady acceleration term characterized by the oscillatory Reynolds number ReT. We illustrate the continuous breakdown of synchronization with the Reynolds number ReT, in analogy to the continuous breakdown of the scallop theorem with decreasing Reynolds number.

Navier-Stokes simulations of unsteady transonic flow phenomena

NASA Technical Reports Server (NTRS)

Atwood, C. A.

1992-01-01

Numerical simulations of two classes of unsteady flows are obtained via the Navier-Stokes equations: a blast-wave/target interaction problem class and a transonic cavity flow problem class. The method developed for the viscous blast-wave/target interaction problem assumes a laminar, perfect gas implemented in a structured finite-volume framework. The approximately factored implicit scheme uses Newton subiterations to obtain the spatially and temporally second-order accurate time history of the blast-waves with stationary targets. The inviscid flux is evaluated using either of two upwind techniques, while the full viscous terms are computed by central differencing. Comparisons of unsteady numerical, analytical, and experimental results are made in two- and three-dimensions for Couette flows, a starting shock-tunnel, and a shock-tube blockage study. The results show accurate wave speed resolution and nonoscillatory discontinuity capturing of the predominantly inviscid flows. Viscous effects were increasingly significant at large post-interaction times. While the blast-wave/target interaction problem benefits from high-resolution methods applied to the Euler terms, the transonic cavity flow problem requires the use of an efficient scheme implemented in a geometrically flexible overset mesh environment. Hence, the Reynolds averaged Navier-Stokes equations implemented in a diagonal form are applied to the cavity flow class of problems. Comparisons between numerical and experimental results are made in two-dimensions for free shear layers and both rectangular and quieted cavities, and in three-dimensions for Stratospheric Observatory For Infrared Astronomy (SOFIA) geometries. The acoustic behavior of the rectangular and three-dimensional cavity flows compare well with experiment in terms of frequency, magnitude, and quieting trends. However, there is a more rapid decrease in computed acoustic energy with frequency than observed experimentally owing to numerical dissipation. In addition, optical phase distortion due to the time-varying density field is modelled using geometrical constructs. The computed optical distortion trends compare with the experimentally inferred result, but underpredicts the fluctuating phase difference magnitude.

Harmonic Balance Computations of Fan Aeroelastic Stability

NASA Technical Reports Server (NTRS)

Bakhle, Milind A.; Reddy, T. S. R.

2010-01-01

A harmonic balance (HB) aeroelastic analysis, which has been recently developed, was used to determine the aeroelastic stability (flutter) characteristics of an experimental fan. To assess the numerical accuracy of this HB aeroelastic analysis, a time-domain aeroelastic analysis was also used to determine the aeroelastic stability characteristics of the same fan. Both of these three-dimensional analysis codes model the unsteady flowfield due to blade vibrations using the Reynolds-averaged Navier-Stokes (RANS) equations. In the HB analysis, the unsteady flow equations are converted to a HB form and solved using a pseudo-time marching method. In the time-domain analysis, the unsteady flow equations are solved using an implicit time-marching approach. Steady and unsteady computations for two vibration modes were carried out at two rotational speeds: 100 percent (design) and 70 percent (part-speed). The steady and unsteady results obtained from the two analysis methods compare well, thus verifying the recently developed HB aeroelastic analysis. Based on the results, the experimental fan was found to have no aeroelastic instability (flutter) at the conditions examined in this study.

Computation of Separated and Unsteady Flows with One- and Two-Equation Turbulence Models

NASA Technical Reports Server (NTRS)

Ekaterinaris, John A.; Menter, Florian R.

1994-01-01

The ability of one- and two-equation turbulence models to predict unsteady separated flows over airfoils is evaluated. An implicit, factorized, upwind-biased numerical scheme is used for the integration of the compressible, Reynolds averaged Navier-Stokes equations. The turbulent eddy viscosity is obtained from the computed mean flowfield by integration of the turbulent field equations. The two-equation turbulence models are discretized in space with an upwind-biased, second order accurate total variation diminishing scheme. One and two-equation turbulence models are first tested for a separated airfoil flow at fixed angle of incidence. The same models are then applied to compute the unsteady flowfields about airfoils undergoing oscillatory motion at low subsonic Mach numbers. Experimental cases where the flow has been tripped at the leading edge and where natural transition was allowed to occur naturally are considered. The more recently developed field-equation turbulence models capture the physics of unsteady separated flow significantly better than the standard kappa-epsilon and kappa-omega models. However, certain differences in the hysteresis effects are obtained. For an untripped high-Reynolds-number flow, it was found necessary to take into account the leading edge transitional flow region in order to capture the correct physical mechanism that leads to dynamic stall.

Large eddy simulation for aerodynamics: status and perspectives.

PubMed

Sagaut, Pierre; Deck, Sébastien

2009-07-28

The present paper provides an up-to-date survey of the use of large eddy simulation (LES) and sequels for engineering applications related to aerodynamics. Most recent landmark achievements are presented. Two categories of problem may be distinguished whether the location of separation is triggered by the geometry or not. In the first case, LES can be considered as a mature technique and recent hybrid Reynolds-averaged Navier-Stokes (RANS)-LES methods do not allow for a significant increase in terms of geometrical complexity and/or Reynolds number with respect to classical LES. When attached boundary layers have a significant impact on the global flow dynamics, the use of hybrid RANS-LES remains the principal strategy to reduce computational cost compared to LES. Another striking observation is that the level of validation is most of the time restricted to time-averaged global quantities, a detailed analysis of the flow unsteadiness being missing. Therefore, a clear need for detailed validation in the near future is identified. To this end, new issues, such as uncertainty and error quantification and modelling, will be of major importance. First results dealing with uncertainty modelling in unsteady turbulent flow simulation are presented.

Flapping Wing Flight Dynamic Modeling

DTIC Science & Technology

2011-08-22

cases. Pesavento and Wang [24] solved the two dimensional Navier-Stokes equations in relation to a piece of free falling paper at Reynolds number near...von Karman, T. and Burgers, J. M., Gerneral Aerodynamic Theory - Perfect Fluids , Vol. II, Julius Springer, Berlin, 1935. [24] Pesavento , U. and Wang...2004, pp. 14. [25] Andersen, A., Pesavento , U., and Wang, Z. J., Unsteady aerodynamics of uttering and tumbling plates, Journal of Fluid Mechanics

Numerical study of the effects of icing on viscous flow over wings

NASA Technical Reports Server (NTRS)

Sankar, L. N.

1994-01-01

An improved hybrid method for computing unsteady compressible viscous flows is presented. This method divides the computational domain into two zones. In the outer zone, the unsteady full-potential equation (FPE) is solved. In the inner zone, the Navier-Stokes equations are solved using a diagonal form of an alternating-direction implicit (ADI) approximate factorization procedure. The two zones are tightly coupled so that steady and unsteady flows may be efficiently solved. Characteristic-based viscous/inviscid interface boundary conditions are employed to avoid spurious reflections at that interface. The resulting CPU times are less than 60 percent of that required for a full-blown Navier-Stokes analysis for steady flow applications and about 60 percent of the Navier-Stokes CPU times for unsteady flows in non-vector processing machines. Applications of the method are presented for a rectangular NACA 0012 wing in low subsonic steady flow at moderate and high angles of attack, and for an F-5 wing in steady and unsteady subsonic and transonic flows. Steady surface pressures are in very good agreement with experimental data and are essentially identical to Navier-Stokes predictions. Density contours show that shocks cross the viscous/inviscid interface smoothly, so that the accuracy of full Navier-Stokes equations can be retained with a significant savings in computational time.

Unsteady Analysis of Turbine Main Flow Coupled with Secondary Air Flow

NASA Technical Reports Server (NTRS)

Hah, Chunill

2006-01-01

Two numerical approaches are used to model the interaction between the turbine main gas flow and the wheelspace cavity seal flow. The 3-D, unsteady Reynolds-averaged Navier-Stokes equations are solved with a CFD code based on a structured grid to study the interaction between the turbine main gas flow and the wheelspace cavity seal flow. A CFD code based on an unstructured grid is used to solve detailed flow feature in the cavity seal which has a complex geometry. The numerical results confirm various observations from earlier experimental studies under similar flow conditions. When the flow rate through the rim cavity seal is increased, the ingestion of the main turbine flow into the rim seal area decreases drastically. However, a small amount of main gas flow is ingested to the rim seal area even with very high level of seal flow rate. This is due to the complex nature of 3-D, unsteady flow interaction near the hub of the turbine stage.

Adjoint-Based Methodology for Time-Dependent Optimization

NASA Technical Reports Server (NTRS)

Yamaleev, N. K.; Diskin, B.; Nielsen, E. J.

2008-01-01

This paper presents a discrete adjoint method for a broad class of time-dependent optimization problems. The time-dependent adjoint equations are derived in terms of the discrete residual of an arbitrary finite volume scheme which approximates unsteady conservation law equations. Although only the 2-D unsteady Euler equations are considered in the present analysis, this time-dependent adjoint method is applicable to the 3-D unsteady Reynolds-averaged Navier-Stokes equations with minor modifications. The discrete adjoint operators involving the derivatives of the discrete residual and the cost functional with respect to the flow variables are computed using a complex-variable approach, which provides discrete consistency and drastically reduces the implementation and debugging cycle. The implementation of the time-dependent adjoint method is validated by comparing the sensitivity derivative with that obtained by forward mode differentiation. Our numerical results show that O(10) optimization iterations of the steepest descent method are needed to reduce the objective functional by 3-6 orders of magnitude for test problems considered.

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.

Comparison of Various Turbulence Models for Unsteady Flow around a Finite Circular Cylinder at Re=20000

NASA Astrophysics Data System (ADS)

Zhang, Di

2017-10-01

This paper compares the performance of eight Reynolds-Averaged Navier-Stokes (RANS) two-equation turbulence models and two sub-grid scale (SGS) large eddy simulation (LES) models in the scenario of unsteady flow around a finite circular cylinder at an aspect ratio (AR) of 1.0 and a Reynolds number of Re=20000. It is found that, among all the eight RANS turbulence models considered, the K-Omega-SST model (viz. SST-V2003) developed by Menter et al. [1, 2] possesses the best overall performance (being closest to the numerical results of the two LES models considered, which can be deemed as the quasi-exact solution in view of the very fine computational mesh employed by the two LES models in this study) in terms of the mean surface pressure coefficient distribution (i.e. C p ), the mean drag coefficient (i.e. C d ), the mean streamline profiles in some characteristic planes (such as the mid-height plane and the symmetry plane of the cylinder) and the distribution of mean bed-shear-stress amplification on the bottom wall.

Development of the Glenn-Heat-Transfer (Glenn-HT) Computer Code to Enable Time-Filtered Navier Stokes (TFNS) Simulations and Application to Film Cooling on a Flat Plate Through Long Cooling Tubes

NASA Technical Reports Server (NTRS)

Ameri, Ali A.; Shyam, Vikram; Rigby, David; Poinsatte, Phillip; Thurman, Douglas; Steinthorsson, Erlendur

2014-01-01

Computational fluid dynamics (CFD) analysis using Reynolds-averaged Navier-Stokes (RANS) formulation for turbomachinery-related flows has enabled improved engine component designs. RANS methodology has limitations that are related to its inability to accurately describe the spectrum of flow phenomena encountered in engines. Examples of flows that are difficult to compute accurately with RANS include phenomena such as laminar/turbulent transition, turbulent mixing due to mixing of streams, and separated flows. Large eddy simulation (LES) can improve accuracy but at a considerably higher cost. In recent years, hybrid schemes that take advantage of both unsteady RANS and LES have been proposed. This study investigated an alternative scheme, the time-filtered Navier-Stokes (TFNS) method applied to compressible flows. The method developed by Shih and Liu was implemented in the Glenn-Heat-Transfer (Glenn-HT) code and applied to film-cooling flows. In this report the method and its implementation is briefly described. The film effectiveness results obtained for film cooling from a row of 30deg holes with a pitch of 3.0 diameters emitting air at a nominal density ratio of unity and two blowing ratios of 0.5 and 1.0 are shown. Flow features under those conditions are also described.

Development of the Glenn Heat-Transfer (Glenn-HT) Computer Code to Enable Time-Filtered Navier-Stokes (TFNS) Simulations and Application to Film Cooling on a Flat Plate Through Long Cooling Tubes

NASA Technical Reports Server (NTRS)

Ameri, Ali; Shyam, Vikram; Rigby, David; Poinsatte, Phillip; Thurman, Douglas; Steinthorsson, Erlendur

2014-01-01

Computational fluid dynamics (CFD) analysis using Reynolds-averaged Navier-Stokes (RANS) formulation for turbomachinery-related flows has enabled improved engine component designs. RANS methodology has limitations that are related to its inability to accurately describe the spectrum of flow phenomena encountered in engines. Examples of flows that are difficult to compute accurately with RANS include phenomena such as laminar/turbulent transition, turbulent mixing due to mixing of streams, and separated flows. Large eddy simulation (LES) can improve accuracy but at a considerably higher cost. In recent years, hybrid schemes that take advantage of both unsteady RANS and LES have been proposed. This study investigated an alternative scheme, the time-filtered Navier-Stokes (TFNS) method applied to compressible flows. The method developed by Shih and Liu was implemented in the Glenn-Heat-Transfer (Glenn-HT) code and applied to film-cooling flows. In this report the method and its implementation is briefly described. The film effectiveness results obtained for film cooling from a row of 30deg holes with a pitch of 3.0 diameters emitting air at a nominal density ratio of unity and two blowing ratios of 0.5 and 1.0 are shown. Flow features under those conditions are also described.

FUN3D Analyses in Support of the Second Aeroelastic Prediction Workshop

NASA Technical Reports Server (NTRS)

Chwalowski, Pawel; Heeg, Jennifer

2016-01-01

This paper presents the computational aeroelastic results generated in support of the second Aeroelastic Prediction Workshop for the Benchmark Supercritical Wing (BSCW) configurations and compares them to the experimental data. The computational results are obtained using FUN3D, an unstructured grid Reynolds- Averaged Navier-Stokes solver developed at NASA Langley Research Center. The analysis results include aerodynamic coefficients and surface pressures obtained for steady-state, static aeroelastic equilibrium, and unsteady flow due to a pitching wing or flutter prediction. Frequency response functions of the pressure coefficients with respect to the angular displacement are computed and compared with the experimental data. The effects of spatial and temporal convergence on the computational results are examined.

Time-Accurate Simulations and Acoustic Analysis of Slat Free-Shear Layer

NASA Technical Reports Server (NTRS)

Khorrami, Mehdi R.; Singer, Bart A.; Berkman, Mert E.

2001-01-01

A detailed computational aeroacoustic analysis of a high-lift flow field is performed. Time-accurate Reynolds Averaged Navier-Stokes (RANS) computations simulate the free shear layer that originates from the slat cusp. Both unforced and forced cases are studied. Preliminary results show that the shear layer is a good amplifier of disturbances in the low to mid-frequency range. The Ffowcs-Williams and Hawkings equation is solved to determine the acoustic field using the unsteady flow data from the RANS calculations. The noise radiated from the excited shear layer has a spectral shape qualitatively similar to that obtained from measurements in a corresponding experimental study of the high-lift system.

Aeroacoustic Simulation of a Nose Landing Gear in an Open Jet Facility Using FUN3D

NASA Technical Reports Server (NTRS)

Vatsa, Veer N.; Lockard, David P.; Khorrami, Mehdi R.; Carlson, Jan-Renee

2012-01-01

Numerical simulations have been performed for a partially-dressed, cavity-closed nose landing gear configuration that was tested in NASA Langley s closed-wall Basic Aerodynamic Research Tunnel (BART) and in the University of Florida s open-jet acoustic facility known as UFAFF. The unstructured-grid flow solver, FUN3D, developed at NASA Langley Research center is used to compute the unsteady flow field for this configuration. A hybrid Reynolds-averaged Navier-Stokes/large eddy simulation (RANS/LES) turbulence model is used for these computations. Time-averaged and instantaneous solutions compare favorably with the measured data. Unsteady flowfield data obtained from the FUN3D code are used as input to a Ffowcs Williams-Hawkings noise propagation code to compute the sound pressure levels at microphones placed in the farfield. Significant improvement in predicted noise levels is obtained when the flowfield data from the open jet UFAFF simulations is used as compared to the case using flowfield data from the closed-wall BART configuration.

A Computational Study of an Oscillating VR-12 Airfoil with a Gurney Flap

NASA Technical Reports Server (NTRS)

Rhee, Myung

2004-01-01

Computations of the flow over an oscillating airfoil with a Gurney-flap are performed using a Reynolds Averaged Navier-Stokes code and compared with recent experimental data. The experimental results have been generated for different sizes of the Gurney flaps. The computations are focused mainly on a configuration. The baseline airfoil without a Gurney flap is computed and compared with the experiments in both steady and unsteady cases for the purpose of initial testing of the code performance. The are carried out with different turbulence models. Effects of the grid refinement are also examined and unsteady cases, in addition to the assessment of solver effects. The results of the comparisons of steady lift and drag computations indicate that the code is reasonably accurate in the attached flow of the steady condition but largely overpredicts the lift and underpredicts the drag in the higher angle steady flow.

Unsteady flow sensing and optimal sensor placement using machine learning

NASA Astrophysics Data System (ADS)

Semaan, Richard

2016-11-01

Machine learning is used to estimate the flow state and to determine the optimal sensor placement over a two-dimensional (2D) airfoil equipped with a Coanda actuator. The analysis is based on flow field data obtained from 2D unsteady Reynolds averaged Navier-Stokes (uRANS) simulations with different jet blowing intensities and actuation frequencies, characterizing different flow separation states. This study shows how the "random forests" algorithm is utilized beyond its typical usage in fluid mechanics estimating the flow state to determine the optimal sensor placement. The results are compared against the current de-facto standard of maximum modal amplitude location and against a brute force approach that scans all possible sensor combinations. The results show that it is possible to simultaneously infer the state of flow and to determine the optimal sensor location without the need to perform proper orthogonal decomposition. Collaborative Research Center (CRC) 880, DFG.

Unsteady Analysis of Separated Aerodynamic Flows Using an Unstructured Multigrid Algorithm

NASA Technical Reports Server (NTRS)

Pelaez, Juan; Mavriplis, Dimitri J.; Kandil, Osama

2001-01-01

An implicit method for the computation of unsteady flows on unstructured grids is presented. The resulting nonlinear system of equations is solved at each time step using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Validation of the code using a one-equation turbulence model is performed for the well-known case of flow over a cylinder. A Detached Eddy Simulation model is also implemented and its performance compared to the one equation Spalart-Allmaras Reynolds Averaged Navier-Stokes (RANS) turbulence model. Validation cases using DES and RANS include flow over a sphere and flow over a NACA 0012 wing including massive stall regimes. The project was driven by the ultimate goal of computing separated flows of aerodynamic interest, such as massive stall or flows over complex non-streamlined geometries.

Re-evaluation of an Optimized Second Order Backward Difference (BDF2OPT) Scheme for Unsteady Flow Applications

NASA Technical Reports Server (NTRS)

Vatsa, Veer N.; Carpenter, Mark H.; Lockard, David P.

2009-01-01

Recent experience in the application of an optimized, second-order, backward-difference (BDF2OPT) temporal scheme is reported. The primary focus of the work is on obtaining accurate solutions of the unsteady Reynolds-averaged Navier-Stokes equations over long periods of time for aerodynamic problems of interest. The baseline flow solver under consideration uses a particular BDF2OPT temporal scheme with a dual-time-stepping algorithm for advancing the flow solutions in time. Numerical difficulties are encountered with this scheme when the flow code is run for a large number of time steps, a behavior not seen with the standard second-order, backward-difference, temporal scheme. Based on a stability analysis, slight modifications to the BDF2OPT scheme are suggested. The performance and accuracy of this modified scheme is assessed by comparing the computational results with other numerical schemes and experimental data.

Prediction of unsteady separated flows on oscillating airfoils

NASA Technical Reports Server (NTRS)

Mccroskey, W. J.

1978-01-01

Techniques for calculating high Reynolds number flow around an airfoil undergoing dynamic stall are reviewed. Emphasis is placed on predicting the values of lift, drag, and pitching moments. Methods discussed include: the discrete potential vortex method; thin boundary layer method; strong interaction between inviscid and viscous flows; and solutions to the Navier-Stokes equations. Empirical methods for estimating unsteady airloads on oscillating airfoils are also described. These methods correlate force and moment data from wind tunnel tests to indicate the effects of various parameters, such as airfoil shape, Mach number, amplitude and frequency of sinosoidal oscillations, mean angle, and type of motion.

Optimized Reduction of Unsteady Radial Forces in a Singlechannel Pump for Wastewater Treatment

NASA Astrophysics Data System (ADS)

Kim, Jin-Hyuk; Cho, Bo-Min; Choi, Young-Seok; Lee, Kyoung-Yong; Peck, Jong-Hyeon; Kim, Seon-Chang

2016-11-01

A single-channel pump for wastewater treatment was optimized to reduce unsteady radial force sources caused by impeller-volute interactions. The steady and unsteady Reynolds- averaged Navier-Stokes equations using the shear-stress transport turbulence model were discretized by finite volume approximations and solved on tetrahedral grids to analyze the flow in the single-channel pump. The sweep area of radial force during one revolution and the distance of the sweep-area center of mass from the origin were selected as the objective functions; the two design variables were related to the internal flow cross-sectional area of the volute. These objective functions were integrated into one objective function by applying the weighting factor for optimization. Latin hypercube sampling was employed to generate twelve design points within the design space. A response-surface approximation model was constructed as a surrogate model for the objectives, based on the objective function values at the generated design points. The optimized results showed considerable reduction in the unsteady radial force sources in the optimum design, relative to those of the reference design.

A comparison between implicit and hybrid methods for the calculation of steady and unsteady inlet flows

NASA Technical Reports Server (NTRS)

Coakley, T. J.; Hsieh, T.

1985-01-01

Numerical simulation of steady and unsteady transonic diffuser flows using two different computer codes are discussed and compared with experimental data. The codes solve the Reynolds-averaged, compressible, Navier-Stokes equations using various turbulence models. One of the codes has been applied extensively to diffuser flows and uses the hybrid method of MacCormack. This code is relatively inefficient numerically. The second code, which was developed more recently, is fully implicit and is relatively efficient numerically. Simulations of steady flows using the implicit code are shown to be in good agreement with simulations using the hybrid code. Both simulations are in good agreement with experimental results. Simulations of unsteady flows using the two codes are in good qualitative agreement with each other, although the quantitative agreement is not as good as in the steady flow cases. The implicit code is shown to be eight times faster than the hybrid code for unsteady flow calculations and up to 32 times faster for steady flow calculations. Results of calculations using alternative turbulence models are also discussed.

Quasi-laminar stability and sensitivity analyses for turbulent flows: Prediction of low-frequency unsteadiness and passive control

NASA Astrophysics Data System (ADS)

Mettot, Clément; Sipp, Denis; Bézard, Hervé

2014-04-01

This article presents a quasi-laminar stability approach to identify in high-Reynolds number flows the dominant low-frequencies and to design passive control means to shift these frequencies. The approach is based on a global linear stability analysis of mean-flows, which correspond to the time-average of the unsteady flows. Contrary to the previous work by Meliga et al. ["Sensitivity of 2-D turbulent flow past a D-shaped cylinder using global stability," Phys. Fluids 24, 061701 (2012)], we use the linearized Navier-Stokes equations based solely on the molecular viscosity (leaving aside any turbulence model and any eddy viscosity) to extract the least stable direct and adjoint global modes of the flow. Then, we compute the frequency sensitivity maps of these modes, so as to predict before hand where a small control cylinder optimally shifts the frequency of the flow. In the case of the D-shaped cylinder studied by Parezanović and Cadot [J. Fluid Mech. 693, 115 (2012)], we show that the present approach well captures the frequency of the flow and recovers accurately the frequency control maps obtained experimentally. The results are close to those already obtained by Meliga et al., who used a more complex approach in which turbulence models played a central role. The present approach is simpler and may be applied to a broader range of flows since it is tractable as soon as mean-flows — which can be obtained either numerically from simulations (Direct Numerical Simulation (DNS), Large Eddy Simulation (LES), unsteady Reynolds-Averaged-Navier-Stokes (RANS), steady RANS) or from experimental measurements (Particle Image Velocimetry - PIV) — are available. We also discuss how the influence of the control cylinder on the mean-flow may be more accurately predicted by determining an eddy-viscosity from numerical simulations or experimental measurements. From a technical point of view, we finally show how an existing compressible numerical simulation code may be used in a black-box manner to extract the global modes and sensitivity maps.

Unsteady viscous calculations of supersonic flows past deep and shallow three-dimensional cavities

NASA Technical Reports Server (NTRS)

Baysal, O.; Srinivasan, S.; Stallings, R. L.

1988-01-01

Computational simulations were performed for supersonic, turbulent flows over deep and shallow three-dimensional cavities. The width and the depth of these cavities were fixed at 2.5 in. and 0.5 in., respectively. Length-to-depth ratio of the deep cavity was 6 and that of the shallow cavity was 16. Freestream values of Mach number and Reynolds number were 1.50 and 2.0 x 10 to the 6th/ft., respectively, at a total temperature of 585 R. The thickness of the turbulent boundary layer at the front lip of the cavity was 0.2 in. Simulations of these oscillatory flows were generated through time-accurate solutions of Reynolds-averaged full Navier-Stokes equations using the explicit MacCormack scheme. The solutions are validated through comparisons with experimental data. The features of open and closed cavity flows and effects of the third dimension are illustrated through computational graphics.

A low-dissipation monotonicity-preserving scheme for turbulent flows in hydraulic turbines

NASA Astrophysics Data System (ADS)

Yang, L.; Nadarajah, S.

2016-11-01

The objective of this work is to improve the inherent dissipation of the numerical schemes under the framework of a Reynolds-averaged Navier-Stokes (RANS) simulation. The governing equations are solved by the finite volume method with the k-ω SST turbulence model. Instead of the van Albada limiter, a novel eddy-preserving limiter is employed in the MUSCL reconstructions to minimize the dissipation of the vortex. The eddy-preserving procedure inactivates the van Albada limiter in the swirl plane and reduces the artificial dissipation to better preserve vortical flow structures. Steady and unsteady simulations of turbulent flows in a straight channel and a straight asymmetric diffuser are demonstrated. Profiles of velocity, Reynolds shear stress and turbulent kinetic energy are presented and compared against large eddy simulation (LES) and/or experimental data. Finally, comparisons are made to demonstrate the capability of the eddy-preserving limiter scheme.

Numerical solution for the velocity-derivative skewness of a low-Reynolds-number decaying Navier-Stokes flow

NASA Technical Reports Server (NTRS)

Deissler, Robert G.

1990-01-01

The variation of the velocity-derivative skewness of a Navier-Stokes flow as the Reynolds number goes toward zero is calculated numerically. The value of the skewness, which has been somewhat controversial, is shown to become small at low Reynolds numbers.

Exact solutions of the Navier-Stokes equations generalized for flow in porous media

NASA Astrophysics Data System (ADS)

Daly, Edoardo; Basser, Hossein; Rudman, Murray

2018-05-01

Flow of Newtonian fluids in porous media is often modelled using a generalized version of the full non-linear Navier-Stokes equations that include additional terms describing the resistance to flow due to the porous matrix. Because this formulation is becoming increasingly popular in numerical models, exact solutions are required as a benchmark of numerical codes. The contribution of this study is to provide a number of non-trivial exact solutions of the generalized form of the Navier-Stokes equations for parallel flow in porous media. Steady-state solutions are derived in the case of flows in a medium with constant permeability along the main direction of flow and a constant cross-stream velocity in the case of both linear and non-linear drag. Solutions are also presented for cases in which the permeability changes in the direction normal to the main flow. An unsteady solution for a flow with velocity driven by a time-periodic pressure gradient is also derived. These solutions form a basis for validating computational models across a wide range of Reynolds and Darcy numbers.

Model for compressible turbulence in hypersonic wall boundary and high-speed mixing layers

NASA Astrophysics Data System (ADS)

Bowersox, Rodney D. W.; Schetz, Joseph A.

1994-07-01

The most common approach to Navier-Stokes predictions of turbulent flows is based on either the classical Reynolds-or Favre-averaged Navier-Stokes equations or some combination. The main goal of the current work was to numerically assess the effects of the compressible turbulence terms that were experimentaly found to be important. The compressible apparent mass mixing length extension (CAMMLE) model, which was based on measured experimental data, was found to produce accurate predictions of the measured compressible turbulence data for both the wall bounded and free mixing layer. Hence, that model was incorporated into a finite volume Navier-Stokes code.

Computation of airfoil buffet boundaries

NASA Technical Reports Server (NTRS)

Levy, L. L., Jr.; Bailey, H. E.

1981-01-01

The ILLIAC IV computer has been programmed with an implicit, finite-difference code for solving the thin layer compressible Navier-Stokes equation. Results presented for the case of the buffet boundaries of a conventional and a supercritical airfoil section at high Reynolds numbers are found to be in agreement with experimentally determined buffet boundaries, especially at the higher freestream Mach numbers and lower lift coefficients where the onset of unsteady flows is associated with shock wave-induced boundary layer separation.

Detached Eddy Simulation for the F-16XL Aircraft Configuration

NASA Technical Reports Server (NTRS)

Elmiligui, Alaa; Abdol-Hamid, Khaled; Parlette, Edward B.

2015-01-01

Numerical simulations for the flow around the F-16XL configuration as a contribution to the Cranked Arrow Wing Aerodynamic Project International 2 (CAWAPI-2) have been performed. The NASA Langley Tetrahedral Unstructured Software System (TetrUSS) with its USM3D solver was used to perform the unsteady flow field simulations for the subsonic high angle-of-attack case corresponding to flight condition (FC) 25. Two approaches were utilized to capture the unsteady vortex flow over the wing of the F-16XL. The first approach was to use Unsteady Reynolds-Averaged Navier-Stokes (URANS) coupled with standard turbulence closure models. The second approach was to use Detached Eddy Simulation (DES), which creates a hybrid model that attempts to combine the most favorable elements of URANS models and Large Eddy Simulation (LES). Computed surface static pressure profiles are presented and compared with flight data. Time-averaged and instantaneous results obtained on coarse, medium and fine grids are compared with the flight data. The intent of this study is to demonstrate that the DES module within the USM3D solver can be used to provide valuable data in predicting vortex-flow physics on a complex configuration.

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.

Pressure drop for inertial flows in elastic porous media

NASA Astrophysics Data System (ADS)

Pauthenet, Martin; Bottaro, Alessandro; Davit, Yohan; Quintard, Michel; porous media Team

2017-11-01

The effect of the porosity and of the elastic properties of anisotropic solid skeletons saturated by a fluid is studied for flows displaying unsteady inertial effects. Insight is achieved by direct numerical simulations of the Navier-Stokes equations for model porous media, with inclusions which can oscillate with respect to their reference positions because of the presence of a restoring elastic force modeled by a spring. The numerical technique is based on the immersed boundary method, to easily allow for the displacement of pores of arbitrary shapes and dimensions. Solid contacts are anelastic. The parameters examined include the local Reynolds number, Red , based on the mean velocity through the reference unit cell and the characteristic size of the inclusions, the direction of the macroscopic forcing pressure gradient, the reduced frequency, f*, ratio of the flow frequency to the natural frequency of the spring-mass system, and the reduced mass, m*, ratio of the solid to the fluid density. Results demonstrate the effect of these parameters, and permit to determine the filtration laws useful for the subsequent macroscopic modeling of these flows through the volume averaged Navier-Stokes equations. IDEX Foundation of the University of Toulouse and HPC resources of the CALMIP supercomputing center.

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 3: Programmer's reference

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 2: User's guide

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This User's Guide describes the program's features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Navier-Stokes Flowfield Simulation of Boeing 747-200 as Platform for SOFIA

NASA Technical Reports Server (NTRS)

Srinivasan, G.R.

1994-01-01

Steady and unsteady viscous, three-dimensional flowfields are calculated using a thin layer approximation of Navier-Stokes equations in conjunction with Chimera overset grids. The finite-difference numerical scheme uses structured grids and a pentadiagonal flow solver called "OVERFLOW". The configuration of Boeing 747-200 has been chosen as one of configurations to be used as a platform for the SOFIA (Stratospheric Observatory For Infrared Astronomy). Initially, the steady flowfield of the full aircraft is calculated for the clean configuration (without a cavity to house telescope). This solution is then used to start the unsteady flowfield of a configuration containing cavity housing the observation telescope and its peripheral units. Analysis of unsteady flowfield in the cavity and its influence on the tail empennage, as well as the noise due to turbulence and optical quality of the flow are the main focus of this study. For the configuration considered here, the telescope housing cavity is located slightly downstream of the portwing. The entire flow-field is carefully constructed using 45 overset grids and consists of nearly 4 million grid points. All the computations axe done at one freestream flow condition of M(sub infinity) = 0.85, alpha = 2.5deg, and a Reynolds of Re = 1.85x10deg

Numerical Investigation of Synthetic-jet based Flow Control on Vertical-axis Wind Turbine Blades

NASA Astrophysics Data System (ADS)

Menon, Ashwin; Tran, Steven; Sahni, Onkar

2013-11-01

Vertical-axis wind turbines encounter large unsteady aerodynamic loads in a sustained fashion due to the continuously varying angle of attack that is experienced by turbine blades during each revolution. Moreover, the detachment of the leading edge vortex at high angles of attack leads to sudden change in aerodynamic loads that result in structural vibrations and fatigue, and possibly failure. This numerical study focuses on using synthetic-jet based fluidic actuation to reduce the unsteady loading on VAWT blades. In the simulations, the jets are placed at the dominant separation location that is observed in the baseline case. We consider different tip-speed ratios, O(2-5), and we also study the effect of blowing ratio (to be in O(0.5-1.5)) and reduced frequency, i.e., ratio of jet frequency to flow frequency (to be in O(5-15)). For all cases, unsteady Reynolds-averaged Navier-Stokes simulations are carried out by using the Spallart-Allamaras turbulence model, where stabilized finite element method is employed for spatial discretization along with an implicit time-integration scheme.

Computational Study of the Impact of Unsteadiness on the Aerodynamic Performance of a Variable- Speed Power Turbine

NASA Technical Reports Server (NTRS)

Welch, Gerard E.

2012-01-01

The design-point and off-design performance of an embedded 1.5-stage portion of a variable-speed power turbine (VSPT) was assessed using Reynolds-Averaged Navier-Stokes (RANS) analyses with mixing-planes and sector-periodic, unsteady RANS analyses. The VSPT provides one means by which to effect the nearly 50 percent main-rotor speed change required for the NASA Large Civil Tilt-Rotor (LCTR) application. The change in VSPT shaft-speed during the LCTR mission results in blade-row incidence angle changes of as high as 55 . Negative incidence levels of this magnitude at takeoff operation give rise to a vortical flow structure in the pressure-side cove of a high-turn rotor that transports low-momentum flow toward the casing endwall. The intent of the effort was to assess the impact of unsteadiness of blade-row interaction on the time-mean flow and, specifically, to identify potential departure from the predicted trend of efficiency with shaft-speed change of meanline and 3-D RANS/mixing-plane analyses used for design.

Mixed convection heat transfer enhancement in a cubic lid-driven cavity containing a rotating cylinder through the introduction of artificial roughness on the heated wall

NASA Astrophysics Data System (ADS)

Kareem, Ali Khaleel; Gao, Shian

2018-02-01

The aim of the present numerical investigation is to comprehensively analyse and understand the heat transfer enhancement process using a roughened, heated bottom wall with two artificial rib types (R-s and R-c) due to unsteady mixed convection heat transfer in a 3D moving top wall enclosure that has a central rotating cylinder, and to compare these cases with the smooth bottom wall case. These different cases (roughened and smooth bottom walls) are considered at various clockwise and anticlockwise rotational speeds, -5 ≤ Ω ≤ 5, and Reynolds numbers of 5000 and 10 000. The top and bottom walls of the lid-driven cavity are differentially heated, whilst the remaining cavity walls are assumed to be stationary and adiabatic. A standard k-ɛ model for the Unsteady Reynolds-Averaged Navier-Stokes equations is used to deal with the turbulent flow. The heat transfer improvement is carefully considered and analysed through the detailed examinations of the flow and thermal fields, the turbulent kinetic energy, the mean velocity profiles, the wall shear stresses, and the local and average Nusselt numbers. It has been concluded that artificial roughness can strongly affect the thermal fields and fluid flow patterns. Ultimately, the heat transfer rate has been dramatically increased by involving the introduced artificial rips. Increasing the cylinder rotational speed or Reynolds number can enhance the heat transfer process, especially when the wall roughness exists.

Computational unsteady aerodynamics for lifting surfaces

NASA Technical Reports Server (NTRS)

Edwards, John W.

1988-01-01

Two dimensional problems are solved using numerical techniques. Navier-Stokes equations are studied both in the vorticity-stream function formulation which appears to be the optimal choice for two dimensional problems, using a storage approach, and in the velocity pressure formulation which minimizes the number of unknowns in three dimensional problems. Analysis shows that compact centered conservative second order schemes for the vorticity equation are the most robust for high Reynolds number flows. Serious difficulties remain in the choice of turbulent models, to keep reasonable CPU efficiency.

Numerical Investigations of Two Typical Unsteady Flows in Turbomachinery Using the Multi-Passage Model

NASA Astrophysics Data System (ADS)

Zhou, Di; Lu, Zhiliang; Guo, Tongqing; Shen, Ennan

2016-06-01

In this paper, the research on two types of unsteady flow problems in turbomachinery including blade flutter and rotor-stator interaction is made by means of numerical simulation. For the former, the energy method is often used to predict the aeroelastic stability by calculating the aerodynamic work per vibration cycle. The inter-blade phase angle (IBPA) is an important parameter in computation and may have significant effects on aeroelastic behavior. For the latter, the numbers of blades in each row are usually not equal and the unsteady rotor-stator interactions could be strong. An effective way to perform multi-row calculations is the domain scaling method (DSM). These two cases share a common point that the computational domain has to be extended to multi passages (MP) considering their respective features. The present work is aimed at modeling these two issues with the developed MP model. Computational fluid dynamics (CFD) technique is applied to resolve the unsteady Reynolds-averaged Navier-Stokes (RANS) equations and simulate the flow fields. With the parallel technique, the additional time cost due to modeling more passages can be largely decreased. Results are presented on two test cases including a vibrating rotor blade and a turbine stage.

Unsteady Flow Dynamics and Acoustics of Two-Outlet Centrifugal Fan Design

NASA Astrophysics Data System (ADS)

Wong, I. Y. W.; Leung, R. C. K.; Law, A. K. Y.

2011-09-01

In this study, a centrifugal fan design with two flow outlets is investigated. This design aims to provide high mass flow rate but low noise performance. Two dimensional unsteady flow simulation with CFD code (FLUENT 6.3) is carried out to analyze the fan flow dynamics and its acoustics. The calculations were done using the unsteady Reynolds averaged Navier Stokes (URANS) approach in which effects of turbulence were accounted for using κ-ɛ model. This work aims to provide an insight how the dominant noise source mechanisms vary with a key fan geometrical paramters, namely, the ratio between cutoff distance and the radius of curvature of the fan housing. Four new fan designs were calculated. Simulation results show that the unsteady flow-induced forces on the fan blades are found to be the main noise sources. The blade force coefficients are then used to build the dipole source terms in Ffowcs Williams and Hawkings (FW-H) Equation for estimating their noise effects. It is found that one design is able to deliver a mass flow 34% more, but with sound pressure level (SPL) 10 dB lower, than the existing design .

Calm water resistance prediction of a bulk carrier using Reynolds averaged Navier-Stokes based solver

NASA Astrophysics Data System (ADS)

Rahaman, Md. Mashiur; Islam, Hafizul; Islam, Md. Tariqul; Khondoker, Md. Reaz Hasan

2017-12-01

Maneuverability and resistance prediction with suitable accuracy is essential for optimum ship design and propulsion power prediction. This paper aims at providing some of the maneuverability characteristics of a Japanese bulk carrier model, JBC in calm water using a computational fluid dynamics solver named SHIP Motion and OpenFOAM. The solvers are based on the Reynolds average Navier-Stokes method (RaNS) and solves structured grid using the Finite Volume Method (FVM). This paper comprises the numerical results of calm water test for the JBC model with available experimental results. The calm water test results include the total drag co-efficient, average sinkage, and trim data. Visualization data for pressure distribution on the hull surface and free water surface have also been included. The paper concludes that the presented solvers predict the resistance and maneuverability characteristics of the bulk carrier with reasonable accuracy utilizing minimum computational resources.

Effect of Reynolds number and turbulence on airfoil aerodynamics at -90-degree incidence

NASA Technical Reports Server (NTRS)

Stremel, Paul M.

1994-01-01

A method has been developed for calculating the viscous flow about airfoils with and without deflected flaps at -90 deg incidence. This method provides for the solution of the unsteady incompressible Navier-Stokes equations by means of an implicit technique. The solution is calculated on a body-fitted computational mesh using a staggered-grid method. The vorticity is defined at the node points, and the velocity components are defined at the mesh-cell sides. The staggered-grid orientation provides for accurate representation of vorticity at the node points and the continuity equation at the mesh-cell centers. The method provides for the noniterative solution of the flowfield and satisfies the continuity equation to machine zero at each time step. The method is evaluated in terms of its stability to predict two-dimensional flow about an airfoil at -90-deg incidence for varying Reynolds number and laminar/turbulent models. The variations of the average loading and surface pressure distribution due to flap deflection, Reynolds number, and laminar or turbulent flow are presented and compared with experimental results. The comparisom indicate that the calculated drag and drag reduction caused by flap deflection and the calculated average surface pressure are in excellent agreement with the measured results at a similar Reynolds number.

Numerical simulation of the vortical flow around a pitching airfoil

NASA Astrophysics Data System (ADS)

Fu, Xiang; Li, Gaohua; Wang, Fuxin

2017-04-01

In order to study the dynamic behaviors of the flapping wing, the vortical flow around a pitching NACA0012 airfoil is investigated. The unsteady flow field is obtained by a very efficient zonal procedure based on the velocity-vorticity formulation and the Reynolds number based on the chord length of the airfoil is set to 1 million. The zonal procedure divides up the whole computation domain in to three zones: potential flow zone, boundary layer zone and Navier-Stokes zone. Since the vorticity is absent in the potential flow zone, the vorticity transport equation needs only to be solved in the boundary layer zone and Navier-Stokes zone. Moreover, the boundary layer equations are solved in the boundary layer zone. This arrangement drastically reduces the computation time against the traditional numerical method. After the flow field computation, the evolution of the vortices around the airfoil is analyzed in detail.

Ensemble Averaged Probability Density Function (APDF) for Compressible Turbulent Reacting Flows

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Liu, Nan-Suey

2012-01-01

In this paper, we present a concept of the averaged probability density function (APDF) for studying compressible turbulent reacting flows. The APDF is defined as an ensemble average of the fine grained probability density function (FG-PDF) with a mass density weighting. It can be used to exactly deduce the mass density weighted, ensemble averaged turbulent mean variables. The transport equation for APDF can be derived in two ways. One is the traditional way that starts from the transport equation of FG-PDF, in which the compressible Navier- Stokes equations are embedded. The resulting transport equation of APDF is then in a traditional form that contains conditional means of all terms from the right hand side of the Navier-Stokes equations except for the chemical reaction term. These conditional means are new unknown quantities that need to be modeled. Another way of deriving the transport equation of APDF is to start directly from the ensemble averaged Navier-Stokes equations. The resulting transport equation of APDF derived from this approach appears in a closed form without any need for additional modeling. The methodology of ensemble averaging presented in this paper can be extended to other averaging procedures: for example, the Reynolds time averaging for statistically steady flow and the Reynolds spatial averaging for statistically homogeneous flow. It can also be extended to a time or spatial filtering procedure to construct the filtered density function (FDF) for the large eddy simulation (LES) of compressible turbulent reacting flows.

Validation of numerical model for cook stove using Reynolds averaged Navier-Stokes based solver

NASA Astrophysics Data System (ADS)

Islam, Md. Moinul; Hasan, Md. Abdullah Al; Rahman, Md. Mominur; Rahaman, Md. Mashiur

2017-12-01

Biomass fired cook stoves, for many years, have been the main cooking appliance for the rural people of developing countries. Several researches have been carried out to the find efficient stoves. In the present study, numerical model of an improved household cook stove is developed to analyze the heat transfer and flow behavior of gas during operation. The numerical model is validated with the experimental results. Computation of the numerical model is executed the using non-premixed combustion model. Reynold's averaged Navier-Stokes (RaNS) equation along with the κ - ɛ model governed the turbulent flow associated within the computed domain. The computational results are in well agreement with the experiment. Developed numerical model can be used to predict the effect of different biomasses on the efficiency of the cook stove.

Computational analysis of water entry of a circular section at constant velocity based on Reynold's averaged Navier-Stokes method

NASA Astrophysics Data System (ADS)

Uddin, M. Maruf; Fuad, Muzaddid-E.-Zaman; Rahaman, Md. Mashiur; Islam, M. Rabiul

2017-12-01

With the rapid decrease in the cost of computational infrastructure with more efficient algorithm for solving non-linear problems, Reynold's averaged Navier-Stokes (RaNS) based Computational Fluid Dynamics (CFD) has been used widely now-a-days. As a preliminary evaluation tool, CFD is used to calculate the hydrodynamic loads on offshore installations, ships, and other structures in the ocean at initial design stages. Traditionally, wedges have been studied more than circular cylinders because cylinder section has zero deadrise angle at the instant of water impact, which increases with increase of submergence. In Present study, RaNS based commercial code ANSYS Fluent is used to simulate the water entry of a circular section at constant velocity. It is seen that present computational results were compared with experiment and other numerical method.

Fluid-structure analysis of a flexible flapping airfoil at low Reynolds number flow

NASA Astrophysics Data System (ADS)

Unger, Ralf; Haupt, Matthias C.; Horst, Peter; Radespiel, Rolf

2012-01-01

In this paper, a coupling simulation methodology is applied to investigate the fluid flow around a light and flexible airfoil based on a handfoil of a seagull. A finite element model of the flexible airfoil is fully coupled to the flow solver by using a load and displacement transfer as well as a fluid grid deformation algorithm. The flow field is characterized by a laminar-turbulent transition at a Reynolds number of Re=100 000, which takes place along a laminar separation bubble. An unsteady Reynolds-averaged Navier-Stokes flow solver is used to take this transition process into account by comparison of a critical N-factor with the N-factor computed by the eN-method. Results of computations have shown that the flexibility of the airfoil has a major influence on the thrust efficiency, the mean drag and lift, and the location of laminar-turbulent transition. The thrust efficiency can be considerably improved by increasing the plunging amplitude and by using a time dependent airfoil stiffness, inspired by the muscle contraction of birds.

Simulations of Bluff Body Flow Interaction for Noise Source Modeling

NASA Technical Reports Server (NTRS)

Khorrami, Medi R.; Lockard David P.; Choudhari, Meelan M.; Jenkins, Luther N.; Neuhart, Dan H.; McGinley, Catherine B.

2006-01-01

The current study is a continuation of our effort to characterize the details of flow interaction between two cylinders in a tandem configuration. This configuration is viewed to possess many of the pertinent flow features of the highly interactive unsteady flow field associated with the main landing gear of large civil transports. The present effort extends our previous two-dimensional, unsteady, Reynolds Averaged Navier-Stokes computations to three dimensions using a quasilaminar, zonal approach, in conjunction with a two-equation turbulence model. Two distinct separation length-to-diameter ratios of L/D = 3.7 and 1.435, representing intermediate and short separation distances between the two cylinders, are simulated. The Mach 0.166 simulations are performed at a Reynolds number of Re = 1.66 105 to match the companion experiments at NASA Langley Research Center. Extensive comparisons with the measured steady and unsteady surface pressure and off-surface particle image velocimetry data show encouraging agreement. Both prominent and some of the more subtle trends in the mean and fluctuating flow fields are correctly predicted. Both computations and the measured data reveal a more robust and energetic shedding process at L/D = 3.7 in comparison with the weaker shedding in the shorter separation case of L/D = 1.435. The vortex shedding frequency based on the computed surface pressure spectra is in reasonable agreement with the measured Strouhal frequency.

In Search of the Physics: NASA's Approach to Airframe Noise

NASA Technical Reports Server (NTRS)

Macaraeg, Michele G.; Lockard, David P.; Streett, Craig L.

1999-01-01

An extensive numerical and experimental study of airframe noise mechanisms associated with a subsonic high-lift system has been performed at NASA Langley Research Center (LaRC). Investigations involving both steady and unsteady computations and experiments on small-scale models with part-span flaps and full-span flaps are presented. Both surface (steady and unsteady pressure measurements, hot films, oil flows, pressure sensitive paint) and off-surface (5 holeprobe, particle-imaged velocimetry, laser velocimetry, laser light sheet measurements) were taken in the LaRC Quiet Flow Facility (QFF) and several hard-wall tunnels. Experiments in the Low Turbulence Pressure Tunnel (LTPT) included Reynolds number variations up to flight conditions. Successful microphone array measurements were also taken providing both acoustic source maps on the model, and quantitative spectra. Critical directivity measurements were obtained in the QFF. NASA Langley unstructured and structured Reynolds-Averaged Navier-Stokes codes modeled the steady aspects of the flows. Excellent comparisons with surface and off-surface experimental data were obtained. Subsequently, these meanflow calculations were utilized in both linear stability and direct numerical simulations of the flow fields to calculate unsteady surface pressures and farfield acoustic spectra. Accurate calculations were critical in obtaining not only noise source characteristics, but shear layer correction data as well. Techniques utilized in these investigations as well as brief overviews of the results are given.

Large Eddy Simulation of a Film Cooling Flow Injected from an Inclined Discrete Cylindrical Hole into a Crossflow with Zero-Pressure Gradient Turbulent Boundary Layer

NASA Technical Reports Server (NTRS)

Johnson, Perry L.; Shyam, Vikram

2012-01-01

A Large Eddy Simulation (LES) is performed of a high blowing ratio (M = 1.7) film cooling flow with density ratio of unity. Mean results are compared with experimental data to show the degree of fidelity achieved in the simulation. While the trends in the LES prediction are a noticeable improvement over Reynolds-Averaged Navier-Stokes (RANS) predictions, there is still a lack a spreading on the underside of the lifted jet. This is likely due to the inability of the LES to capture the full range of influential eddies on the underside of the jet due to their smaller structure. The unsteady structures in the turbulent coolant jet are also explored and related to turbulent mixing characteristics

Control of pseudo-shock oscillation in scramjet inlet-isolator using periodical excitation

NASA Astrophysics Data System (ADS)

Su, Wei-Yi; Chen, Yun; Zhang, Feng-Rui; Tang, Piao-Ping

2018-02-01

To suppress the pressure oscillation, stabilize the shock train in the scramjet isolator and delay the hypersonic inlet unstart, flow control using periodic excitation was investigated with unsteady Reynolds averaged Navier-Stokes simulations. The results showed that by injecting air to manipulate the cowl reflected shock wave, the separation bubble induced by it was diminished and the pressure oscillations of the shock train were markedly suppressed. The power spectral density and standard deviation of wall pressure were significantly reduced. The simulations revealed that this active control method can raise the critical back pressure by 17.5% compared with the baseline, which would successfully delay the hypersonic inlet unstarts. The results demonstrated that this active control method is effective in suppressing pressure oscillation and delaying hypersonic inlet unstarts.

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.

Numerical analysis of flow about a total temperature sensor

NASA Technical Reports Server (NTRS)

Von Lavante, Ernst; Bruns, Russell L., Jr.; Sanetrik, Mark D.; Lam, Tim

1989-01-01

The unsteady flowfield about an airfoil-shaped inlet temperature sensor has been investigated using the thin-layer and full Navier-Stokes equations. A finite-volume formulation of the governing equations was used in conjunction with a Runge-Kutta time stepping scheme to analyze the flow about the sensor. Flow characteristics for this configuration were established at Mach numbers of 0.5 and 0.8 for different Reynolds numbers. The results were obtained for configurations of increasing complexity; important physical phenomena such as shock formation, boundary-layer separation, and unsteady wake formation were noted. Based on the computational results, recommendations for further study and refinement of the inlet temperature sensor were made.

Numerical investigation on the self-induced unsteadiness in tip leakage flow of a micro-axial fan rotor

NASA Astrophysics Data System (ADS)

Chen, Jinxin; Lai, Huanxin

2015-06-01

The self-induced unsteadiness in tip leakage flow (TLF) of a micro-axial fan rotor is numerically studied by solvingReynolds-averaged Navier-Stokes equations. The micro-axial fan, which is widely used in cooling systems of electronic devices, has a tip clearance of 6% of the axial chord length of the blade. At the design rotation speed, four cases near the peak efficiency point (PEP) with self-induced unsteadiness and four steady cases which have much weaker pressure fluctuations are investigated Using the "interface" separating the incoming main flow and the TLF defined by Du et al. [1], an explanation based on the propagation of the low energy spot and its multi-passing through the high gradient zone of the relativetotal pressure, is proposed to clarify the originating mechanism of the unsteadiness. At the operating points near the PEP, the main flow is weaker than the TLF and the interface moves upstream. The low energy spot which propagates along in the close behind of the interface has opportunity to circulate in the circumferential direction and passes through the sensitive interfaces several times, a slight perturbation therefore may be magnified significantlyand develops into the self-induced unsteadiness. The explanation is demonstrated by numerical results

Properties of the Residual Stress of the Temporally Filtered Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Pruett, C. D.; Gatski, T. B.; Grosch, C. E.; Thacker, W. D.

2002-01-01

The development of a unifying framework among direct numerical simulations, large-eddy simulations, and statistically averaged formulations of the Navier-Stokes equations, is of current interest. Toward that goal, the properties of the residual (subgrid-scale) stress of the temporally filtered Navier-Stokes equations are carefully examined. Causal time-domain filters, parameterized by a temporal filter width 0 less than Delta less than infinity, are considered. For several reasons, the differential forms of such filters are preferred to their corresponding integral forms; among these, storage requirements for differential forms are typically much less than for integral forms and, for some filters, are independent of Delta. The behavior of the residual stress in the limits of both vanishing and in infinite filter widths is examined. It is shown analytically that, in the limit Delta to 0, the residual stress vanishes, in which case the Navier-Stokes equations are recovered from the temporally filtered equations. Alternately, in the limit Delta to infinity, the residual stress is equivalent to the long-time averaged stress, and the Reynolds-averaged Navier-Stokes equations are recovered from the temporally filtered equations. The predicted behavior at the asymptotic limits of filter width is further validated by numerical simulations of the temporally filtered forced, viscous Burger's equation. Finally, finite filter widths are also considered, and a priori analyses of temporal similarity and temporal approximate deconvolution models of the residual stress are conducted.

Aerothermodynamic Analyses of Towed Ballutes

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.; Buck, Greg; Moss, James N.; Nielsen, Eric; Berger, Karen; Jones, William T.; Rudavsky, Rena

2006-01-01

A ballute (balloon-parachute) is an inflatable, aerodynamic drag device for application to planetary entry vehicles. Two challenging aspects of aerothermal simulation of towed ballutes are considered. The first challenge, simulation of a complete system including inflatable tethers and a trailing toroidal ballute, is addressed using the unstructured-grid, Navier-Stokes solver FUN3D. Auxiliary simulations of a semi-infinite cylinder using the rarefied flow, Direct Simulation Monte Carlo solver, DSV2, provide additional insight into limiting behavior of the aerothermal environment around tethers directly exposed to the free stream. Simulations reveal pressures higher than stagnation and corresponding large heating rates on the tether as it emerges from the spacecraft base flow and passes through the spacecraft bow shock. The footprint of the tether shock on the toroidal ballute is also subject to heating amplification. Design options to accommodate or reduce these environments are discussed. The second challenge addresses time-accurate simulation to detect the onset of unsteady flow interactions as a function of geometry and Reynolds number. Video of unsteady interactions measured in the Langley Aerothermodynamic Laboratory 20-Inch Mach 6 Air Tunnel and CFD simulations using the structured grid, Navier-Stokes solver LAURA are compared for flow over a rigid spacecraft-sting-toroid system. The experimental data provides qualitative information on the amplitude and onset of unsteady motion which is captured in the numerical simulations. The presence of severe unsteady fluid - structure interactions is undesirable and numerical simulation must be able to predict the onset of such motion.

The Sensitivity Analysis for the Flow Past Obstacles Problem with Respect to the Reynolds Number

PubMed Central

Ito, Kazufumi; Li, Zhilin; Qiao, Zhonghua

2013-01-01

In this paper, numerical sensitivity analysis with respect to the Reynolds number for the flow past obstacle problem is presented. To carry out such analysis, at each time step, we need to solve the incompressible Navier-Stokes equations on irregular domains twice, one for the primary variables; the other is for the sensitivity variables with homogeneous boundary conditions. The Navier-Stokes solver is the augmented immersed interface method for Navier-Stokes equations on irregular domains. One of the most important contribution of this paper is that our analysis can predict the critical Reynolds number at which the vortex shading begins to develop in the wake of the obstacle. Some interesting experiments are shown to illustrate how the critical Reynolds number varies with different geometric settings. PMID:24910780

The Sensitivity Analysis for the Flow Past Obstacles Problem with Respect to the Reynolds Number.

PubMed

Ito, Kazufumi; Li, Zhilin; Qiao, Zhonghua

2012-02-01

In this paper, numerical sensitivity analysis with respect to the Reynolds number for the flow past obstacle problem is presented. To carry out such analysis, at each time step, we need to solve the incompressible Navier-Stokes equations on irregular domains twice, one for the primary variables; the other is for the sensitivity variables with homogeneous boundary conditions. The Navier-Stokes solver is the augmented immersed interface method for Navier-Stokes equations on irregular domains. One of the most important contribution of this paper is that our analysis can predict the critical Reynolds number at which the vortex shading begins to develop in the wake of the obstacle. Some interesting experiments are shown to illustrate how the critical Reynolds number varies with different geometric settings.

Analysis of Unsteady Tip and Endwall Heat Transfer in a Highly Loaded Transonic Turbine Stage

NASA Technical Reports Server (NTRS)

Shyam, Vikram; Ameri, Ali; Chen, Jen-Ping

2010-01-01

In a previous study, vane-rotor shock interactions and heat transfer on the rotor blade of a highly loaded transonic turbine stage were simulated. The geometry consists of a high pressure turbine vane and downstream rotor blade. This study focuses on the physics of flow and heat transfer in the rotor tip, casing and hub regions. The simulation was performed using the Unsteady Reynolds-Averaged Navier-Stokes (URANS) code MSU-TURBO. A low Reynolds number k-epsilon model was utilized to model turbulence. The rotor blade in question has a tip gap height of 2.1 percent of the blade height. The Reynolds number of the flow is approximately 3x10(exp 6) per meter. Unsteadiness was observed at the tip surface that results in intermittent "hot spots". It is demonstrated that unsteadiness in the tip gap is governed by inviscid effects due to high speed flow and is not strongly dependent on pressure ratio across the tip gap contrary to published observations that have primarily dealt with subsonic tip flows. The high relative Mach numbers in the tip gap lead to a choking of the leakage flow that translates to a relative attenuation of losses at higher loading. The efficacy of new tip geometry is discussed to minimize heat flux at the tip while maintaining choked conditions. In addition, an explanation is provided that shows the mechanism behind the rise in stagnation temperature on the casing to values above the absolute total temperature at the inlet. It is concluded that even in steady mode, work transfer to the near tip fluid occurs due to relative shearing by the casing. This is believed to be the first such explanation of the work transfer phenomenon in the open literature. The difference in pattern between steady and time-averaged heat flux at the hub is also explained.

About the coupling of turbulence closure models with averaged Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Vandromme, D.; Ha Minh, H.

1986-01-01

The MacCormack implicit predictor-corrector model (1981) for numerical solution of the coupled Navier-Stokes equations for turbulent flows is extended to nonconservative multiequation turbulence models, as well as the inclusion of second-order Reynolds stress turbulence closure. A scalar effective pressure turbulent contribution to the pressure field is defined to approximate the effects of the Reynolds stress in strongly sheared flows. The Jacobian matrices of the transport equations are diagonalized to reduce the required computer memory and run time. Techniques are defined for including turbulence in the diagonalization. Application of the method is demonstrated with solutions generated for transonic nozzle flow and for the interaction between a supersonic flat plate boundary layer and a 12 deg compression-expansion ramp.

Basic lubrication equations

NASA Technical Reports Server (NTRS)

Hamrock, B. J.; Dowson, D.

1981-01-01

Lubricants, usually Newtonian fluids, are assumed to experience laminar flow. The basic equations used to describe the flow are the Navier-Stokes equation of motion. The study of hydrodynamic lubrication is, from a mathematical standpoint, the application of a reduced form of these Navier-Stokes equations in association with the continuity equation. The Reynolds equation can also be derived from first principles, provided of course that the same basic assumptions are adopted in each case. Both methods are used in deriving the Reynolds equation, and the assumptions inherent in reducing the Navier-Stokes equations are specified. Because the Reynolds equation contains viscosity and density terms and these properties depend on temperature and pressure, it is often necessary to couple the Reynolds with energy equation. The lubricant properties and the energy equation are presented. Film thickness, a parameter of the Reynolds equation, is a function of the elastic behavior of the bearing surface. The governing elasticity equation is therefore presented.

A numerical study of the 2- and 3-dimensional unsteady Navier-Stokes equations in velocity-vorticity variables using compact difference schemes

NASA Technical Reports Server (NTRS)

Gatski, T. B.; Grosch, C. E.

1984-01-01

A compact finite-difference approximation to the unsteady Navier-Stokes equations in velocity-vorticity variables is used to numerically simulate a number of flows. These include two-dimensional laminar flow of a vortex evolving over a flat plate with an embedded cavity, the unsteady flow over an elliptic cylinder, and aspects of the transient dynamics of the flow over a rearward facing step. The methodology required to extend the two-dimensional formulation to three-dimensions is presented.

Performance of Reynolds Averaged Navier-Stokes Models in Predicting Separated Flows: Study of the Hump Flow Model Problem

NASA Technical Reports Server (NTRS)

Cappelli, Daniele; Mansour, Nagi N.

2012-01-01

Separation can be seen in most aerodynamic flows, but accurate prediction of separated flows is still a challenging problem for computational fluid dynamics (CFD) tools. The behavior of several Reynolds Averaged Navier-Stokes (RANS) models in predicting the separated ow over a wall-mounted hump is studied. The strengths and weaknesses of the most popular RANS models (Spalart-Allmaras, k-epsilon, k-omega, k-omega-SST) are evaluated using the open source software OpenFOAM. The hump ow modeled in this work has been documented in the 2004 CFD Validation Workshop on Synthetic Jets and Turbulent Separation Control. Only the baseline case is treated; the slot flow control cases are not considered in this paper. Particular attention is given to predicting the size of the recirculation bubble, the position of the reattachment point, and the velocity profiles downstream of the hump.

Flow and axial dispersion in a sinusoidal-walled tube: Effects of inertial and unsteady flows

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

Richmond, Marshall C.; Perkins, William A.; Scheibe, Timothy D.

2013-12-01

Dispersion in porous media flows has been the subject of much experimental, theoretical and numerical study. Here we consider a wavy-walled tube (a three-dimensional tube with sinusoidally-varying diameter) as a simplified conceptualization of flow in porous media, where constrictions represent pore throats and expansions pore bodies. A theoretical model for effective (macroscopic) longitudinal dispersion in this system has been developed by volume averaging the microscale velocity field. Direct numerical simulation using computational fluid dynamics (CFD) methods was used to compute velocity fields by solving the Navier-Stokes equations, and also to numerically solve the volume averaging closure problem, for a rangemore » of Reynolds numbers (Re) spanning the low-Re to inertial flow regimes, including one simulation at Re = 449 for which unsteady flow was observed. Dispersion values were computed using both the volume averaging solution and a random walk particle tracking method, and results of the two methods were shown to be consistent. Our results are compared to experimental measurements of dispersion in porous media and to previous theoretical results for the low-Re, Stokes flow regime. In the steady inertial regime we observe an power-law increase in effective longitudinal dispersion (DL) with Re, consistent with previous results. This rapid rate of increase is caused by trapping of solute in expansions due to flow separation (eddies). For the unsteady case (Re = 449), the rate of increase of DL with Re was smaller than that observed at lower Re. Velocity fluctuations in this regime lead to increased rates of solute mass transfer between the core flow and separated flow regions, thus diminishing the amount of tailing caused by solute trapping in eddies and thereby reducing longitudinal dispersion.« less

Influence of the dispersive and dissipative scales alpha and beta on the energy spectrum of the Navier-Stokes alphabeta equations.

PubMed

Chen, Xuemei; Fried, Eliot

2008-10-01

Lundgren's vortex model for the intermittent fine structure of high-Reynolds-number turbulence is applied to the Navier-Stokes alphabeta equations and specialized to the Navier-Stokes alpha equations. The Navier-Stokes alphabeta equations involve dispersive and dissipative length scales alpha and beta, respectively. Setting beta equal to alpha reduces the Navier-Stokes alphabeta equations to the Navier-Stokes alpha equations. For the Navier-Stokes alpha equations, the energy spectrum is found to obey Kolmogorov's -5/3 law in a range of wave numbers identical to that determined by Lundgren for the Navier-Stokes equations. For the Navier-Stokes alphabeta equations, Kolmogorov's -5/3 law is also recovered. However, granted that beta < alpha, the range of wave numbers for which this law holds is extended by a factor of alphabeta . This suggests that simulations based on the Navier-Stokes alphabeta equations may have the potential to resolve features smaller than those obtainable using the Navier-Stokes alpha equations.

Unsteady Flowfield in a High-Pressure Turbine Modeled by TURBO

NASA Technical Reports Server (NTRS)

Bakhle, Milind A.; Mehmed, Oral

2003-01-01

Forced response, or resonant vibrations, in turbomachinery components can cause blades to crack or fail because of the large vibratory blade stresses and subsequent high-cycle fatigue. Forced-response vibrations occur when turbomachinery blades are subjected to periodic excitation at a frequency close to their natural frequency. Rotor blades in a turbine are constantly subjected to periodic excitations when they pass through the spatially nonuniform flowfield created by upstream vanes. Accurate numerical prediction of the unsteady aerodynamics phenomena that cause forced-response vibrations can lead to an improved understanding of the problem and offer potential approaches to reduce or eliminate specific forced-response problems. The objective of the current work was to validate an unsteady aerodynamics code (named TURBO) for the modeling of the unsteady blade row interactions that can cause forced response vibrations. The three-dimensional, unsteady, multi-blade-row, Reynolds-averaged Navier-Stokes turbomachinery code named TURBO was used to model a high-pressure turbine stage for which benchmark data were recently acquired under a NASA contract by researchers at the Ohio State University. The test article was an initial design for a high-pressure turbine stage that experienced forced-response vibrations which were eliminated by increasing the axial gap. The data, acquired in a short duration or shock tunnel test facility, included unsteady blade surface pressures and vibratory strains.

Three-dimensional unsteady flow calculations in an advanced gas generator turbine

NASA Technical Reports Server (NTRS)

Rangwalla, Akil A.

1993-01-01

This paper deals with the application of a three-dimensional, unsteady Navier-Stokes code for predicting the unsteady flow in a single stage of an advanced gas generator turbine. The numerical method solves the three-dimensional thin-layer Navier-Stokes equations, using a system of overlaid grids, which allow for relative motion between the rotor and stator airfoils. Results in the form of time averaged pressures and pressure amplitudes on the airfoil surfaces will be shown. In addition, instantaneous contours of pressure, Mach number, etc. will be presented in order to provide a greater understanding of the inviscid as well as the viscous aspects of the flowfield. Also, relevant secondary flow features such as cross-plane velocity vectors and total pressure contours will be presented. Prior work in two-dimensions has indicated that for the advanced designs, the unsteady interactions can play a significant role in turbine performance. These interactions affect not only the stage efficiency but can substantially alter the time-averaged features of the flow. This work is a natural extension of the work done in two-dimensions and hopes to address some of the issues raised by the two-dimensional calculations. These calculations are being performed as an integral part of an actual design process and demonstrate the value of unsteady rotor-stator interaction calculations in the design of turbomachines.

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 1: Analysis description

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. The governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models are described in detail.

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 1: Analysis description

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 3D has been developed to solve the three dimensional, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort has been to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation have been emphasized. The governing equations are solved in generalized non-orthogonal body-fitted coordinates by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. It describes in detail the governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models.

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 2: User's guide

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the User's Guide, and describes the program's features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Experimental and Computational Study of the Flow past a Simplified Geometry of an Engine/Pylon/Wing Installation at low velocity/moderate incidence flight conditions

NASA Astrophysics Data System (ADS)

Bury, Yannick; Lucas, Matthieu; Bonnaud, Cyril; Joly, Laurent; ISAE Team; Airbus Team

2014-11-01

We study numerically and experimentally the vortices that develop past a model geometry of a wing equipped with pylon-mounted engine at low speed/moderate incidence flight conditions. For such configuration, the presence of the powerplant installation under the wing initiates a complex, unsteady vortical flow field at the nacelle/pylon/wing junctions. Its interaction with the upper wing boundary layer causes a drop of aircraft performances. In order to decipher the underlying physics, this study is initially conducted on a simplified geometry at a Reynolds number of 200000, based on the chord wing and on the freestream velocity. Two configurations of angle of attack and side-slip angle are investigated. This work relies on unsteady Reynolds Averaged Navier Stokes computations, oil flow visualizations and stereoscopic Particle Image Velocimetry measurements. The vortex dynamics thus produced is described in terms of vortex core position, intensity, size and turbulent intensity thanks to a vortex tracking approach. In addition, the analysis of the velocity flow fields obtained from PIV highlights the influence of the longitudinal vortex initiated at the pylon/wing junction on the separation process of the boundary layer near the upper wing leading-edge.

Implementation of algebraic stress models in a general 3-D Navier-Stokes method (PAB3D)

NASA Technical Reports Server (NTRS)

Abdol-Hamid, Khaled S.

1995-01-01

A three-dimensional multiblock Navier-Stokes code, PAB3D, which was developed for propulsion integration and general aerodynamic analysis, has been used extensively by NASA Langley and other organizations to perform both internal (exhaust) and external flow analysis of complex aircraft configurations. This code was designed to solve the simplified Reynolds Averaged Navier-Stokes equations. A two-equation k-epsilon turbulence model has been used with considerable success, especially for attached flows. Accurate predicting of transonic shock wave location and pressure recovery in separated flow regions has been more difficult. Two algebraic Reynolds stress models (ASM) have been recently implemented in the code that greatly improved the code's ability to predict these difficult flow conditions. Good agreement with Direct Numerical Simulation (DNS) for a subsonic flat plate was achieved with ASM's developed by Shih, Zhu, and Lumley and Gatski and Speziale. Good predictions were also achieved at subsonic and transonic Mach numbers for shock location and trailing edge boattail pressure recovery on a single-engine afterbody/nozzle model.

Comparison Between Navier-Stokes and Thin-Layer Computations for Separated Supersonic Flow

NASA Technical Reports Server (NTRS)

Degani, David; Steger, Joseph L.

1983-01-01

In the numerical simulation of high Reynolds-number flow, one can frequently supply only enough grid points to resolve the viscous terms in a thin layer. As a consequence, a body-or stream-aligned coordinate system is frequently used and viscous terms in this direction are discarded. It is argued that these terms cannot be resolved and computational efficiency is gained by their neglect. Dropping the streamwise viscous terms in this manner has been termed the thin-layer approximation. The thin-layer concept is an old one, and similar viscous terms are dropped, for example, in parabolized Navier-Stokes schemes. However, such schemes also make additional assumptions so that the equations can be marched in space, and such a restriction is not usually imposed on a thin-layer model. The thin-layer approximation can be justified in much the same way as the boundary-layer approximation; it requires, therefore, a body-or stream-aligned coordinate and a high Reynolds number. Unlike the boundary-layer approximation, the same equations are used throughout, so there is no matching problem. Furthermore, the normal momentum equation is not simplified and the convection terms are not one-sided differenced for marching. Consequently, the thin-layer equations are numerically well behaved at separation and require no special treatment there. Nevertheless, the thin-layer approximation receives criticism. It has been suggested that the approximation is invalid at separation and, more recently, that it is inadequate for unsteady transonic flow. Although previous comparisons between the thin-layer and Navier-Stokes equations have been made, these comparisons have not been adequately documented.

Predicting Flutter and Forced Response in Turbomachinery

NASA Technical Reports Server (NTRS)

VanZante, Dale E.; Adamczyk, John J.; Srivastava, Rakesh; Bakhle, Milind A.; Shabbir, Aamir; Chen, Jen-Ping; Janus, J. Mark; To, Wai-Ming; Barter, John

2005-01-01

TURBO-AE is a computer code that enables detailed, high-fidelity modeling of aeroelastic and unsteady aerodynamic characteristics for prediction of flutter, forced response, and blade-row interaction effects in turbomachinery. Flow regimes that can be modeled include subsonic, transonic, and supersonic, with attached and/or separated flow fields. The three-dimensional Reynolds-averaged Navier-Stokes equations are solved numerically to obtain extremely accurate descriptions of unsteady flow fields in multistage turbomachinery configurations. Blade vibration is simulated by use of a dynamic-grid-deformation technique to calculate the energy exchange for determining the aerodynamic damping of vibrations of blades. The aerodynamic damping can be used to assess the stability of a blade row. TURBO-AE also calculates the unsteady blade loading attributable to such external sources of excitation as incoming gusts and blade-row interactions. These blade loadings, along with aerodynamic damping, are used to calculate the forced responses of blades to predict their fatigue lives. Phase-lagged boundary conditions based on the direct-store method are used to calculate nonzero interblade phase-angle oscillations; this practice eliminates the need to model multiple blade passages, and, hence, enables large savings in computational resources.

Investigation of unsteadiness in Shock-particle cloud interaction: Fully resolved two-dimensional simulation and one-dimensional modeling

NASA Astrophysics Data System (ADS)

Hosseinzadeh-Nik, Zahra; Regele, Jonathan D.

2015-11-01

Dense compressible particle-laden flow, which has a complex nature, exists in various engineering applications. Shock waves impacting a particle cloud is a canonical problem to investigate this type of flow. It has been demonstrated that large flow unsteadiness is generated inside the particle cloud from the flow induced by the shock passage. It is desirable to develop models for the Reynolds stress to capture the energy contained in vortical structures so that volume-averaged models with point particles can be simulated accurately. However, the previous work used Euler equations, which makes the prediction of vorticity generation and propagation innacurate. In this work, a fully resolved two dimensional (2D) simulation using the compressible Navier-Stokes equations with a volume penalization method to model the particles has been performed with the parallel adaptive wavelet-collocation method. The results still show large unsteadiness inside and downstream of the particle cloud. A 1D model is created for the unclosed terms based upon these 2D results. The 1D model uses a two-phase simple low dissipation AUSM scheme (TSLAU) developed by coupled with the compressible two phase kinetic energy equation.

Simulation of blood flow through an artificial heart

NASA Technical Reports Server (NTRS)

Kiris, Cetin; Chang, I-Dee; Rogers, Stuart E.; Kwak, Dochan

1991-01-01

A numerical simulation of the incompressible viscous flow through a prosthetic tilting disk heart valve is presented in order to demonstrate the current capability to model unsteady flows with moving boundaries. Both steady state and unsteady flow calculations are done by solving the incompressible Navier-Stokes equations in 3-D generalized curvilinear coordinates. In order to handle the moving boundary problems, the chimera grid embedding scheme which decomposes a complex computational domain into several simple subdomains is used. An algebraic turbulence model for internal flows is incorporated to reach the physiological values of Reynolds number. Good agreement is obtained between the numerical results and experimental measurements. It is found that the tilting disk valve causes large regions of separated flow, and regions of high shear.

Effect of Turbulence Modeling on an Excited Jet

NASA Technical Reports Server (NTRS)

Brown, Clifford A.; Hixon, Ray

2010-01-01

The flow dynamics in a high-speed jet are dominated by unsteady turbulent flow structures in the plume. Jet excitation seeks to control these flow structures through the natural instabilities present in the initial shear layer of the jet. Understanding and optimizing the excitation input, for jet noise reduction or plume mixing enhancement, requires many trials that may be done experimentally or computationally at a significant cost savings. Numerical simulations, which model various parts of the unsteady dynamics to reduce the computational expense of the simulation, must adequately capture the unsteady flow dynamics in the excited jet for the results are to be used. Four CFD methods are considered for use in an excited jet problem, including two turbulence models with an Unsteady Reynolds Averaged Navier-Stokes (URANS) solver, one Large Eddy Simulation (LES) solver, and one URANS/LES hybrid method. Each method is used to simulate a simplified excited jet and the results are evaluated based on the flow data, computation time, and numerical stability. The knowledge gained about the effect of turbulence modeling and CFD methods from these basic simulations will guide and assist future three-dimensional (3-D) simulations that will be used to understand and optimize a realistic excited jet for a particular application.

Caution: Precision Error in Blade Alignment Results in Faulty Unsteady CFD Simulation

NASA Astrophysics Data System (ADS)

Lewis, Bryan; Cimbala, John; Wouden, Alex

2012-11-01

Turbomachinery components experience unsteady loads at several frequencies. The rotor frequency corresponds to the time for one rotor blade to rotate between two stator vanes, and is normally dominant for rotor torque oscillations. The guide vane frequency corresponds to the time for two rotor blades to pass by one guide vane. The machine frequency corresponds to the machine RPM. Oscillations at the machine frequency are always present due to minor blade misalignments and imperfections resulting from manufacturing defects. However, machine frequency oscillations should not be present in CFD simulations if the mesh is free of both blade misalignment and surface imperfections. The flow through a Francis hydroturbine was modeled with unsteady Reynolds-Averaged Navier-Stokes (URANS) CFD simulations and a dynamic rotating grid. Spectral analysis of the unsteady torque on the rotor blades revealed a large component at the machine frequency. Close examination showed that one blade was displaced by 0 .0001° due to round-off errors during mesh generation. A second mesh without blade misalignment was then created. Subsequently, large machine frequency oscillations were not observed for this mesh. These results highlight the effect of minor geometry imperfections on CFD solutions. This research was supported by a grant from the DoE and a National Defense Science and Engineering Graduate Fellowship.

Slat Cove Noise Modeling: A Posteriori Analysis of Unsteady RANS Simulations

NASA Technical Reports Server (NTRS)

Choudhari, Meelan; Khorrami, Mehdi R.; Lockard, David P.; Atkins, Harold L.; Lilley, Geoffrey M.

2002-01-01

A companion paper by Khorrami et al demonstrates the feasibility of simulating the (nominally) self-sustained, large-scale unsteadiness within the leading-edge slat-cove region of multi-element airfoils using unsteady Reynolds-Averaged Navier-Stokes (URANS) equations, provided that the turbulence production term in the underlying two-equation turbulence model is switched off within the cove region. In conjunction with a FfowesWilliams-Hawkings solver, the URANS computations were shown to capture the dominant portion of the acoustic spectrum attributed to slat noise, as well as reproducing the increased intensity of slat cove motions (and, correspondingly, far-field noise as well) at the lower angles of attack. This paper examines that simulation database, augmented by additional simulations, with the objective of transitioning this apparent success to aeroacoustic predictions in an engineering context. As a first step towards this goal, the simulated flow and acoustic fields are compared with experiment and simplified analytical model. Rather intense near-field fluctuations in the simulated flow are found to be associated with unsteady separation along the slat bottom surface, relatively close to the slat cusp. Accuracy of the laminar-cove simulations in this near-wall region is raised to be an open issue. The adjoint Green's function approach is also explored in an attempt to identify the most efficient noise source locations.

Slat Cove Unsteadiness Effect of 3D Flow Structures

NASA Technical Reports Server (NTRS)

Choudhari, Meelan M.; Khorrami, Mehdi R.

2006-01-01

Previous studies have indicated that 2D, time accurate computations based on a pseudo-laminar zonal model of the slat cove region (within the framework of the Reynolds-Averaged Navier-Stokes equations) are inadequate for predicting the full unsteady dynamics of the slat cove flow field. Even though such computations could capture the large-scale, unsteady vorticity structures in the slat cove region without requiring any external forcing, the simulated vortices were excessively strong and the recirculation zone was unduly energetic in comparison with the PIV measurements for a generic high-lift configuration. To resolve this discrepancy and to help enable physics based predictions of slat aeroacoustics, the present paper is focused on 3D simulations of the slat cove flow over a computational domain of limited spanwise extent. Maintaining the pseudo-laminar approach, current results indicate that accounting for the three-dimensionality of flow fluctuations leads to considerable improvement in the accuracy of the unsteady, nearfield solution. Analysis of simulation data points to the likely significance of turbulent fluctuations near the reattachment region toward the generation of broadband slat noise. The computed acoustic characteristics (in terms of the frequency spectrum and spatial distribution) within short distances from the slat resemble the previously reported, subscale measurements of slat noise.

Unsteady RANS/DES analysis of flow around helicopter rotor blades at forword flight conditions

NASA Astrophysics Data System (ADS)

Zhang, Zhenyu; Qian, Yaoru

2018-05-01

In this paper, the complex flows around forward-flying helicopter blades are numerically investigated. Both the Reynolds-averaged Navier-Stokes (RANS) and the Detached Eddy Simulation (DES) methods are used for the analysis of characteristics like local dynamic flow separation, effects of radial sweeping and reversed flow. The flow was solved by a highly efficient finite volume solver with multi-block structured grids. Focusing upon the complexity of the advance ratio effects, above properties are fully recognized. The current results showed significant agreements between both RANS and DES methods at phases with attached flow phases. Detailed information of separating flow near the withdrawal phases are given by DES results. The flow analysis of these blades under reversed flow reveals a significant interaction between the reversed flow and the span-wise sweeping.

Recent Enhancements To The FUN3D Flow Solver For Moving-Mesh Applications

NASA Technical Reports Server (NTRS)

Biedron, Robert T,; Thomas, James L.

2009-01-01

An unsteady Reynolds-averaged Navier-Stokes solver for unstructured grids has been extended to handle general mesh movement involving rigid, deforming, and overset meshes. Mesh deformation is achieved through analogy to elastic media by solving the linear elasticity equations. A general method for specifying the motion of moving bodies within the mesh has been implemented that allows for inherited motion through parent-child relationships, enabling simulations involving multiple moving bodies. Several example calculations are shown to illustrate the range of potential applications. For problems in which an isolated body is rotating with a fixed rate, a noninertial reference-frame formulation is available. An example calculation for a tilt-wing rotor is used to demonstrate that the time-dependent moving grid and noninertial formulations produce the same results in the limit of zero time-step size.

Statistical-mechanical predictions and Navier-Stokes dynamics of two-dimensional flows on a bounded domain.

PubMed

Brands, H; Maassen, S R; Clercx, H J

1999-09-01

In this paper the applicability of a statistical-mechanical theory to freely decaying two-dimensional (2D) turbulence on a bounded domain is investigated. We consider an ensemble of direct numerical simulations in a square box with stress-free boundaries, with a Reynolds number that is of the same order as in experiments on 2D decaying Navier-Stokes turbulence. The results of these simulations are compared with the corresponding statistical equilibria, calculated from different stages of the evolution. It is shown that the statistical equilibria calculated from early times of the Navier-Stokes evolution do not correspond to the dynamical quasistationary states. At best, the global topological structure is correctly predicted from a relatively late time in the Navier-Stokes evolution, when the quasistationary state has almost been reached. This failure of the (basically inviscid) statistical-mechanical theory is related to viscous dissipation and net leakage of vorticity in the Navier-Stokes dynamics at moderate values of the Reynolds number.

International journal of computational fluid dynamics real-time prediction of unsteady flow based on POD reduced-order model and particle filter

NASA Astrophysics Data System (ADS)

Kikuchi, Ryota; Misaka, Takashi; Obayashi, Shigeru

2016-04-01

An integrated method consisting of a proper orthogonal decomposition (POD)-based reduced-order model (ROM) and a particle filter (PF) is proposed for real-time prediction of an unsteady flow field. The proposed method is validated using identical twin experiments of an unsteady flow field around a circular cylinder for Reynolds numbers of 100 and 1000. In this study, a PF is employed (ROM-PF) to modify the temporal coefficient of the ROM based on observation data because the prediction capability of the ROM alone is limited due to the stability issue. The proposed method reproduces the unsteady flow field several orders faster than a reference numerical simulation based on Navier-Stokes equations. Furthermore, the effects of parameters, related to observation and simulation, on the prediction accuracy are studied. Most of the energy modes of the unsteady flow field are captured, and it is possible to stably predict the long-term evolution with ROM-PF.

Some practical turbulence modeling options for Reynolds-averaged full Navier-Stokes calculations of three-dimensional flows

NASA Technical Reports Server (NTRS)

Bui, Trong T.

1993-01-01

New turbulence modeling options recently implemented for the 3-D version of Proteus, a Reynolds-averaged compressible Navier-Stokes code, are described. The implemented turbulence models include: the Baldwin-Lomax algebraic model, the Baldwin-Barth one-equation model, the Chien k-epsilon model, and the Launder-Sharma k-epsilon model. Features of this turbulence modeling package include: well documented and easy to use turbulence modeling options, uniform integration of turbulence models from different classes, automatic initialization of turbulence variables for calculations using one- or two-equation turbulence models, multiple solid boundaries treatment, and fully vectorized L-U solver for one- and two-equation models. Validation test cases include the incompressible and compressible flat plate turbulent boundary layers, turbulent developing S-duct flow, and glancing shock wave/turbulent boundary layer interaction. Good agreement is obtained between the computational results and experimental data. Sensitivity of the compressible turbulent solutions with the method of y(sup +) computation, the turbulent length scale correction, and some compressibility corrections are examined in detail. The test cases show that the highly optimized one-and two-equation turbulence models can be used in routine 3-D Navier-Stokes computations with no significant increase in CPU time as compared with the Baldwin-Lomax algebraic model.

Isogeometric Divergence-conforming B-splines for the Unsteady Navier-Stokes Equations

DTIC Science & Technology

2012-04-01

space and S a positive real number, we define Lq(0, S;X) as the space consisting of all strongly measurable functions φ : (0, S)→ X with ‖φ...Introduction The unsteady incompressible Navier-Stokes equations are infused with vast geometric structure, evidenced by a wide array of balance laws for...analy- sis in conjunction with a Variational Multiscale (VMS) methodology. In these papers, it was found that the increased continuity of

Development of a High-Order Space-Time Matrix-Free Adjoint Solver

NASA Technical Reports Server (NTRS)

Ceze, Marco A.; Diosady, Laslo T.; Murman, Scott M.

2016-01-01

The growth in computational power and algorithm development in the past few decades has granted the science and engineering community the ability to simulate flows over complex geometries, thus making Computational Fluid Dynamics (CFD) tools indispensable in analysis and design. Currently, one of the pacing items limiting the utility of CFD for general problems is the prediction of unsteady turbulent ows.1{3 Reynolds-averaged Navier-Stokes (RANS) methods, which predict a time-invariant mean flowfield, struggle to provide consistent predictions when encountering even mild separation, such as the side-of-body separation at a wing-body junction. NASA's Transformative Tools and Technologies project is developing both numerical methods and physical modeling approaches to improve the prediction of separated flows. A major focus of this e ort is efficient methods for resolving the unsteady fluctuations occurring in these flows to provide valuable engineering data of the time-accurate flow field for buffet analysis, vortex shedding, etc. This approach encompasses unsteady RANS (URANS), large-eddy simulations (LES), and hybrid LES-RANS approaches such as Detached Eddy Simulations (DES). These unsteady approaches are inherently more expensive than traditional engineering RANS approaches, hence every e ort to mitigate this cost must be leveraged. Arguably, the most cost-effective approach to improve the efficiency of unsteady methods is the optimal placement of the spatial and temporal degrees of freedom (DOF) using solution-adaptive methods.

A nonperturbative approximation for the moderate Reynolds number Navier-Stokes equations.

PubMed

Roper, Marcus; Brenner, Michael P

2009-03-03

The nonlinearity of the Navier-Stokes equations makes predicting the flow of fluid around rapidly moving small bodies highly resistant to all approaches save careful experiments or brute force computation. Here, we show how a linearization of the Navier-Stokes equations captures the drag-determining features of the flow and allows simplified or analytical computation of the drag on bodies up to Reynolds number of order 100. We illustrate the utility of this linearization in 2 practical problems that normally can only be tackled with sophisticated numerical methods: understanding flow separation in the flow around a bluff body and finding drag-minimizing shapes.

A direct method for the solution of unsteady two-dimensional incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ghia, K. N.; Osswald, G. A.; Ghia, U.

1983-01-01

The unsteady incompressible Navier-Stokes equations are formulated in terms of vorticity and stream function in generalized curvilinear orthogonal coordinates to facilitiate analysis of flow configurations with general geometries. The numerical method developed solves the conservative form of the transport equation using the alternating-direction implicit method, whereas the stream-function equation is solved by direct block Gaussian elimination. The method is applied to a model problem of flow over a back-step in a doubly infinite channel, using clustered conformal coordinates. One-dimensional stretching functions, dependent on the Reynolds number and the asymptotic behavior of the flow, are used to provide suitable grid distribution in the separation and reattachment regions, as well as in the inflow and outflow regions. The optimum grid distribution selected attempts to honor the multiple length scales of the separated-flow model problem. The asymptotic behavior of the finite-differenced transport equation near infinity is examined and the numerical method is carefully developed so as to lead to spatially second-order accurate wiggle-free solutions, i.e., with minimum dispersive error. Results have been obtained in the entire laminar range for the backstep channel and are in good agreement with the available experimental data for this flow problem.

Overview of the Aeroelastic Prediction Workshop

NASA Technical Reports Server (NTRS)

Heeg, Jennifer; Chwalowski, Pawel; Florance, Jennifer P.; Wieseman, Carol D.; Schuster, David M.; Perry, Raleigh B.

2013-01-01

The Aeroelastic Prediction Workshop brought together an international community of computational fluid dynamicists as a step in defining the state of the art in computational aeroelasticity. This workshop's technical focus was prediction of unsteady pressure distributions resulting from forced motion, benchmarking the results first using unforced system data. The most challenging aspects of the physics were identified as capturing oscillatory shock behavior, dynamic shock-induced separated flow and tunnel wall boundary layer influences. The majority of the participants used unsteady Reynolds-averaged Navier Stokes codes. These codes were exercised at transonic Mach numbers for three configurations and comparisons were made with existing experimental data. Substantial variations were observed among the computational solutions as well as differences relative to the experimental data. Contributing issues to these differences include wall effects and wall modeling, non-standardized convergence criteria, inclusion of static aeroelastic deflection, methodology for oscillatory solutions, post-processing methods. Contributing issues pertaining principally to the experimental data sets include the position of the model relative to the tunnel wall, splitter plate size, wind tunnel expansion slot configuration, spacing and location of pressure instrumentation, and data processing methods.

Large-Amplitude, High-Rate Roll Oscillations of a 65 deg Delta Wing at High Incidence

NASA Technical Reports Server (NTRS)

Chaderjian, Neal M.; Schiff, Lewis B.

2000-01-01

The IAR/WL 65 deg delta wing experimental results provide both detail pressure measurements and a wide range of flow conditions covering from simple attached flow, through fully developed vortex and vortex burst flow, up to fully-stalled flow at very high incidence. Thus, the Computational Unsteady Aerodynamics researchers can use it at different level of validating the corresponding code. In this section a range of CFD results are provided for the 65 deg delta wing at selected flow conditions. The time-dependent, three-dimensional, Reynolds-averaged, Navier-Stokes (RANS) equations are used to numerically simulate the unsteady vertical flow. Two sting angles and two large- amplitude, high-rate, forced-roll motions and a damped free-to-roll motion are presented. The free-to-roll motion is computed by coupling the time-dependent RANS equations to the flight dynamic equation of motion. The computed results are compared with experimental pressures, forces, moments and roll angle time history. In addition, surface and off-surface flow particle streaks are also presented.

Large Eddy Simulations using oodlesDST

DTIC Science & Technology

2016-01-01

Research Agency DST-Group-TR-3205 ABSTRACT The oodlesDST code is based on OpenFOAM software and performs Large Eddy Simulations of......maritime platforms using a variety of simulation techniques. He is currently using OpenFOAM software to perform both Reynolds Averaged Navier-Stokes

Evaluation of a research circulation control airfoil using Navier-Stokes methods

NASA Technical Reports Server (NTRS)

Shrewsbury, George D.

1987-01-01

The compressible Reynolds time averaged Navier-Stokes equations were used to obtain solutions for flows about a two dimensional circulation control airfoil. The governing equations were written in conservation form for a body-fitted coordinate system and solved using an Alternating Direction Implicit (ADI) procedure. A modified algebraic eddy viscosity model was used to define the turbulent characteristics of the flow, including the wall jet flow over the Coanda surface at the trailing edge. Numerical results are compared to experimental data obtained for a research circulation control airfoil geometry. Excellent agreement with the experimental results was obtained.

A fast Poisson solver for unsteady incompressible Navier-Stokes equations on the half-staggered grid

NASA Technical Reports Server (NTRS)

Golub, G. H.; Huang, L. C.; Simon, H.; Tang, W. -P.

1995-01-01

In this paper, a fast Poisson solver for unsteady, incompressible Navier-Stokes equations with finite difference methods on the non-uniform, half-staggered grid is presented. To achieve this, new algorithms for diagonalizing a semi-definite pair are developed. Our fast solver can also be extended to the three dimensional case. The motivation and related issues in using this second kind of staggered grid are also discussed. Numerical testing has indicated the effectiveness of this algorithm.

Sea Butterfly Swimming: Time-resolved Tomographic PIV measurements

NASA Astrophysics Data System (ADS)

Murphy, David; Zheng, Lingxiao; Mittal, Rajat; Webster, Donald; Yen, Jeannette

2011-11-01

The planktonic sea butterfly Limacina helicina swims by flapping its flexible, wing-like parapodia. The appendage stroke kinematics of this shell-bearing pteropod are three-dimensional and likely contain elements of both drag-based (rowing) and lift-based (flapping) propulsion. Unsteady lift-generating mechanisms such as clap-and-fling may also be present. Upstroke and downstroke motions both propel the animal upward and roll it forwards and backwards, resulting in a sawtooth trajectory. We present time-resolved, tomographic PIV measurements of flow generated by free-swimming pteropods (Limacina helicina) moving upwards with average swimming speeds of 5 - 17 mm/s. The pteropods beat their appendages with a stroke frequency of 4 - 5 Hz. With a size range of 1 - 2 mm, the animals filmed in this study operate in a viscous environment with a Reynolds number of 5 to 20. The volumetric flow measurements provide insight into the three dimensional nature of the flow and into the relative importance of drag- and lift-based propulsion at this low Reynolds number. Preliminary results from Navier-Stokes simulations of the flow associated with the swimming of this organism will also be presented.

Numerical Issues for Circulation Control Calculations

NASA Technical Reports Server (NTRS)

Swanson, Roy C., Jr.; Rumsey, Christopher L.

2006-01-01

Steady-state and time-accurate two-dimensional solutions of the compressible Reynolds-averaged Navier- Stokes equations are obtained for flow over the Lockheed circulation control (CC) airfoil and the General Aviation CC (GACC) airfoil. Numerical issues in computing circulation control flows such as the effects of grid resolution, boundary and initial conditions, and unsteadiness are addressed. For the Lockheed CC airfoil computed solutions are compared with detailed experimental data, which include velocity and Reynolds stress profiles. Three turbulence models, having either one or two transport equations, are considered. Solutions are obtained on a sequence of meshes, with mesh refinement primarily concentrated on the airfoil circular trailing edge. Several effects related to mesh refinement are identified. For example, sometimes sufficient mesh resolution can exclude nonphysical solutions, which can occur in CC airfoil calculations. Also, sensitivities of the turbulence models with mesh refinement are discussed. In the case of the GACC airfoil the focus is on the difference between steady-state and time-accurate solutions. A specific objective is to determine if there is self-excited vortex shedding from the jet slot lip.

Computational fluid dynamics challenges for hybrid air vehicle applications

NASA Astrophysics Data System (ADS)

Carrin, M.; Biava, M.; Steijl, R.; Barakos, G. N.; Stewart, D.

2017-06-01

This paper begins by comparing turbulence models for the prediction of hybrid air vehicle (HAV) flows. A 6 : 1 prolate spheroid is employed for validation of the computational fluid dynamics (CFD) method. An analysis of turbulent quantities is presented and the Shear Stress Transport (SST) k-ω model is compared against a k-ω Explicit Algebraic Stress model (EASM) within the unsteady Reynolds-Averaged Navier-Stokes (RANS) framework. Further comparisons involve Scale Adaptative Simulation models and a local transition transport model. The results show that the flow around the vehicle at low pitch angles is sensitive to transition effects. At high pitch angles, the vortices generated on the suction side provide substantial lift augmentation and are better resolved by EASMs. The validated CFD method is employed for the flow around a shape similar to the Airlander aircraft of Hybrid Air Vehicles Ltd. The sensitivity of the transition location to the Reynolds number is demonstrated and the role of each vehicle£s component is analyzed. It was found that the ¦ns contributed the most to increase the lift and drag.

Reynolds-Averaged Navier-Stokes Simulation of a 2D Circulation Control Wind Tunnel Experiment

NASA Technical Reports Server (NTRS)

Allan, Brian G.; Jones, Greg; Lin, John C.

2011-01-01

Numerical simulations are performed using a Reynolds-averaged Navier-Stokes (RANS) flow solver for a circulation control airfoil. 2D and 3D simulation results are compared to a circulation control wind tunnel test conducted at the NASA Langley Basic Aerodynamics Research Tunnel (BART). The RANS simulations are compared to a low blowing case with a jet momentum coefficient, C(sub u), of 0:047 and a higher blowing case of 0.115. Three dimensional simulations of the model and tunnel walls show wall effects on the lift and airfoil surface pressures. These wall effects include a 4% decrease of the midspan sectional lift for the C(sub u) 0.115 blowing condition. Simulations comparing the performance of the Spalart Allmaras (SA) and Shear Stress Transport (SST) turbulence models are also made, showing the SST model compares best to the experimental data. A Rotational/Curvature Correction (RCC) to the turbulence model is also evaluated demonstrating an improvement in the CFD predictions.

Dynamic stall study of a multi-element airfoil

NASA Technical Reports Server (NTRS)

Tung, Chee; Mcalister, Kenneth W.; Wang, Clin M.

1992-01-01

Unsteady flow behavior and load characteristics of a VR-7 airfoil with and without a slat were studied in the water tunnel of the Aeroflightdynamics Directorate, NASA Ames Research Center. Both airfoils were oscillated sinusoidally between 5 and 25 degrees at a Reynolds number of 200,000 to obtain the unsteady lift, drag and pitching moment data. A fluorescing dye was released from an orifice located at the leading edge of the airfoil for the purpose of visualizing the boundary layer and wake flow. The flow field and load predictions of an incompressible Navier-Stokes code based on a velocity-vorticity formulation were compared with the test data. The test and predictions both confirm that the slatted VR-7 airfoil delays both static and dynamic stall as compared to the VR-7 airfoil alone.

Investigation of Turbulent Tip Leakage Vortex in an Axial Water Jet Pump with Large Eddy Simulation

NASA Technical Reports Server (NTRS)

Hah, Chunill; Katz, Joseph

2012-01-01

Detailed steady and unsteady numerical studies were performed to investigate tip clearance flow in an axial water jet pump. The primary objective is to understand physics of unsteady tip clearance flow, unsteady tip leakage vortex, and cavitation inception in an axial water jet pump. Steady pressure field and resulting steady tip leakage vortex from a steady flow analysis do not seem to explain measured cavitation inception correctly. The measured flow field near the tip is unsteady and measured cavitation inception is highly transient. Flow visualization with cavitation bubbles shows that the leakage vortex is oscillating significantly and many intermittent vortex ropes are present between the suction side of the blade and the tip leakage core vortex. Although the flow field is highly transient, the overall flow structure is stable and a characteristic frequency seems to exist. To capture relevant flow physics as much as possible, a Reynolds-averaged Navier-Stokes (RANS) calculation and a Large Eddy Simulation (LES) were applied for the current investigation. The present study reveals that several vortices from the tip leakage vortex system cross the tip gap of the adjacent blade periodically. Sudden changes in local pressure field inside tip gap due to these vortices create vortex ropes. The instantaneous pressure filed inside the tip gap is drastically different from that of the steady flow simulation. Unsteady flow simulation which can calculate unsteady vortex motion is necessary to calculate cavitation inception accurately even at design flow condition in such a water jet pump.

Efficiency and Accuracy of Time-Accurate Turbulent Navier-Stokes Computations

NASA Technical Reports Server (NTRS)

Rumsey, Christopher L.; Sanetrik, Mark D.; Biedron, Robert T.; Melson, N. Duane; Parlette, Edward B.

1995-01-01

The accuracy and efficiency of two types of subiterations in both explicit and implicit Navier-Stokes codes are explored for unsteady laminar circular-cylinder flow and unsteady turbulent flow over an 18-percent-thick circular-arc (biconvex) airfoil. Grid and time-step studies are used to assess the numerical accuracy of the methods. Nonsubiterative time-stepping schemes and schemes with physical time subiterations are subject to time-step limitations in practice that are removed by pseudo time sub-iterations. Computations for the circular-arc airfoil indicate that a one-equation turbulence model predicts the unsteady separated flow better than an algebraic turbulence model; also, the hysteresis with Mach number of the self-excited unsteadiness due to shock and boundary-layer separation is well predicted.

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.

Numerical simulation and comparison of symmetrical/supercritical airfoils for the near tip region of a helicopter in forward flight

NASA Technical Reports Server (NTRS)

Badavi, F. F.

1989-01-01

Aerodynamic loads on a multi-bladed helicopter rotor in forward flight at transonic tip conditions are calculated. The unsteady, three-dimensional, time-accurate compressible Reynolds-averaged thin layer Navier-Stokes equations are solved in a rotating coordinate system on a body-conformed, curvilinear grid of C-H topology. Detailed boundary layer and global numerical comparisons of NACA-0012 symmetrical and CAST7-158 supercritical airfoils are made under identical forward flight conditions. The rotor wake effects are modeled by applying a correction to the geometric angle of attack of the blade. This correction is obtained by computing the local induced downwash velocity with a free wake analysis program. The calculations are performed on the Numerical Aerodynamic Simulation Cray 2 and the VPS32 (a derivative of a Cyber 205 at the Langley Research Center) for a model helicopter rotor in forward flight.

Reliability of numerical wind tunnels for VAWT simulation

NASA Astrophysics Data System (ADS)

Raciti Castelli, M.; Masi, M.; Battisti, L.; Benini, E.; Brighenti, A.; Dossena, V.; Persico, G.

2016-09-01

Computational Fluid Dynamics (CFD) based on the Unsteady Reynolds Averaged Navier Stokes (URANS) equations have long been widely used to study vertical axis wind turbines (VAWTs). Following a comprehensive experimental survey on the wakes downwind of a troposkien-shaped rotor, a campaign of bi-dimensional simulations is presented here, with the aim of assessing its reliability in reproducing the main features of the flow, also identifying areas needing additional research. Starting from both a well consolidated turbulence model (k-ω SST) and an unstructured grid typology, the main simulation settings are here manipulated in a convenient form to tackle rotating grids reproducing a VAWT operating in an open jet wind tunnel. The dependence of the numerical predictions from the selected grid spacing is investigated, thus establishing the less refined grid size that is still capable of capturing some relevant flow features such as integral quantities (rotor torque) and local ones (wake velocities).

Blade Displacement Predictions for the Full-Scale UH-60A Airloads Rotor

NASA Technical Reports Server (NTRS)

Bledron, Robert T.; Lee-Rausch, Elizabeth M.

2014-01-01

An unsteady Reynolds-Averaged Navier-Stokes solver for unstructured grids is loosely coupled to a rotorcraft comprehensive code and used to simulate two different test conditions from a wind-tunnel test of a full-scale UH-60A rotor. Performance data and sectional airloads from the simulation are compared with corresponding tunnel data to assess the level of fidelity of the aerodynamic aspects of the simulation. The focus then turns to a comparison of the blade displacements, both rigid (blade root) and elastic. Comparisons of computed root motions are made with data from three independent measurement systems. Finally, comparisons are made between computed elastic bending and elastic twist, and the corresponding measurements obtained from a photogrammetry system. Overall the correlation between computed and measured displacements was good, especially for the root pitch and lag motions and the elastic bending deformation. The correlation of root lead-lag motion and elastic twist deformation was less favorable.

RANS simulation of cavitation and hull pressure fluctuation for marine propeller operating behind-hull condition

NASA Astrophysics Data System (ADS)

Paik, Kwang-Jun; Park, Hyung-Gil; Seo, Jongsoo

2013-12-01

Simulations of cavitation flow and hull pressure fluctuation for a marine propeller operating behind a hull using the unsteady Reynolds-Averaged Navier-Stokes equations (RANS) are presented. A full hull body submerged under the free surface is modeled in the computational domain to simulate directly the wake field of the ship at the propeller plane. Simulations are performed in design and ballast draught conditions to study the effect of cavitation number. And two propellers with slightly different geometry are simulated to validate the detectability of the numerical simulation. All simulations are performed using a commercial CFD software FLUENT. Cavitation patterns of the simulations show good agreement with the experimental results carried out in Samsung CAvitation Tunnel (SCAT). The simulation results for the hull pressure fluctuation induced by a propeller are also compared with the experimental results showing good agreement in the tendency and amplitude, especially, for the first blade frequency.

The Prediction of Scattered Broadband Shock-Associated Noise

NASA Technical Reports Server (NTRS)

Miller, Steven A. E.

2015-01-01

A mathematical model is developed for the prediction of scattered broadband shock-associated noise. Model arguments are dependent on the vector Green's function of the linearized Euler equations, steady Reynolds-averaged Navier-Stokes solutions, and the two-point cross-correlation of the equivalent source. The equivalent source is dependent on steady Reynolds-averaged Navier-Stokes solutions of the jet flow, that capture the nozzle geometry and airframe surface. Contours of the time-averaged streamwise velocity component and turbulent kinetic energy are examined with varying airframe position relative to the nozzle exit. Propagation effects are incorporated by approximating the vector Green's function of the linearized Euler equations. This approximation involves the use of ray theory and an assumption that broadband shock-associated noise is relatively unaffected by the refraction of the jet shear layer. A non-dimensional parameter is proposed that quantifies the changes of the broadband shock-associated noise source with varying jet operating condition and airframe position. Scattered broadband shock-associated noise possesses a second set of broadband lobes that are due to the effect of scattering. Presented predictions demonstrate relatively good agreement compared to a wide variety of measurements.

Large Eddy/Reynolds-Averaged Navier-Stokes Simulations of CUBRC Base Heating Experiments

NASA Technical Reports Server (NTRS)

Salazar, Giovanni; Edwards, Jack R.; Amar, Adam J.

2012-01-01

ven with great advances in computational techniques and computing power during recent decades, the modeling of unsteady separated flows, such as those encountered in the wake of a re-entry vehicle, continues to be one of the most challenging problems in CFD. Of most interest to the aerothermodynamics community is accurately predicting transient heating loads on the base of a blunt body, which would result in reduced uncertainties and safety margins when designing a re-entry vehicle. However, the prediction of heat transfer can vary widely depending on the turbulence model employed. Therefore, selecting a turbulence model which realistically captures as much of the flow physics as possible will result in improved results. Reynolds Averaged Navier Stokes (RANS) models have become increasingly popular due to their good performance with attached flows, and the relatively quick turnaround time to obtain results. However, RANS methods cannot accurately simulate unsteady separated wake flows, and running direct numerical simulation (DNS) on such complex flows is currently too computationally expensive. Large Eddy Simulation (LES) techniques allow for the computation of the large eddies, which contain most of the Reynolds stress, while modeling the smaller (subgrid) eddies. This results in models which are more computationally expensive than RANS methods, but not as prohibitive as DNS. By complimenting an LES approach with a RANS model, a hybrid LES/RANS method resolves the larger turbulent scales away from surfaces with LES, and switches to a RANS model inside boundary layers. As pointed out by Bertin et al., this type of hybrid approach has shown a lot of promise for predicting turbulent flows, but work is needed to verify that these models work well in hypersonic flows. The very limited amounts of flight and experimental data available presents an additional challenge for researchers. Recently, a joint study by NASA and CUBRC has focused on collecting heat transfer data on the backshell of a scaled model of the Orion Multi-Purpose Crew Vehicle (MPCV). Heat augmentation effects due to the presence of cavities and RCS jet firings were also investigated. The high quality data produced by this effort presents a new set of data which can be used to assess the performance of CFD methods. In this work, a hybrid LES/RANS model developed at North Carolina State University (NCSU) is used to simulate several runs from these experiments, and evaluate the performance of high fidelity methods as compared to more typical RANS models. .

Characterization of Unsteady Flow Structures Around Tandem Cylinders for Component Interaction Studies in Airframe Noise

NASA Technical Reports Server (NTRS)

Jenkins, Luther N.; Khorrami, Mehdi R.; Choudhari, Meelan M.; McGinley, Catherine B.

2005-01-01

A joint computational and experimental study has been performed at NASA Langley Research Center to investigate the unsteady flow generated by the components of an aircraft landing gear system. Because the flow field surrounding a full landing gear is so complex, the study was conducted on a simplified geometry consisting of two cylinders in tandem arrangement to isolate and characterize the pertinent flow phenomena. This paper focuses on the experimental effort where surface pressures, 2-D Particle Image Velocimetry, and hot-wire anemometry were used to document the flow interaction around the two cylinders at a Reynolds Number of 1.66 x 10(exp 5), based on cylinder diameter, and cylinder spacing-todiameter ratios, L/D, of 1.435 and 3.70. Transition strips were applied to the forward cylinder to produce a turbulent boundary layer upstream of the flow separation. For these flow conditions and L/D ratios, surface pressures on both the forward and rear cylinders show the effects of L/D on flow symmetry, base pressure, and the location of flow separation and attachment. Mean velocities and instantaneous vorticity obtained from the PIV data are used to examine the flow structure between and aft of the cylinders. Shedding frequencies and spectra obtained using hot-wire anemometry are presented. These results are compared with unsteady, Reynolds-Averaged Navier-Stokes (URANS) computations for the same configuration in a companion paper by Khorrami, Choudhari, Jenkins, and McGinley (2005). The experimental dataset produced in this study provides information to better understand the mechanisms associated with component interaction noise, develop and validate time-accurate computer methods used to calculate the unsteady flow field, and assist in modeling of the radiated noise from landing gears.

Navier-Stokes calculations on multi-element airfoils using a chimera-based solver

NASA Technical Reports Server (NTRS)

Jasper, Donald W.; Agrawal, Shreekant; Robinson, Brian A.

1993-01-01

A study of Navier-Stokes calculations of flows about multielement airfoils using a chimera grid approach is presented. The chimera approach utilizes structured, overlapped grids which allow great flexibility of grid arrangement and simplifies grid generation. Calculations are made for two-, three-, and four-element airfoils, and modeling of the effect of gap distance between elements is demonstrated for a two element case. Solutions are obtained using the thin-layer form of the Reynolds averaged Navier-Stokes equations with turbulence closure provided by the Baldwin-Lomax algebraic model or the Baldwin-Barth one equation model. The Baldwin-Barth turbulence model is shown to provide better agreement with experimental data and to dramatically improve convergence rates for some cases. Recently developed, improved farfield boundary conditions are incorporated into the solver for greater efficiency. Computed results show good comparison with experimental data which include aerodynamic forces, surface pressures, and boundary layer velocity profiles.

Reynolds-Averaged Navier-Stokes Solutions to Flat Plate Film Cooling Scenarios

NASA Technical Reports Server (NTRS)

Johnson, Perry L.; Shyam, Vikram; Hah, Chunill

2011-01-01

The predictions of several Reynolds-Averaged Navier-Stokes solutions for a baseline film cooling geometry are analyzed and compared with experimental data. The Fluent finite volume code was used to perform the computations with the realizable k-epsilon turbulence model. The film hole was angled at 35 to the crossflow with a Reynolds number of 17,400. Multiple length-to-diameter ratios (1.75 and 3.5) as well as momentum flux ratios (0.125 and 0.5) were simulated with various domains, boundary conditions, and grid refinements. The coolant to mainstream density ratio was maintained at 2.0 for all scenarios. Computational domain and boundary condition variations show the ability to reduce the computational cost as compared to previous studies. A number of grid refinement and coarsening variations are compared for further insights into the reduction of computational cost. Liberal refinement in the near hole region is valuable, especially for higher momentum jets that tend to lift-off and create a recirculating flow. A lack of proper refinement in the near hole region can severely diminish the accuracy of the solution, even in the far region. The effects of momentum ratio and hole length-to-diameter ratio are also discussed.

Parallel computing techniques for rotorcraft aerodynamics

NASA Astrophysics Data System (ADS)

Ekici, Kivanc

The modification of unsteady three-dimensional Navier-Stokes codes for application on massively parallel and distributed computing environments is investigated. The Euler/Navier-Stokes code TURNS (Transonic Unsteady Rotor Navier-Stokes) was chosen as a test bed because of its wide use by universities and industry. For the efficient implementation of TURNS on parallel computing systems, two algorithmic changes are developed. First, main modifications to the implicit operator, Lower-Upper Symmetric Gauss Seidel (LU-SGS) originally used in TURNS, is performed. Second, application of an inexact Newton method, coupled with a Krylov subspace iterative method (Newton-Krylov method) is carried out. Both techniques have been tried previously for the Euler equations mode of the code. In this work, we have extended the methods to the Navier-Stokes mode. Several new implicit operators were tried because of convergence problems of traditional operators with the high cell aspect ratio (CAR) grids needed for viscous calculations on structured grids. Promising results for both Euler and Navier-Stokes cases are presented for these operators. For the efficient implementation of Newton-Krylov methods to the Navier-Stokes mode of TURNS, efficient preconditioners must be used. The parallel implicit operators used in the previous step are employed as preconditioners and the results are compared. The Message Passing Interface (MPI) protocol has been used because of its portability to various parallel architectures. It should be noted that the proposed methodology is general and can be applied to several other CFD codes (e.g. OVERFLOW).

The effect of Reynolds number and turbulence on airfoil aerodynamics at -90 degrees incidence

NASA Technical Reports Server (NTRS)

Stremel, Paul M.

1993-01-01

A method has been developed for calculating the viscous flow about airfoils in with and without deflected flaps at -90 deg incidence. This method provides for the solution of the unsteady incompressible Navier-Stokes equations by means of an implicit technique. The solution is calculated on a body-fitted computational mesh using a staggered grid method. The vorticity is defined at the node points, and the velocity components are defined at the mesh-cell sides. The staggered-grid orientation provides for accurate representation of vorticity at the node points and the continuity equation at the mesh-cell centers. The method provides for the direct solution of the flow field and satisfies the continuity equation to machine zero at each time-step. The method is evaluated in terms of its ability to predict two-dimensional flow about an airfoil at -90 degrees incidence for varying Reynolds number and different boundary layer models. A laminar and a turbulent boundary layer models. A laminar and a turbulent boundary layer model are considered in the evaluation of the method. The variation of the average loading and surface pressure distribution due to flap deflection, Reynolds number, and laminar or turbulent flow are presented and compared with experimental results. The comparisons indicate that the calculated drag and drag reduction caused by flap deflection and the calculated average surface pressure are in excellent agreement with the measured results at a similar Reynolds number.

Development Of A Navier-Stokes Computer Code

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan; Kwak, Dochan

1993-01-01

Report discusses aspects of development of CENS3D computer code, solving three-dimensional Navier-Stokes equations of compressible, viscous, unsteady flow. Implements implicit finite-difference or finite-volume numerical-integration scheme, called "lower-upper symmetric-Gauss-Seidel" (LU-SGS), offering potential for very low computer time per iteration and for fast convergence.

An Edge-Based Method for the Incompressible Navier-Stokes Equations on Polygonal Meshes

NASA Astrophysics Data System (ADS)

Wright, Jeffrey A.; Smith, Richard W.

2001-05-01

A pressure-based method is presented for discretizing the unsteady incompressible Navier-Stokes equations using hybrid unstructured meshes. The edge-based data structure and assembly procedure adopted lead naturally to a strictly conservative discretization, which is valid for meshes composed of n-sided polygons. Particular attention is given to the construction of a pressure-velocity coupling procedure which is supported by edge data, resulting in a relatively simple numerical method that is consistent with the boundary and initial conditions required by the incompressible Navier-Stokes equations. Edge formulas are presented for assembling the momentum equations, which are based on an upwind-biased linear reconstruction of the velocity field. Similar formulas are presented for assembling the pressure equation. The method is demonstrated to be second-order accurate in space and time for two Navier-Stokes problems admitting an exact solution. Results for several other well-known problems are also presented, including lid-driven cavity flow, impulsively started cylinder flow, and unsteady vortex shedding from a circular cylinder. Although the method is by construction minimalist, it is shown to be accurate and robust for the problems considered.

Parallel performance investigations of an unstructured mesh Navier-Stokes solver

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.

2000-01-01

A Reynolds-averaged Navier-Stokes solver based on unstructured mesh techniques for analysis of high-lift configurations is described. The method makes use of an agglomeration multigrid solver for convergence acceleration. Implicit line-smoothing is employed to relieve the stiffness associated with highly stretched meshes. A GMRES technique is also implemented to speed convergence at the expense of additional memory usage. The solver is cache efficient and fully vectorizable, and is parallelized using a two-level hybrid MPI-OpenMP implementation suitable for shared and/or distributed memory architectures, as well as clusters of shared memory machines. Convergence and scalability results are illustrated for various high-lift cases.

Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Anderson, W. Kyle

1998-01-01

A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences. Several simplifying approximations to the complete linearization of the residual are also presented, and the resulting accuracy of the derivatives is examined. Demonstration optimizations for both compressible and incompressible flows are given.

Unsteady numerical simulation of the flow in the U9 Kaplan turbine model

NASA Astrophysics Data System (ADS)

Javadi, Ardalan; Nilsson, Håkan

2014-03-01

The Reynolds-averaged Navier-Stokes equations with the RNG k-ε turbulence model closure are utilized to simulate the unsteady turbulent flow throughout the whole flow passage of the U9 Kaplan turbine model. The U9 Kaplan turbine model comprises 20 stationary guide vanes and 6 rotating blades (696.3 RPM), working at best efficiency load (0.71 m3/s). The computations are conducted using a general finite volume method, using the OpenFOAM CFD code. A dynamic mesh is used together with a sliding GGI interface to include the effect of the rotating runner. The clearance is included in the guide vane. The hub and tip clearances are also included in the runner. An analysis is conducted of the unsteady behavior of the flow field, the pressure fluctuation in the draft tube, and the coherent structures of the flow. The tangential and axial velocity distributions at three sections in the draft tube are compared against LDV measurements. The numerical result is in reasonable agreement with the experimental data, and the important flow physics close to the hub in the draft tube is captured. The hub and tip vortices and an on-axis forced vortex are captured. The numerical results show that the frequency of the forced vortex in 1/5 of the runner rotation.

CFD Based Added Mass Prediction in Cruise Condition of Underwater Vehicle Dynamic

NASA Astrophysics Data System (ADS)

Agoes Moelyadi, Mochammad; Bambang Riswandi, Bagus

2018-04-01

One of the unsteady flow behavior on the hydrodynamic characteristics of underwater vehicle is the presence of added mass. In cruising conditions, the underwater vehicle may require the addition of speed or experience the disturbance in the form of unsteady flow so that cause the hydrodynamic interaction between the surface of the vehicle with the surrounding fluid. This leads to the rise of local velocity of flow and the great changes of hydrodynamic forces which are very influential on the stability of the underwater vehicle. One of the result is an additional force called added mass. It is very useful parameter to control underwater vehicle dynamic.This paper reports the research on the added mass coefficient of underwater vehicles obtained through the Computational Fluid Dynmaic (CFD) simulation method using CFX software. Added mass coefficient is calculated by performing an unsteady simulation or known as transient simulation. Computational simulations are based on the Reynold Average Navier- Stokes (RANS) equation solution. The simulated vehicle moves forward and backward according to the sinus function, with a frequency of 0.25 Hz, a 2 m amplitude, a cruising depth of 10 m below sea level, and Vcruise 1.54 m / s (Re = 9.000.000). Simulation result data includes velocity contour, variation of force and acceleration to frequency, and added mass coefficient.

SIERRA/Aero Theory Manual Version 4.46.

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

Sierra Thermal/Fluid Team

2017-09-01

SIERRA/Aero is a two and three dimensional, node-centered, edge-based finite volume code that approximates the compressible Navier-Stokes equations on unstructured meshes. It is applicable to inviscid and high Reynolds number laminar and turbulent flows. Currently, two classes of turbulence models are provided: Reynolds Averaged Navier-Stokes (RANS) and hybrid methods such as Detached Eddy Simulation (DES). Large Eddy Simulation (LES) models are currently under development. The gas may be modeled either as ideal, or as a non-equilibrium, chemically reacting mixture of ideal gases. This document describes the mathematical models contained in the code, as well as certain implementation details. First, themore » governing equations are presented, followed by a description of the spatial discretization. Next, the time discretization is described, and finally the boundary conditions. Throughout the document, SIERRA/ Aero is referred to simply as Aero for brevity.« less

SIERRA/Aero Theory Manual Version 4.44

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

Sierra Thermal /Fluid Team

2017-04-01

SIERRA/Aero is a two and three dimensional, node-centered, edge-based finite volume code that approximates the compressible Navier-Stokes equations on unstructured meshes. It is applicable to inviscid and high Reynolds number laminar and turbulent flows. Currently, two classes of turbulence models are provided: Reynolds Averaged Navier-Stokes (RANS) and hybrid methods such as Detached Eddy Simulation (DES). Large Eddy Simulation (LES) models are currently under development. The gas may be modeled either as ideal, or as a non-equilibrium, chemically reacting mixture of ideal gases. This document describes the mathematical models contained in the code, as well as certain implementation details. First, themore » governing equations are presented, followed by a description of the spatial discretization. Next, the time discretization is described, and finally the boundary conditions. Throughout the document, SIERRA/ Aero is referred to simply as Aero for brevity.« less

Validation of High-Fidelity CFD Simulations for Rocket Injector Design

NASA Technical Reports Server (NTRS)

Tucker, P. Kevin; Menon, Suresh; Merkle, Charles L.; Oefelein, Joseph C.; Yang, Vigor

2008-01-01

Computational fluid dynamics (CFD) has the potential to improve the historical rocket injector design process by evaluating the sensitivity of performance and injector-driven thermal environments to the details of the injector geometry and key operational parameters. Methodical verification and validation efforts on a range of coaxial injector elements have shown the current production CFD capability must be improved in order to quantitatively impact the injector design process. This paper documents the status of a focused effort to compare and understand the predictive capabilities and computational requirements of a range of CFD methodologies on a set of single element injector model problems. The steady Reynolds-Average Navier-Stokes (RANS), unsteady Reynolds-Average Navier-Stokes (URANS) and three different approaches using the Large Eddy Simulation (LES) technique were used to simulate the initial model problem, a single element coaxial injector using gaseous oxygen and gaseous hydrogen propellants. While one high-fidelity LES result matches the experimental combustion chamber wall heat flux very well, there is no monotonic convergence to the data with increasing computational tool fidelity. Systematic evaluation of key flow field regions such as the flame zone, the head end recirculation zone and the downstream near wall zone has shed significant, though as of yet incomplete, light on the complex, underlying causes for the performance level of each technique. 1 Aerospace Engineer and Combustion CFD Team Leader, MS ER42, NASA MSFC, AL 35812, Senior Member, AIAA. 2 Professor and Director, Computational Combustion Laboratory, School of Aerospace Engineering, 270 Ferst Dr., Atlanta, GA 30332, Associate Fellow, AIAA. 3 Reilly Professor of Engineering, School of Mechanical Engineering, 585 Purdue Mall, West Lafayette, IN 47907, Fellow, AIAA. 4 Principal Member of Technical Staff, Combustion Research Facility, 7011 East Avenue, MS9051, Livermore, CA 94550, Associate Fellow, AIAA. 5 J. L. and G. H. McCain Endowed Chair, Mechanical Engineering, 104 Research Building East, University Park, PA 16802, Fellow, AIAA. American Institute of Aeronautics and Astronautics 1

Analysis of Massively Separated Flows of Aircraft Using Detached Eddy Simulation

NASA Astrophysics Data System (ADS)

Morton, Scott

2002-08-01

An important class of turbulent flows of aerodynamic interest are those characterized by massive separation, e.g., the flow around an aircraft at high angle of attack. Numerical simulation is an important tool for analysis, though traditional models used in the solution of the Reynolds-averaged Navier-Stokes (RANS) equations appear unable to accurately account for the time-dependent and three-dimensional motions governing flows with massive separation. Large-eddy simulation (LES) is able to resolve these unsteady three-dimensional motions, yet is cost prohibitive for high Reynolds number wall-bounded flows due to the need to resolve the small scale motions in the boundary layer. Spalart et. al. proposed a hybrid technique, Detached-Eddy Simulation (DES), which takes advantage of the often adequate performance of RANS turbulence models in the "thin," typically attached regions of the flow. In the separated regions of the flow the technique becomes a Large Eddy Simulation, directly resolving the time-dependent and unsteady features that dominate regions of massive separation. The current work applies DES to a 70 degree sweep delta wing at 27 degrees angle of attack, a geometrically simple yet challenging flowfield that exhibits the unsteady three-dimensional massively separated phenomena of vortex breakdown. After detailed examination of this basic flowfield, the method is demonstrated on three full aircraft of interest characterized by massive separation, the F-16 at 45 degrees angle of attack, the F-15 at 65 degree angle of attack (with comparison to flight test), and the C-130 in a parachute drop condition at near stall speed with cargo doors open.

Highly turbulent solutions of the Lagrangian-averaged Navier-Stokes alpha model and their large-eddy-simulation potential.

PubMed

Pietarila Graham, Jonathan; Holm, Darryl D; Mininni, Pablo D; Pouquet, Annick

2007-11-01

We compute solutions of the Lagrangian-averaged Navier-Stokes alpha - (LANS alpha ) model for significantly higher Reynolds numbers (up to Re approximately 8300 ) than have previously been accomplished. This allows sufficient separation of scales to observe a Navier-Stokes inertial range followed by a second inertial range specific to the LANS alpha model. Both fully helical and nonhelical flows are examined, up to Reynolds numbers of approximately 1300. Analysis of the third-order structure function scaling supports the predicted l3 scaling; it corresponds to a k-1 scaling of the energy spectrum for scales smaller than alpha. The energy spectrum itself shows a different scaling, which goes as k1. This latter spectrum is consistent with the absence of stretching in the subfilter scales due to the Taylor frozen-in hypothesis employed as a closure in the derivation of the LANS alpha model. These two scalings are conjectured to coexist in different spatial portions of the flow. The l3 [E(k) approximately k-1] scaling is subdominant to k1 in the energy spectrum, but the l3 scaling is responsible for the direct energy cascade, as no cascade can result from motions with no internal degrees of freedom. We demonstrate verification of the prediction for the size of the LANS alpha attractor resulting from this scaling. From this, we give a methodology either for arriving at grid-independent solutions for the LANS alpha model, or for obtaining a formulation of the large eddy simulation optimal in the context of the alpha models. The fully converged grid-independent LANS alpha model may not be the best approximation to a direct numerical simulation of the Navier-Stokes equations, since the minimum error is a balance between truncation errors and the approximation error due to using the LANS alpha instead of the primitive equations. Furthermore, the small-scale behavior of the LANS alpha model contributes to a reduction of flux at constant energy, leading to a shallower energy spectrum for large alpha. These small-scale features, however, do not preclude the LANS alpha model from reproducing correctly the intermittency properties of the high-Reynolds-number flow.

Supersonic quasi-axisymmetric vortex breakdown

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; Kandil, Hamdy A.; Liu, C. H.

1991-01-01

An extensive computational study of supersonic quasi-axisymmetric vortex breakdown in a configured circular duct is presented. The unsteady, compressible, full Navier-Stokes (NS) equations are used. The NS equations are solved for the quasi-axisymmetric flows using an implicit, upwind, flux difference splitting, finite volume scheme. The quasi-axisymmetric solutions are time accurate and are obtained by forcing the components of the flowfield vector to be equal on two axial planes, which are in close proximity of each other. The effect of Reynolds number, for laminar flows, on the evolution and persistence of vortex breakdown, is studied. Finally, the effect of swirl ration at the duct inlet is investigated.

A numerical study of three-dimensional vortex breakdown

NASA Technical Reports Server (NTRS)

Spall, Robert E.; Ash, Robert L.

1987-01-01

A numerical simulation of bubble-type vortex breakdown using a unique discrete form of the full 3-D, unsteady incompressible Navier-Stokes equations was performed. The Navier-Stokes equations were written in a vorticity-velocity form and the physical problem was not restricted to axisymmetric flow. The problem was parametized on a Rossby- Reynolds-number basis. Utilization of this parameter duo was shown to dictate the form of the free-field boundary condition specification and allowed control of axial breakdown location within the computational domain. The structure of the breakdown bubble was studied through time evolution plots of planar projected velocity vectors as well as through plots of particle traces and vortex lines. These results compared favorably with previous experimental studies. In addition, profiles of all three velocity components are presented at various axial stations and a Fourier analysis was performed to identify the dominant circumferential modes. The dynamics of the breakdown process were studied through plots of axial variation of rate of change of integrated total energy and rate of change of integrated enstrophy, as well as through contour plots of velocity, vorticity and pressure.

Stable boundary conditions and difference schemes for Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Dutt, P.

1985-01-01

The Navier-Stokes equations can be viewed as an incompletely elliptic perturbation of the Euler equations. By using the entropy function for the Euler equations as a measure of energy for the Navier-Stokes equations, it was possible to obtain nonlinear energy estimates for the mixed initial boundary value problem. These estimates are used to derive boundary conditions which guarantee L2 boundedness even when the Reynolds number tends to infinity. Finally, a new difference scheme for modelling the Navier-Stokes equations in multidimensions for which it is possible to obtain discrete energy estimates exactly analogous to those we obtained for the differential equation was proposed.

A novel VLES model accounting for near-wall turbulence: physical rationale and applications

NASA Astrophysics Data System (ADS)

Jakirlic, Suad; Chang, Chi-Yao; Kutej, Lukas; Tropea, Cameron

2014-11-01

A novel VLES (Very Large Eddy Simulation) model whose non-resolved residual turbulence is modelled by using an advanced near-wall eddy-viscosity model accounting for the near-wall Reynolds stress anisotropy influence on the turbulence viscosity by modelling appropriately the velocity scale in the relevant formulation (Hanjalic et al., 2004) is proposed. It represents a variable resolution Hybrid LES/RANS (Reynolds-Averaged Navier-Stokes) computational scheme enabling a seamless transition from RANS to LES depending on the ratio of the turbulent viscosities associated with the unresolved scales corresponding to the LES cut-off and the `unsteady' scales pertinent to the turbulent properties of the VLES residual motion, which varies within the flow domain. The VLES method is validated interactively in the process of the model derivation by computing fully-developed flow in a plane channel (important representative of wall-bounded flows, underlying the log-law for the velocity field, for studying near-wall Reynolds stress anisotropy) and a separating flow over a periodic arrangement of smoothly-contoured 2-D hills. The model performances are also assessed in capturing the natural decay of the homogeneous isotropic turbulence. The model is finally applied to swirling flow in a vortex tube, flow in an IC-engine configuration and flow past a realistic car model.

Numerical Prediction Methods (Reynolds-Averaged Navier-Stokes Simulations of Transonic Separated Flows)

NASA Technical Reports Server (NTRS)

Mehta, Unmeel; Lomax, Harvard

1981-01-01

During the past five years, numerous pioneering archival publications have appeared that have presented computer solutions of the mass-weighted, time-averaged Navier-Stokes equations for transonic problems pertinent to the aircraft industry. These solutions have been pathfinders of developments that could evolve into a major new technological capability, namely the computational Navier-Stokes technology, for the aircraft industry. So far these simulations have demonstrated that computational techniques, and computer capabilities have advanced to the point where it is possible to solve forms of the Navier-Stokes equations for transonic research problems. At present there are two major shortcomings of the technology: limited computer speed and memory, and difficulties in turbulence modelling and in computation of complex three-dimensional geometries. These limitations and difficulties are the pacing items of the continuing developments, although the one item that will most likely turn out to be the most crucial to the progress of this technology is turbulence modelling. The objective of this presentation is to discuss the state of the art of this technology and suggest possible future areas of research. We now discuss some of the flow conditions for which the Navier-Stokes equations appear to be required. On an airfoil there are four different types of interaction of a shock wave with a boundary layer: (1) shock-boundary-layer interaction with no separation, (2) shock-induced turbulent separation with immediate reattachment (we refer to this as a shock-induced separation bubble), (3) shock-induced turbulent separation without reattachment, and (4) shock-induced separation bubble with trailing edge separation.

Discrete adjoint of fractional step Navier-Stokes solver in generalized coordinates

NASA Astrophysics Data System (ADS)

Wang, Mengze; Mons, Vincent; Zaki, Tamer

2017-11-01

Optimization and control in transitional and turbulent flows require evaluation of gradients of the flow state with respect to the problem parameters. Using adjoint approaches, these high-dimensional gradients can be evaluated with a similar computational cost as the forward Navier-Stokes simulations. The adjoint algorithm can be obtained by discretizing the continuous adjoint Navier-Stokes equations or by deriving the adjoint to the discretized Navier-Stokes equations directly. The latter algorithm is necessary when the forward-adjoint relations must be satisfied to machine precision. In this work, our forward model is the fractional step solution to the Navier-Stokes equations in generalized coordinates, proposed by Rosenfeld, Kwak & Vinokur. We derive the corresponding discrete adjoint equations. We also demonstrate the accuracy of the combined forward-adjoint model, and its application to unsteady wall-bounded flows. This work has been partially funded by the Office of Naval Research (Grant N00014-16-1-2542).

The space-time solution element method: A new numerical approach for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Scott, James R.; Chang, Sin-Chung

1995-01-01

This paper is one of a series of papers describing the development of a new numerical method for the Navier-Stokes equations. Unlike conventional numerical methods, the current method concentrates on the discrete simulation of both the integral and differential forms of the Navier-Stokes equations. Conservation of mass, momentum, and energy in space-time is explicitly provided for through a rigorous enforcement of both the integral and differential forms of the governing conservation laws. Using local polynomial expansions to represent the discrete primitive variables on each cell, fluxes at cell interfaces are evaluated and balanced using exact functional expressions. No interpolation or flux limiters are required. Because of the generality of the current method, it applies equally to the steady and unsteady Navier-Stokes equations. In this paper, we generalize and extend the authors' 2-D, steady state implicit scheme. A general closure methodology is presented so that all terms up through a given order in the local expansions may be retained. The scheme is also extended to nonorthogonal Cartesian grids. Numerous flow fields are computed and results are compared with known solutions. The high accuracy of the scheme is demonstrated through its ability to accurately resolve developing boundary layers on coarse grids. Finally, we discuss applications of the current method to the unsteady Navier-Stokes equations.

Progress in incompressible Navier-Stokes computations for propulsion flows and its dual-use applications

NASA Technical Reports Server (NTRS)

Kiris, Cetin

1995-01-01

Development of an incompressible Navier-Stokes solution procedure was performed for the analysis of a liquid rocket engine pump components and for the mechanical heart assist devices. The solution procedure for the propulsion systems is applicable to incompressible Navier-Stokes flows in a steadily rotating frame of reference for any general complex configurations. The computer codes were tested on different complex configurations such as liquid rocket engine inducer and impellers. As a spin-off technology from the turbopump component simulations, the flow analysis for an axial heart pump was conducted. The baseline Left Ventricular Assist Device (LVAD) design was improved by adding an inducer geometry by adapting from the liquid rocket engine pump. The time-accurate mode of the incompressible Navier-Stokes code was validated with flapping foil experiment by using different domain decomposition methods. In the flapping foil experiment, two upstream NACA 0025 foils perform high-frequency synchronized motion and generate unsteady flow conditions for a downstream larger stationary foil. Fairly good agreement was obtained between unsteady experimental data and numerical results from two different moving boundary procedures. Incompressible Navier-Stokes code (INS3D) has been extended for heat transfer applications. The temperature equation was written for both forced and natural convection phenomena. Flow in a square duct case was used for the validation of the code in both natural and forced convection.

3-D Wave-Structure Interaction with Coastal Sediments - A Multi-Physics/Multi-Solution-Techniques Approach

DTIC Science & Technology

2008-01-01

element method (BEM). Reynolds averaged Navier-Stokes (RANS) and the particle finite element method ( PFEM ) will be used in the water/mine/sand domain...and deformable sandy seabed (median grain diameter: 0.2 mm) 12 SOLID/FEM SAND/SPH GEOMATERIALS FNPF/BEM FNPF/BEMRANS/ PFEM

Turbulence modeling

NASA Technical Reports Server (NTRS)

Bardina, Jorge E.

1995-01-01

The objective of this work is to develop, verify, and incorporate the baseline two-equation turbulence models which account for the effects of compressibility into the three-dimensional Reynolds averaged Navier-Stokes (RANS) code and to provide documented descriptions of the models and their numerical procedures so that they can be implemented into 3-D CFD codes for engineering applications.

Analysis of vegetation effect on waves using a vertical 2-D RANS model

USDA-ARS?s Scientific Manuscript database

A vertical two-dimensional (2-D) model has been applied in the simulation of wave propagation through vegetated water bodies. The model is based on an existing model SOLA-VOF which solves the Reynolds-Averaged Navier-Stokes (RANS) equations with the finite difference method on a staggered rectangula...

Whole-annulus aeroelasticity analysis of a 17-bladerow WRF compressor using an unstructured Navier Stokes solver

NASA Astrophysics Data System (ADS)

Wu, X.; Vahdati, M.; Sayma, A.; Imregun, M.

2005-03-01

This paper describes a large-scale aeroelasticity computation for an aero-engine core compressor. The computational domain includes all 17 bladerows, resulting in a mesh with over 68 million points. The Favre-averaged Navier Stokes equations are used to represent the flow in a non-linear time-accurate fashion on unstructured meshes of mixed elements. The structural model of the first two rotor bladerows is based on a standard finite element representation. The fluid mesh is moved at each time step according to the structural motion so that changes in blade aerodynamic damping and flow unsteadiness can be accommodated automatically. An efficient domain decomposition technique, where special care was taken to balance the memory requirement across processors, was developed as part of the work. The calculation was conducted in parallel mode on 128 CPUs of an SGI Origin 3000. Ten vibration cycles were obtained using over 2.2 CPU years, though the elapsed time was a week only. Steady-state flow measurements and predictions were found to be in good agreement. A comparison of the averaged unsteady flow and the steady-state flow revealed some discrepancies. It was concluded that, in due course, the methodology would be adopted by industry to perform routine numerical simulations of the unsteady flow through entire compressor assemblies with vibrating blades not only to minimise engine and rig tests but also to improve performance predictions.

Design optimization using adjoint of Long-time LES for the trailing edge of a transonic turbine vane

NASA Astrophysics Data System (ADS)

Talnikar, Chaitanya; Wang, Qiqi

2017-11-01

Adjoint-based design optimization methods have been applied to low-fidelity simulation methods like Reynolds Averaged Navier-Stokes (RANS) and are useful for designing fluid machinery components. But to reliably capture the complex flow phenomena involved in turbomachinery, high fidelity simulations like large eddy simulation (LES) are required. Unfortunately due to the chaotic dynamics of turbulence, the unsteady adjoint method for LES diverges and produces incorrect gradients. Using a viscosity stabilized unsteady adjoint method developed for LES, the gradient can be obtained with reasonable accuracy. In this paper, design of the trailing edge of a gas turbine inlet guide vane is performed with the objective to reduce stagnation pressure loss and heat transfer over the surface of the vane. Slight changes in the shape of trailing edge can significantly impact these quantities by altering the boundary layer development process and separation points. The trailing edge is parameterized using a linear combination of 5 convex designs. Bayesian optimization is used as a global optimizer with the objective function evaluated from the LES and gradients obtained using the viscosity adjoint method. Results from the optimization, performed on the supercomputer Mira, are presented.

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.

Navier-Stokes and Comprehensive Analysis Performance Predictions of the NREL Phase VI Experiment

NASA Technical Reports Server (NTRS)

Duque, Earl P. N.; Burklund, Michael D.; Johnson, Wayne

2003-01-01

A vortex lattice code, CAMRAD II, and a Reynolds-Averaged Navier-Stoke code, OVERFLOW-D2, were used to predict the aerodynamic performance of a two-bladed horizontal axis wind turbine. All computations were compared with experimental data that was collected at the NASA Ames Research Center 80- by 120-Foot Wind Tunnel. Computations were performed for both axial as well as yawed operating conditions. Various stall delay models and dynamics stall models were used by the CAMRAD II code. Comparisons between the experimental data and computed aerodynamic loads show that the OVERFLOW-D2 code can accurately predict the power and spanwise loading of a wind turbine rotor.

Navier-Stokes solution of transonic cascade flows using nonperiodic C-type grids

NASA Technical Reports Server (NTRS)

Arnone, Andrea; Liou, Meng-Sing; Povinelli, Louis A.

1992-01-01

A new kind of C-type grid is proposed, this grid is non-periodic on the wake and allows minimum skewness for cascades with high turning and large camber. Reynolds-averaged Navier-Stokes equations are solved on this type of grid using a finite volume discretization and a full multigrid method which uses Runge-Kutta stepping as the driving scheme. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. A detailed numerical study is proposed for a highly loaded transonic blade. A grid independence analysis is presented in terms of pressure distribution, exit flow angles, and loss coefficient. Comparison with experiments clearly demonstrates the capability of the proposed procedure.

Introduction to COFFE: The Next-Generation HPCMP CREATE-AV CFD Solver

NASA Technical Reports Server (NTRS)

Glasby, Ryan S.; Erwin, J. Taylor; Stefanski, Douglas L.; Allmaras, Steven R.; Galbraith, Marshall C.; Anderson, W. Kyle; Nichols, Robert H.

2016-01-01

HPCMP CREATE-AV Conservative Field Finite Element (COFFE) is a modular, extensible, robust numerical solver for the Navier-Stokes equations that invokes modularity and extensibility from its first principles. COFFE implores a flexible, class-based hierarchy that provides a modular approach consisting of discretization, physics, parallelization, and linear algebra components. These components are developed with modern software engineering principles to ensure ease of uptake from a user's or developer's perspective. The Streamwise Upwind/Petrov-Galerkin (SU/PG) method is utilized to discretize the compressible Reynolds-Averaged Navier-Stokes (RANS) equations tightly coupled with a variety of turbulence models. The mathematics and the philosophy of the methodology that makes up COFFE are presented.

Unsteady swimming of small organisms

NASA Astrophysics Data System (ADS)

Wang, Shiyan; Ardekani, Arezoo

2012-11-01

Small planktonic organisms ubiquitously display unsteady or impulsive motion to attack a prey or escape a predator in natural environments. Despite this, the role of unsteady hydrodynamic forces such as history and added mass forces on the low Reynolds number propulsion of small organisms is poorly understood. In this paper, we derive the fundamental equation of motion for an organism swimming by the means of surface distortion in a nonuniform flow at a low Reynolds number regime. We show that the history and added mass forces, that where traditionally neglected in the literature for small swimming organisms, cannot be neglected as the Stokes number increases above unity. For example, these unsteady inertial forces are of the same order as quasi-steady Stokes forces for Paramecium. Finally, we quantify the effects of convective inertial forces in the limit of small, but nonzero, Reynolds number regime. This work is supported by NSF grant CBET-1066545.

A systematic comparison of two-equation Reynolds-averaged Navier-Stokes turbulence models applied to shock-cloud interactions

NASA Astrophysics Data System (ADS)

Goodson, Matthew D.; Heitsch, Fabian; Eklund, Karl; Williams, Virginia A.

2017-07-01

Turbulence models attempt to account for unresolved dynamics and diffusion in hydrodynamical simulations. We develop a common framework for two-equation Reynolds-averaged Navier-Stokes turbulence models, and we implement six models in the athena code. We verify each implementation with the standard subsonic mixing layer, although the level of agreement depends on the definition of the mixing layer width. We then test the validity of each model into the supersonic regime, showing that compressibility corrections can improve agreement with experiment. For models with buoyancy effects, we also verify our implementation via the growth of the Rayleigh-Taylor instability in a stratified medium. The models are then applied to the ubiquitous astrophysical shock-cloud interaction in three dimensions. We focus on the mixing of shock and cloud material, comparing results from turbulence models to high-resolution simulations (up to 200 cells per cloud radius) and ensemble-averaged simulations. We find that the turbulence models lead to increased spreading and mixing of the cloud, although no two models predict the same result. Increased mixing is also observed in inviscid simulations at resolutions greater than 100 cells per radius, which suggests that the turbulent mixing begins to be resolved.

The accuracy of the compressible Reynolds equation for predicting the local pressure in gas-lubricated textured parallel slider bearings

PubMed Central

Qiu, Mingfeng; Bailey, Brian N.; Stoll, Rob

2014-01-01

The validity of the compressible Reynolds equation to predict the local pressure in a gas-lubricated, textured parallel slider bearing is investigated. The local bearing pressure is numerically simulated using the Reynolds equation and the Navier-Stokes equations for different texture geometries and operating conditions. The respective results are compared and the simplifying assumptions inherent in the application of the Reynolds equation are quantitatively evaluated. The deviation between the local bearing pressure obtained with the Reynolds equation and the Navier-Stokes equations increases with increasing texture aspect ratio, because a significant cross-film pressure gradient and a large velocity gradient in the sliding direction develop in the lubricant film. Inertia is found to be negligible throughout this study. PMID:25049440

FUN3D Analyses in Support of the First Aeroelastic Prediction Workshop

NASA Technical Reports Server (NTRS)

Chwalowski, Pawel; Heeg, Jennifer; Wieseman, Carol D.; Florance, Jennifer P.

2013-01-01

This paper presents the computational aeroelastic results generated in support of the first Aeroelastic Prediction Workshop for the Benchmark Supercritical Wing (BSCW) and the HIgh REynolds Number AeroStructural Dynamics (HIRENASD) configurations and compares them to the experimental data. The computational results are obtained using FUN3D, an unstructured grid Reynolds-averaged Navier-Stokes solver developed at NASA Langley Research Center. The analysis results for both configurations include aerodynamic coefficients and surface pressures obtained for steady-state or static aeroelastic equilibrium (BSCW and HIRENASD, respectively) and for unsteady flow due to a pitching wing (BSCW) or modally-excited wing (HIRENASD). Frequency response functions of the pressure coefficients with respect to displacement are computed and compared with the experimental data. For the BSCW, the shock location is computed aft of the experimentally-located shock position. The pressure distribution upstream of this shock is in excellent agreement with the experimental data, but the pressure downstream of the shock in the separated flow region does not match as well. For HIRENASD, very good agreement between the numerical results and the experimental data is observed at the mid-span wing locations.

Computational fluid mechanics

NASA Technical Reports Server (NTRS)

Hassan, H. A.

1993-01-01

Two papers are included in this progress report. In the first, the compressible Navier-Stokes equations have been used to compute leading edge receptivity of boundary layers over parabolic cylinders. Natural receptivity at the leading edge was simulated and Tollmien-Schlichting waves were observed to develop in response to an acoustic disturbance, applied through the farfield boundary conditions. To facilitate comparison with previous work, all computations were carried out at a free stream Mach number of 0.3. The spatial and temporal behavior of the flowfields are calculated through the use of finite volume algorithms and Runge-Kutta integration. The results are dominated by strong decay of the Tollmien-Schlichting wave due to the presence of the mean flow favorable pressure gradient. The effects of numerical dissipation, forcing frequency, and nose radius are studied. The Strouhal number is shown to have the greatest effect on the unsteady results. In the second paper, a transition model for low-speed flows, previously developed by Young et al., which incorporates first-mode (Tollmien-Schlichting) disturbance information from linear stability theory has been extended to high-speed flow by incorporating the effects of second mode disturbances. The transition model is incorporated into a Reynolds-averaged Navier-Stokes solver with a one-equation turbulence model. Results using a variable turbulent Prandtl number approach demonstrate that the current model accurately reproduces available experimental data for first and second-mode dominated transitional flows. The performance of the present model shows significant improvement over previous transition modeling attempts.

Asymptotic behavior of solutions of the renormalization group K-epsilon turbulence model

NASA Technical Reports Server (NTRS)

Yakhot, A.; Staroselsky, I.; Orszag, S. A.

1994-01-01

Presently, the only efficient way to calculate turbulent flows in complex geometries of engineering interest is to use Reynolds-average Navier-Stokes (RANS) equations. As compared to the original Navier-Stokes problem, these RANS equations posses much more complicated nonlinear structure and may exhibit far more complex nonlinear behavior. In certain cases, the asymptotic behavior of such models can be studied analytically which, aside from being an interesting fundamental problem, is important for better understanding of the internal structure of the models as well as to improve their performances. The renormalization group (RNG) K-epsilon turbulence model, derived directly from the incompresible Navier-Stokes equations, is analyzed. It has already been used to calculate a variety of turbulent and transitional flows in complex geometries. For large values of the RNG viscosity parameter, the model may exhibit singular behavior. In the form of the RNG K-epsilon model that avoids the use of explicit wall functions, a = 1, so the RNG viscosity parameter must be smaller than 23.62 to avoid singularities.

Incompressible Navier-Stokes and parabolized Navier-Stokes solution procedures and computational techniques

NASA Technical Reports Server (NTRS)

Rubin, S. G.

1982-01-01

Recent developments with finite-difference techniques are emphasized. The quotation marks reflect the fact that any finite discretization procedure can be included in this category. Many so-called finite element collocation and galerkin methods can be reproduced by appropriate forms of the differential equations and discretization formulas. Many of the difficulties encountered in early Navier-Stokes calculations were inherent not only in the choice of the different equations (accuracy), but also in the method of solution or choice of algorithm (convergence and stability, in the manner in which the dependent variables or discretized equations are related (coupling), in the manner that boundary conditions are applied, in the manner that the coordinate mesh is specified (grid generation), and finally, in recognizing that for many high Reynolds number flows not all contributions to the Navier-Stokes equations are necessarily of equal importance (parabolization, preferred direction, pressure interaction, asymptotic and mathematical character). It is these elements that are reviewed. Several Navier-Stokes and parabolized Navier-Stokes formulations are also presented.

Assessment of an Explicit Algebraic Reynolds Stress Model

NASA Technical Reports Server (NTRS)

Carlson, Jan-Renee

2005-01-01

This study assesses an explicit algebraic Reynolds stress turbulence model in the in the three-dimensional Reynolds averaged Navier-Stokes (RANS) solver, ISAAC (Integrated Solution Algorithm for Arbitrary Con gurations). Additionally, it compares solutions for two select configurations between ISAAC and the RANS solver PAB3D. This study compares with either direct numerical simulation data, experimental data, or empirical models for several different geometries with compressible, separated, and high Reynolds number flows. In general, the turbulence model matched data or followed experimental trends well, and for the selected configurations, the computational results of ISAAC closely matched those of PAB3D using the same turbulence model.

Hydrodynamics of Fishlike Swimming: Effects of swimming kinematics and Reynolds number

NASA Astrophysics Data System (ADS)

Gilmanov, Anvar; Posada, Nicolas; Sotiropoulos, Fotis

2003-11-01

We carry out a series of numerical simulations to investigate the effects of swimming kinematics and Reynolds number on the flow past a three-dimensional fishlike body undergoing undulatory motion. The simulated body shape is that of a real mackerel fish. The mackerel was frozen and subsequently sliced in several thin fillets whose dimensions were carefully measured and used to construct the fishlike body shape used in the simulations. The flow induced by the undulating body is simulated by solving the 3D, unsteady, incompressible Navier-Stokes equations with the second-order accurate, hybrid Cartesian/Immersed Boundary formulation of Gilmanov and Sotiropoulos (J. Comp. Physics, under review, 2003). We consider in-line swimming at constant speed and carry out simulations for various types of swimming kinematics, varying the tailbeat amplitude, frequency, and Reynolds number (300

Low Mass-Damping Vortex-Induced Vibrations of a Single Cylinder at Moderate Reynolds Number.

PubMed

Jus, Y; Longatte, E; Chassaing, J-C; Sagaut, P

2014-10-01

The feasibility and accuracy of large eddy simulation is investigated for the case of three-dimensional unsteady flows past an elastically mounted cylinder at moderate Reynolds number. Although these flow problems are unconfined, complex wake flow patterns may be observed depending on the elastic properties of the structure. An iterative procedure is used to solve the structural dynamic equation to be coupled with the Navier-Stokes system formulated in a pseudo-Eulerian way. A moving mesh method is involved to deform the computational domain according to the motion of the fluid structure interface. Numerical simulations of vortex-induced vibrations are performed for a freely vibrating cylinder at Reynolds number 3900 in the subcritical regime under two low mass-damping conditions. A detailed physical analysis is provided for a wide range of reduced velocities, and the typical three-branch response of the amplitude behavior usually reported in the experiments is exhibited and reproduced by numerical simulation.

RANS Simulations using OpenFOAM Software

DTIC Science & Technology

2016-01-01

Averaged Navier- Stokes (RANS) simulations is described and illustrated by applying the simpleFoam solver to two case studies; two dimensional flow...to run in parallel over large processor arrays. The purpose of this report is to illustrate and test the use of the steady-state Reynolds Averaged ...Group in the Maritime Platforms Division he has been simulating fluid flow around ships and submarines using finite element codes, Lagrangian vortex

A least-squares finite element method for incompressible Navier-Stokes problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan

1992-01-01

A least-squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady incompressible Navier-Stokes problems. This method leads to a minimization problem rather than to a saddle-point problem by the classic mixed method and can thus accommodate equal-order interpolations. This method has no parameter to tune. The associated algebraic system is symmetric, and positive definite. Numerical results for the cavity flow at Reynolds number up to 10,000 and the backward-facing step flow at Reynolds number up to 900 are presented.

Three-Dimensional Navier-Stokes Method with Two-Equation Turbulence Models for Efficient Numerical Simulation of Hypersonic Flows

NASA Technical Reports Server (NTRS)

Bardina, J. E.

1994-01-01

A new computational efficient 3-D compressible Reynolds-averaged implicit Navier-Stokes method with advanced two equation turbulence models for high speed flows is presented. All convective terms are modeled using an entropy satisfying higher-order Total Variation Diminishing (TVD) scheme based on implicit upwind flux-difference split approximations and arithmetic averaging procedure of primitive variables. This method combines the best features of data management and computational efficiency of space marching procedures with the generality and stability of time dependent Navier-Stokes procedures to solve flows with mixed supersonic and subsonic zones, including streamwise separated flows. Its robust stability derives from a combination of conservative implicit upwind flux-difference splitting with Roe's property U to provide accurate shock capturing capability that non-conservative schemes do not guarantee, alternating symmetric Gauss-Seidel 'method of planes' relaxation procedure coupled with a three-dimensional two-factor diagonal-dominant approximate factorization scheme, TVD flux limiters of higher-order flux differences satisfying realizability, and well-posed characteristic-based implicit boundary-point a'pproximations consistent with the local characteristics domain of dependence. The efficiency of the method is highly increased with Newton Raphson acceleration which allows convergence in essentially one forward sweep for supersonic flows. The method is verified by comparing with experiment and other Navier-Stokes methods. Here, results of adiabatic and cooled flat plate flows, compression corner flow, and 3-D hypersonic shock-wave/turbulent boundary layer interaction flows are presented. The robust 3-D method achieves a better computational efficiency of at least one order of magnitude over the CNS Navier-Stokes code. It provides cost-effective aerodynamic predictions in agreement with experiment, and the capability of predicting complex flow structures in complex geometries with good accuracy.

Three-dimensional Navier-Stokes simulations of turbine rotor-stator interaction

NASA Technical Reports Server (NTRS)

Rai, Man Mohan

1988-01-01

Fluid flows within turbomachinery tend to be extremely complex in nature. Understanding such flows is crucial to improving current designs of turbomachinery. The computational approach can be used to great advantage in understanding flows in turbomachinery. A finite difference, unsteady, thin layer, Navier-Stokes approach to calculating the flow within an axial turbine stage is presented. The relative motion between the stator and rotor airfoils is made possible with the use of patched grids that move relative to each other. The calculation includes endwall and tip leakage effects. An introduction to the rotor-stator problem and sample results in the form of time averaged surface pressures are presented. The numerical data are compared with experimental data and the agreement between the two is found to be good.

The CMC:3DPNS computer program for prediction of three-dimensional, subsonic, turbulent aerodynamic juncture region flow. Volume 1: Theoretical

NASA Technical Reports Server (NTRS)

Baker, A. J.

1982-01-01

An order-of-magnitude analysis of the subsonic three dimensional steady time averaged Navier-Stokes equations, for semibounded aerodynamic juncture geometries, yields the parabolic Navier-Stokes simplification. The numerical solution of the resultant pressure Poisson equation is cast into complementary and particular parts, yielding an iterative interaction algorithm with an exterior three dimensional potential flow solution. A parabolic transverse momentum equation set is constructed, wherein robust enforcement of first order continuity effects is accomplished using a penalty differential constraint concept within a finite element solution algorithm. A Reynolds stress constitutive equation, with low turbulence Reynolds number wall functions, is employed for closure, using parabolic forms of the two-equation turbulent kinetic energy-dissipation equation system. Numerical results document accuracy, convergence, and utility of the developed finite element algorithm, and the CMC:3DPNS computer code applied to an idealized wing-body juncture region. Additional results document accuracy aspects of the algorithm turbulence closure model.

CFD-based design load analysis of 5MW offshore wind turbine

NASA Astrophysics Data System (ADS)

Tran, T. T.; Ryu, G. J.; Kim, Y. H.; Kim, D. H.

2012-11-01

The structure and aerodynamic loads acting on NREL 5MW reference wind turbine blade are calculated and analyzed based on advanced Computational Fluid Dynamics (CFD) and unsteady Blade Element Momentum (BEM). A detailed examination of the six force components has been carried out (three force components and three moment components). Structure load (gravity and inertia load) and aerodynamic load have been obtained by additional structural calculations (CFD or BEM, respectively,). In CFD method, the Reynolds Average Navier-Stokes approach was applied to solve the continuity equation of mass conservation and momentum balance so that the complex flow around wind turbines was modeled. Written in C programming language, a User Defined Function (UDF) code which defines transient velocity profile according to the Extreme Operating Gust condition was compiled into commercial FLUENT package. Furthermore, the unsteady BEM with 3D stall model has also adopted to investigate load components on wind turbine rotor. The present study introduces a comparison between advanced CFD and unsteady BEM for determining load on wind turbine rotor. Results indicate that there are good agreements between both present methods. It is importantly shown that six load components on wind turbine rotor is significant effect under Extreme Operating Gust (EOG) condition. Using advanced CFD and additional structural calculations, this study has succeeded to construct accuracy numerical methodology to estimate total load of wind turbine that compose of aerodynamic load and structure load.

Aeroelastic Computations of a Compressor Stage Using the Harmonic Balance Method

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.

2010-01-01

The aeroelastic characteristics of a compressor stage were analyzed using a computational fluid dynamic (CFD) solver that uses the harmonic balance method to solve the governing equations. The three dimensional solver models the unsteady flow field due to blade vibration using the Reynolds-Averaged Navier-Stokes equations. The formulation enables the study of the effect of blade row interaction through the inclusion of coupling modes between blade rows. It also enables the study of nonlinear effects of high amplitude blade vibration by the inclusion of higher harmonics of the fundamental blade vibration frequency. In the present work, the solver is applied to study in detail the aeroelastic characteristics of a transonic compressor stage. Various parameters were included in the study: number of coupling modes, blade row axial spacing, and operating speeds. Only the first vibration mode is considered with amplitude of oscillation in the linear range. Both aeroelastic stability (flutter) of rotor blade and unsteady loading on the stator are calculated. The study showed that for the stage considered, the rotor aerodynamic damping is not influenced by the presence of the stator even when the axial spacing is reduced by nearly 25 percent. However, the study showed that blade row interaction effects become important for the unsteady loading on the stator when the axial spacing is reduced by the same amount.

Characterization of Unsteady Flow Structures Near Leading-Edge Slat. Part 1; PIV Measurements

NASA Technical Reports Server (NTRS)

Jenkins, Luther N.; Khorrami, Mehdi R.; Choudhari, Meelan

2004-01-01

A comprehensive computational and experimental study has been performed at the NASA Langley Research Center as part of the Quiet Aircraft Technology (QAT) Program to investigate the unsteady flow near a leading-edge slat of a two-dimensional, high-lift system. This paper focuses on the experimental effort conducted in the NASA Langley Basic Aerodynamics Research Tunnel (BART) where Particle Image Velocimetry (PIV) data was acquired in the slat cove and at the slat trailing edge of a three-element, high-lift model at 4, 6, and 8 degrees angle of attack and a freestream Mach Number of 0.17. Instantaneous velocities obtained from PIV images are used to obtain mean and fluctuating components of velocity and vorticity. The data show the recirculation in the cove, reattachment of the shear layer on the slat lower surface, and discrete vortical structures within the shear layer emanating from the slat cusp and slat trailing edge. Detailed measurements are used to examine the shear layer formation at the slat cusp, vortex shedding at the slat trailing edge, and convection of vortical structures through the slat gap. Selected results are discussed and compared with unsteady, Reynolds-Averaged Navier-Stokes (URANS) computations for the same configuration in a companion paper by Khorrami, Choudhari, and Jenkins (2004). The experimental dataset provides essential flow-field information for the validation of near-field inputs to noise prediction tools.

Unsteady Thick Airfoil Aerodynamics: Experiments, Computation, and Theory

NASA Technical Reports Server (NTRS)

Strangfeld, C.; Rumsey, C. L.; Mueller-Vahl, H.; Greenblatt, D.; Nayeri, C. N.; Paschereit, C. O.

2015-01-01

An experimental, computational and theoretical investigation was carried out to study the aerodynamic loads acting on a relatively thick NACA 0018 airfoil when subjected to pitching and surging, individually and synchronously. Both pre-stall and post-stall angles of attack were considered. Experiments were carried out in a dedicated unsteady wind tunnel, with large surge amplitudes, and airfoil loads were estimated by means of unsteady surface mounted pressure measurements. Theoretical predictions were based on Theodorsen's and Isaacs' results as well as on the relatively recent generalizations of van der Wall. Both two- and three-dimensional computations were performed on structured grids employing unsteady Reynolds-averaged Navier-Stokes (URANS). For pure surging at pre-stall angles of attack, the correspondence between experiments and theory was satisfactory; this served as a validation of Isaacs theory. Discrepancies were traced to dynamic trailing-edge separation, even at low angles of attack. Excellent correspondence was found between experiments and theory for airfoil pitching as well as combined pitching and surging; the latter appears to be the first clear validation of van der Wall's theoretical results. Although qualitatively similar to experiment at low angles of attack, two-dimensional URANS computations yielded notable errors in the unsteady load effects of pitching, surging and their synchronous combination. The main reason is believed to be that the URANS equations do not resolve wake vorticity (explicitly modeled in the theory) or the resulting rolled-up un- steady flow structures because high values of eddy viscosity tend to \\smear" the wake. At post-stall angles, three-dimensional computations illustrated the importance of modeling the tunnel side walls.

Numerical study of aero-excitation of steam-turbine rotor blade self-oscillations

NASA Astrophysics Data System (ADS)

Galaev, S. A.; Makhnov, V. Yu.; Ris, V. V.; Smirnov, E. M.

2018-05-01

Blade aero-excitation increment is evaluated by numerical solution of the full 3D unsteady Reynolds-averaged Navier-Stokes equations governing wet steam flow in a powerful steam-turbine last stage. The equilibrium wet steam model was adopted. Blade surfaces oscillations are defined by eigen-modes of a row of blades bounded by a shroud. Grid dependency study was performed with a reduced model being a set of blades multiple an eigen-mode nodal diameter. All other computations were carried out for the entire blade row. Two cases are considered, with an original-blade row and with a row of modified (reinforced) blades. Influence of eigen-mode nodal diameter and blade reinforcing on aero-excitation increment is analyzed. It has been established, in particular, that maximum value of the aero-excitation increment for the reinforced-blade row is two times less as compared with the original-blade row. Generally, results of the study point definitely to less probability of occurrence of blade self-oscillations in case of the reinforced blade-row.

Adjoint Sensitivity Analysis for Scale-Resolving Turbulent Flow Solvers

NASA Astrophysics Data System (ADS)

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

2017-11-01

Adjoint-based sensitivity analysis methods are powerful design tools for engineers who use computational fluid dynamics. In recent years, these engineers have started to use scale-resolving simulations like large-eddy simulations (LES) and direct numerical simulations (DNS), which resolve more scales in complex flows with unsteady separation and jets than the widely-used Reynolds-averaged Navier-Stokes (RANS) methods. However, the conventional adjoint method computes large, unusable sensitivities for scale-resolving simulations, which unlike RANS simulations exhibit the chaotic dynamics inherent in turbulent flows. Sensitivity analysis based on least-squares shadowing (LSS) avoids the issues encountered by conventional adjoint methods, but has a high computational cost even for relatively small simulations. The following talk discusses a more computationally efficient formulation of LSS, ``non-intrusive'' LSS, and its application to turbulent flows simulated with a discontinuous-Galkerin spectral-element-method LES/DNS solver. Results are presented for the minimal flow unit, a turbulent channel flow with a limited streamwise and spanwise domain.

Computational fluid dynamics simulation of sound propagation through a blade row.

PubMed

Zhao, Lei; Qiao, Weiyang; Ji, Liang

2012-10-01

The propagation of sound waves through a blade row is investigated numerically. A wave splitting method in a two-dimensional duct with arbitrary mean flow is presented, based on which pressure amplitude of different wave mode can be extracted at an axial plane. The propagation of sound wave through a flat plate blade row has been simulated by solving the unsteady Reynolds average Navier-Stokes equations (URANS). The transmission and reflection coefficients obtained by Computational Fluid Dynamics (CFD) are compared with semi-analytical results. It indicates that the low order URANS scheme will cause large errors if the sound pressure level is lower than -100 dB (with as reference pressure the product of density, main flow velocity, and speed of sound). The CFD code has sufficient precision when solving the interaction of sound wave and blade row providing the boundary reflections have no substantial influence. Finally, the effects of flow Mach number, blade thickness, and blade turning angle on sound propagation are studied.

Fluidic Vectoring of a Planar Incompressible Jet Flow

NASA Astrophysics Data System (ADS)

Mendez, Miguel Alfonso; Scelzo, Maria Teresa; Enache, Adriana; Buchlin, Jean-Marie

2018-06-01

This paper presents an experimental, a numerical and a theoretical analysis of the performances of a fluidic vectoring device for controlling the direction of a turbulent, bi-dimensional and low Mach number (incompressible) jet flow. The investigated design is the co-flow secondary injection with Coanda surface, which allows for vectoring angles up to 25° with no need of moving mechanical parts. A simple empirical model of the vectoring process is presented and validated via experimental and numerical data. The experiments consist of flow visualization and image processing for the automatic detection of the jet centerline; the numerical simulations are carried out solving the Unsteady Reynolds Average Navier- Stokes (URANS) closed with the k - ω SST turbulence model, using the PisoFoam solver from OpenFOAM. The experimental validation on three different geometrical configurations has shown that the model is capable of providing a fast and reliable evaluation of the device performance as a function of the operating conditions.

Numerical studies of the fluid and optical fields associated with complex cavity flows

NASA Technical Reports Server (NTRS)

Atwood, Christopher A.

1992-01-01

Numerical solutions for the flowfield about several cavity configurations have been computed using the Reynolds averaged Navier-Stokes equations. Comparisons between numerical and experimental results are made in two dimensions for free shear layers and a rectangular cavity, and in three dimensions for the transonic aero-window problem of the Stratospheric Observatory for Infrared Astronomy (SOFIA). Results show that dominant acoustic frequencies and magnitudes of the self excited resonant cavity flows compare well with the experiment. In addition, solution sensitivity to artificial dissipation and grid resolution levels are determined. Optical path distortion due to the flow field is modelled geometrically and is found to match the experiment. The fluid field was computed using a diagonalized scheme within an overset mesh framework. An existing code, OVERFLOW, was utilized with the additions of characteristic boundary condition and output routines required for reduction of the unsteady data. The newly developed code is directly applicable to a generalized three dimensional structured grid zone. Details are provided in a paper included in Appendix A.

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.

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.

Evaluation of Full Reynolds Stress Turbulence Models in FUN3D

NASA Technical Reports Server (NTRS)

Dudek, Julianne C.; Carlson, Jan-Renee

2017-01-01

Full seven-equation Reynolds stress turbulence models are a relatively new and promising tool for todays aerospace technology challenges. This paper uses two stress-omega full Reynolds stress models to evaluate challenging flows including shock-wave boundary layer interactions, separation and mixing layers. The Wilcox and the SSG/LRR full second-moment Reynolds stress models have been implemented into the FUN3D (Fully Unstructured Navier-Stokes Three Dimensional) unstructured Navier-Stokes code and are evaluated for four problems: a transonic two-dimensional diffuser, a supersonic axisymmetric compression corner, a compressible planar shear layer, and a subsonic axisymmetric jet. Simulation results are compared with experimental data and results using the more commonly used Spalart-Allmaras (SA) one-equation and the Menter Shear Stress Transport (SST-V) two-equation turbulence models.

Flow and axial dispersion in a sinusoidal-walled tube: Effects of inertial and unsteady flows

NASA Astrophysics Data System (ADS)

Richmond, Marshall C.; Perkins, William A.; Scheibe, Timothy D.; Lambert, Adam; Wood, Brian D.

2013-12-01

In this work, we consider a sinusoidal-walled tube (a three-dimensional tube with sinusoidally-varying diameter) as a simplified conceptualization of flow in porous media. Direct numerical simulation using computational fluid dynamics (CFD) methods was used to compute velocity fields by solving the Navier-Stokes equations, and also to numerically solve the volume averaging closure problem, for a range of Reynolds numbers (Re) spanning the low-Re to inertial flow regimes, including one simulation at Re=449 for which unsteady flow was observed. The longitudinal dispersion observed for the flow was computed using a random walk particle tracking method, and this was compared to the longitudinal dispersion predicted from a volume-averaged macroscopic mass balance using the method of volume averaging; the results of the two methods were consistent. Our results are compared to experimental measurements of dispersion in porous media and to previous theoretical results for both the low-Re, Stokes flow regime and for values of Re representing the steady inertial regime. In the steady inertial regime, a power-law increase in the effective longitudinal dispersion (DL) with Re was found, and this is consistent with previous results. This rapid rate of increase is caused by trapping of solute in expansions due to flow separation (eddies). One unsteady (but non-turbulent) flow case (Re=449) was also examined. For this case, the rate of increase of DL with Re was smaller than that observed at lower Re. Velocity fluctuations in this regime lead to increased rates of solute mass transfer between the core flow and separated flow regions, thus diminishing the amount of tailing caused by solute trapping in eddies and thereby reducing longitudinal dispersion. The observed tailing was further explored through analysis of concentration skewness (third moment) and its assymptotic convergence to conventional advection-dispersion behavior (skewness = 0). The method of volume averaging was applied to develop a skewness model, and demonstrated that the skewness decreases as a function of inverse square root of time. Our particle tracking simulation results were shown to conform to this theoretical result in most of the cases considered.

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.

Effects of Turbulence Model on Prediction of Hot-Gas Lateral Jet Interaction in a Supersonic Crossflow

DTIC Science & Technology

2015-07-01

performance computing time from the US Department of Defense (DOD) High Performance Computing Modernization program at the US Army Research Laboratory...Approved OMB No. 0704-0188 Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time ...dimensional, compressible, Reynolds-averaged Navier-Stokes (RANS) equations are solved using a finite volume method. A point-implicit time - integration

Unsteady Navier-Stokes computations over airfoils using both fixed and dynamic meshes

NASA Technical Reports Server (NTRS)

Rumsey, Christopher L.; Anderson, W. Kyle

1989-01-01

A finite volume implicit approximate factorization method which solves the thin layer Navier-Stokes equations was used to predict unsteady turbulent flow airfoil behavior. At a constant angle of attack of 16 deg, the NACA 0012 airfoil exhibits an unsteady periodic flow field with the lift coefficient oscillating between 0.89 and 1.60. The Strouhal number is 0.028. Results are similar at 18 deg, with a Strouhal number of 0.033. A leading edge vortex is shed periodically near maximum lift. Dynamic mesh solutions for unstalled airfoil flows show general agreement with experimental pressure coefficients. However, moment coefficients and the maximum lift value are underpredicted. The deep stall case shows some agreement with experiment for increasing angle of attack, but is only qualitatively comparable past stall and for decreasing angle of attack.

Effect of Turbulence Modeling on Hovering Rotor Flows

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan; Chaderjian, Neal M.; Pulliam, Thomas H.; Holst, Terry L.

2015-01-01

The effect of turbulence models in the off-body grids on the accuracy of solutions for rotor flows in hover has been investigated. Results from the Reynolds-Averaged Navier-Stokes and Laminar Off-Body models are compared. Advection of turbulent eddy viscosity has been studied to find the mechanism leading to inaccurate solutions. A coaxial rotor result is also included.

Turbulence modeling for hypersonic flight

NASA Technical Reports Server (NTRS)

Bardina, Jorge E.

1993-01-01

The objective of the proposed work is to continue to develop, verify, and incorporate the baseline two-equation turbulence models, which account for the effects of compressibility at high speeds, into a three-dimensional Reynolds averaged Navier-Stokes (RANS) code. Additionally, we plan to provide documented descriptions of the models and their numerical procedures so that they can be implemented into the NASP CFD codes.

Semiannual Report October 1, 1999 through March 31, 2000

DTIC Science & Technology

2000-04-01

Mark Carpenter (NASA Langley). Textbook Multigrid Efficiency for the Navier-Stokes Equations Boris Diskin A typical modern Reynolds-Averaged...defined as textbook multigrid efficiency (TME), meaning the solutions to the governing system of equations are attained in a computational work...basic elements of the barriers to be overcome in extending textbook efficiencies to the compressible RANS equations, namely entering flows, far wake

Numerical Investigation of a Model Scramjet Combustor Using DDES

NASA Astrophysics Data System (ADS)

Shin, Junsu; Sung, Hong-Gye

2017-04-01

Non-reactive flows moving through a model scramjet were investigated using a delayed detached eddy simulation (DDES), which is a hybrid scheme combining Reynolds averaged Navier-Stokes scheme and a large eddy simulation. The three dimensional Navier-Stokes equations were solved numerically on a structural grid using finite volume methods. An in-house was developed. This code used a monotonic upstream-centered scheme for conservation laws (MUSCL) with an advection upstream splitting method by pressure weight function (AUSMPW+) for space. In addition, a 4th order Runge-Kutta scheme was used with preconditioning for time integration. The geometries and boundary conditions of a scramjet combustor operated by DLR, a German aerospace center, were considered. The profiles of the lower wall pressure and axial velocity obtained from a time-averaged solution were compared with experimental results. Also, the mixing efficiency and total pressure recovery factor were provided in order to inspect the performance of the combustor.

Hypersonic Viscous Flow Over Large Roughness Elements

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan; Choudhari, Meelan M.

2009-01-01

Viscous flow over discrete or distributed surface roughness has great implications for hypersonic flight due to aerothermodynamic considerations related to laminar-turbulent transition. Current prediction capability is greatly hampered by the limited knowledge base for such flows. To help fill that gap, numerical computations are used to investigate the intricate flow physics involved. An unstructured mesh, compressible Navier-Stokes code based on the space-time conservation element, solution element (CESE) method is used to perform time-accurate Navier-Stokes calculations for two roughness shapes investigated in wind tunnel experiments at NASA Langley Research Center. It was found through 2D parametric study that at subcritical Reynolds numbers, spontaneous absolute instability accompanying by sustained vortex shedding downstream of the roughness is likely to take place at subsonic free-stream conditions. On the other hand, convective instability may be the dominant mechanism for supersonic boundary layers. Three-dimensional calculations for both a rectangular and a cylindrical roughness element at post-shock Mach numbers of 4.1 and 6.5 also confirm that no self-sustained vortex generation from the top face of the roughness is observed, despite the presence of flow unsteadiness for the smaller post-shock Mach number case.

The structure of supersonic jet flow and its radiated sound

NASA Technical Reports Server (NTRS)

Mankbadi, Reda R.; Hayder, M. E.; Povinelli, Louis A.

1993-01-01

Large-eddy simulation of a supersonic jet is presented with emphasis on capturing the unsteady features of the flow pertinent to sound emission. A high-accuracy numerical scheme is used to solve the filtered, unsteady, compressible Navier-Stokes equations while modelling the subgrid-scale turbulence. For random inflow disturbance, the wave-like feature of the large-scale structure is demonstrated. The large-scale structure was then enhanced by imposing harmonic disturbances to the inflow. The limitation of using the full Navier-Stokes equation to calculate the far-field sound is discussed. Application of Lighthill's acoustic analogy is given with the objective of highlighting the difficulties that arise from the non-compactness of the source term.

A stable penalty method for the compressible Navier-Stokes equations. 1: Open boundary conditions

NASA Technical Reports Server (NTRS)

Hesthaven, J. S.; Gottlieb, D.

1994-01-01

The purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible Navier-Stokes equations in three spatial dimensions. The treatment uses the conservation form of the Navier-Stokes equations and utilizes linearization and localization at the boundaries based on these variables. The proposed boundary conditions are applied through a penalty procedure, thus ensuring correct behavior of the scheme as the Reynolds number tends to infinity. The versatility of this method is demonstrated for the problem of a compressible flow past a circular cylinder.

Time-Filtered Navier-Stokes Approach and Emulation of Turbulence-Chemistry Interaction

NASA Technical Reports Server (NTRS)

Liu, Nan-Suey; Wey, Thomas; Shih, Tsan-Hsing

2013-01-01

This paper describes the time-filtered Navier-Stokes approach capable of capturing unsteady flow structures important for turbulent mixing and an accompanying subgrid model directly accounting for the major processes in turbulence-chemistry interaction. They have been applied to the computation of two-phase turbulent combustion occurring in a single-element lean-direct-injection combustor. Some of the preliminary results from this computational effort are presented in this paper.

Aerofoil broadband and tonal noise modelling using stochastic sound sources and incorporated large scale fluctuations

NASA Astrophysics Data System (ADS)

Proskurov, S.; Darbyshire, O. R.; Karabasov, S. A.

2017-12-01

The present work discusses modifications to the stochastic Fast Random Particle Mesh (FRPM) method featuring both tonal and broadband noise sources. The technique relies on the combination of incorporated vortex-shedding resolved flow available from Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulation with the fine-scale turbulence FRPM solution generated via the stochastic velocity fluctuations in the context of vortex sound theory. In contrast to the existing literature, our method encompasses a unified treatment for broadband and tonal acoustic noise sources at the source level, thus, accounting for linear source interference as well as possible non-linear source interaction effects. When sound sources are determined, for the sound propagation, Acoustic Perturbation Equations (APE-4) are solved in the time-domain. Results of the method's application for two aerofoil benchmark cases, with both sharp and blunt trailing edges are presented. In each case, the importance of individual linear and non-linear noise sources was investigated. Several new key features related to the unsteady implementation of the method were tested and brought into the equation. Encouraging results have been obtained for benchmark test cases using the new technique which is believed to be potentially applicable to other airframe noise problems where both tonal and broadband parts are important.

Predicted and experimental steady and unsteady transonic flows about a biconvex airfoil

NASA Technical Reports Server (NTRS)

Levy, L. L., Jr.

1981-01-01

Results of computer code time dependent solutions of the two dimensional compressible Navier-Stokes equations and the results of independent experiments are compared to verify the Mach number range for instabilities in the transonic flow field about a 14 percent thick biconvex airfoil at an angle of attack of 0 deg and a Reynolds number of 7 million. The experiments were conducted in a transonic, slotted wall wind tunnel. The computer code included an algebraic eddy viscosity turbulence model developed for steady flows, and all computations were made using free flight boundary conditions. All of the features documented experimentally for both steady and unsteady flows were predicted qualitatively; even with the above simplifications, the predictions were, on the whole, in good quantitative agreement with experiment. In particular, predicted time histories of shock wave position, surface pressures, lift, and pitching moment were found to be in very good agreement with experiment for an unsteady flow. Depending upon the free stream Mach number for steady flows, the surface pressure downstream of the shock wave or the shock wave location was not well predicted.

Numerical Studies of Boundary-Layer Receptivity

NASA Technical Reports Server (NTRS)

Reed, Helen L.

1995-01-01

Direct numerical simulations (DNS) of the acoustic receptivity process on a semi-infinite flat plate with a modified-super-elliptic (MSE) leading edge are performed. The incompressible Navier-Stokes equations are solved in stream-function/vorticity form in a general curvilinear coordinate system. The steady basic-state solution is found by solving the governing equations using an alternating direction implicit (ADI) procedure which takes advantage of the parallelism present in line-splitting techniques. Time-harmonic oscillations of the farfield velocity are applied as unsteady boundary conditions to the unsteady disturbance equations. An efficient time-harmonic scheme is used to produce the disturbance solutions. Buffer-zone techniques have been applied to eliminate wave reflection from the outflow boundary. The spatial evolution of Tollmien-Schlichting (T-S) waves is analyzed and compared with experiment and theory. The effects of nose-radius, frequency, Reynolds number, angle of attack, and amplitude of the acoustic wave are investigated. This work is being performed in conjunction with the experiments at the Arizona State University Unsteady Wind Tunnel under the direction of Professor William Saric. The simulations are of the same configuration and parameters used in the wind-tunnel experiments.

Flow in Atherosclerotic Blood Vessels

NASA Astrophysics Data System (ADS)

Berger, Stanley A.; Stroud, Jenn S.

2000-11-01

Atherosclerotic lesions occur in arteries where there are major changes in flow structure, e.g. bifurcations and junctions. The reduction of vessel lumen alters the flow, including the mechanical forces on the walls. We have examined the flow in carotid artery bifurcations with realistic plaque contours. The unsteady, incompressible, Navier-Stokes equations are solved in finite-volume form. Steady and pulsatile flows have been analyzed for laminar and turbulent flows, using for the latter a low-Reynolds number k- ɛ model and a k-ω model. Non-Newtonian viscosity is also considered using a power-law model. In general the very irregular contours of the vessels lead to recirculating regions, strong spatial variations of wall shear stresses, and in some cases, vortex shedding. Even steady inlet flow exhibits fluctuating, unsteady behavior. Neither turbulence models captures all the physics of the flow. The flow, in fact, appears to be transitional and not fully turbulent. For unsteady flow, there are also strong temporal variations of normal and shear stresses, which together with the strong spatial variations, has important implications for the onset and progression of atherosclerotic disease.

Three-dimensional Navier-Stokes analysis of turbine passage heat transfer

NASA Technical Reports Server (NTRS)

Ameri, Ali A.; Arnone, Andrea

1991-01-01

The three-dimensional Reynolds-averaged Navier-Stokes equations are numerically solved to obtain the pressure distribution and heat transfer rates on the endwalls and the blades of two linear turbine cascades. The TRAF3D code which has recently been developed in a joint project between researchers from the University of Florence and NASA Lewis Research Center is used. The effect of turbulence is taken into account by using the eddy viscosity hypothesis and the two-layer mixing length model of Baldwin and Lomax. Predictions of surface heat transfer are made for Langston's cascade and compared with the data obtained for that cascade by Graziani. The comparison was found to be favorable. The code is also applied to a linear transonic rotor cascade to predict the pressure distributions and heat transfer rates.

CCM Continuity Constraint Method: A finite-element computational fluid dynamics algorithm for incompressible Navier-Stokes fluid flows

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

Williams, P. T.

1993-09-01

As the field of computational fluid dynamics (CFD) continues to mature, algorithms are required to exploit the most recent advances in approximation theory, numerical mathematics, computing architectures, and hardware. Meeting this requirement is particularly challenging in incompressible fluid mechanics, where primitive-variable CFD formulations that are robust, while also accurate and efficient in three dimensions, remain an elusive goal. This dissertation asserts that one key to accomplishing this goal is recognition of the dual role assumed by the pressure, i.e., a mechanism for instantaneously enforcing conservation of mass and a force in the mechanical balance law for conservation of momentum. Provingmore » this assertion has motivated the development of a new, primitive-variable, incompressible, CFD algorithm called the Continuity Constraint Method (CCM). The theoretical basis for the CCM consists of a finite-element spatial semi-discretization of a Galerkin weak statement, equal-order interpolation for all state-variables, a 0-implicit time-integration scheme, and a quasi-Newton iterative procedure extended by a Taylor Weak Statement (TWS) formulation for dispersion error control. Original contributions to algorithmic theory include: (a) formulation of the unsteady evolution of the divergence error, (b) investigation of the role of non-smoothness in the discretized continuity-constraint function, (c) development of a uniformly H 1 Galerkin weak statement for the Reynolds-averaged Navier-Stokes pressure Poisson equation, (d) derivation of physically and numerically well-posed boundary conditions, and (e) investigation of sparse data structures and iterative methods for solving the matrix algebra statements generated by the algorithm.« less

Unsteady Airfoil Flow Solutions on Moving Zonal Grids

DTIC Science & Technology

1992-12-17

for the angle-of-attack of 15.5’, the comparisons diverge. This happens because of the different turbulence models used . At this angle- of attack, the...downstream in the wake . This vortex shedding phenomenon alters the chordwise pressure distribution on the upper surface of the airfoil resulting in higher...in- terest, turbulence modeling is used . Turbulence models are implemented with the time-averaged forms of the Navier-Stokes equations. Two widely

Generalized Knudsen Number for Unsteady Fluid Flow.

PubMed

Kara, V; Yakhot, V; Ekinci, K L

2017-02-17

We explore the scaling behavior of an unsteady flow that is generated by an oscillating body of finite size in a gas. If the gas is gradually rarefied, the Navier-Stokes equations begin to fail and a kinetic description of the flow becomes more appropriate. The failure of the Navier-Stokes equations can be thought to take place via two different physical mechanisms: either the continuum hypothesis breaks down as a result of a finite size effect or local equilibrium is violated due to the high rate of strain. By independently tuning the relevant linear dimension and the frequency of the oscillating body, we can experimentally observe these two different physical mechanisms. All the experimental data, however, can be collapsed using a single dimensionless scaling parameter that combines the relevant linear dimension and the frequency of the body. This proposed Knudsen number for an unsteady flow is rooted in a fundamental symmetry principle, namely, Galilean invariance.

Generalized Knudsen Number for Unsteady Fluid Flow

NASA Astrophysics Data System (ADS)

Kara, V.; Yakhot, V.; Ekinci, K. L.

2017-02-01

We explore the scaling behavior of an unsteady flow that is generated by an oscillating body of finite size in a gas. If the gas is gradually rarefied, the Navier-Stokes equations begin to fail and a kinetic description of the flow becomes more appropriate. The failure of the Navier-Stokes equations can be thought to take place via two different physical mechanisms: either the continuum hypothesis breaks down as a result of a finite size effect or local equilibrium is violated due to the high rate of strain. By independently tuning the relevant linear dimension and the frequency of the oscillating body, we can experimentally observe these two different physical mechanisms. All the experimental data, however, can be collapsed using a single dimensionless scaling parameter that combines the relevant linear dimension and the frequency of the body. This proposed Knudsen number for an unsteady flow is rooted in a fundamental symmetry principle, namely, Galilean invariance.

Studying Turbulence Using Numerical Simulation Databases - X Proceedings of the 2004 Summer Program

NASA Technical Reports Server (NTRS)

Moin, Parviz; Mansour, Nagi N.

2004-01-01

This Proceedings volume contains 32 papers that span a wide range of topics that reflect the ubiquity of turbulence. The papers have been divided into six groups: 1) Solar Simulations; 2) Magnetohydrodynamics (MHD); 3) Large Eddy Simulation (LES) and Numerical Simulations; 4) Reynolds Averaged Navier Stokes (RANS) Modeling and Simulations; 5) Stability and Acoustics; 6) Combustion and Multi-Phase Flow.

Hydrocarbon-Fueled Scramjet Research at Hypersonic Mach Numbers

DTIC Science & Technology

2005-03-31

oxide O atomic oxygen 02 molecular oxygen OH hydroxyl radical ppm parts per million PD photodiode PLLF planar laser-induced fluorescence PMT...photomultiplier tube RAM random access memory RANS Reynolds-averaged Navier-Stokes RET rotational energy transfer TDLAS tunable diode laser absorption...here extend this knowledge base to flight at Mach 11.5. Griffiths (2004) used a tunable diode laser absorption spectroscopy ( TDLAS ) system to measure

CFL3D User's Manual (Version 5.0)

NASA Technical Reports Server (NTRS)

Krist, Sherrie L.; Biedron, Robert T.; Rumsey, Christopher L.

1998-01-01

This document is the User's Manual for the CFL3D computer code, a thin-layer Reynolds-averaged Navier-Stokes flow solver for structured multiple-zone grids. Descriptions of the code's input parameters, non-dimensionalizations, file formats, boundary conditions, and equations are included. Sample 2-D and 3-D test cases are also described, and many helpful hints for using the code are provided.

Gas Generator Feedline Orifice Sizing Methodology: Effects of Unsteadiness and Non-Axisymmetric Flow

NASA Technical Reports Server (NTRS)

Rothermel, Jeffry; West, Jeffrey S.

2011-01-01

Engine LH2 and LO2 gas generator feed assemblies were modeled with computational fluid dynamics (CFD) methods at 100% rated power level, using on-center square- and round-edge orifices. The purpose of the orifices is to regulate the flow of fuel and oxidizer to the gas generator, enabling optimal power supply to the turbine and pump assemblies. The unsteady Reynolds-Averaged Navier-Stokes equations were solved on unstructured grids at second-order spatial and temporal accuracy. The LO2 model was validated against published experimental data and semi-empirical relationships for thin-plate orifices over a range of Reynolds numbers. Predictions for the LO2 square- and round-edge orifices precisely match experiment and semi-empirical formulas, despite complex feedline geometry whereby a portion of the flow from the engine main feedlines travels at a right-angle through a smaller-diameter pipe containing the orifice. Predictions for LH2 square- and round-edge orifice designs match experiment and semi-empirical formulas to varying degrees depending on the semi-empirical formula being evaluated. LO2 mass flow rate through the square-edge orifice is predicted to be 25 percent less than the flow rate budgeted in the original engine balance, which was subsequently modified. LH2 mass flow rate through the square-edge orifice is predicted to be 5 percent greater than the flow rate budgeted in the engine balance. Since CFD predictions for LO2 and LH2 square-edge orifice pressure loss coefficients, K, both agree with published data, the equation for K has been used to define a procedure for orifice sizing.

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.

Navier-Stokes Solutions for Spin-Up from Rest in a Cylindrical Container

DTIC Science & Technology

1979-09-01

CONDITIONS The calculations employ a finite - difference analog of the unsteady axisyimetric Navier-Stokes equations formulated in cylindrical coordinates...derivatives are approximated by second- order accurate one-sided difference formulae involving three time levels. * The following finite - difference ...equation are identical in form to Equations (13). The finite - difference representations for the ?-equation are: "(i)[aJ~lk " /i’,J-l2k] T (14a) •g I

Current Trends in Modeling Research for Turbulent Aerodynamic Flows

NASA Technical Reports Server (NTRS)

Gatski, Thomas B.; Rumsey, Christopher L.; Manceau, Remi

2007-01-01

The engineering tools of choice for the computation of practical engineering flows have begun to migrate from those based on the traditional Reynolds-averaged Navier-Stokes approach to methodologies capable, in theory if not in practice, of accurately predicting some instantaneous scales of motion in the flow. The migration has largely been driven by both the success of Reynolds-averaged methods over a wide variety of flows as well as the inherent limitations of the method itself. Practitioners, emboldened by their ability to predict a wide-variety of statistically steady, equilibrium turbulent flows, have now turned their attention to flow control and non-equilibrium flows, that is, separation control. This review gives some current priorities in traditional Reynolds-averaged modeling research as well as some methodologies being applied to a new class of turbulent flow control problems.

Scale Adaptive Simulation Model for the Darrieus Wind Turbine

NASA Astrophysics Data System (ADS)

Rogowski, K.; Hansen, M. O. L.; Maroński, R.; Lichota, P.

2016-09-01

Accurate prediction of aerodynamic loads for the Darrieus wind turbine using more or less complex aerodynamic models is still a challenge. One of the problems is the small amount of experimental data available to validate the numerical codes. The major objective of the present study is to examine the scale adaptive simulation (SAS) approach for performance analysis of a one-bladed Darrieus wind turbine working at a tip speed ratio of 5 and at a blade Reynolds number of 40 000. The three-dimensional incompressible unsteady Navier-Stokes equations are used. Numerical results of aerodynamic loads and wake velocity profiles behind the rotor are compared with experimental data taken from literature. The level of agreement between CFD and experimental results is reasonable.

On the utility of GPU accelerated high-order methods for unsteady flow simulations: A comparison with industry-standard tools

NASA Astrophysics Data System (ADS)

Vermeire, B. C.; Witherden, F. D.; Vincent, P. E.

2017-04-01

First- and second-order accurate numerical methods, implemented for CPUs, underpin the majority of industrial CFD solvers. Whilst this technology has proven very successful at solving steady-state problems via a Reynolds Averaged Navier-Stokes approach, its utility for undertaking scale-resolving simulations of unsteady flows is less clear. High-order methods for unstructured grids and GPU accelerators have been proposed as an enabling technology for unsteady scale-resolving simulations of flow over complex geometries. In this study we systematically compare accuracy and cost of the high-order Flux Reconstruction solver PyFR running on GPUs and the industry-standard solver STAR-CCM+ running on CPUs when applied to a range of unsteady flow problems. Specifically, we perform comparisons of accuracy and cost for isentropic vortex advection (EV), decay of the Taylor-Green vortex (TGV), turbulent flow over a circular cylinder, and turbulent flow over an SD7003 aerofoil. We consider two configurations of STAR-CCM+: a second-order configuration, and a third-order configuration, where the latter was recommended by CD-adapco for more effective computation of unsteady flow problems. Results from both PyFR and STAR-CCM+ demonstrate that third-order schemes can be more accurate than second-order schemes for a given cost e.g. going from second- to third-order, the PyFR simulations of the EV and TGV achieve 75× and 3× error reduction respectively for the same or reduced cost, and STAR-CCM+ simulations of the cylinder recovered wake statistics significantly more accurately for only twice the cost. Moreover, advancing to higher-order schemes on GPUs with PyFR was found to offer even further accuracy vs. cost benefits relative to industry-standard tools.

On Parametric Sensitivity of Reynolds-Averaged Navier-Stokes SST Turbulence Model: 2D Hypersonic Shock-Wave Boundary Layer Interactions

NASA Technical Reports Server (NTRS)

Brown, James L.

2014-01-01

Examined is sensitivity of separation extent, wall pressure and heating to variation of primary input flow parameters, such as Mach and Reynolds numbers and shock strength, for 2D and Axisymmetric Hypersonic Shock Wave Turbulent Boundary Layer interactions obtained by Navier-Stokes methods using the SST turbulence model. Baseline parametric sensitivity response is provided in part by comparison with vetted experiments, and in part through updated correlations based on free interaction theory concepts. A recent database compilation of hypersonic 2D shock-wave/turbulent boundary layer experiments extensively used in a prior related uncertainty analysis provides the foundation for this updated correlation approach, as well as for more conventional validation. The primary CFD method for this work is DPLR, one of NASA's real-gas aerothermodynamic production RANS codes. Comparisons are also made with CFL3D, one of NASA's mature perfect-gas RANS codes. Deficiencies in predicted separation response of RANS/SST solutions to parametric variations of test conditions are summarized, along with recommendations as to future turbulence approach.

Distributed Relaxation Multigrid and Defect Correction Applied to the Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Thomas, J. L.; Diskin, B.; Brandt, A.

1999-01-01

The distributed-relaxation multigrid and defect- correction methods are applied to the two- dimensional compressible Navier-Stokes equations. The formulation is intended for high Reynolds number applications and several applications are made at a laminar Reynolds number of 10,000. A staggered- grid arrangement of variables is used; the coupled pressure and internal energy equations are solved together with multigrid, requiring a block 2x2 matrix solution. Textbook multigrid efficiencies are attained for incompressible and slightly compressible simulations of the boundary layer on a flat plate. Textbook efficiencies are obtained for compressible simulations up to Mach numbers of 0.7 for a viscous wake simulation.

Shock-Wave/Boundary-Layer Interactions in Hypersonic Low Density Flows

NASA Technical Reports Server (NTRS)

Moss, James N.; Olejniczak, Joseph

2004-01-01

Results of numerical simulations of Mach 10 air flow over a hollow cylinder-flare and a double-cone are presented where viscous effects are significant. The flow phenomena include shock-shock and shock- boundary-layer interactions with accompanying flow separation, recirculation, and reattachment. The purpose of this study is to promote an understanding of the fundamental gas dynamics resulting from such complex interactions and to clarify the requirements for meaningful simulations of such flows when using the direct simulation Monte Carlo (DSMC) method. Particular emphasis is placed on the sensitivity of computed results to grid resolution. Comparisons of the DSMC results for the hollow cylinder-flare (30 deg.) configuration are made with the results of experimental measurements conducted in the ONERA RSCh wind tunnel for heating, pressure, and the extent of separation. Agreement between computations and measurements for various quantities is good except that for pressure. For the same flow conditions, the double- cone geometry (25 deg.- 65 deg.) produces much stronger interactions, and these interactions are investigated numerically using both DSMC and Navier-Stokes codes. For the double-cone computations, a two orders of magnitude variation in free-stream density (with Reynolds numbers from 247 to 24,7 19) is investigated using both computational methods. For this range of flow conditions, the computational results are in qualitative agreement for the extent of separation with the DSMC method always predicting a smaller separation region. Results from the Navier-Stokes calculations suggest that the flow for the highest density double-cone case may be unsteady; however, the DSMC solution does not show evidence of unsteadiness.

Numerical Solution of Incompressible Navier-Stokes Equations Using a Fractional-Step Approach

NASA Technical Reports Server (NTRS)

Kiris, Cetin; Kwak, Dochan

1999-01-01

A fractional step method for the solution of steady and unsteady incompressible Navier-Stokes equations is outlined. The method is based on a finite volume formulation and uses the pressure in the cell center and the mass fluxes across the faces of each cell as dependent variables. Implicit treatment of convective and viscous terms in the momentum equations enables the numerical stability restrictions to be relaxed. The linearization error in the implicit solution of momentum equations is reduced by using three subiterations in order to achieve second order temporal accuracy for time-accurate calculations. In spatial discretizations of the momentum equations, a high-order (3rd and 5th) flux-difference splitting for the convective terms and a second-order central difference for the viscous terms are used. The resulting algebraic equations are solved with a line-relaxation scheme which allows the use of large time step. A four color ZEBRA scheme is employed after the line-relaxation procedure in the solution of the Poisson equation for pressure. This procedure is applied to a Couette flow problem using a distorted computational grid to show that the method minimizes grid effects. Additional benchmark cases include the unsteady laminar flow over a circular cylinder for Reynolds Numbers of 200, and a 3-D, steady, turbulent wingtip vortex wake propagation study. The solution algorithm does a very good job in resolving the vortex core when 5th-order upwind differencing and a modified production term in the Baldwin-Barth one-equation turbulence model are used with adequate grid resolution.

Evaluation of Full Reynolds Stress Turbulence Models in FUN3D

NASA Technical Reports Server (NTRS)

Dudek, Julianne C.; Carlson, Jan-Renee

2017-01-01

Full seven-equation Reynolds stress turbulence models are promising tools for today’s aerospace technology challenges. This paper examines two such models for computing challenging turbulent flows including shock-wave boundary layer interactions, separation and mixing layers. The Wilcox and the SSG/LRR full second-moment Reynolds stress models have been implemented into the FUN3D (Fully Unstructured Navier-Stokes Three Dimensional) unstructured Navier-Stokes code and were evaluated for four problems: a transonic two-dimensional diffuser, a supersonic axisymmetric compression corner, a compressible planar shear layer, and a subsonic axisymmetric jet. Simulation results are compared with experimental data and results computed using the more commonly used Spalart-Allmaras (SA) one-equation and the Menter Shear Stress Transport (SST-V) two-equation turbulence models.

Direct Numerical Simulation of Pebble Bed Flows: Database Development and Investigation of Low-Frequency Temporal Instabilities

DOE PAGES

Fick, Lambert H.; Merzari, Elia; Hassan, Yassin A.

2017-02-20

Computational analyses of fluid flow through packed pebble bed domains using the Reynolds-averaged NavierStokes framework have had limited success in the past. Because of a lack of high-fidelity experimental or computational data, optimization of Reynolds-averaged closure models for these geometries has not been extensively developed. In the present study, direct numerical simulation was employed to develop a high-fidelity database that can be used for optimizing Reynolds-averaged closure models for pebble bed flows. A face-centered cubic domain with periodic boundaries was used. Flow was simulated at a Reynolds number of 9308 and cross-verified by using available quasi-DNS data. During the simulations,more » low-frequency instability modes were observed that affected the stationary solution. Furthermore, these instabilities were investigated by using the method of proper orthogonal decomposition, and a correlation was found between the time-dependent asymmetry of the averaged velocity profile data and the behavior of the highest energy eigenmodes.« less

Direct Numerical Simulation of Pebble Bed Flows: Database Development and Investigation of Low-Frequency Temporal Instabilities

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

Fick, Lambert H.; Merzari, Elia; Hassan, Yassin A.

Computational analyses of fluid flow through packed pebble bed domains using the Reynolds-averaged NavierStokes framework have had limited success in the past. Because of a lack of high-fidelity experimental or computational data, optimization of Reynolds-averaged closure models for these geometries has not been extensively developed. In the present study, direct numerical simulation was employed to develop a high-fidelity database that can be used for optimizing Reynolds-averaged closure models for pebble bed flows. A face-centered cubic domain with periodic boundaries was used. Flow was simulated at a Reynolds number of 9308 and cross-verified by using available quasi-DNS data. During the simulations,more » low-frequency instability modes were observed that affected the stationary solution. Furthermore, these instabilities were investigated by using the method of proper orthogonal decomposition, and a correlation was found between the time-dependent asymmetry of the averaged velocity profile data and the behavior of the highest energy eigenmodes.« less

Compressible Boundary Layer Predictions at High Reynolds Number using Hybrid LES/RANS Methods

NASA Technical Reports Server (NTRS)

Choi, Jung-Il; Edwards, Jack R.; Baurle, Robert A.

2008-01-01

Simulations of compressible boundary layer flow at three different Reynolds numbers (Re(sub delta) = 5.59x10(exp 4), 1.78x10(exp 5), and 1.58x10(exp 6) are performed using a hybrid large-eddy/Reynolds-averaged Navier-Stokes method. Variations in the recycling/rescaling method, the higher-order extension, the choice of primitive variables, the RANS/LES transition parameters, and the mesh resolution are considered in order to assess the model. The results indicate that the present model can provide good predictions of the mean flow properties and second-moment statistics of the boundary layers considered. Normalized Reynolds stresses in the outer layer are found to be independent of Reynolds number, similar to incompressible turbulent boundary layers.

Receptivity of Supersonic Boundary Layers Due To Acoustic Disturbances Over Blunt Cones

NASA Technical Reports Server (NTRS)

Balakumar, P.

2007-01-01

Receptivity and stability of supersonic boundary layers over a 5-degree straight cone with a blunt tip are numerically investigated at a free stream Mach number of 3.5 and at a high Reynolds number of 106/inch. Both the steady and unsteady solutions are obtained by solving the full Navier-Stokes equations using the 5th-order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using third-order total-variation-diminishing (TVD) Runge-Kutta scheme for time integration. The linear stability results showed that bluntness has less stabilizing effects on the stability of boundary layers over cones than on flat plates and wedges. The unsteady simulations of the interaction of plane threedimensional acoustic waves with the cone showed that the modulation of wavelength and the generation of instability waves first occurred near the leading edge in the plane where the constant acoustic phase lines are perpendicular to the cone axis. Further downstream, this instability region spreads in the azimuthal direction from this plane.

TURNS - A free-wake Euler/Navier-Stokes numerical method for helicopter rotors

NASA Technical Reports Server (NTRS)

Srinivasan, G. R.; Baeder, J. D.

1993-01-01

Computational capabilities of a numerical procedure, called TURNS (transonic unsteady rotor Navier-Stokes), to calculate the aerodynamics and acoustics (high-speed impulsive noise) out to several rotor diameters are summarized. The procedure makes it possible to obtain the aerodynamics and acoustics information in one single calculation. The vortical wave and its influence, as well as the acoustics, are captured as part of the overall flowfield solution. The accuracy and suitability of the TURNS method is demonstrated through comparisons with experimental data.

A new flux conserving Newton's method scheme for the two-dimensional, steady Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Scott, James R.; Chang, Sin-Chung

1993-01-01

A new numerical method is developed for the solution of the two-dimensional, steady Navier-Stokes equations. The method that is presented differs in significant ways from the established numerical methods for solving the Navier-Stokes equations. The major differences are described. First, the focus of the present method is on satisfying flux conservation in an integral formulation, rather than on simulating conservation laws in their differential form. Second, the present approach provides a unified treatment of the dependent variables and their unknown derivatives. All are treated as unknowns together to be solved for through simulating local and global flux conservation. Third, fluxes are balanced at cell interfaces without the use of interpolation or flux limiters. Fourth, flux conservation is achieved through the use of discrete regions known as conservation elements and solution elements. These elements are not the same as the standard control volumes used in the finite volume method. Fifth, the discrete approximation obtained on each solution element is a functional solution of both the integral and differential form of the Navier-Stokes equations. Finally, the method that is presented is a highly localized approach in which the coupling to nearby cells is only in one direction for each spatial coordinate, and involves only the immediately adjacent cells. A general third-order formulation for the steady, compressible Navier-Stokes equations is presented, and then a Newton's method scheme is developed for the solution of incompressible, low Reynolds number channel flow. It is shown that the Jacobian matrix is nearly block diagonal if the nonlinear system of discrete equations is arranged approximately and a proper pivoting strategy is used. Numerical results are presented for Reynolds numbers of 100, 1000, and 2000. Finally, it is shown that the present scheme can resolve the developing channel flow boundary layer using as few as six to ten cells per channel width, depending on the Reynolds number.

Aeroacoustic Simulations of a Nose Landing Gear Using FUN3D on Pointwise Unstructured Grids

NASA Technical Reports Server (NTRS)

Vatsa, Veer N.; Khorrami, Mehdi R.; Rhoads, John; Lockard, David P.

2015-01-01

Numerical simulations have been performed for a partially-dressed, cavity-closed (PDCC) nose landing gear configuration that was tested in the University of Florida's open-jet acoustic facility known as the UFAFF. The unstructured-grid flow solver FUN3D is used to compute the unsteady flow field for this configuration. Mixed-element grids generated using the Pointwise(TradeMark) grid generation software are used for these simulations. Particular care is taken to ensure quality cells and proper resolution in critical areas of interest in an effort to minimize errors introduced by numerical artifacts. A hybrid Reynolds-averaged Navier-Stokes/large eddy simulation (RANS/LES) turbulence model is used for these simulations. Solutions are also presented for a wall function model coupled to the standard turbulence model. Time-averaged and instantaneous solutions obtained on these Pointwise grids are compared with the measured data and previous numerical solutions. The resulting CFD solutions are used as input to a Ffowcs Williams-Hawkings noise propagation code to compute the farfield noise levels in the flyover and sideline directions. The computed noise levels compare well with previous CFD solutions and experimental data.

Effects of Non-Uniform Inlet Temperature Distribution on High-Pressure Turbine Blade Loading

NASA Astrophysics Data System (ADS)

Smith, Craig I.; Chang, Dongil; Tavoularis, Stavros

2012-09-01

The effects of a non-uniform inlet field on the performance of a commercial, transonic, single-stage, high-pressure, axial turbine with a curved inlet duct have been investigated numerically by solving the unsteady Reynolds-averaged Navier-Stokes equations with the shear stress transport (SST) turbulence model. By adjusting the alignment of the experimentally-based inlet temperature field with respect to the stator vanes, two clocking configurations were generated: a Vane-Impinging (VI) case, in which each hot streak impinged on a vane and a Mid-Pitch (MP) case, in which each hot streak passed between two vanes. An additional case with a purely radial (PR) variation of inlet temperature was also investigated. In the VI case, it was observed that, as the hot streaks impinged on the stator vanes, they spread spanwise due to the actions of the casing passage vortices and the radial pressure gradient; this resulted in a stream entering the rotor with relatively low temperature variations. In the MP case, the hot streaks were convected undisturbed past the relatively cool vane section. Relatively high time-averaged enthalpy values were found to occur on the pressure side of the blades in the MP configuration.

A High-Order, Adaptive, Discontinuous Galerkin Finite Element Method for the Reynolds-Averaged Navier-Stokes Equations

DTIC Science & Technology

2008-09-01

Element Method. Wellesley- Cambridge Press, Wellesly, MA, 1988. [97] E. F. Toro . Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical...introducing additional state variables, are generally asymptotically dual consistent. Numerical results are presented to confirm the results of the analysis...dependence on the state gradient is handled by introducing additional state variables, are generally asymptotically dual consistent. Numerical results are

A comparative study of Rosenbrock-type and implicit Runge-Kutta time integration for discontinuous Galerkin method for unsteady 3D compressible Navier-Stokes equations

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

Liu, Xiaodong; Xia, Yidong; Luo, Hong

A comparative study of two classes of third-order implicit time integration schemes is presented for a third-order hierarchical WENO reconstructed discontinuous Galerkin (rDG) method to solve the 3D unsteady compressible Navier-Stokes equations: — 1) the explicit first stage, single diagonally implicit Runge-Kutta (ESDIRK3) scheme, and 2) the Rosenbrock-Wanner (ROW) schemes based on the differential algebraic equations (DAEs) of Index-2. Compared with the ESDIRK3 scheme, a remarkable feature of the ROW schemes is that, they only require one approximate Jacobian matrix calculation every time step, thus considerably reducing the overall computational cost. A variety of test cases, ranging from inviscid flowsmore » to DNS of turbulent flows, are presented to assess the performance of these schemes. Here, numerical experiments demonstrate that the third-order ROW scheme for the DAEs of index-2 can not only achieve the designed formal order of temporal convergence accuracy in a benchmark test, but also require significantly less computing time than its ESDIRK3 counterpart to converge to the same level of discretization errors in all of the flow simulations in this study, indicating that the ROW methods provide an attractive alternative for the higher-order time-accurate integration of the unsteady compressible Navier-Stokes equations.« less

A comparative study of Rosenbrock-type and implicit Runge-Kutta time integration for discontinuous Galerkin method for unsteady 3D compressible Navier-Stokes equations

DOE PAGES

Liu, Xiaodong; Xia, Yidong; Luo, Hong; ...

2016-10-05

A comparative study of two classes of third-order implicit time integration schemes is presented for a third-order hierarchical WENO reconstructed discontinuous Galerkin (rDG) method to solve the 3D unsteady compressible Navier-Stokes equations: — 1) the explicit first stage, single diagonally implicit Runge-Kutta (ESDIRK3) scheme, and 2) the Rosenbrock-Wanner (ROW) schemes based on the differential algebraic equations (DAEs) of Index-2. Compared with the ESDIRK3 scheme, a remarkable feature of the ROW schemes is that, they only require one approximate Jacobian matrix calculation every time step, thus considerably reducing the overall computational cost. A variety of test cases, ranging from inviscid flowsmore » to DNS of turbulent flows, are presented to assess the performance of these schemes. Here, numerical experiments demonstrate that the third-order ROW scheme for the DAEs of index-2 can not only achieve the designed formal order of temporal convergence accuracy in a benchmark test, but also require significantly less computing time than its ESDIRK3 counterpart to converge to the same level of discretization errors in all of the flow simulations in this study, indicating that the ROW methods provide an attractive alternative for the higher-order time-accurate integration of the unsteady compressible Navier-Stokes equations.« less

Reynolds number scaling of velocity increments in isotropic turbulence.

PubMed

Iyer, Kartik P; Sreenivasan, Katepalli R; Yeung, P K

2017-02-01

Using the largest database of isotropic turbulence available to date, generated by the direct numerical simulation (DNS) of the Navier-Stokes equations on an 8192^{3} periodic box, we show that the longitudinal and transverse velocity increments scale identically in the inertial range. By examining the DNS data at several Reynolds numbers, we infer that the contradictory results of the past on the inertial-range universality are artifacts of low Reynolds number and residual anisotropy. We further show that both longitudinal and transverse velocity increments scale on locally averaged dissipation rate, just as postulated by Kolmogorov's refined similarity hypothesis, and that, in isotropic turbulence, a single independent scaling adequately describes fluid turbulence in the inertial range.

External heat transfer predictions in a highly loaded transonic linear turbine guide vane cascade using an upwind biased Navier-Stokes solver

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

Gehrer, A.; Jericha, H.

External heat transfer predictions are performed for two-dimensional turbine blade cascades. The Reynolds-averaged Navier-Stokes equations with algebraic (Arnone and Pacciani, 1998), one-equation (Spalart and Allmaras, 1994), and two-equation (low-Re {kappa}-{epsilon}, Biswas and Fukuyama, 1994) turbulence closures are solved with a fully implicit time-marching finite volume method. Comparisons with measurements (Arts et al., 1990; Arts, 1994) for a highly loaded transonic turbine nozzle guide vane cascade show good agreement in some cases, but also reveal problems with transition prediction and turbulence modeling. Special attention has been focused on the low-Re {kappa}-{epsilon} model concerning the influence of the inlet boundary condition formore » the {epsilon}-equation and problems in the stagnation point region.« less

Study of Near-Stall Flow Behavior in a Modern Transonic Fan with Composite Sweep

NASA Technical Reports Server (NTRS)

Hah, Chunill; Shin, Hyoun-Woo

2011-01-01

Detailed flow behavior in a modern transonic fan with a composite sweep is investigated in this paper. Both unsteady Reynolds-averaged Navier-Stokes (URANS) and Large Eddy Simulation (LES) methods are applied to investigate the flow field over a wide operating range. The calculated flow fields are compared with the data from an array of high-frequency response pressure transducers embedded in the fan casing. The current study shows that a relatively fine computational grid is required to resolve the flow field adequately and to calculate the pressure rise across the fan correctly. The calculated flow field shows detailed flow structure near the fan rotor tip region. Due to the introduction of composite sweep toward the rotor tip, the flow structure at the rotor tip is much more stable compared to that of the conventional blade design. The passage shock stays very close to the leading edge at the rotor tip even at the throttle limit. On the other hand, the passage shock becomes stronger and detaches earlier from the blade passage at the radius where the blade sweep is in the opposite direction. The interaction between the tip clearance vortex and the passage shock becomes intense as the fan operates toward the stall limit, and tip clearance vortex breakdown occurs at near-stall operation. URANS calculates the time-averaged flow field fairly well. Details of measured RMS static pressure are not calculated with sufficient accuracy with URANS. On the other hand, LES calculates details of the measured unsteady flow features in the current transonic fan with composite sweep fairly well and reveals the flow mechanism behind the measured unsteady flow field.

Numerical study of unsteady shockwave reflections using an upwind TVD scheme

NASA Technical Reports Server (NTRS)

Hsu, Andrew T.; Liou, Meng-Sing

1990-01-01

An unsteady TVD Navier-Stokes solver was developed and applied to the problem of shock reflection on a circular cylinder. The obtained numerical results were compared with the Schlieren photos from an experimental study. These results show that the present computer code has the ability of capturing moving shocks.

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

NASA Technical Reports Server (NTRS)

Sankar, Lakshmi N.; Hixon, Duane

1992-01-01

The development of efficient iterative solution methods for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations is discussed. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. In this work, another approach based on the classical conjugate gradient method, known as the Generalized Minimum Residual (GMRES) algorithm is investigated. The GMRES algorithm has been used in the past by a number of researchers for solving steady viscous and inviscid flow problems. Here, we investigate the suitability of this algorithm for solving the system of non-linear equations that arise in unsteady Navier-Stokes solvers at each time step.

Falling paper: Navier-Stokes solutions, model of fluid forces, and center of mass elevation.

PubMed

Pesavento, Umberto; Wang, Z Jane

2004-10-01

We investigate the problem of falling paper by solving the two dimensional Navier-Stokes equations subject to the motion of a free-falling body at Reynolds numbers around 10(3). The aerodynamic lift on a tumbling plate is found to be dominated by the product of linear and angular velocities rather than velocity squared, as appropriate for an airfoil. This coupling between translation and rotation provides a mechanism for a brief elevation of center of mass near the cusplike turning points. The Navier-Stokes solutions further provide the missing quantity in the classical theory of lift, the instantaneous circulation, and suggest a revised model for the fluid forces.

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

NASA Technical Reports Server (NTRS)

Obayashi, Shigeru

1991-01-01

A streamwise upwind algorithm for solving the unsteady 3-D Navier-Stokes equations was extended to handle the moving grid system. It is noted that the finite volume concept is essential to extend the algorithm. The resulting algorithm is conservative for any motion of the coordinate system. Two extensions to an implicit method were considered and the implicit extension that makes the algorithm computationally efficient is implemented into Ames's aeroelasticity code, ENSAERO. The new flow solver has been validated through the solution of test problems. Test cases include three-dimensional problems with fixed and moving grids. The first test case shown is an unsteady viscous flow over an F-5 wing, while the second test considers the motion of the leading edge vortex as well as the motion of the shock wave for a clipped delta wing. The resulting algorithm has been implemented into ENSAERO. The upwind version leads to higher accuracy in both steady and unsteady computations than the previously used central-difference method does, while the increase in the computational time is small.

High fidelity CFD-CSD aeroelastic analysis of slender bladed horizontal-axis wind turbine

NASA Astrophysics Data System (ADS)

Sayed, M.; Lutz, Th.; Krämer, E.; Shayegan, Sh.; Ghantasala, A.; Wüchner, R.; Bletzinger, K.-U.

2016-09-01

The aeroelastic response of large multi-megawatt slender horizontal-axis wind turbine blades is investigated by means of a time-accurate CFD-CSD coupling approach. A loose coupling approach is implemented and used to perform the simulations. The block- structured CFD solver FLOWer is utilized to obtain the aerodynamic blade loads based on the time-accurate solution of the unsteady Reynolds-averaged Navier-Stokes equations. The CSD solver Carat++ is applied to acquire the blade elastic deformations based on non-linear beam elements. In this contribution, the presented coupling approach is utilized to study the aeroelastic response of the generic DTU 10MW wind turbine. Moreover, the effect of the coupled results on the wind turbine performance is discussed. The results are compared to the aeroelastic response predicted by FLOWer coupled to the MBS tool SIMPACK as well as the response predicted by SIMPACK coupled to a Blade Element Momentum code for aerodynamic predictions. A comparative study among the different modelling approaches for this coupled problem is discussed to quantify the coupling effects of the structural models on the aeroelastic response.

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.

Overview of the Aeroelastic Prediction Workshop

NASA Technical Reports Server (NTRS)

Heeg, Jennifer; Chwalowski, Pawel; Schuster, David M.; Dalenbring, Mats

2013-01-01

The AIAA Aeroelastic Prediction Workshop (AePW) was held in April, 2012, bringing together communities of aeroelasticians and computational fluid dynamicists. The objective in conducting this workshop on aeroelastic prediction was to assess state-of-the-art computational aeroelasticity methods as practical tools for the prediction of static and dynamic aeroelastic phenomena. No comprehensive aeroelastic benchmarking validation standard currently exists, greatly hindering validation and state-of-the-art assessment objectives. The workshop was a step towards assessing the state of the art in computational aeroelasticity. This was an opportunity to discuss and evaluate the effectiveness of existing computer codes and modeling techniques for unsteady flow, and to identify computational and experimental areas needing additional research and development. Three configurations served as the basis for the workshop, providing different levels of geometric and flow field complexity. All cases considered involved supercritical airfoils at transonic conditions. The flow fields contained oscillating shocks and in some cases, regions of separation. The computational tools principally employed Reynolds-Averaged Navier Stokes solutions. The successes and failures of the computations and the experiments are examined in this paper.

Transonic aeroelastic analysis of launch vehicle configurations. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Filgueirasdeazevedo, Joao Luiz

1988-01-01

A numerical study of the aeroelastic stability of typical launch vehicle configurations in transonic flight is performed. Recent computational fluid dynamics techniques are used to simulate the transonic aerodynamic flow fields, as opposed to relying on experimental data for the unsteady aerodynamic pressures. The flow solver is coupled to an appropriate structural representation of the vehicle. The aerodynamic formulation is based on the thin layer approximation to the Reynolds-Averaged Navier-Stokes equations, where the account for turbulent mixing is done by the two-layer Baldwin and Lomax algebraic eddy viscosity model. The structural-dynamic equations are developed considering free-free flexural vibration of an elongated beam with variable properties and are cast in modal form. Aeroelastic analyses are performed by integrating simultaneously in the two sets of equations. By tracing the growth or decay of a perturbed oscillation, the aeroelastic stability of a given constant configuration can be ascertained. The method is described in detail, and results that indicate its application are presented. Applications include some validation cases for the algorithm developed, as well as the study of configurations known to have presented flutter programs in the past.

Introduction. Computational aerodynamics.

PubMed

Tucker, Paul G

2007-10-15

The wide range of uses of computational fluid dynamics (CFD) for aircraft design is discussed along with its role in dealing with the environmental impact of flight. Enabling technologies, such as grid generation and turbulence models, are also considered along with flow/turbulence control. The large eddy simulation, Reynolds-averaged Navier-Stokes and hybrid turbulence modelling approaches are contrasted. The CFD prediction of numerous jet configurations occurring in aerospace are discussed along with aeroelasticity for aeroengine and external aerodynamics, design optimization, unsteady flow modelling and aeroengine internal and external flows. It is concluded that there is a lack of detailed measurements (for both canonical and complex geometry flows) to provide validation and even, in some cases, basic understanding of flow physics. Not surprisingly, turbulence modelling is still the weak link along with, as ever, a pressing need for improved (in terms of robustness, speed and accuracy) solver technology, grid generation and geometry handling. Hence, CFD, as a truly predictive and creative design tool, seems a long way off. Meanwhile, extreme practitioner expertise is still required and the triad of computation, measurement and analytic solution must be judiciously used.

A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Ronquist, Einar M.

1989-01-01

A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.

Turbulent kinetic energy and a possible hierarchy of length scales in a generalization of the Navier-Stokes alpha theory.

PubMed

Fried, Eliot; Gurtin, Morton E

2007-05-01

We present a continuum-mechanical formulation and generalization of the Navier-Stokes alpha theory based on a general framework for fluid-dynamical theories with gradient dependencies. Our flow equation involves two additional problem-dependent length scales alpha and beta. The first of these scales enters the theory through the internal kinetic energy, per unit mass, alpha2|D|2, where D is the symmetric part of the gradient of the filtered velocity. The remaining scale is associated with a dissipative hyperstress which depends linearly on the gradient of the filtered vorticity. When alpha and beta are equal, our flow equation reduces to the Navier-Stokes alpha equation. In contrast to the original derivation of the Navier-Stokes alpha equation, which relies on Lagrangian averaging, our formulation delivers boundary conditions. For a confined flow, our boundary conditions involve an additional length scale l characteristic of the eddies found near walls. Based on a comparison with direct numerical simulations for fully developed turbulent flow in a rectangular channel of height 2h, we find that alphabeta approximately Re(0.470) and lh approximately Re(-0.772), where Re is the Reynolds number. The first result, which arises as a consequence of identifying the internal kinetic energy with the turbulent kinetic energy, indicates that the choice alpha=beta required to reduce our flow equation to the Navier-Stokes alpha equation is likely to be problematic. The second result evinces the classical scaling relation eta/L approximately Re(-3/4) for the ratio of the Kolmogorov microscale eta to the integral length scale L . The numerical data also suggests that l < or = beta . We are therefore led to conjecture a tentative hierarchy, l < or = beta < alpha , involving the three length scales entering our theory.

A solution to the Navier-Stokes equations based upon the Newton Kantorovich method

NASA Technical Reports Server (NTRS)

Davis, J. E.; Gabrielsen, R. E.; Mehta, U. B.

1977-01-01

An implicit finite difference scheme based on the Newton-Kantorovich technique was developed for the numerical solution of the nonsteady, incompressible, two-dimensional Navier-Stokes equations in conservation-law form. The algorithm was second-order-time accurate, noniterative with regard to the nonlinear terms in the vorticity transport equation except at the earliest few time steps, and spatially factored. Numerical results were obtained with the technique for a circular cylinder at Reynolds number 15. Results indicate that the technique is in excellent agreement with other numerical techniques for all geometries and Reynolds numbers investigated, and indicates a potential for significant reduction in computation time over current iterative techniques.

Transonic Navier-Stokes wing solutions using a zonal approach. Part 2: High angle-of-attack simulation

NASA Technical Reports Server (NTRS)

Chaderjian, N. M.

1986-01-01

A computer code is under development whereby the thin-layer Reynolds-averaged Navier-Stokes equations are to be applied to realistic fighter-aircraft configurations. This transonic Navier-Stokes code (TNS) utilizes a zonal approach in order to treat complex geometries and satisfy in-core computer memory constraints. The zonal approach has been applied to isolated wing geometries in order to facilitate code development. Part 1 of this paper addresses the TNS finite-difference algorithm, zonal methodology, and code validation with experimental data. Part 2 of this paper addresses some numerical issues such as code robustness, efficiency, and accuracy at high angles of attack. Special free-stream-preserving metrics proved an effective way to treat H-mesh singularities over a large range of severe flow conditions, including strong leading-edge flow gradients, massive shock-induced separation, and stall. Furthermore, lift and drag coefficients have been computed for a wing up through CLmax. Numerical oil flow patterns and particle trajectories are presented both for subcritical and transonic flow. These flow simulations are rich with complex separated flow physics and demonstrate the efficiency and robustness of the zonal approach.

Computational flow development for unsteady viscous flows: Foundation of the numerical method

NASA Technical Reports Server (NTRS)

Bratanow, T.; Spehert, T.

1978-01-01

A procedure is presented for effective consideration of viscous effects in computational development of high Reynolds number flows. The procedure is based on the interpretation of the Navier-Stokes equations as vorticity transport equations. The physics of the flow was represented in a form suitable for numerical analysis. Lighthill's concept for flow development for computational purposes was adapted. The vorticity transport equations were cast in a form convenient for computation. A statement for these equations was written using the method of weighted residuals and applying the Galerkin criterion. An integral representation of the induced velocity was applied on the basis of the Biot-Savart law. Distribution of new vorticity, produced at wing surfaces over small computational time intervals, was assumed to be confined to a thin region around the wing surfaces.

Proper Orthogonal Decomposition in Optimal Control of Fluids

NASA Technical Reports Server (NTRS)

Ravindran, S. S.

1999-01-01

In this article, we present a reduced order modeling approach suitable for active control of fluid dynamical systems based on proper orthogonal decomposition (POD). The rationale behind the reduced order modeling is that numerical simulation of Navier-Stokes equations is still too costly for the purpose of optimization and control of unsteady flows. We examine the possibility of obtaining reduced order models that reduce computational complexity associated with the Navier-Stokes equations while capturing the essential dynamics by using the POD. The POD allows extraction of certain optimal set of basis functions, perhaps few, from a computational or experimental data-base through an eigenvalue analysis. The solution is then obtained as a linear combination of these optimal set of basis functions by means of Galerkin projection. This makes it attractive for optimal control and estimation of systems governed by partial differential equations. We here use it in active control of fluid flows governed by the Navier-Stokes equations. We show that the resulting reduced order model can be very efficient for the computations of optimization and control problems in unsteady flows. Finally, implementational issues and numerical experiments are presented for simulations and optimal control of fluid flow through channels.

On solving the compressible Navier-Stokes equations for unsteady flows at very low Mach numbers

NASA Technical Reports Server (NTRS)

Pletcher, R. H.; Chen, K.-H.

1993-01-01

The properties of a preconditioned, coupled, strongly implicit finite difference scheme for solving the compressible Navier-Stokes equations in primitive variables are investigated for two unsteady flows at low speeds, namely the impulsively started driven cavity and the startup of pipe flow. For the shear-driven cavity flow, the computational effort was observed to be nearly independent of Mach number, especially at the low end of the range considered. This Mach number independence was also observed for steady pipe flow calculations; however, rather different conclusions were drawn for the unsteady calculations. In the pressure-driven pipe startup problem, the compressibility of the fluid began to significantly influence the physics of the flow development at quite low Mach numbers. The present scheme was observed to produce the expected characteristics of completely incompressible flow when the Mach number was set at very low values. Good agreement with incompressible results available in the literature was observed.

Numerical and Experimental Investigation of Confined Turbulent Multiple Transverse Jets (Briefing Charts)

DTIC Science & Technology

2014-07-29

14.3. The momentum and scalar mixing is investigated through the solution of the Reynolds-Averaged Navier Stokes (RANS) equations. The mean scalar...demonstrated symmetry , only a one-half section of the geometry is considered. All numerical simulations capture salient flow structures such as the counter...distribution unlimited Symmetry Plane Walls Diluents’ Inlet Vy = 100 m/s Previous Numerical Work at AFRL: Air-to-Air Experimental Configuration

Prediction of Flows about Forebodies at High-Angle-of-Attack Dynamic Conditions

NASA Technical Reports Server (NTRS)

Fremaux, C. M.; vanDam, C. P.; Saephan, S.; DalBello, T.

2003-01-01

A Reynolds-average Navier Stokes method developed for rotorcraft type of flow problems is applied for predicting the forces and moments of forebody models at high-angle-of-attack dynamic conditions and for providing insight into the flow characteristics at these conditions. Wind-tunnel results from rotary testing on generic forebody models conducted by NASA Langley and DERA are used for comparison. This paper focuses on the steady-state flow problem.

Detached-Eddy Simulations of Attached and Detached Boundary Layers

NASA Astrophysics Data System (ADS)

Caruelle, B.; Ducros, F.

2003-12-01

This article presents Detached-Eddy Simulations (DESs) of attached and detached turbulent boundary layers. This hybrid Reynolds Averaged Navier-Stokes (RANS) / Large Eddy Simulation (LES) model goes continuously from RANS to LES according to the mesh definition. We propose a parametric study of the model over two "academic" configurations, in order to get information on the influence of the mesh to correctly treat complex flow with attached and detached boundary layers.

Numerical investigation of airflow in an idealised human extra-thoracic airway: a comparison study

PubMed Central

Chen, Jie; Gutmark, Ephraim

2013-01-01

Large eddy simulation (LES) technique is employed to numerically investigate the airflow through an idealised human extra-thoracic airway under different breathing conditions, 10 l/min, 30 l/min, and 120 l/min. The computational results are compared with single and cross hot-wire measurements, and with time-averaged flow field computed by standard k-ω and k-ω-SST Reynolds averaged Navier-Stokes (RANS) models and the Lattice-Boltzmann method (LBM). The LES results are also compared to root-mean-square (RMS) flow field computed by the Reynolds stress model (RSM) and LBM. LES generally gives better prediction of the time-averaged flow field than RANS models and LBM. LES also provides better estimation of the RMS flow field than both the RSM and the LBM. PMID:23619907

Towards LES Models of Jets and Plumes

NASA Technical Reports Server (NTRS)

Webb, A. T.; Mansour, N. N.

2000-01-01

As pointed out by Rodi standard integral solutions for jets and plumes developed for discharge into infinite, quiescent ambient are difficult to extend to complex situations, particularly in the presence of boundaries such as the sea floor or ocean surface. In such cases the assumption of similarity breaks down and it is impossible to find a suitable entrainment coefficient. The models are also incapable of describing any but the most slowly varying unsteady motions. There is therefore a need for full time-dependent modeling of the flow field for which there are three main approaches: (1) Reynolds averaged numerical simulation (RANS), (2) large eddy simulation (LES), and (3) direct numerical simulation (DNS). Rodi applied RANS modeling to both jets and plumes with considerable success, the test being a match with experimental data for time-averaged velocity and temperature profiles as well as turbulent kinetic energy and rms axial turbulent velocity fluctuations. This model still relies on empirical constants, some eleven in the case of the buoyant jet, and so would not be applicable to a partly laminar plume, may have limited use in the presence of boundaries, and would also be unsuitable if one is after details of the unsteady component of the flow (the turbulent eddies). At the other end of the scale DNS modeling includes all motions down to the viscous scales. Boersma et al. have built such a model for the non-buoyant case which also compares well with measured data for mean and turbulent velocity components. The model demonstrates its versatility by application to a laminar flow case. As its name implies, DNS directly models the Navier-Stokes equations without recourse to subgrid modeling so for flows with a broad spectrum of motions (high Re) the cost can be prohibitive - the number of required grid points scaling with Re(exp 9/4) and the number of time steps with Re(exp 3/4). The middle road is provided by LES whereby the Navier-Stokes equations are formally filtered with the filter chosen to only exclude the smallest turbulent motions. If successful, LES should provide much of the detail available to DNS but at more bearable cost. Fatica et al. in comparing LES with DNS for a low Reynolds number jet showed that the LES could simulate the temporally evolving behavior including growth of the jet thickness. It is the intention of this report to explore the application of an LES model to jets and plumes. As always, before tackling complex situations, the model must be tested for the simplest of cases and so we address only two, a non-buoyant axisymmetric jet issuing steadily from an orifice into a semi-infinite stationary environment and a buoyant jet in the same environment. The work is a continuation of Basu and Mansour.

Simulation of separated flow past a bluff body using Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ghia, K. N.; Ghia, U.; Osswald, G. A.; Liu, C. A.

1987-01-01

Two-dimensional flow past a bluff body is presently simulated on the basis of an analysis that employs the incompressible, unsteady Navier-Stokes equations in terms of vorticity and stream function. The fully implicit, time-marching, alternating-direction, implicit-block Gaussian elimination used is a direct method with second-order spatial accuracy; this allows it to avoid the introduction of any artificial viscosity. Attention is given to the simulation of flow past a circular cylinder with and without symmetry, requiring the use of either the half or the full cylinder, respectively.

Computational studies of an impulsively started viscous flow

NASA Technical Reports Server (NTRS)

Davis, Sanford S.

1988-01-01

Progress in validating incompressible Navier-Stokes codes is described using a predictor/corrector scheme. The flow field under study is the impulsive start of a circular cylinder and the unsteady evolution of the separation bubble. In the current code, a uniform asymptotic expansion is used as an initial condition in order to correctly capture the initial growth of the vortex sheet. Volocity fields at selected instants of time are decomposed into vectorial representations of Navier-Stokes equations which are then used to analyze dominant contributions in the boundary-layer region.

Analysis and Design of Rotors at Ultra-Low Reynolds Numbers

NASA Technical Reports Server (NTRS)

Kunz, Peter J.; Strawn, Roger C.

2003-01-01

Design tools have been developed for ultra-low Reynolds number rotors, combining enhanced actuator-ring / blade-element theory with airfoil section data based on two-dimensional Navier-Stokes calculations. This performance prediction method is coupled with an optimizer for both design and analysis applications. Performance predictions from these tools have been compared with three-dimensional Navier Stokes analyses and experimental data for a 2.5 cm diameter rotor with chord Reynolds numbers below 10,000. Comparisons among the analyses and experimental data show reasonable agreement both in the global thrust and power required, but the spanwise distributions of these quantities exhibit significant deviations. The study also reveals that three-dimensional and rotational effects significantly change local airfoil section performance. The magnitude of this issue, unique to this operating regime, may limit the applicability of blade-element type methods for detailed rotor design at ultra-low Reynolds numbers, but these methods are still useful for evaluating concept feasibility and rapidly generating initial designs for further analysis and optimization using more advanced tools.

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.

Turbulence modeling for hypersonic flight

NASA Technical Reports Server (NTRS)

Bardina, Jorge E.

1992-01-01

The objective of the present work is to develop, verify, and incorporate two equation turbulence models which account for the effect of compressibility at high speeds into a three dimensional Reynolds averaged Navier-Stokes code and to provide documented model descriptions and numerical procedures so that they can be implemented into the National Aerospace Plane (NASP) codes. A summary of accomplishments is listed: (1) Four codes have been tested and evaluated against a flat plate boundary layer flow and an external supersonic flow; (2) a code named RANS was chosen because of its speed, accuracy, and versatility; (3) the code was extended from thin boundary layer to full Navier-Stokes; (4) the K-omega two equation turbulence model has been implemented into the base code; (5) a 24 degree laminar compression corner flow has been simulated and compared to other numerical simulations; and (6) work is in progress in writing the numerical method of the base code including the turbulence model.

Numerical solutions of Navier-Stokes equations for compressible turbulent two/three dimensional flows in terminal shock region of an inlet/diffuser

NASA Technical Reports Server (NTRS)

Liu, N. S.; Shamroth, S. J.; Mcdonald, H.

1983-01-01

The multidimensional ensemble averaged compressible time dependent Navier Stokes equations in conjunction with mixing length turbulence model and shock capturing technique were used to study the terminal shock type of flows in various flight regimes occurring in a diffuser/inlet model. The numerical scheme for solving the governing equations is based on a linearized block implicit approach and the following high Reynolds number calculations were carried out: (1) 2 D, steady, subsonic; (2) 2 D, steady, transonic with normal shock; (3) 2 D, steady, supersonic with terminal shock; (4) 2 D, transient process of shock development and (5) 3 D, steady, transonic with normal shock. The numerical results obtained for the 2 D and 3 D transonic shocked flows were compared with corresponding experimental data; the calculated wall static pressure distributions agree well with the measured data.

An efficient nonlinear relaxation technique for the three-dimensional, Reynolds-averaged Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Edwards, Jack R.; Mcrae, D. S.

1993-01-01

An efficient implicit method for the computation of steady, three-dimensional, compressible Navier-Stokes flowfields is presented. A nonlinear iteration strategy based on planar Gauss-Seidel sweeps is used to drive the solution toward a steady state, with approximate factorization errors within a crossflow plane reduced by the application of a quasi-Newton technique. A hybrid discretization approach is employed, with flux-vector splitting utilized in the streamwise direction and central differences with artificial dissipation used for the transverse fluxes. Convergence histories and comparisons with experimental data are presented for several 3-D shock-boundary layer interactions. Both laminar and turbulent cases are considered, with turbulent closure provided by a modification of the Baldwin-Barth one-equation model. For the problems considered (175,000-325,000 mesh points), the algorithm provides steady-state convergence in 900-2000 CPU seconds on a single processor of a Cray Y-MP.

An Evaluation of Parameters Influencing Jet Mixing Using the WIND Navier-stokes Code

NASA Technical Reports Server (NTRS)

Dembowski, Mary Ann; Georgiadis, Nicholas J.

2002-01-01

The WIND code, a Reynolds-averaged Navier-Stokes solver used for a variety of aerospace flow simulations, was investigated for a Mach 2 nozzle at a series of nozzle stagnation temperatures. Comparisons of WIND calculations are made to experimental measurements of axial velocity, Mach number, and stagnation temperature along the jet centerline. The primary objective was to investigate the capabilities of the two-equation turbulence models available in WIND, version 4.0, for the analysis of heated supersonic nozzle flows. The models examined were the Menter Shear Stress Transport (SST) model and the Chien k-epsilon model, with and without the compressibility correction due to Sarkar. It was observed that all of the turbulence models investigated produced solutions that did not agree well with the experimental measurements. The effects of freestream Mach number and turbulent Prandtl number specifications were also investigated.

Direct Numerical Simulation of Flows over an NACA-0012 Airfoil at Low and Moderate Reynolds Numbers

NASA Technical Reports Server (NTRS)

Balakumar, P.

2017-01-01

Direct numerical simulations (DNS) of flow over an NACA-0012 airfoil are performed at a low and a moderate Reynolds numbers of Re(sub c)=50 times10(exp 3) and 1times 10(exp 6). The angles of attack are 5 and 15 degrees at the low and the moderate Reynolds number cases respectively. The three-dimensional unsteady compressible Navier-Stokes equations are solved using higher order compact schemes. The flow field in the low Reynolds number case consists of a long separation bubble near the leading-edge region and an attached boundary layer on the aft part of the airfoil. The shear layer that formed in the separated region persisted up to the end of the airfoil. The roles of the turbulent diffusion, advection, and dissipation terms in the turbulent kinetic-energy balance equation change as the boundary layer evolves over the airfoil. In the higher Reynolds number case, the leading-edge separation bubble is very small in length and in height. A fully developed turbulent boundary layer is observed in a short distance downstream of the reattachment point. The boundary layer velocity near the wall gradually decreases along the airfoil. Eventually, the boundary layer separates near the trailing edge. The Reynolds stresses peak in the outer part of the boundary layer and the maximum amplitude also gradually increases along the chord.

Application of a Navier-Stokes Solver to the Analysis of Multielement Airfoils and Wings Using Multizonal Grid Techniques

NASA Technical Reports Server (NTRS)

Jones, Kenneth M.; Biedron, Robert T.; Whitlock, Mark

1995-01-01

A computational study was performed to determine the predictive capability of a Reynolds averaged Navier-Stokes code (CFL3D) for two-dimensional and three-dimensional multielement high-lift systems. Three configurations were analyzed: a three-element airfoil, a wing with a full span flap and a wing with a partial span flap. In order to accurately model these complex geometries, two different multizonal structured grid techniques were employed. For the airfoil and full span wing configurations, a chimera or overset grid technique was used. The results of the airfoil analysis illustrated that although the absolute values of lift were somewhat in error, the code was able to predict reasonably well the variation with Reynolds number and flap position. The full span flap analysis demonstrated good agreement with experimental surface pressure data over the wing and flap. Multiblock patched grids were used to model the partial span flap wing. A modification to an existing patched- grid algorithm was required to analyze the configuration as modeled. Comparisons with experimental data were very good, indicating the applicability of the patched-grid technique to analyses of these complex geometries.

Turbulence and deterministic chaos. [computational fluid dynamics

NASA Technical Reports Server (NTRS)

Deissler, Robert G.

1992-01-01

Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, largest Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low Reynolds number fully developed turbulence are compared. Several flows are noted: fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, only fully chaotic is classified as turbulent. Besides the sustained flows, a flow which decays as it becomes turbulent is examined. For the finest grid, 128(exp 3) points, the spatial resolution appears to be quite good. As a final note, the variation of the velocity derivatives skewness of a Navier-Stokes flow as the Reynolds number goes to zero is calculated numerically. The value of the skewness is shown to become small at low Reynolds numbers, in agreement with intuitive arguments that nonlinear terms should be negligible.

Investigation of laminar to turbulent transition phenomena effects on impingement heat transfer

NASA Astrophysics Data System (ADS)

Isman, Mustafa Kemal; Morris, Philip J.; Can, Muhiddin

2016-10-01

Turbulent impinging air flow is investigated numerically by using the ANSYS-CFX® code. All computations are performed by considering three-dimensional, steady, and incompressible flow. Three different Reynolds averaged Navier-Stokes (RANS) turbulence models and two Reynolds stress models (RSM's) are employed. Furthermore three different laminar to turbulent transition (LTT) models are employed with the shear stress transport (SST) and the baseline (BSL) models. Results show that predictions of the SST and two RSM's are very close each other and these models' results are in better agreement with the experimental data when all Reynolds numbers used in this study are considered. Secondary maxima in Nusselt number can be seen only if the LTT formula is employed with SST and BSL models.

A comparative study of turbulence models in predicting hypersonic inlet flows

NASA Technical Reports Server (NTRS)

Kapoor, Kamlesh

1993-01-01

A computational study has been conducted to evaluate the performance of various turbulence models. The NASA P8 inlet, which represents cruise condition of a typical hypersonic air-breathing vehicle, was selected as a test case for the study; the PARC2D code, which solves the full two dimensional Reynolds-averaged Navier-Stokes equations, was used. Results are presented for a total of six versions of zero- and two-equation turbulence models. Zero-equation models tested are the Baldwin-Lomax model, the Thomas model, and a combination of the two. Two-equation models tested are low-Reynolds number models (the Chien model and the Speziale model) and a high-Reynolds number model (the Launder and Spalding model).

Prediction of Very High Reynolds Number Compressible Skin Friction

NASA Technical Reports Server (NTRS)

Carlson, John R.

1998-01-01

Flat plate skin friction calculations over a range of Mach numbers from 0.4 to 3.5 at Reynolds numbers from 16 million to 492 million using a Navier Stokes method with advanced turbulence modeling are compared with incompressible skin friction coefficient correlations. The semi-empirical correlation theories of van Driest; Cope; Winkler and Cha; and Sommer and Short T' are used to transform the predicted skin friction coefficients of solutions using two algebraic Reynolds stress turbulence models in the Navier-Stokes method PAB3D. In general, the predicted skin friction coefficients scaled well with each reference temperature theory though, overall the theory by Sommer and Short appeared to best collapse the predicted coefficients. At the lower Reynolds number 3 to 30 million, both the Girimaji and Shih, Zhu and Lumley turbulence models predicted skin-friction coefficients within 2% of the semi-empirical correlation skin friction coefficients. At the higher Reynolds numbers of 100 to 500 million, the turbulence models by Shih, Zhu and Lumley and Girimaji predicted coefficients that were 6% less and 10% greater, respectively, than the semi-empirical coefficients.

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.

Large Eddy Simulation and Reynolds-Averaged Navier-Stokes modeling of flow in a realistic pharyngeal airway model: an investigation of obstructive sleep apnea.

PubMed

Mihaescu, Mihai; Murugappan, Shanmugam; Kalra, Maninder; Khosla, Sid; Gutmark, Ephraim

2008-07-19

Computational fluid dynamics techniques employing primarily steady Reynolds-Averaged Navier-Stokes (RANS) methodology have been recently used to characterize the transitional/turbulent flow field in human airways. The use of RANS implies that flow phenomena are averaged over time, the flow dynamics not being captured. Further, RANS uses two-equation turbulence models that are not adequate for predicting anisotropic flows, flows with high streamline curvature, or flows where separation occurs. A more accurate approach for such flow situations that occur in the human airway is Large Eddy Simulation (LES). The paper considers flow modeling in a pharyngeal airway model reconstructed from cross-sectional magnetic resonance scans of a patient with obstructive sleep apnea. The airway model is characterized by a maximum narrowing at the site of retropalatal pharynx. Two flow-modeling strategies are employed: steady RANS and the LES approach. In the RANS modeling framework both k-epsilon and k-omega turbulence models are used. The paper discusses the differences between the airflow characteristics obtained from the RANS and LES calculations. The largest discrepancies were found in the axial velocity distributions downstream of the minimum cross-sectional area. This region is characterized by flow separation and large radial velocity gradients across the developed shear layers. The largest difference in static pressure distributions on the airway walls was found between the LES and the k-epsilon data at the site of maximum narrowing in the retropalatal pharynx.

LES/RANS Simulation of a Supersonic Reacting Wall Jet

NASA Technical Reports Server (NTRS)

Edwards, Jack R.; Boles, John A.; Baurle, Robert A.

2010-01-01

This work presents results from large-eddy / Reynolds-averaged Navier-Stokes (LES/RANS) simulations of the well-known Burrows-Kurkov supersonic reacting wall-jet experiment. Generally good agreement with experimental mole fraction, stagnation temperature, and Pitot pressure profiles is obtained for non-reactive mixing of the hydrogen jet with a non-vitiated air stream. A lifted flame, stabilized between 10 and 22 cm downstream of the hydrogen jet, is formed for hydrogen injected into a vitiated air stream. Flame stabilization occurs closer to the hydrogen injection location when a three-dimensional combustor geometry (with boundary layer development resolved on all walls) is considered. Volumetric expansion of the reactive shear layer is accompanied by the formation of large eddies which interact strongly with the reaction zone. Time averaged predictions of the reaction zone structure show an under-prediction of the peak water concentration and stagnation temperature, relative to experimental data and to results from a Reynolds-averaged Navier-Stokes calculation. If the experimental data can be considered as being accurate, this result indicates that the present LES/RANS method does not correctly capture the cascade of turbulence scales that should be resolvable on the present mesh. Instead, energy is concentrated in the very largest scales, which provide an over-mixing effect that excessively cools and strains the flame. Predictions improve with the use of a low-dissipation version of the baseline piecewise parabolic advection scheme, which captures the formation of smaller-scale structures superimposed on larger structures of the order of the shear-layer width.

Numerical Prediction of Periodic Vortex Shedding in Subsonic and Transonic Turbine Cascade Flows

NASA Astrophysics Data System (ADS)

Mensink, C.

1996-05-01

Periodic vortex shedding at the trailing edge of a turbine cascade has been investigated numerically for a subsonic and a transonic cascade flow. The numerical investigation was carried out by a finite volume multiblock code, solving the 2D compressible Reynolds-averaged Navier-Stokes equations on a set of non-overlapping grid blocks that are connected in a conservative way. Comparisons are made with experimental results previously obtained by Sieverding and Heinemann.

Numerical Prediction of Non-Reacting and Reacting Flow in a Model Gas Turbine Combustor

NASA Technical Reports Server (NTRS)

Davoudzadeh, Farhad; Liu, Nan-Suey

2005-01-01

The three-dimensional, viscous, turbulent, reacting and non-reacting flow characteristics of a model gas turbine combustor operating on air/methane are simulated via an unstructured and massively parallel Reynolds-Averaged Navier-Stokes (RANS) code. This serves to demonstrate the capabilities of the code for design and analysis of real combustor engines. The effects of some design features of combustors are examined. In addition, the computed results are validated against experimental data.

Numerical Study Comparing RANS and LES Approaches on a Circulation Control Airfoil

NASA Technical Reports Server (NTRS)

Rumsey, Christopher L.; Nishino, Takafumi

2011-01-01

A numerical study over a nominally two-dimensional circulation control airfoil is performed using a large-eddy simulation code and two Reynolds-averaged Navier-Stokes codes. Different Coanda jet blowing conditions are investigated. In addition to investigating the influence of grid density, a comparison is made between incompressible and compressible flow solvers. The incompressible equations are found to yield negligible differences from the compressible equations up to at least a jet exit Mach number of 0.64. The effects of different turbulence models are also studied. Models that do not account for streamline curvature effects tend to predict jet separation from the Coanda surface too late, and can produce non-physical solutions at high blowing rates. Three different turbulence models that account for streamline curvature are compared with each other and with large eddy simulation solutions. All three models are found to predict the Coanda jet separation location reasonably well, but one of the models predicts specific flow field details near the Coanda surface prior to separation much better than the other two. All Reynolds-averaged Navier-Stokes computations produce higher circulation than large eddy simulation computations, with different stagnation point location and greater flow acceleration around the nose onto the upper surface. The precise reasons for the higher circulation are not clear, although it is not solely a function of predicting the jet separation location correctly.

A Priori Analysis of a Compressible Flamelet Model using RANS Data for a Dual-Mode Scramjet Combustor

NASA Technical Reports Server (NTRS)

Quinlan, Jesse R.; Drozda, Tomasz G.; McDaniel, James C.; Lacaze, Guilhem; Oefelein, Joseph

2015-01-01

In an effort to make large eddy simulation of hydrocarbon-fueled scramjet combustors more computationally accessible using realistic chemical reaction mechanisms, a compressible flamelet/progress variable (FPV) model was proposed that extends current FPV model formulations to high-speed, compressible flows. Development of this model relied on observations garnered from an a priori analysis of the Reynolds-Averaged Navier-Stokes (RANS) data obtained for the Hypersonic International Flight Research and Experimentation (HI-FiRE) dual-mode scramjet combustor. The RANS data were obtained using a reduced chemical mechanism for the combustion of a JP-7 surrogate and were validated using avail- able experimental data. These RANS data were then post-processed to obtain, in an a priori fashion, the scalar fields corresponding to an FPV-based modeling approach. In the current work, in addition to the proposed compressible flamelet model, a standard incompressible FPV model was also considered. Several candidate progress variables were investigated for their ability to recover static temperature and major and minor product species. The effects of pressure and temperature on the tabulated progress variable source term were characterized, and model coupling terms embedded in the Reynolds- averaged Navier-Stokes equations were studied. Finally, results for the novel compressible flamelet/progress variable model were presented to demonstrate the improvement attained by modeling the effects of pressure and flamelet boundary conditions on the combustion.

Reynolds-Averaged Navier-Stokes Simulations of Two Partial-Span Flap Wing Experiments

NASA Technical Reports Server (NTRS)

Takalluk, M. A.; Laflin, Kelly R.

1998-01-01

Structured Reynolds Averaged Navier-Stokes simulations of two partial-span flap wing experiments were performed. The high-lift aerodynamic and aeroacoustic wind-tunnel experiments were conducted at both the NASA Ames 7-by 10-Foot Wind Tunnel and at the NASA Langley Quiet Flow Facility. The purpose of these tests was to accurately document the acoustic and aerodynamic characteristics associated with the principle airframe noise sources, including flap side-edge noise. Specific measurements were taken that can be used to validate analytic and computational models of the noise sources and associated aerodynamic for configurations and conditions approximating flight for transport aircraft. The numerical results are used to both calibrate a widely used CFD code, CFL3D, and to obtain details of flap side-edge flow features not discernible from experimental observations. Both experimental set-ups were numerically modeled by using multiple block structured grids. Various turbulence models, grid block-interface interaction methods and grid topologies were implemented. Numerical results of both simulations are in excellent agreement with experimental measurements and flow visualization observations. The flow field in the flap-edge region was adequately resolved to discern some crucial information about the flow physics and to substantiate the merger of the two vortical structures. As a result of these investigations, airframe noise modelers have proposed various simplified models which use the results obtained from the steady-state computations as input.

A Comparative Analysis of Reynolds-Averaged Navier-Stokes Model Predictions for Rayleigh-Taylor Instability and Mixing with Constant and Complex Accelerations

NASA Astrophysics Data System (ADS)

Schilling, Oleg

2016-11-01

Two-, three- and four-equation, single-velocity, multicomponent Reynolds-averaged Navier-Stokes (RANS) models, based on the turbulent kinetic energy dissipation rate or lengthscale, are used to simulate At = 0 . 5 Rayleigh-Taylor turbulent mixing with constant and complex accelerations. The constant acceleration case is inspired by the Cabot and Cook (2006) DNS, and the complex acceleration cases are inspired by the unstable/stable and unstable/neutral cases simulated using DNS (Livescu, Wei & Petersen 2011) and the unstable/stable/unstable case simulated using ILES (Ramaprabhu, Karkhanis & Lawrie 2013). The four-equation models couple equations for the mass flux a and negative density-specific volume correlation b to the K- ɛ or K- L equations, while the three-equation models use a two-fluid algebraic closure for b. The lengthscale-based models are also applied with no buoyancy production in the L equation to explore the consequences of neglecting this term. Predicted mixing widths, turbulence statistics, fields, and turbulent transport equation budgets are compared among these models to identify similarities and differences in the turbulence production, dissipation and diffusion physics represented by the closures used in these models. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Active Aerodynamic Load Reduction on a Rotorcraft Fuselage With Rotor Effects: A CFD Validation Effort

NASA Technical Reports Server (NTRS)

Allan, Brian G.; Schaeffler, Norman W.; Jenkins, Luther N.; Yao, Chung-Sheng; Wong, Oliver D.; Tanner, Philip E.

2015-01-01

A rotorcraft fuselage is typically designed with an emphasis on operational functionality with aerodynamic efficiency being of secondary importance. This results in a significant amount of drag during high-speed forward flight that can be a limiting factor for future high-speed rotorcraft designs. To enable higher speed flight, while maintaining a functional fuselage design (i.e., a large rear cargo ramp door), the NASA Rotary Wing Project has conducted both experimental and computational investigations to assess active flow control as an enabling technology for fuselage drag reduction. This paper will evaluate numerical simulations of a flow control system on a generic rotorcraft fuselage with a rotor in forward flight using OVERFLOW, a structured mesh Reynolds-averaged Navier-Stokes flow solver developed at NASA. The results are compared to fuselage forces, surface pressures, and PN flow field data obtained in a wind tunnel experiment conducted at the NASA Langley 14-by 22-Foot Subsonic Tunnel where significant drag and download reductions were demonstrated using flow control. This comparison showed that the Reynolds-averaged Navier-Stokes flow solver was unable to predict the fuselage forces and pressure measurements on the ramp for the baseline and flow control cases. While the CFD was able to capture the flow features, it was unable to accurately predict the performance of the flow control.

Textbook Multigrid Efficiency for Computational Fluid Dynamics Simulations

NASA Technical Reports Server (NTRS)

Brandt, Achi; Thomas, James L.; Diskin, Boris

2001-01-01

Considerable progress over the past thirty years has been made in the development of large-scale computational fluid dynamics (CFD) solvers for the Euler and Navier-Stokes equations. Computations are used routinely to design the cruise shapes of transport aircraft through complex-geometry simulations involving the solution of 25-100 million equations; in this arena the number of wind-tunnel tests for a new design has been substantially reduced. However, simulations of the entire flight envelope of the vehicle, including maximum lift, buffet onset, flutter, and control effectiveness have not been as successful in eliminating the reliance on wind-tunnel testing. These simulations involve unsteady flows with more separation and stronger shock waves than at cruise. The main reasons limiting further inroads of CFD into the design process are: (1) the reliability of turbulence models; and (2) the time and expense of the numerical simulation. Because of the prohibitive resolution requirements of direct simulations at high Reynolds numbers, transition and turbulence modeling is expected to remain an issue for the near term. The focus of this paper addresses the latter problem by attempting to attain optimal efficiencies in solving the governing equations. Typically current CFD codes based on the use of multigrid acceleration techniques and multistage Runge-Kutta time-stepping schemes are able to converge lift and drag values for cruise configurations within approximately 1000 residual evaluations. An optimally convergent method is defined as having textbook multigrid efficiency (TME), meaning the solutions to the governing system of equations are attained in a computational work which is a small (less than 10) multiple of the operation count in the discretized system of equations (residual equations). In this paper, a distributed relaxation approach to achieving TME for Reynolds-averaged Navier-Stokes (RNAS) equations are discussed along with the foundations that form the basis of this approach. Because the governing equations are a set of coupled nonlinear conservation equations with discontinuities (shocks, slip lines, etc.) and singularities (flow- or grid-induced), the difficulties are many. This paper summarizes recent progress towards the attainment of TME in basic CFD simulations.

Upscaling the Navier-Stokes Equation for Turbulent Flows in Porous Media Using a Volume Averaging Method

NASA Astrophysics Data System (ADS)

Wood, Brian; He, Xiaoliang; Apte, Sourabh

2017-11-01

Turbulent flows through porous media are encountered in a number of natural and engineered systems. Many attempts to close the Navier-Stokes equation for such type of flow have been made, for example using RANS models and double averaging. On the other hand, Whitaker (1996) applied volume averaging theorem to close the macroscopic N-S equation for low Re flow. In this work, the volume averaging theory is extended into the turbulent flow regime to posit a relationship between the macroscale velocities and the spatial velocity statistics in terms of the spatial averaged velocity only. Rather than developing a Reynolds stress model, we propose a simple algebraic closure, consistent with generalized effective viscosity models (Pope 1975), to represent the spatial fluctuating velocity and pressure respectively. The coefficients (one 1st order, two 2nd order and one 3rd order tensor) of the linear functions depend on averaged velocity and gradient. With the data set from DNS, performed with inertial and turbulent flows (pore Re of 300, 500 and 1000) through a periodic face centered cubic (FCC) unit cell, all the unknown coefficients can be computed and the closure is complete. The macroscopic quantity calculated from the averaging is then compared with DNS data to verify the upscaling. NSF Project Numbers 1336983, 1133363.

Use of DNS Data for the Evaluation of Closure Models for Rotating Turbulent Channel Flow

NASA Astrophysics Data System (ADS)

Hsieh, Alan; Biringen, Sedat; Kucala, Alec

2013-11-01

A direct numerical simulation (DNS) of a turbulent channel flow rotating about the spanwise axis was conducted at a Reynolds number (based on the centerline velocity and channel half height) 8000, Prandtl number 0.71, and Rossby number 26. Several Reynolds-Averaged Navier-Stokes (RANS) based turbulence models for rotating flows were analyzed and tested. It was shown that the closure approximations in the pressure-strain correlation term proposed by the Speziale, Sarkar, and Gatski (SSG) RSM model were more accurate than the Girimaji EARSM model. The Reynolds stresses, primarily the shear stresses, produced by the Girimaji model were compared to the DNS data and revealed an evident discontinuity in the modeled Reynolds stress profiles; consequently, a smoothing function was generated and applied as a correction so that there is significantly better agreement between the Reynolds shear stress profiles produced by the DNS data and the modified Girimaji model.

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Jothiprasad, Giridhar; Mavriplis, Dimitri J.; Caughey, David A.

2002-01-01

The rapid increase in available computational power over the last decade has enabled higher resolution flow simulations and more widespread use of unstructured grid methods for complex geometries. While much of this effort has been focused on steady-state calculations in the aerodynamics community, the need to accurately predict off-design conditions, which may involve substantial amounts of flow separation, points to the need to efficiently simulate unsteady flow fields. Accurate unsteady flow simulations can easily require several orders of magnitude more computational effort than a corresponding steady-state simulation. For this reason, techniques for improving the efficiency of unsteady flow simulations are required in order to make such calculations feasible in the foreseeable future. The purpose of this work is to investigate possible reductions in computer time due to the choice of an efficient time-integration scheme from a series of schemes differing in the order of time-accuracy, and by the use of more efficient techniques to solve the nonlinear equations which arise while using implicit time-integration schemes. This investigation is carried out in the context of a two-dimensional unstructured mesh laminar Navier-Stokes solver.

High-resolution multi-code implementation of unsteady Navier-Stokes flow solver based on paralleled overset adaptive mesh refinement and high-order low-dissipation hybrid schemes

NASA Astrophysics Data System (ADS)

Li, Gaohua; Fu, Xiang; Wang, Fuxin

2017-10-01

The low-dissipation high-order accurate hybrid up-winding/central scheme based on fifth-order weighted essentially non-oscillatory (WENO) and sixth-order central schemes, along with the Spalart-Allmaras (SA)-based delayed detached eddy simulation (DDES) turbulence model, and the flow feature-based adaptive mesh refinement (AMR), are implemented into a dual-mesh overset grid infrastructure with parallel computing capabilities, for the purpose of simulating vortex-dominated unsteady detached wake flows with high spatial resolutions. The overset grid assembly (OGA) process based on collection detection theory and implicit hole-cutting algorithm achieves an automatic coupling for the near-body and off-body solvers, and the error-and-try method is used for obtaining a globally balanced load distribution among the composed multiple codes. The results of flows over high Reynolds cylinder and two-bladed helicopter rotor show that the combination of high-order hybrid scheme, advanced turbulence model, and overset adaptive mesh refinement can effectively enhance the spatial resolution for the simulation of turbulent wake eddies.

On a modified form of navier-stokes equations for three-dimensional flows.

PubMed

Venetis, J

2015-01-01

A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces.

On a Modified Form of Navier-Stokes Equations for Three-Dimensional Flows

PubMed Central

Venetis, J.

2015-01-01

A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces. PMID:25918743

A three dimensional multigrid multiblock multistage time stepping scheme for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Elmiligui, Alaa; Cannizzaro, Frank; Melson, N. D.

1991-01-01

A general multiblock method for the solution of the three-dimensional, unsteady, compressible, thin-layer Navier-Stokes equations has been developed. The convective and pressure terms are spatially discretized using Roe's flux differencing technique while the viscous terms are centrally differenced. An explicit Runge-Kutta method is used to advance the solution in time. Local time stepping, adaptive implicit residual smoothing, and the Full Approximation Storage (FAS) multigrid scheme are added to the explicit time stepping scheme to accelerate convergence to steady state. Results for three-dimensional test cases are presented and discussed.

Transient Performance of a Vertical Axis Wind Turbine

NASA Astrophysics Data System (ADS)

Onol, Aykut; Yesilyurt, Serhat

2016-11-01

A coupled CFD/rotor dynamics modeling approach is presented for the analysis of realistic transient behavior of a height-normalized, three-straight-bladed VAWT subject to inertial effects of the rotor and generator load which is manipulated by a feedback control under standardized wind gusts. The model employs the k- ɛ turbulence model to approximate unsteady Reynolds-averaged Navier-Stokes equations and is validated with data from field measurements. As distinct from related studies, here, the angular velocity is calculated from the rotor's equation of motion; thus, the dynamic response of the rotor is taken into account. Results include the following: First, the rotor's inertia filters large amplitude oscillations in the wind torque owing to the first-order dynamics. Second, the generator and wind torques differ especially during wind transients subject to the conservation of angular momentum of the rotor. Third, oscillations of the power coefficient exceed the Betz limit temporarily due to the energy storage in the rotor, which acts as a temporary buffer that stores the kinetic energy like a flywheel in short durations. Last, average of transient power coefficients peaks at a smaller tip-speed ratio for wind gusts than steady winds. This work was supported by the Sabanci University Internal Research Grant Program (SU-IRG-985).

Aeroacoustic Simulations of a Nose Landing Gear with FUN3D: A Grid Refinement Study

NASA Technical Reports Server (NTRS)

Vatsa, Veer N.; Khorrami, Mehdi R.; Lockard, David P.

2017-01-01

A systematic grid refinement study is presented for numerical simulations of a partially-dressed, cavity-closed (PDCC) nose landing gear configuration that was tested in the University of Florida's open-jet acoustic facility known as the UFAFF. The unstructured-grid flow solver FUN3D is used to compute the unsteady flow field for this configuration. Mixed-element grids generated using the Pointwise (Registered Trademark) grid generation software are used for numerical simulations. Particular care is taken to ensure quality cells and proper resolution in critical areas of interest in an effort to minimize errors introduced by numerical artifacts. A set of grids was generated in this manner to create a family of uniformly refined grids. The finest grid was then modified to coarsen the wall-normal spacing to create a grid suitable for the wall-function implementation in FUN3D code. A hybrid Reynolds-averaged Navier-Stokes/large eddy simulation (RANS/LES) turbulence modeling approach is used for these simulations. Time-averaged and instantaneous solutions obtained on these grids are compared with the measured data. These CFD solutions are used as input to a FfowcsWilliams-Hawkings (FW-H) noise propagation code to compute the farfield noise levels. The agreement of the computed results with the experimental data improves as the grid is refined.

Aeroacoustic Simulation of Nose Landing Gear on Adaptive Unstructured Grids With FUN3D

NASA Technical Reports Server (NTRS)

Vatsa, Veer N.; Khorrami, Mehdi R.; Park, Michael A.; Lockard, David P.

2013-01-01

Numerical simulations have been performed for a partially-dressed, cavity-closed nose landing gear configuration that was tested in NASA Langley s closed-wall Basic Aerodynamic Research Tunnel (BART) and in the University of Florida's open-jet acoustic facility known as the UFAFF. The unstructured-grid flow solver FUN3D, developed at NASA Langley Research center, is used to compute the unsteady flow field for this configuration. Starting with a coarse grid, a series of successively finer grids were generated using the adaptive gridding methodology available in the FUN3D code. A hybrid Reynolds-averaged Navier-Stokes/large eddy simulation (RANS/LES) turbulence model is used for these computations. Time-averaged and instantaneous solutions obtained on these grids are compared with the measured data. In general, the correlation with the experimental data improves with grid refinement. A similar trend is observed for sound pressure levels obtained by using these CFD solutions as input to a FfowcsWilliams-Hawkings noise propagation code to compute the farfield noise levels. In general, the numerical solutions obtained on adapted grids compare well with the hand-tuned enriched fine grid solutions and experimental data. In addition, the grid adaption strategy discussed here simplifies the grid generation process, and results in improved computational efficiency of CFD simulations.

Analogy between the Navier-Stokes equations and Maxwell's equations: Application to turbulence

NASA Astrophysics Data System (ADS)

Marmanis, Haralambos

1998-06-01

A new theory of turbulence is initiated, based on the analogy between electromagnetism and turbulent hydrodynamics, for the purpose of describing the dynamical behavior of averaged flow quantities in incompressible fluid flows of high Reynolds numbers. The starting point is the recognition that the vorticity (w=∇×u) and the Lamb vector (l=w×u) should be taken as the kernel of a dynamical theory of turbulence. The governing equations for these fields can be obtained by the Navier-Stokes equations, which underlie the whole evolution. Then whatever parts are not explicitly expressed as a function of w or l only are gathered and treated as source terms. This is done by introducing the concepts of turbulent charge and turbulent current. Thus we are led to a closed set of linear equations for the averaged field quantities. The premise is that the earlier introduced sources will be apt for modeling, in the sense that their distribution will depend only on the geometry and the total energetics of the flow. The dynamics described in the preceding manner is what we call the metafluid dynamics.

Navier-Stokes relaxation to sinh-Poisson states at finite Reynolds numbers

NASA Technical Reports Server (NTRS)

Montgomery, David; Shan, Xiaowen; Matthaeus, William H.

1993-01-01

A mathematical framework is proposed in which it seems possible to justify the computationally-observed relaxation of a two-dimensional Navier-Stokes fluid to a 'most probable', or maximum entropy, state. The relaxation occurs at large but finite Reynolds numbers, and involves substantial decay of higher-order ideal invariants such as enstrophy. A two-fluid formulation, involving interpenetrating positive and negative vorticity fluxes (continuous and square integrable) is developed, and is shown to be intimately related to the passive scalar decay problem. Increasing interpenetration of the two fluids corresponds to the decay of vorticity flux due to viscosity. It is demonstrated numerically that, in two dimensions, passive scalars decay rapidly, relative to mean-square vorticity (enstrophy). This observation provides a basis for assigning initial data to the two-fluid field variables.

Navier-Stokes Flow Past a Rigid Body: Attainability of Steady Solutions as Limits of Unsteady Weak Solutions, Starting and Landing Cases

NASA Astrophysics Data System (ADS)

Hishida, Toshiaki; Maremonti, Paolo

2017-11-01

Consider the Navier-Stokes flow in 3-dimensional exterior domains, where a rigid body is translating with prescribed translational velocity - h(t)u_∞ with constant vector u_∞ \\in R^3{\\setminus }{0}. Finn raised the question whether his steady solutions are attainable as limits for t→ ∞ of unsteady solutions starting from motionless state when h(t)=1 after some finite time and h(0)=0 (starting problem). This was affirmatively solved by Galdi et al. (Arch Ration Mech Anal 138:307-318, 1997) for small u_∞. We study some generalized situation in which unsteady solutions start from large motions being in L^3 . We then conclude that the steady solutions for small u_∞ are still attainable as limits of evolution of those fluid motions which are found as a sort of weak solutions. The opposite situation, in which h(t)=0 after some finite time and h(0)=1 (landing problem), is also discussed. In this latter case, the rest state is attainable no matter how large u_∞ is.

Navier-Stokes Flow Past a Rigid Body: Attainability of Steady Solutions as Limits of Unsteady Weak Solutions, Starting and Landing Cases

NASA Astrophysics Data System (ADS)

Hishida, Toshiaki; Maremonti, Paolo

2018-06-01

Consider the Navier-Stokes flow in 3-dimensional exterior domains, where a rigid body is translating with prescribed translational velocity - h(t)u_∞ with constant vector u_∞ \\in R^3{\\setminus }{0}. Finn raised the question whether his steady solutions are attainable as limits for t→ ∞ of unsteady solutions starting from motionless state when h(t)=1 after some finite time and h(0)=0 (starting problem). This was affirmatively solved by Galdi et al. (Arch Ration Mech Anal 138:307-318, 1997) for small u_∞. We study some generalized situation in which unsteady solutions start from large motions being in L^3. We then conclude that the steady solutions for small u_∞ are still attainable as limits of evolution of those fluid motions which are found as a sort of weak solutions. The opposite situation, in which h(t)=0 after some finite time and h(0)=1 (landing problem), is also discussed. In this latter case, the rest state is attainable no matter how large u_∞ is.

An ODE-Based Wall Model for Turbulent Flow Simulations

NASA Technical Reports Server (NTRS)

Berger, Marsha J.; Aftosmis, Michael J.

2017-01-01

Fully automated meshing for Reynolds-Averaged Navier-Stokes Simulations, Mesh generation for complex geometry continues to be the biggest bottleneck in the RANS simulation process; Fully automated Cartesian methods routinely used for inviscid simulations about arbitrarily complex geometry; These methods lack of an obvious & robust way to achieve near wall anisotropy; Goal: Extend these methods for RANS simulation without sacrificing automation, at an affordable cost; Note: Nothing here is limited to Cartesian methods, and much becomes simpler in a body-fitted setting.

Exhaust plumes and their interaction with missile airframes - A new viewpoint

NASA Technical Reports Server (NTRS)

Dash, S. M.; Sinha, N.

1992-01-01

The present, novel treatment of missile airframe-exhaust plume interactions emphasizes their simulation via a formal solution of the Reynolds-averaged Navier-Stokes (RNS) equation and is accordingly able to address the simulation requirements of novel missiles with nonconventional/integrated propulsion systems. The method is made possible by implicit RNS codes with improved artificial dissipation models, generalized geometric capabilities, and improved two-equation turbulence models, as well as by such codes' recent incorporation of plume thermochemistry and multiphase flow effects.

Aeroelastic Analysis of a Distributed Electric Propulsion Wing

NASA Technical Reports Server (NTRS)

Massey, Steven J.; Stanford, Bret K.; Wieseman, Carol D.; Heeg, Jennifer

2017-01-01

An aeroelastic analysis of a prototype distributed electric propulsion wing is presented. Results using MSC Nastran (Registered Trademark) doublet lattice aerodynamics are compared to those based on FUN3D Reynolds Averaged Navier- Stokes aerodynamics. Four levels of grid refinement were examined for the FUN3D solutions and solutions were seen to be well converged. It was found that no oscillatory instability existed, only that of divergence, which occurred in the first bending mode at a dynamic pressure of over three times the flutter clearance condition.

Computational Aeroacoustic Analysis of Slat Trailing-Edge Flow

NASA Technical Reports Server (NTRS)

Singer, Bart A.; Lockard, David P.; Brentner, Kenneth S.; Khorrami, Mehdi R.; Berkman, Mert E.; Choudhari, Meelan

2000-01-01

An acoustic analysis based on the Ffowcs Williams and Hawkings equation was performed for a high-lift system. As input, the acoustic analysis used un- steady flow data obtained from a highly resolved, time-dependent, Reynolds-averaged Navier-Stokes calculation. The analysis strongly suggests that vor- tex shedding from the trailing edge of the slat results in a high-amplitude, high-frequency acoustic signal, similar to that which was observed in a correspond- ing experimental study of the high-lift system.

Budget of Turbulent Kinetic Energy in a Shock Wave Boundary-Layer Interaction

NASA Technical Reports Server (NTRS)

Vyas, Manan; Waindim, Mbu; Gaitonde, Datta

2016-01-01

Implicit large-eddy simulation (ILES) of a shock wave boundary-layer interaction (SBLI) was performed. Quantities present in the exact equation of the turbulent kinetic energy (TKE) transport were accumulated. These quantities will be used to calculate the components of TKE-like production, dissipation, transport, and dilatation. Correlations of these terms will be presented to study the growth and interaction between various terms. A comparison with its RANS (Reynolds-Averaged Navier-Stokes) counterpart will also be presented.

Viscous Incompressible Flow Computations for 3-D Steady and Unsteady Flows

NASA Technical Reports Server (NTRS)

Kwak, Dochan

2001-01-01

This viewgraph presentation gives an overview of viscous incompressible flow computations for three-dimensional steady and unsteady flows. Details are given on the use of computational fluid dynamics (CFD) as an engineering tool, solution methods for incompressible Navier-Stokes equations, numerical and physical characteristics of the primitive variable approach, and the role of CFD in the past and in current engineering and research applications.

Finite length Taylor Couette flow

NASA Technical Reports Server (NTRS)

Streett, C. L.; Hussaini, M. Y.

1987-01-01

Axisymmetric numerical solutions of the unsteady Navier-Stokes equations for flow between concentric rotating cylinders of finite length are obtained by a spectral collocation method. These representative results pertain to two-cell/one-cell exchange process, and are compared with recent experiments.

Unsteady, Transonic Flow Around Delta Wings Undergoing Coupled and Natural Modes Response: A Multidisciplinary Problem

NASA Technical Reports Server (NTRS)

Menzies, Margaret Anne

1996-01-01

The unsteady, three-dimensional Navier-Stokes equations coupled with the Euler equations of rigid-body dynamics are sequentially solved to simulate and analyze the aerodynamic response of a high angle of attack delta wing undergoing oscillatory motion. The governing equations of fluid flow and dynamics of the multidisciplinary problem are solved using a time-accurate solution of the laminar, unsteady, compressible, full Navier- Stokes equations with the implicit, upwind, Roe flux-difference splitting, finite-volume scheme and a four-stage Runge-Kutta scheme, respectively. The primary model under consideration consists of a 65 deg swept, sharp-edged, cropped delta wing of zero thickness at 20 deg angle of attack. In a freestream of Mach 0.85 and Reynolds number of 3.23 x 10(exp 6), the flow over the upper surface of the wing develops a complex shock system which interacts with the leading-edge primary vortices producing vortex breakdown. The effect of the oscillatory motion of the wing on the vortex breakdown and overall aerodynamic response is detailed to provide insight to the complicated physics associated with unsteady flows and the phenomenon of wing rock. Forced sinusoidal single and coupled mode rolling and pitching motion is presented for the wing in a transonic freestream. The Reynolds number, frequency of oscillation, and the phase angle are varied. Comparison between the single and coupled mode forced rolling and pitching oscillation cases illustrate the effects of coupling the motion. This investigation shows that even when coupled, forced rolling oscillation at a reduced frequency of 2(pi) eliminates the vortex breakdown which results in an increase in lift. The coupling effect for in phase forced oscillations show that the lift coefficient of the pitching-alone case and the rolling-moment coefficient of the rolling-alone case dominate the resulting response. However, with a phase lead in the pitching motion, the coupled motion results in a non-periodic response of the rolling moment. The second class of problems involve releasing the wing in roll to respond to the flowfield. Two models of sharp-edged delta wings, the previous 65 deg swept model and an 80 deg swept, sharp-edged delta wing, are used to observe the aerodynamic response of a wing free to roll in a transonic and subsonic freestream, respectively. These cases demonstrate damped oscillations, self-sustained limit cycle oscillations, and divergent rolling oscillations. Ultimately, an active control model using a mass injection system was applied on the surface of the wing to suppress the self-sustained limit cycle oscillation known as wing rock. Comparisons with experimental investigations complete this study, validating the analysis and illustrating the complex details afforded by computational investigations.

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.

Inlet Development for a Rocket Based Combined Cycle, Single Stage to Orbit Vehicle Using Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

DeBonis, J. R.; Trefny, C. J.; Steffen, C. J., Jr.

1999-01-01

Design and analysis of the inlet for a rocket based combined cycle engine is discussed. Computational fluid dynamics was used in both the design and subsequent analysis. Reynolds averaged Navier-Stokes simulations were performed using both perfect gas and real gas assumptions. An inlet design that operates over the required Mach number range from 0 to 12 was produced. Performance data for cycle analysis was post processed using a stream thrust averaging technique. A detailed performance database for cycle analysis is presented. The effect ot vehicle forebody compression on air capture is also examined.

Comprehensive Approaches to Multiphase Flows in Geophysics - Application to nonisothermal, nonhomogenous, unsteady, large-scale, turbulent dusty clouds I. Hydrodynamic and Thermodynamic RANS and LES Models

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

S. Dartevelle

2005-09-05

The objective of this manuscript is to fully derive a geophysical multiphase model able to ''accommodate'' different multiphase turbulence approaches; viz., the Reynolds Averaged Navier-Stokes (RANS), the Large Eddy Simulation (LES), or hybrid RANSLES. This manuscript is the first part of a larger geophysical multiphase project--lead by LANL--that aims to develop comprehensive modeling tools for large-scale, atmospheric, transient-buoyancy dusty jets and plume (e.g., plinian clouds, nuclear ''mushrooms'', ''supercell'' forest fire plumes) and for boundary-dominated geophysical multiphase gravity currents (e.g., dusty surges, diluted pyroclastic flows, dusty gravity currents in street canyons). LES is a partially deterministic approach constructed on either amore » spatial- or a temporal-separation between the large and small scales of the flow, whereas RANS is an entirely probabilistic approach constructed on a statistical separation between an ensemble-averaged mean and higher-order statistical moments (the so-called ''fluctuating parts''). Within this specific multiphase context, both turbulence approaches are built up upon the same phasic binary-valued ''function of presence''. This function of presence formally describes the occurrence--or not--of any phase at a given position and time and, therefore, allows to derive the same basic multiphase Navier-Stokes model for either the RANS or the LES frameworks. The only differences between these turbulence frameworks are the closures for the various ''turbulence'' terms involving the unknown variables from the fluctuating (RANS) or from the subgrid (LES) parts. Even though the hydrodynamic and thermodynamic models for RANS and LES have the same set of Partial Differential Equations, the physical interpretations of these PDEs cannot be the same, i.e., RANS models an averaged field, while LES simulates a filtered field. In this manuscript, we also demonstrate that this multiphase model fully fulfills the second law of thermodynamics and fulfills the necessary requirements for a well-posed initial-value problem. In the next manuscripts, we will further develop specific closures for multiphase RANS, LES, and hybrid-LES.« less

Multi-fluid Dynamics for Supersonic Jet-and-Crossflows and Liquid Plug Rupture

NASA Astrophysics Data System (ADS)

Hassan, Ezeldin A.

Multi-fluid dynamics simulations require appropriate numerical treatments based on the main flow characteristics, such as flow speed, turbulence, thermodynamic state, and time and length scales. In this thesis, two distinct problems are investigated: supersonic jet and crossflow interactions; and liquid plug propagation and rupture in an airway. Gaseous non-reactive ethylene jet and air crossflow simulation represents essential physics for fuel injection in SCRAMJET engines. The regime is highly unsteady, involving shocks, turbulent mixing, and large-scale vortical structures. An eddy-viscosity-based multi-scale turbulence model is proposed to resolve turbulent structures consistent with grid resolution and turbulence length scales. Predictions of the time-averaged fuel concentration from the multi-scale model is improved over Reynolds-averaged Navier-Stokes models originally derived from stationary flow. The response to the multi-scale model alone is, however, limited, in cases where the vortical structures are small and scattered thus requiring prohibitively expensive grids in order to resolve the flow field accurately. Statistical information related to turbulent fluctuations is utilized to estimate an effective turbulent Schmidt number, which is shown to be highly varying in space. Accordingly, an adaptive turbulent Schmidt number approach is proposed, by allowing the resolved field to adaptively influence the value of turbulent Schmidt number in the multi-scale turbulence model. The proposed model estimates a time-averaged turbulent Schmidt number adapted to the computed flowfield, instead of the constant value common to the eddy-viscosity-based Navier-Stokes models. This approach is assessed using a grid-refinement study for the normal injection case, and tested with 30 degree injection, showing improved results over the constant turbulent Schmidt model both in mean and variance of fuel concentration predictions. For the incompressible liquid plug propagation and rupture study, numerical simulations are conducted using an Eulerian-Lagrangian approach with a continuous-interface method. A reconstruction scheme is developed to allow topological changes during plug rupture by altering the connectivity information of the interface mesh. Rupture time is shown to be delayed as the initial precursor film thickness increases. During the plug rupture process, a sudden increase of mechanical stresses on the tube wall is recorded, which can cause tissue damage.

Assessment of the Partially Resolved Numerical Simulation (PRNS) Approach in the National Combustion Code (NCC) for Turbulent Nonreacting and Reacting Flows

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Liu, Nan-Suey

2008-01-01

This paper describes an approach which aims at bridging the gap between the traditional Reynolds-averaged Navier-Stokes (RANS) approach and the traditional large eddy simulation (LES) approach. It has the characteristics of the very large eddy simulation (VLES) and we call this approach the partially-resolved numerical simulation (PRNS). Systematic simulations using the National Combustion Code (NCC) have been carried out for fully developed turbulent pipe flows at different Reynolds numbers to evaluate the PRNS approach. Also presented are the sample results of two demonstration cases: nonreacting flow in a single injector flame tube and reacting flow in a Lean Direct Injection (LDI) hydrogen combustor.

Computations of Combustion-Powered Actuation for Dynamic Stall Suppression

NASA Technical Reports Server (NTRS)

Jee, Solkeun; Bowles, Patrick O.; Matalanis, Claude G.; Min, Byung-Young; Wake, Brian E.; Crittenden, Tom; Glezer, Ari

2016-01-01

A computational framework for the simulation of dynamic stall suppression with combustion-powered actuation (COMPACT) is validated against wind tunnel experimental results on a VR-12 airfoil. COMPACT slots are located at 10% chord from the leading edge of the airfoil and directed tangentially along the suction-side surface. Helicopter rotor-relevant flow conditions are used in the study. A computationally efficient two-dimensional approach, based on unsteady Reynolds-averaged Navier-Stokes (RANS), is compared in detail against the baseline and the modified airfoil with COMPACT, using aerodynamic forces, pressure profiles, and flow-field data. The two-dimensional RANS approach predicts baseline static and dynamic stall very well. Most of the differences between the computational and experimental results are within two standard deviations of the experimental data. The current framework demonstrates an ability to predict COMPACT efficacy across the experimental dataset. Enhanced aerodynamic lift on the downstroke of the pitching cycle due to COMPACT is well predicted, and the cycleaveraged lift enhancement computed is within 3% of the test data. Differences with experimental data are discussed with a focus on three-dimensional features not included in the simulations and the limited computational model for COMPACT.

Pressure pulsation in Kaplan turbines: Prototype-CFD comparison

NASA Astrophysics Data System (ADS)

Rivetti, A.; Lucino1, C.; Liscia, S.; Muguerza, D.; Avellan, F.

2012-11-01

Pressure pulsation phenomena in a large Kaplan turbine are investigated by means of numerical simulations (CFD) and prototype measurements in order to study the dynamic behavior of flow due to the blade passage and its interaction with other components of the turbine. Numerical simulations are performed with the commercial software Ansys CFX code, solving the incompressible Unsteady Reynolds-Averaged-Navier Stokes equations under a finite volume scheme. The computational domain involves the entire machine at prototype scale. Special care is taken in the discretization of the wicket gate overhang and runner blade gap. Prototype measurements are performed using pressure transducers at different locations among the wicket gate outlet and the draft tube inlet. Then, CFD results are compared with temporary signals of prototype measurements at identical locations to validate the numerical model. A detailed analysis was focused on the tip gap flow and the pressure field at the discharge ring. From a rotating reference frame perspective, it is found that the mean pressure fluctuates accordingly the wicket gate passage. Moreover, in prototype measurements the pressure frequency that reveals the presence of modulated cavitation at the discharge ring is distinguished, as also verified from the shape of erosion patches in concordance with the number of wicket gates.

Design of Shrouded Airborne Wind Turbine & CFD Analysis

NASA Astrophysics Data System (ADS)

Anbreen, Faiqa; Faiqa Anbreen Collaboration

2015-11-01

The focus is to design a shrouded airborne wind turbine, capable to generate 70 kW to propel a leisure boat. The idea of designing an airborne turbine is to take the advantage of different velocity layers in the atmosphere. The blades have been designed using NREL S826 airfoil, which has coefficient of lift CL of 1.4 at angle of attack, 6°. The value selected for CP is 0.8. The rotor diameter is 7.4 m. The balloon (shroud) has converging-diverging nozzle design, to increase the mass flow rate through the rotor. The ratio of inlet area to throat area, Ai/At is 1.31 and exit area to throat area, Ae/At is1.15. The Solidworks model has been analyzed numerically using CFD. The software used is StarCCM +. The Unsteady Reynolds Averaged Navier Stokes Simulation (URANS) K- ɛ model has been selected, to study the physical properties of the flow, with emphasis on the performance of the turbine. Stress analysis has been done using Nastran. From the simulations, the torque generated by the turbine is approximately 800N-m and angular velocity is 21 rad/s.

The effect of undulating leading-edge modifications on NACA 0021 airfoil characteristics

NASA Astrophysics Data System (ADS)

Rostamzadeh, N.; Kelso, R. M.; Dally, B. B.; Hansen, K. L.

2013-11-01

In spite of its mammoth physical size, the humpback whale's manoeuvrability in hunting has captured the attention of biologists as well as fluid mechanists. It has now been established that the protrusions on the leading-edges of the humpback's pectoral flippers, known as tubercles, account for this species' agility and manoeuvrability. In the present work, Prandtl's nonlinear lifting-line theory was employed to propose a hypothesis that the favourable traits observed in the performance of tubercled lifting bodies are not exclusive to this form of leading-edge configuration. Accordingly, a novel alternative to tubercles was introduced and incorporated into the design of four airfoils that underwent wind tunnel force and pressure measurement tests in the transitional flow regime. In addition, a Computation Fluid Dynamics study was performed using the Shear Stress Transport transitional model in the context of unsteady Reynolds-Averaged Navier-Stokes at several attack angles. The results from the numerical investigation are in reasonable agreement with those of the experiments, and suggest the presence of features that are also observed in flows over tubercled foils, most notably a distinct pair of streamwise vortices for each wavelength of the tubercle-like feature.

Numerical Study of Winter Diurnal Convection Over the City of Krasnoyarsk: Effects of Non-freezing River, Undulating Fog and Steam Devils

NASA Astrophysics Data System (ADS)

Hrebtov, M.; Hanjalić, K.

2017-06-01

We performed a numerical simulation of penetrative convection of an inversion-topped weakly stratified atmospheric boundary layer over urban terrain with a strong localized source of heat and moisture. With some simplifications, the case mimics the real environment of the Krasnoyarsk region in Russia where the non-freezing river Yenisei acts as a thermal and humidity source during winter, generating an undulating fog pattern along the river accompanied with scattered `steam devils'. An idealized full diurnal cycle was simulated using an unsteady Reynolds-averaged Navier-Stokes (RANS) three-equation algebraic flux model and the novel buoyancy-accounting functions for treating the ground boundary conditions. The results show a significant effect of the river on the net temperature and moisture distribution. The localized heat and moisture source leads to strong horizontal convection and marked non-uniformity of humidity concentration in the air. An interplay of several distinct large-scale vortex systems leads to a wavy pattern of moisture plumes over the river. The simulations deal with rare natural phenomena and show the capability of the RANS turbulence closure to capture the main features of flow and scalar fields on an affordable, relatively coarse, computational grid.

Sensitivity of LES results from turbine rim seals to changes in grid resolution and sector size

NASA Astrophysics Data System (ADS)

O'Mahoney, T.; Hills, N.; Chew, J.

2012-07-01

Large-Eddy Simulations (LES) were carried out for a turbine rim seal and the sensitivity of the results to changes in grid resolution and the size of the computational domain are investigated. Ingestion of hot annulus gas into the rotor-stator cavity is compared between LES results and against experiments and Unsteady Reynolds-Averaged Navier-Stokes (URANS) calculations. The LES calculations show greater ingestion than the URANS calculation and show better agreement with experiments. Increased grid resolution shows a small improvement in ingestion predictions whereas increasing the sector model size has little effect on the results. The contrast between the different CFD models is most stark in the inner cavity, where the URANS shows almost no ingestion. Particular attention is also paid to the presence of low frequency oscillations in the disc cavity. URANS calculations show such low frequency oscillations at different frequencies than the LES. The oscillations also take a very long time to develop in the LES. The results show that the difficult problem of estimating ingestion through rim seals could be overcome by using LES but that the computational requirements were still restrictive.

CFD analysis of gas explosions vented through relief pipes.

PubMed

Ferrara, G; Di Benedetto, A; Salzano, E; Russo, G

2006-09-21

Vent devices for gas and dust explosions are often ducted to safe locations by means of relief pipes. However, the presence of the duct increases the severity of explosion if compared to simply vented vessels (i.e. compared to cases where no duct is present). Besides, the identification of the key phenomena controlling the violence of explosion has not yet been gained. Multidimensional models coupling, mass, momentum and energy conservation equations can be valuable tools for the analysis of such complex explosion phenomena. In this work, gas explosions vented through ducts have been modelled by a two-dimensional (2D) axi-symmetric computational fluid dynamic (CFD) model based on the unsteady Reynolds Averaged Navier Stokes (RANS) approach in which the laminar, flamelet and distributed combustion models have been implemented. Numerical test have been carried out by varying ignition position, duct diameter and length. Results have evidenced that the severity of ducted explosions is mainly driven by the vigorous secondary explosion occurring in the duct (burn-up) rather than by the duct flow resistance or acoustic enhancement. Moreover, it has been found out that the burn-up affects explosion severity due to the reduction of venting rate rather than to the burning rate enhancement through turbulization.

Off-design Performance Analysis of Multi-Stage Transonic Axial Compressors

NASA Astrophysics Data System (ADS)

Du, W. H.; Wu, H.; Zhang, L.

Because of the complex flow fields and component interaction in modern gas turbine engines, they require extensive experiment to validate performance and stability. The experiment process can become expensive and complex. Modeling and simulation of gas turbine engines are way to reduce experiment costs, provide fidelity and enhance the quality of essential experiment. The flow field of a transonic compressor contains all the flow aspects, which are difficult to present-boundary layer transition and separation, shock-boundary layer interactions, and large flow unsteadiness. Accurate transonic axial compressor off-design performance prediction is especially difficult, due in large part to three-dimensional blade design and the resulting flow field. Although recent advancements in computer capacity have brought computational fluid dynamics to forefront of turbomachinery design and analysis, the grid and turbulence model still limit Reynolds-average Navier-Stokes (RANS) approximations in the multi-stage transonic axial compressor flow field. Streamline curvature methods are still the dominant numerical approach as an important tool for turbomachinery to analyze and design, and it is generally accepted that streamline curvature solution techniques will provide satisfactory flow prediction as long as the losses, deviation and blockage are accurately predicted.

Toward Supersonic Retropropulsion CFD Validation

NASA Technical Reports Server (NTRS)

Kleb, Bil; Schauerhamer, D. Guy; Trumble, Kerry; Sozer, Emre; Barnhardt, Michael; Carlson, Jan-Renee; Edquist, Karl

2011-01-01

This paper begins the process of verifying and validating computational fluid dynamics (CFD) codes for supersonic retropropulsive flows. Four CFD codes (DPLR, FUN3D, OVERFLOW, and US3D) are used to perform various numerical and physical modeling studies toward the goal of comparing predictions with a wind tunnel experiment specifically designed to support CFD validation. Numerical studies run the gamut in rigor from code-to-code comparisons to observed order-of-accuracy tests. Results indicate that this complex flowfield, involving time-dependent shocks and vortex shedding, design order of accuracy is not clearly evident. Also explored is the extent of physical modeling necessary to predict the salient flowfield features found in high-speed Schlieren images and surface pressure measurements taken during the validation experiment. Physical modeling studies include geometric items such as wind tunnel wall and sting mount interference, as well as turbulence modeling that ranges from a RANS (Reynolds-Averaged Navier-Stokes) 2-equation model to DES (Detached Eddy Simulation) models. These studies indicate that tunnel wall interference is minimal for the cases investigated; model mounting hardware effects are confined to the aft end of the model; and sparse grid resolution and turbulence modeling can damp or entirely dissipate the unsteadiness of this self-excited flow.

An Euler-Lagrange method considering bubble radial dynamics for modeling sonochemical reactors.

PubMed

Jamshidi, Rashid; Brenner, Gunther

2014-01-01

Unsteady numerical computations are performed to investigate the flow field, wave propagation and the structure of bubbles in sonochemical reactors. The turbulent flow field is simulated using a two-equation Reynolds-Averaged Navier-Stokes (RANS) model. The distribution of the acoustic pressure is solved based on the Helmholtz equation using a finite volume method (FVM). The radial dynamics of a single bubble are considered by applying the Keller-Miksis equation to consider the compressibility of the liquid to the first order of acoustical Mach number. To investigate the structure of bubbles, a one-way coupling Euler-Lagrange approach is used to simulate the bulk medium and the bubbles as the dispersed phase. Drag, gravity, buoyancy, added mass, volume change and first Bjerknes forces are considered and their orders of magnitude are compared. To verify the implemented numerical algorithms, results for one- and two-dimensional simplified test cases are compared with analytical solutions. The results show good agreement with experimental results for the relationship between the acoustic pressure amplitude and the volume fraction of the bubbles. The two-dimensional axi-symmetric results are in good agreement with experimentally observed structure of bubbles close to sonotrode. Copyright © 2013 Elsevier B.V. All rights reserved.

Hybrid Large Eddy Simulation / Reynolds Averaged Navier-Stokes Modeling in Directed Energy Applications

NASA Astrophysics Data System (ADS)

Zilberter, Ilya Alexandrovich

In this work, a hybrid Large Eddy Simulation / Reynolds-Averaged Navier Stokes (LES/RANS) turbulence model is applied to simulate two flows relevant to directed energy applications. The flow solver blends the Menter Baseline turbulence closure near solid boundaries with a Lenormand-type subgrid model in the free-stream with a blending function that employs the ratio of estimated inner and outer turbulent length scales. A Mach 2.2 mixing nozzle/diffuser system representative of a gas laser is simulated under a range of exit pressures to assess the ability of the model to predict the dynamics of the shock train. The simulation captures the location of the shock train responsible for pressure recovery but under-predicts the rate of pressure increase. Predicted turbulence production at the wall is found to be highly sensitive to the behavior of the RANS turbulence model. A Mach 2.3, high-Reynolds number, three-dimensional cavity flow is also simulated in order to compute the wavefront aberrations of an optical beam passing thorough the cavity. The cavity geometry is modeled using an immersed boundary method, and an auxiliary flat plate simulation is performed to replicate the effects of the wind-tunnel boundary layer on the computed optical path difference. Pressure spectra extracted on the cavity walls agree with empirical predictions based on Rossiter's formula. Proper orthogonal modes of the wavefront aberrations in a beam originating from the cavity center agree well with experimental data despite uncertainty about in flow turbulence levels and boundary layer thicknesses over the wind tunnel window. Dynamic mode decomposition of a planar wavefront spanning the cavity reveals that wavefront distortions are driven by shear layer oscillations at the Rossiter frequencies; these disturbances create eddy shocklets that propagate into the free-stream, creating additional optical wavefront distortion.

Towards Petascale DNS of High Reynolds-Number Turbulent Boundary Layer

NASA Astrophysics Data System (ADS)

Webster, Keegan R.

In flight vehicles, a large portion of fuel consumption is due to skin-friction drag. Reduction of this drag will significantly reduce the fuel consumption of flight vehicles and help our nation to reduce CO 2 emissions. In order to reduce skin-friction drag, an increased understanding of wall-turbulence is needed. Direct numerical simulation (DNS) of spatially developing turbulent boundary layers (SDTBL) can provide the fundamental understanding of wall-turbulence in order to produce models for Reynolds averaged Navier-Stokes (RANS) and large-eddy simulations (LES). DNS of SDTBL over a flat plate at Retheta = 1430 - 2900 were performed. Improvements were made to the DNS code allowing for higher Reynolds number simulations towards petascale DNS of turbulent boundary layers. Mesh refinement and improvements to the inflow and outflow boundary conditions have resulted in turbulence statistics that match more closely to experimental results. The Reynolds stresses and the terms of their evolution equations are reported.

Evaluation of a Multigrid Scheme for the Incompressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Swanson, R. C.

2004-01-01

A fast multigrid solver for the steady, incompressible Navier-Stokes equations is presented. The multigrid solver is based upon a factorizable discrete scheme for the velocity-pressure form of the Navier-Stokes equations. This scheme correctly distinguishes between the advection-diffusion and elliptic parts of the operator, allowing efficient smoothers to be constructed. To evaluate the multigrid algorithm, solutions are computed for flow over a flat plate, parabola, and a Karman-Trefftz airfoil. Both nonlifting and lifting airfoil flows are considered, with a Reynolds number range of 200 to 800. Convergence and accuracy of the algorithm are discussed. Using Gauss-Seidel line relaxation in alternating directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of Runge-Kutta and implicit upwind based multigrid methods.

Convergence Acceleration of Runge-Kutta Schemes for Solving the Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Swanson, Roy C., Jr.; Turkel, Eli; Rossow, C.-C.

2007-01-01

The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 can be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. This RK/implicit scheme is used as a smoother for multigrid. Fourier analysis is applied to determine damping properties. Numerical dissipation operators based on the Roe scheme, a matrix dissipation, and the CUSP scheme are considered in evaluating the RK/implicit scheme. In addition, the effect of the number of RK stages is examined. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. Turbulent flows over an airfoil and wing at subsonic and transonic conditions are computed. The effects of the cell aspect ratio on convergence are investigated for Reynolds numbers between 5:7 x 10(exp 6) and 100 x 10(exp 6). It is demonstrated that the implicit preconditioner can reduce the computational time of a well-tuned standard RK scheme by a factor between four and ten.

Diaphragm opening effects on shock wave formation and acceleration in a rectangular cross section channel

NASA Astrophysics Data System (ADS)

Pakdaman, S. A.; Garcia, M.; Teh, E.; Lincoln, D.; Trivedi, M.; Alves, M.; Johansen, C.

2016-11-01

Shock wave formation and acceleration in a high-aspect ratio cross section shock tube were studied experimentally and numerically. The relative importance of geometric effects and diaphragm opening time on shock formation are assessed. The diaphragm opening time was controlled through the use of slit-type (fast opening time) and petal-type (slow opening time) diaphragms. A novel method of fabricating the petal-type diaphragms, which results in a consistent burst pressure and symmetric opening without fragmentation, is presented. High-speed schlieren photography was used to visualize the unsteady propagation of the lead shock wave and trailing gas dynamic structures. Surface-mounted pressure sensors were used to capture the spatial and temporal development of the pressure field. Unsteady Reynolds-Averaged Navier-Stokes simulation predictions using the shear-stress-transport turbulence model are compared to the experimental data. Simulation results are used to explain the presence of high-frequency pressure oscillations observed experimentally in the driver section as well as the cause of the initial acceleration and subsequent rapid decay of shock velocity measured along the top and bottom channel surfaces. A one-dimensional theoretical model predicting the effect of the finite opening time of the diaphragm on the rate of driver depressurization and shock acceleration is proposed. The model removes the large amount of empiricism that accompanies existing models published in the literature. Model accuracy is assessed through comparisons with experiments and simulations. Limitations of and potential improvements in the model are discussed.

An Investigation of Transonic Resonance in a Mach 2.2 Round Convergent-Divergent Nozzle

NASA Technical Reports Server (NTRS)

Dippold, Vance F., III; Zaman, Khairul B. M. Q.

2015-01-01

Hot-wire and acoustic measurements were taken for a round convergent nozzle and a round convergent-divergent (C-D) nozzle at a jet Mach number of 0.61. The C-D nozzle had a design Mach number of 2.2. Compared to the convergent nozzle jet flow, the Mach 2.2 nozzle jet flow produced excess broadband noise (EBBN). It also produced a transonic resonance tone at 1200 Herz. Computational simulations were performed for both nozzle flows. A steady Reynolds-Averaged Navier-Stokes simulation was performed for the convergent nozzle jet flow. For the Mach 2.2 nozzle flow, a steady RANS simulation, an unsteady RANS (URANS) simulation, and an unsteady Detached Eddy Simulation (DES) were performed. The RANS simulation of the convergent nozzle showed good agreement with the hot-wire velocity and turbulence measurements, though the decay of the potential core was over-predicted. The RANS simulation of the Mach 2.2 nozzle showed poor agreement with the experimental data, and more closely resembled an ideally-expanded jet. The URANS simulation also showed qualitative agreement with the hot-wire data, but predicted a transonic resonance at 1145 Herz. The DES showed good agreement with the hot-wire velocity and turbulence data. The DES also produced a transonic tone at 1135 Herz. The DES solution showed that the destabilization of the shock-induced separation region inside the nozzle produced increased levels of turbulence intensity. This is likely the source of the EBBN.

Effects of nonuniform Mach-number entrance on scramjet nozzle flowfield and performance

NASA Astrophysics Data System (ADS)

Zhang, Pu; Xu, Jinglei; Quan, Zhibin; Mo, Jianwei

2016-12-01

Considering the non-uniformities of nozzle entrance influenced by the upstream, the effects of nonuniform Mach-number coupled with shock and expansion-wave on the flowfield and performances of single expansion ramp nozzle (SERN) are numerically studied using Reynolds-Averaged Navier-Stokes equations. The adopted Reynolds-averaged Navier-Stokes methodology is validated by comparing the numerical results with the cold experimental data, and the average method used in this paper is discussed. Uniform and nonuniform facility nozzles are designed to generate different Mach-number profile for the inlet of SERN, which is direct-connected with different facility nozzle, and the whole flowfield is simulated. Because of the coupling of shock and expansion-wave, flow direction of nonuniform SERN entrance is distorted. Compared with Mach contour of uniform case, the line is more curved for coupling shock-wave entrance (SWE) case, and flatter for the coupling expansion-wave entrance (EWE) case. Wall pressure distribution of SWE case appears rising region, whereas decreases like stairs of EWE case. The numerical results reveal that the coupled shock and expansion-wave play significant roles on nozzle performances. Compared with the SERN performances of uniform entrance case at the same work conditions, the thrust of nonuniform entrance cases reduces by 3-6%, pitch moment decreases by 2.5-7%. The negative lift presents an incremental trend with EWE while the situation is the opposite with SWE. These results confirm that considering the entrance flow parameter nonuniformities of a scramjet nozzle coupled with shock or expansion-wave from the upstream is necessary.

F-16XL Hybrid Reynolds-Averaged Navier-Stokes/Large Eddy Simulation on Unstructured Grids

NASA Technical Reports Server (NTRS)

Park, Michael A.; Abdol-Hamid, Khaled S.; Elmiligui, Alaa

2015-01-01

This study continues the Cranked Arrow Wing Aerodynamics Program, International (CAWAPI) investigation with the FUN3D and USM3D flow solvers. CAWAPI was established to study the F-16XL, because it provides a unique opportunity to fuse fight test, wind tunnel test, and simulation to understand the aerodynamic features of swept wings. The high-lift performance of the cranked-arrow wing planform is critical for recent and past supersonic transport design concepts. Simulations of the low speed high angle of attack Flight Condition 25 are compared: Detached Eddy Simulation (DES), Modi ed Delayed Detached Eddy Simulation (MDDES), and the Spalart-Allmaras (SA) RANS model. Iso- surfaces of Q criterion show the development of coherent primary and secondary vortices on the upper surface of the wing that spiral, burst, and commingle. SA produces higher pressure peaks nearer to the leading-edge of the wing than flight test measurements. Mean DES and MDDES pressures better predict the flight test measurements, especially on the outer wing section. Vorticies and vortex-vortex interaction impact unsteady surface pressures. USM3D showed many sharp tones in volume points spectra near the wing apex with low broadband noise and FUN3D showed more broadband noise with weaker tones. Spectra of the volume points near the outer wing leading-edge was primarily broadband for both codes. Without unsteady flight measurements, the flight pressure environment can not be used to validate the simulations containing tonal or broadband spectra. Mean forces and moment are very similar between FUN3D models and between USM3D models. Spectra of the unsteady forces and moment are broadband with a few sharp peaks for USM3D.

Simulation of Turbine Tone Noise Generation Using a Turbomachinery Aerodynamics Solver

NASA Technical Reports Server (NTRS)

VanZante, Dale; Envia, Edmane

2010-01-01

As turbofan engine bypass ratios continue to increase, the contribution of the turbine to the engine noise signature is receiving more attention. Understanding the relative importance of the various turbine noise generation mechanisms and the characteristics of the turbine acoustic transmission loss are essential ingredients in developing robust reduced-order models for predicting the turbine noise signature. A computationally based investigation has been undertaken to help guide the development of a turbine noise prediction capability that does not rely on empiricism. As proof-of-concept for this approach, two highly detailed numerical simulations of the unsteady flow field inside the first stage of a modern high-pressure turbine were carried out. The simulations were computed using TURBO, which is an unsteady Reynolds-Averaged Navier-Stokes code capable of multi-stage simulations. Spectral and modal analysis of the unsteady pressure data from the numerical simulation of the turbine stage show a circumferential modal distribution that is consistent with the Tyler-Sofrin rule. Within the high-pressure turbine, the interaction of velocity, pressure and temperature fluctuations with the downstream blade rows are all possible tone noise source mechanisms. We have taken the initial step in determining the source strength hierarchy by artificially reducing the level of temperature fluctuations in the turbine flowfield. This was accomplished by changing the vane cooling flow temperature in order to mitigate the vane thermal wake in the second of the two simulations. The results indicated that, despite a dramatic change in the vane cooling flow, the computed modal levels changed very little indicating that the contribution of temperature fluctuations to the overall pressure field is rather small compared with the viscous and potential field interaction mechanisms.

Computational Analysis for Rocket-Based Combined-Cycle Systems During Rocket-Only Operation

NASA Technical Reports Server (NTRS)

Steffen, C. J., Jr.; Smith, T. D.; Yungster, S.; Keller, D. J.

2000-01-01

A series of Reynolds-averaged Navier-Stokes calculations were employed to study the performance of rocket-based combined-cycle systems operating in an all-rocket mode. This parametric series of calculations were executed within a statistical framework, commonly known as design of experiments. The parametric design space included four geometric and two flowfield variables set at three levels each, for a total of 729 possible combinations. A D-optimal design strategy was selected. It required that only 36 separate computational fluid dynamics (CFD) solutions be performed to develop a full response surface model, which quantified the linear, bilinear, and curvilinear effects of the six experimental variables. The axisymmetric, Reynolds-averaged Navier-Stokes simulations were executed with the NPARC v3.0 code. The response used in the statistical analysis was created from Isp efficiency data integrated from the 36 CFD simulations. The influence of turbulence modeling was analyzed by using both one- and two-equation models. Careful attention was also given to quantify the influence of mesh dependence, iterative convergence, and artificial viscosity upon the resulting statistical model. Thirteen statistically significant effects were observed to have an influence on rocket-based combined-cycle nozzle performance. It was apparent that the free-expansion process, directly downstream of the rocket nozzle, can influence the Isp efficiency. Numerical schlieren images and particle traces have been used to further understand the physical phenomena behind several of the statistically significant results.

Evaluation of machine learning algorithms for prediction of regions of high Reynolds averaged Navier Stokes uncertainty

DOE PAGES

Ling, Julia; Templeton, Jeremy Alan

2015-08-04

Reynolds Averaged Navier Stokes (RANS) models are widely used in industry to predict fluid flows, despite their acknowledged deficiencies. Not only do RANS models often produce inaccurate flow predictions, but there are very limited diagnostics available to assess RANS accuracy for a given flow configuration. If experimental or higher fidelity simulation results are not available for RANS validation, there is no reliable method to evaluate RANS accuracy. This paper explores the potential of utilizing machine learning algorithms to identify regions of high RANS uncertainty. Three different machine learning algorithms were evaluated: support vector machines, Adaboost decision trees, and random forests.more » The algorithms were trained on a database of canonical flow configurations for which validated direct numerical simulation or large eddy simulation results were available, and were used to classify RANS results on a point-by-point basis as having either high or low uncertainty, based on the breakdown of specific RANS modeling assumptions. Classifiers were developed for three different basic RANS eddy viscosity model assumptions: the isotropy of the eddy viscosity, the linearity of the Boussinesq hypothesis, and the non-negativity of the eddy viscosity. It is shown that these classifiers are able to generalize to flows substantially different from those on which they were trained. As a result, feature selection techniques, model evaluation, and extrapolation detection are discussed in the context of turbulence modeling applications.« less

On the control of the chaotic attractors of the 2-d Navier-Stokes equations.

PubMed

Smaoui, Nejib; Zribi, Mohamed

2017-03-01

The control problem of the chaotic attractors of the two dimensional (2-d) Navier-Stokes (N-S) equations is addressed in this paper. First, the Fourier Galerkin method based on a reduced-order modelling approach developed by Chen and Price is applied to the 2-d N-S equations to construct a fifth-order system of nonlinear ordinary differential equations (ODEs). The dynamics of the fifth-order system was studied by analyzing the system's attractor for different values of Reynolds number, R e . Then, control laws are proposed to drive the states of the ODE system to a desired attractor. Finally, an adaptive controller is designed to synchronize two reduced order ODE models having different Reynolds numbers and starting from different initial conditions. Simulation results indicate that the proposed control schemes work well.

On the control of the chaotic attractors of the 2-d Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Smaoui, Nejib; Zribi, Mohamed

2017-03-01

The control problem of the chaotic attractors of the two dimensional (2-d) Navier-Stokes (N-S) equations is addressed in this paper. First, the Fourier Galerkin method based on a reduced-order modelling approach developed by Chen and Price is applied to the 2-d N-S equations to construct a fifth-order system of nonlinear ordinary differential equations (ODEs). The dynamics of the fifth-order system was studied by analyzing the system's attractor for different values of Reynolds number, Re. Then, control laws are proposed to drive the states of the ODE system to a desired attractor. Finally, an adaptive controller is designed to synchronize two reduced order ODE models having different Reynolds numbers and starting from different initial conditions. Simulation results indicate that the proposed control schemes work well.

Assessment of Reduced-Kinetics Mechanisms for Combustion of Jet Fuel in CFD Applications

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Kundu, Krihna P.; Yungster, Shaye J.

2014-01-01

A computational effort was undertaken to analyze the details of fluid flow in Lean-Direct Injection (LDI) combustors for next-generation LDI design. The National Combustor Code (NCC) was used to perform reacting flow computations on single-element LDI injector configurations. The feasibility of using a reduced chemical-kinetics approach, which optimizes the reaction rates and species to model the emissions characteristics typical of lean-burning gas-turbine combustors, was assessed. The assessments were performed with Reynolds- Averaged Navier-Stokes (RANS) and Time-Filtered Navier Stokes (TFNS) time-integration, with a Lagrangian spray model with the NCC code. The NCC predictions for EINOx and combustor exit temperature were compared with experimental data for two different single-element LDI injector configurations, with 60deg and 45deg axially swept swirler vanes. The effects of turbulence-chemistry interaction on the predicted flow in a typical LDI combustor were studied with detailed comparisons of NCC TFNS with experimental data.

Multitasking a three-dimensional Navier-Stokes algorithm on the Cray-2

NASA Technical Reports Server (NTRS)

Swisshelm, Julie M.

1989-01-01

A three-dimensional computational aerodynamics algorithm has been multitasked for efficient parallel execution on the Cray-2. It provides a means for examining the multitasking performance of a complete CFD application code. An embedded zonal multigrid scheme is used to solve the Reynolds-averaged Navier-Stokes equations for an internal flow model problem. The explicit nature of each component of the method allows a spatial partitioning of the computational domain to achieve a well-balanced task load for MIMD computers with vector-processing capability. Experiments have been conducted with both two- and three-dimensional multitasked cases. The best speedup attained by an individual task group was 3.54 on four processors of the Cray-2, while the entire solver yielded a speedup of 2.67 on four processors for the three-dimensional case. The multiprocessing efficiency of various types of computational tasks is examined, performance on two Cray-2s with different memory access speeds is compared, and extrapolation to larger problems is discussed.

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.

A pressure-gradient mechanism for vortex shedding in constricted channels

PubMed Central

Boghosian, M. E.; Cassel, K. W.

2013-01-01

Numerical simulations of the unsteady, two-dimensional, incompressible Navier–Stokes equations are performed for a Newtonian fluid in a channel having a symmetric constriction modeled by a two-parameter Gaussian distribution on both channel walls. The Reynolds number based on inlet half-channel height and mean inlet velocity ranges from 1 to 3000. Constriction ratios based on the half-channel height of 0.25, 0.5, and 0.75 are considered. The results show that both the Reynolds number and constriction geometry have a significant effect on the behavior of the post-constriction flow field. The Navier–Stokes solutions are observed to experience a number of bifurcations: steady attached flow, steady separated flow (symmetric and asymmetric), and unsteady vortex shedding downstream of the constriction depending on the Reynolds number and constriction ratio. A sequence of events is described showing how a sustained spatially growing flow instability, reminiscent of a convective instability, leads to the vortex shedding phenomenon via a proposed streamwise pressure-gradient mechanism. PMID:24399860

Large Scale Flutter Data for Design of Rotating Blades Using Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Guruswamy, Guru P.

2012-01-01

A procedure to compute flutter boundaries of rotating blades is presented; a) Navier-Stokes equations. b) Frequency domain method compatible with industry practice. Procedure is initially validated: a) Unsteady loads with flapping wing experiment. b) Flutter boundary with fixed wing experiment. Large scale flutter computation is demonstrated for rotating blade: a) Single job submission script. b) Flutter boundary in 24 hour wall clock time with 100 cores. c) Linearly scalable with number of cores. Tested with 1000 cores that produced data in 25 hrs for 10 flutter boundaries. Further wall-clock speed-up is possible by performing parallel computations within each case.

Parallelization of Unsteady Adaptive Mesh Refinement for Unstructured Navier-Stokes Solvers

NASA Technical Reports Server (NTRS)

Schwing, Alan M.; Nompelis, Ioannis; Candler, Graham V.

2014-01-01

This paper explores the implementation of the MPI parallelization in a Navier-Stokes solver using adaptive mesh re nement. Viscous and inviscid test problems are considered for the purpose of benchmarking, as are implicit and explicit time advancement methods. The main test problem for comparison includes e ects from boundary layers and other viscous features and requires a large number of grid points for accurate computation. Ex- perimental validation against double cone experiments in hypersonic ow are shown. The adaptive mesh re nement shows promise for a staple test problem in the hypersonic com- munity. Extension to more advanced techniques for more complicated ows is described.

Status and future prospects of using numerical methods to study complex flows at High Reynolds numbers

NASA Technical Reports Server (NTRS)

Maccormack, R. W.

1978-01-01

The calculation of flow fields past aircraft configuration at flight Reynolds numbers is considered. Progress in devising accurate and efficient numerical methods, in understanding and modeling the physics of turbulence, and in developing reliable and powerful computer hardware is discussed. Emphasis is placed on efficient solutions to the Navier-Stokes equations.

Bayesian parameter estimation of a k-ε model for accurate jet-in-crossflow simulations

DOE PAGES

Ray, Jaideep; Lefantzi, Sophia; Arunajatesan, Srinivasan; ...

2016-05-31

Reynolds-averaged Navier–Stokes models are not very accurate for high-Reynolds-number compressible jet-in-crossflow interactions. The inaccuracy arises from the use of inappropriate model parameters and model-form errors in the Reynolds-averaged Navier–Stokes model. In this study, the hypothesis is pursued that Reynolds-averaged Navier–Stokes predictions can be significantly improved by using parameters inferred from experimental measurements of a supersonic jet interacting with a transonic crossflow.

The first effects of fluid inertia on flows in ordered and random arrays of spheres

NASA Astrophysics Data System (ADS)

Hill, Reghan J.; Koch, Donald L.; Ladd, Anthony J. C.

2001-12-01

Theory and lattice-Boltzmann simulations are used to examine the effects of fluid inertia, at small Reynolds numbers, on flows in simple cubic, face-centred cubic and random arrays of spheres. The drag force on the spheres, and hence the permeability of the arrays, is determined at small but finite Reynolds numbers, at solid volume fractions up to the close-packed limits of the arrays. For small solid volume fraction, the simulations are compared to theory, showing that the first inertial contribution to the drag force, when scaled with the Stokes drag force on a single sphere in an unbounded fluid, is proportional to the square of the Reynolds number. The simulations show that this scaling persists at solid volume fractions up to the close-packed limits of the arrays, and that the first inertial contribution to the drag force relative to the Stokes-flow drag force decreases with increasing solid volume fraction. The temporal evolution of the spatially averaged velocity and the drag force is examined when the fluid is accelerated from rest by a constant average pressure gradient toward a steady Stokes flow. Theory for the short- and long-time behaviour is in good agreement with simulations, showing that the unsteady force is dominated by quasi-steady drag and added-mass forces. The short- and long-time added-mass coefficients are obtained from potential-flow and quasi-steady viscous-flow approximations, respectively.

Computational fluid dynamics analysis of cyclist aerodynamics: performance of different turbulence-modelling and boundary-layer modelling approaches.

PubMed

Defraeye, Thijs; Blocken, Bert; Koninckx, Erwin; Hespel, Peter; Carmeliet, Jan

2010-08-26

This study aims at assessing the accuracy of computational fluid dynamics (CFD) for applications in sports aerodynamics, for example for drag predictions of swimmers, cyclists or skiers, by evaluating the applied numerical modelling techniques by means of detailed validation experiments. In this study, a wind-tunnel experiment on a scale model of a cyclist (scale 1:2) is presented. Apart from three-component forces and moments, also high-resolution surface pressure measurements on the scale model's surface, i.e. at 115 locations, are performed to provide detailed information on the flow field. These data are used to compare the performance of different turbulence-modelling techniques, such as steady Reynolds-averaged Navier-Stokes (RANS), with several k-epsilon and k-omega turbulence models, and unsteady large-eddy simulation (LES), and also boundary-layer modelling techniques, namely wall functions and low-Reynolds number modelling (LRNM). The commercial CFD code Fluent 6.3 is used for the simulations. The RANS shear-stress transport (SST) k-omega model shows the best overall performance, followed by the more computationally expensive LES. Furthermore, LRNM is clearly preferred over wall functions to model the boundary layer. This study showed that there are more accurate alternatives for evaluating flow around bluff bodies with CFD than the standard k-epsilon model combined with wall functions, which is often used in CFD studies in sports. 2010 Elsevier Ltd. All rights reserved.

Analysis of Highly-Resolved Simulations of 2-D Humps Toward Improvement of Second-Moment Closures

NASA Technical Reports Server (NTRS)

Jeyapaul, Elbert; Rumsey Christopher

2013-01-01

Fully resolved simulation data of flow separation over 2-D humps has been used to analyze the modeling terms in second-moment closures of the Reynolds-averaged Navier- Stokes equations. Existing models for the pressure-strain and dissipation terms have been analyzed using a priori calculations. All pressure-strain models are incorrect in the high-strain region near separation, although a better match is observed downstream, well into the separated-flow region. Near-wall inhomogeneity causes pressure-strain models to predict incorrect signs for the normal components close to the wall. In a posteriori computations, full Reynolds stress and explicit algebraic Reynolds stress models predict the separation point with varying degrees of success. However, as with one- and two-equation models, the separation bubble size is invariably over-predicted.

Comparative study of turbulence models in predicting hypersonic inlet flows

NASA Technical Reports Server (NTRS)

Kapoor, Kamlesh; Anderson, Bernhard H.; Shaw, Robert J.

1992-01-01

A numerical study was conducted to analyze the performance of different turbulence models when applied to the hypersonic NASA P8 inlet. Computational results from the PARC2D code, which solves the full two-dimensional Reynolds-averaged Navier-Stokes equation, were compared with experimental data. The zero-equation models considered for the study were the Baldwin-Lomax model, the Thomas model, and a combination of the Baldwin-Lomax and Thomas models; the two-equation models considered were the Chien model, the Speziale model (both low Reynolds number), and the Launder and Spalding model (high Reynolds number). The Thomas model performed best among the zero-equation models, and predicted good pressure distributions. The Chien and Speziale models compared wery well with the experimental data, and performed better than the Thomas model near the walls.

Comparative study of turbulence models in predicting hypersonic inlet flows

NASA Technical Reports Server (NTRS)

Kapoor, Kamlesh; Anderson, Bernhard H.; Shaw, Robert J.

1992-01-01

A numerical study was conducted to analyze the performance of different turbulence models when applied to the hypersonic NASA P8 inlet. Computational results from the PARC2D code, which solves the full two-dimensional Reynolds-averaged Navier-Stokes equation, were compared with experimental data. The zero-equation models considered for the study were the Baldwin-Lomax model, the Thomas model, and a combination of the Baldwin-Lomax and Thomas models; the two-equation models considered were the Chien model, the Speziale model (both low Reynolds number), and the Launder and Spalding model (high Reynolds number). The Thomas model performed best among the zero-equation models, and predicted good pressure distributions. The Chien and Speziale models compared very well with the experimental data, and performed better than the Thomas model near the walls.

Large-eddy and unsteady RANS simulations of a shock-accelerated heavy gas cylinder

DOE PAGES

Morgan, B. E.; Greenough, J. A.

2015-04-08

Two-dimensional numerical simulations of the Richtmyer–Meshkov unstable “shock-jet” problem are conducted using both large-eddy simulation (LES) and unsteady Reynolds-averaged Navier–Stokes (URANS) approaches in an arbitrary Lagrangian–Eulerian hydrodynamics code. Turbulence statistics are extracted from LES by running an ensemble of simulations with multimode perturbations to the initial conditions. Detailed grid convergence studies are conducted, and LES results are found to agree well with both experiment and high-order simulations conducted by Shankar et al. (Phys Fluids 23, 024102, 2011). URANS results using a k–L approach are found to be highly sensitive to initialization of the turbulence lengthscale L and to the timemore » at which L becomes resolved on the computational mesh. As a result, it is observed that a gradient diffusion closure for turbulent species flux is a poor approximation at early times, and a new closure based on the mass-flux velocity is proposed for low-Reynolds-number mixing.« less

Lubrication Flows.

ERIC Educational Resources Information Center

Papanastasiou, Tasos C.

1989-01-01

Discusses fluid mechanics for undergraduates including the differential Navier-Stokes equations, dimensional analysis and simplified dimensionless numbers, control volume principles, the Reynolds lubrication equation for confined and free surface flows, capillary pressure, and simplified perturbation techniques. Provides a vertical dip coating…

Comparisons of Flutter Analyses for an Experimental Fan

NASA Technical Reports Server (NTRS)

Bakhle, Milind A.; Reddy, T. S. R.; Stefko, George L.

2010-01-01

Two propulsion aeroelasticity codes were used to model the aeroelastic characteristics of an experimental forward-swept fan that encountered flutter during wind tunnel testing. Both of these three-dimensional codes model the unsteady flowfield due to blade vibrations using the Navier-Stokes equations. In the first approach, the unsteady flow equations are solved using an implicit time-marching approach. In the second approach, the unsteady flow equations are converted to a harmonic balance form and solved using a pseudo-time marching method. This paper describes the flutter calculations and compares the results to experimental measurements.

An investigation of several numerical procedures for time-asymptotic compressible Navier-Stokes solutions

NASA Technical Reports Server (NTRS)

Rudy, D. H.; Morris, D. J.; Blanchard, D. K.; Cooke, C. H.; Rubin, S. G.

1975-01-01

The status of an investigation of four numerical techniques for the time-dependent compressible Navier-Stokes equations is presented. Results for free shear layer calculations in the Reynolds number range from 1000 to 81000 indicate that a sequential alternating-direction implicit (ADI) finite-difference procedure requires longer computing times to reach steady state than a low-storage hopscotch finite-difference procedure. A finite-element method with cubic approximating functions was found to require excessive computer storage and computation times. A fourth method, an alternating-direction cubic spline technique which is still being tested, is also described.

Navier-Stokes Analysis of a High Wing Transport High-Lift Configuration with Externally Blown Flaps

NASA Technical Reports Server (NTRS)

Slotnick, Jeffrey P.; An, Michael Y.; Mysko, Stephen J.; Yeh, David T.; Rogers, Stuart E.; Roth, Karlin; Baker, M.David; Nash, S.

2000-01-01

Insights and lessons learned from the aerodynamic analysis of the High Wing Transport (HWT) high-lift configuration are presented. Three-dimensional Navier-Stokes CFD simulations using the OVERFLOW flow solver are compared with high Reynolds test data obtained in the NASA Ames 12 Foot Pressure Wind Tunnel (PWT) facility. Computational analysis of the baseline HWT high-lift configuration with and without Externally Blown Flap (EBF) jet effects is highlighted. Several additional aerodynamic investigations, such as nacelle strake effectiveness and wake vortex studies, are presented. Technical capabilities and shortcomings of the computational method are discussed and summarized.

Numerical solution of the unsteady Navier-Stokes equation

NASA Technical Reports Server (NTRS)

Osher, Stanley J.; Engquist, Bjoern

1985-01-01

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws are discussed. These schemes share many desirable properties with total variation diminishing schemes, but TVD schemes have at most first-order accuracy, in the sense of truncation error, at extrema of the solution. In this paper a uniformly second-order approximation is constructed, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

Comparison of NACA 0012 Laminar Flow Solutions: Structured and Unstructured Grid Methods

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Langer, S.

2016-01-01

In this paper we consider the solution of the compressible Navier-Stokes equations for a class of laminar airfoil flows. The principal objective of this paper is to demonstrate that members of this class of laminar flows have steady-state solutions. These laminar airfoil flow cases are often used to evaluate accuracy, stability and convergence of numerical solution algorithms for the Navier-Stokes equations. In recent years, such flows have also been used as test cases for high-order numerical schemes. While generally consistent steady-state solutions have been obtained for these flows using higher order schemes, a number of results have been published with various solutions, including unsteady ones. We demonstrate with two different numerical methods and a range of meshes with a maximum density that exceeds 8 × 106 grid points that steady-state solutions are obtained. Furthermore, numerical evidence is presented that even when solving the equations with an unsteady algorithm, one obtains steady-state solutions.

A self-contained, automated methodology for optimal flow control validated for transition delay

NASA Technical Reports Server (NTRS)

Joslin, Ronald D.; Gunzburger, Max D.; Nicolaides, R. A.; Erlebacher, Gordon; Hussaini, M. Yousuff

1995-01-01

This paper describes a self-contained, automated methodology for flow control along with a validation of the methodology for the problem of boundary layer instability suppression. The objective of control is to match the stress vector along a portion of the boundary to a given vector; instability suppression is achieved by choosing the given vector to be that of a steady base flow, e.g., Blasius boundary layer. Control is effected through the injection or suction of fluid through a single orifice on the boundary. The present approach couples the time-dependent Navier-Stokes system with an adjoint Navier-Stokes system and optimality conditions from which optimal states, i.e., unsteady flow fields, and control, e.g., actuators, may be determined. The results demonstrate that instability suppression can be achieved without any a priori knowledge of the disturbance, which is significant because other control techniques have required some knowledge of the flow unsteadiness such as frequencies, instability type, etc.

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Jothiprasad, Giridhar; Mavriplis, Dimitri J.; Caughey, David A.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The efficiency gains obtained using higher-order implicit Runge-Kutta schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each timestep are presented. The first algorithm (NMG) is a pseudo-time-stepping scheme which employs a non-linear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on Inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the Generalized Minimal Residual method. Results demonstrating the relative superiority of these Newton's methods based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes with the more efficient nonlinear solvers.

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.

Reducing RANS Model Error Using Random Forest

NASA Astrophysics Data System (ADS)

Wang, Jian-Xun; Wu, Jin-Long; Xiao, Heng; Ling, Julia

2016-11-01

Reynolds-Averaged Navier-Stokes (RANS) models are still the work-horse tools in the turbulence modeling of industrial flows. However, the model discrepancy due to the inadequacy of modeled Reynolds stresses largely diminishes the reliability of simulation results. In this work we use a physics-informed machine learning approach to improve the RANS modeled Reynolds stresses and propagate them to obtain the mean velocity field. Specifically, the functional forms of Reynolds stress discrepancies with respect to mean flow features are trained based on an offline database of flows with similar characteristics. The random forest model is used to predict Reynolds stress discrepancies in new flows. Then the improved Reynolds stresses are propagated to the velocity field via RANS equations. The effects of expanding the feature space through the use of a complete basis of Galilean tensor invariants are also studied. The flow in a square duct, which is challenging for standard RANS models, is investigated to demonstrate the merit of the proposed approach. The results show that both the Reynolds stresses and the propagated velocity field are improved over the baseline RANS predictions. SAND Number: SAND2016-7437 A

Analysis of Low-Speed Stall Aerodynamics of a Business Jets Wing Using STAR-CCM+

NASA Technical Reports Server (NTRS)

Bui, Trong

2016-01-01

Reynolds-Averaged Navier-Stokes (RANS) computational fluid dynamics (CFD) analysis was conducted: to study the low-speed stall aerodynamics of a GIII aircrafts swept wing modified with (1) a laminar-flow wing glove, or (2) a seamless flap. The stall aerodynamics of these two different wing configurations were analyzed and compared with the unmodified baseline wing for low-speed flight. The Star-CCM+ polyhedral unstructured CFD code was first validated for wing stall predictions using the wing-body geometry from the First AIAA CFD High-Lift Prediction Workshop.

Evaluation of Turbulence-Model Performance as Applied to Jet-Noise Prediction

NASA Technical Reports Server (NTRS)

Woodruff, S. L.; Seiner, J. M.; Hussaini, M. Y.; Erlebacher, G.

1998-01-01

The accurate prediction of jet noise is possible only if the jet flow field can be predicted accurately. Predictions for the mean velocity and turbulence quantities in the jet flowfield are typically the product of a Reynolds-averaged Navier-Stokes solver coupled with a turbulence model. To evaluate the effectiveness of solvers and turbulence models in predicting those quantities most important to jet noise prediction, two CFD codes and several turbulence models were applied to a jet configuration over a range of jet temperatures for which experimental data is available.

Summary of EASM Turbulence Models in CFL3D With Validation Test Cases

NASA Technical Reports Server (NTRS)

Rumsey, Christopher L.; Gatski, Thomas B.

2003-01-01

This paper summarizes the Explicit Algebraic Stress Model in k-omega form (EASM-ko) and in k-epsilon form (EASM-ke) in the Reynolds-averaged Navier-Stokes code CFL3D. These models have been actively used over the last several years in CFL3D, and have undergone some minor modifications during that time. Details of the equations and method for coding the latest versions of the models are given, and numerous validation cases are presented. This paper serves as a validation archive for these models.

Experimental Validation Data for Computational Fluid Dynamics of Forced Convection on a Vertical Flat Plate

DOE PAGES

Harris, Jeff R.; Lance, Blake W.; Smith, Barton L.

2015-08-10

We present computational fluid dynamics (CFD) validation dataset for turbulent forced convection on a vertical plate. The design of the apparatus is based on recent validation literature and provides a means to simultaneously measure boundary conditions (BCs) and system response quantities (SRQs). Important inflow quantities for Reynolds-Averaged Navier-Stokes (RANS). CFD are also measured. Data are acquired at two heating conditions and cover the range 40,000 < Re x < 300,000, 357 < Re δ2 < 813, and 0.02 < Gr/Re 2 < 0.232.

Numerical viscosity and resolution of high-order weighted essentially nonoscillatory schemes for compressible flows with high Reynolds numbers.

PubMed

Zhang, Yong-Tao; Shi, Jing; Shu, Chi-Wang; Zhou, Ye

2003-10-01

A quantitative study is carried out in this paper to investigate the size of numerical viscosities and the resolution power of high-order weighted essentially nonoscillatory (WENO) schemes for solving one- and two-dimensional Navier-Stokes equations for compressible gas dynamics with high Reynolds numbers. A one-dimensional shock tube problem, a one-dimensional example with parameters motivated by supernova and laser experiments, and a two-dimensional Rayleigh-Taylor instability problem are used as numerical test problems. For the two-dimensional Rayleigh-Taylor instability problem, or similar problems with small-scale structures, the details of the small structures are determined by the physical viscosity (therefore, the Reynolds number) in the Navier-Stokes equations. Thus, to obtain faithful resolution to these small-scale structures, the numerical viscosity inherent in the scheme must be small enough so that the physical viscosity dominates. A careful mesh refinement study is performed to capture the threshold mesh for full resolution, for specific Reynolds numbers, when WENO schemes of different orders of accuracy are used. It is demonstrated that high-order WENO schemes are more CPU time efficient to reach the same resolution, both for the one-dimensional and two-dimensional test problems.

Numerical solution of the Navier-Stokes equations for blunt nosed bodies in supersonic flows

NASA Technical Reports Server (NTRS)

Warsi, Z. U. A.; Devarayalu, K.; Thompson, J. F.

1978-01-01

A time dependent, two dimensional Navier-Stokes code employing the method of body fitted coordinate technique was developed for supersonic flows past blunt bodies of arbitrary shapes. The bow shock ahead of the body is obtained as part of the solution, viz., by shock capturing. A first attempt at mesh refinement in the shock region was made by using the forcing function in the coordinate generating equations as a linear function of the density gradients. The technique displaces a few lines from the neighboring region into the shock region. Numerical calculations for Mach numbers 2 and 4.6 and Reynolds numbers from 320 to 10,000 were performed for a circular cylinder with and without a fairing. Results of Mach number 4.6 and Reynolds number 10,000 for an isothermal wall temperature of 556 K are presented in detail.

Investigation of Unsteady Flow Interaction Between an Ultra-Compact Inlet and a Transonic Fan

NASA Technical Reports Server (NTRS)

Hah, Chunill; Rabe, Douglas; Scribben, Angie

2015-01-01

In the study presented, unsteady flow interaction between an ultra-compact inlet and a transonic fan stage is investigated. Future combat aircraft engines require ultra-compact inlet ducts as part of an integrated, advanced propulsion system to improve air vehicle capability and effectiveness to meet future mission needs. The main purpose of the current study is to advance the understanding of the flow interaction between a modern ultra-compact inlet and a transonic fan for future design applications. Many experimental/ analytical studies have been reported on the aerodynamics of compact inlets in aircraft engines. On the other hand, very few studies have been reported on the effects of flow distortion from these inlets on the performance of the following fan/compressor stages. The primary goal of the study presented is to investigate how flow interaction between an ultra-compact inlet and a transonic compressor influence the operating margin of the compressor. Both Unsteady Reynolds-averaged Navier-Stokes (URANS) and Large Eddy Simulation (LES) approaches are used to calculate the unsteady flow field, and the numerical results are used to study the flow interaction. The present study indicates that stall inception of the following compressor stage is affected directly based on how the distortion pattern evolves before it interacts with the fan/compressor face. For the present compressor, the stall initiates at the tip section with clean inlet flow and distortion pattern away from the casing itself seems to have limited impacts on the stall inception of the compressor. A counter-rotating swirl, which is generated due to flow separation inside the s-shaped compact duct, generates an increased flow angle near the blade tip. This increased flow angle near the rotor tip due to the secondary flow from the counter-rotating vortices is the primary reason for the reduced compressor stall margin.

Reynolds-averaged Navier-Stokes investigation of high-lift low-pressure turbine blade aerodynamics at low Reynolds number

NASA Astrophysics Data System (ADS)

Arko, Bryan M.

Design trends for the low-pressure turbine (LPT) section of modern gas turbine engines include increasing the loading per airfoil, which promises a decreased airfoil count resulting in reduced manufacturing and operating costs. Accurate Reynolds-Averaged Navier-Stokes predictions of separated boundary layers and transition to turbulence are needed, as the lack of an economical and reliable computational model has contributed to this high-lift concept not reaching its full potential. Presented here for what is believed to be the first time applied to low-Re computations of high-lift linear cascade simulations is the Abe-Kondoh-Nagano (AKN) linear low-Re two-equation turbulence model which utilizes the Kolmogorov velocity scale for improved predictions of separated boundary layers. A second turbulence model investigated is the Kato-Launder modified version of the AKN, denoted MPAKN, which damps turbulent production in highly strained regions of flow. Fully Laminar solutions have also been calculated in an effort to elucidate the transitional quality of the turbulence model solutions. Time accurate simulations of three modern high-lift blades at a Reynolds number of 25,000 are compared to experimental data and higher-order computations in order to judge the accuracy of the results, where it is shown that the RANS simulations with highly refined grids can produce both quantitatively and qualitatively similar separation behavior as found in experiments. In particular, the MPAKN model is shown to predict the correct boundary layer behavior for all three blades, and evidence of transition is found through inspection of the components of the Reynolds Stress Tensor, spectral analysis, and the turbulence production parameter. Unfortunately, definitively stating that transition is occurring becomes an uncertain task, as similar evidence of the transition process is found in the Laminar predictions. This reveals that boundary layer reattachment may be a result of laminar vortex shedding interaction with the blade surface, or that application of Laminar solvers with highly refined grids may be valid for investigations of transitional flow. It is recommended that this be studied in the future along with further studies of the turbulence models presented, which have proved to be worthy of additional study in the present application.

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.

Two-Dimensional Computational Model for Wave Rotor Flow Dynamics

NASA Technical Reports Server (NTRS)

Welch, Gerard E.

1996-01-01

A two-dimensional (theta,z) Navier-Stokes solver for multi-port wave rotor flow simulation is described. The finite-volume form of the unsteady thin-layer Navier-Stokes equations are integrated in time on multi-block grids that represent the stationary inlet and outlet ports and the moving rotor passages of the wave rotor. Computed results are compared with three-port wave rotor experimental data. The model is applied to predict the performance of a planned four-port wave rotor experiment. Two-dimensional flow features that reduce machine performance and influence rotor blade and duct wall thermal loads are identified. The performance impact of rounding the inlet port wall, to inhibit separation during passage gradual opening, is assessed.

A comparative study of Full Navier-Stokes and Reduced Navier-Stokes analyses for separating flows within a diffusing inlet S-duct

NASA Technical Reports Server (NTRS)

Anderson, B. H.; Reddy, D. R.; Kapoor, K.

1993-01-01

A three-dimensional implicit Full Navier-Stokes (FNS) analysis and a 3D Reduced Navier Stokes (RNS) initial value space marching solution technique has been applied to a class of separated flow problems within a diffusing S-duct configuration characterized by vortex-liftoff. Both the FNS and the RNS solution technique were able to capture the overall flow physics of vortex lift-off, and gave remarkably similar results which agreed reasonably well with the experimental measured averaged performance parameters of engine face total pressure recovery and distortion. However, the Full Navier-Stokes and Reduced Navier-Stokes also consistently predicted separation further downstream in the M2129 inlet S-duct than was indicated by experimental data, thus compensating errors were present in the two Navier-Stokes analyses. The difficulties encountered in the Navier-Stokes separations analyses of the M2129 inlet S-duct center primarily on turbulence model issues, and these focused on two distinct but different phenomena, namely, (1) characterization of low skin friction adverse pressure gradient flows, and (2) description of the near wall behavior of flows characterized by vortex lift-off.

LES and URANS predictions of the hydrodynamic loads on a tension-leg platform

NASA Astrophysics Data System (ADS)

Abrishamchi, A.; Younis, B. A.

2012-01-01

This paper reports on the prediction of the unsteady hydrodynamic forces that act on a floating Tension-Leg Platform (TLP) due to the action of a steady current. The results were obtained by solving the three-dimensional, time-dependent form of the equations governing conservation of mass and momentum. Movement of the free surface was tracked using the volume of fluid algorithm. The effects of turbulence were accounted for using two very different approaches: Large-Eddy Simulations (LES) and Unsteady Reynolds-Averaged Navier-Stokes (URANS). The latter approach utilized a two-equation turbulence closure that has been extended to capture the occurrence and consequences of vortex shedding from bluff bodies. The primary objective of the work was to explore the merits and de-merits of each modeling approach when applied to a large-scale structure of the type frequently encountered in practice. The test case chosen for this purposes of this assessment was the case of a conventional TLP in steady current at Reynolds numbers (based on column diameter) of 7.5×106 and 7.5×107. These values are representative of those encountered in deep-sea operations. Experiments and field observations have indicated that the resulting flows exhibit a number of complicated features due to the interactions between the shed vortices and the various structural components of the TLP. Many but not all of these features were captured by the present computations. In addition to a critical assessment of the two modeling approaches, the paper reports on a number of practical experiences gained in the course of conducting this study, including an assessment of the importance of allowing for the movement of the free surface (as opposed to adopting the usual solid-lid approximation) and an illustration of the effects of the current's angle of incidence on the computed hydrodynamic loads.

Magnetic Resonance Velocimetry analysis of an angled impinging jet

NASA Astrophysics Data System (ADS)

Irhoud, Alexandre; Benson, Michael; Verhulst, Claire; van Poppel, Bret; Elkins, Chris; Helmer, David

2016-11-01

Impinging jets are used to achieve high heat transfer rates in applications ranging from gas turbine engines to electronics. Despite the importance and relative simplicity of the geometry, simulations historically fail to accurately predict the flow behavior in the vicinity of the flow impingement. In this work, we present results from a novel experimental technique, Magnetic Resonance Velocimetry (MRV), which measures three-dimensional time-averaged velocity without the need for optical access. The geometry considered in this study is a circular jet angled at 45 degrees and impinging on a flat plate, with a separation of approximately seven jet diameters between the jet exit and the impingement location. Two flow conditions are considered, with Reynolds numbers of roughly 800 and 14,000. Measurements from the MRV experiment are compared to predictions from Reynolds Averaged Navier Stokes (RANS) simulations, thus demonstrating the utility of MRV for validation of numerical analyses of impinging jet flow.

High Reynolds number analysis of flat plate and separated afterbody flow using non-linear turbulence models

NASA Technical Reports Server (NTRS)

Carlson, John R.

1996-01-01

The ability of the three-dimensional Navier-Stokes method, PAB3D, to simulate the effect of Reynolds number variation using non-linear explicit algebraic Reynolds stress turbulence modeling was assessed. Subsonic flat plate boundary-layer flow parameters such as normalized velocity distributions, local and average skin friction, and shape factor were compared with DNS calculations and classical theory at various local Reynolds numbers up to 180 million. Additionally, surface pressure coefficient distributions and integrated drag predictions on an axisymmetric nozzle afterbody were compared with experimental data from 10 to 130 million Reynolds number. The high Reynolds data was obtained from the NASA Langley 0.3m Transonic Cryogenic Tunnel. There was generally good agreement of surface static pressure coefficients between the CFD and measurement. The change in pressure coefficient distributions with varying Reynolds number was similar to the experimental data trends, though slightly over-predicting the effect. The computational sensitivity of viscous modeling and turbulence modeling are shown. Integrated afterbody pressure drag was typically slightly lower than the experimental data. The change in afterbody pressure drag with Reynolds number was small both experimentally and computationally, even though the shape of the distribution was somewhat modified with Reynolds number.

Three-Dimensional Navier-Stokes Simulations with Two-Equation Turbulence Models of Intersecting Shock-Waves/Turbulent Boundary Layer at Mach 8.3

NASA Technical Reports Server (NTRS)

Bardina, J. E.; Coakley, T. J.

1994-01-01

An investigation of the numerical simulation with two-equation turbulence models of a three-dimensional hypersonic intersecting (SWTBL) shock-wave/turbulent boundary layer interaction flow is presented. The flows are solved with an efficient implicit upwind flux-difference split Reynolds-averaged Navier-Stokes code. Numerical results are compared with experimental data for a flow at Mach 8.28 and Reynolds number 5.3x10(exp 6) with crossing shock-waves and expansion fans generated by two lateral 15 fins located on top of a cold-wall plate. This experiment belongs to the hypersonic database for modeling validation. Simulations show the development of two primary counter-rotating cross-flow vortices and secondary turbulent structures under the main vortices and in each corner singularity inside the turbulent boundary layer. A significant loss of total pressure is produced by the complex interaction between the main vortices and the uplifted jet stream of the boundary layer. The overall agreement between computational and experimental data is generally good. The turbulence modeling corrections show improvements in the predictions of surface heat transfer distribution and an increase in the strength of the cross-flow vortices. Accurate predictions of the outflow flowfield is found to require accurate modeling of the laminar/turbulent boundary layers on the fin walls.

A self-sustaining process model of inertial layer dynamics in high Reynolds number turbulent wall flows.

PubMed

Chini, G P; Montemuro, B; White, C M; Klewicki, J

2017-03-13

Field observations and laboratory experiments suggest that at high Reynolds numbers Re the outer region of turbulent boundary layers self-organizes into quasi-uniform momentum zones (UMZs) separated by internal shear layers termed 'vortical fissures' (VFs). Motivated by this emergent structure, a conceptual model is proposed with dynamical components that collectively have the potential to generate a self-sustaining interaction between a single VF and adjacent UMZs. A large-Re asymptotic analysis of the governing incompressible Navier-Stokes equation is performed to derive reduced equation sets for the streamwise-averaged and streamwise-fluctuating flow within the VF and UMZs. The simplified equations reveal the dominant physics within-and isolate possible coupling mechanisms among-these different regions of the flow.This article is part of the themed issue 'Toward the development of high-fidelity models of wall turbulence at large Reynolds number'. © 2017 The Author(s).

The Variation of Slat Noise with Mach and Reynolds Numbers

NASA Technical Reports Server (NTRS)

Lockard, David P.; Choudhari, Meelan M.

2011-01-01

The slat noise from the 30P30N high-lift system has been computed using a computational fluid dynamics code in conjunction with a Ffowcs Williams-Hawkings solver. By varying the Mach number from 0.13 to 0.25, the noise was found to vary roughly with the 5th power of the speed. Slight changes in the behavior with directivity angle could easily account for the different speed dependencies reported in the literature. Varying the Reynolds number from 1.4 to 2.4 million resulted in almost no differences, and primarily served to demonstrate the repeatability of the results. However, changing the underlying hybrid Reynolds-averaged-Navier-Stokes/Large-Eddy-Simulation turbulence model significantly altered the mean flow because of changes in the flap separation. However, the general trends observed in both the acoustics and near-field fluctuations were similar for both models.

Rocket Engine Turbine Blade Surface Pressure Distributions Experiment and Computations

NASA Technical Reports Server (NTRS)

Hudson, Susan T.; Zoladz, Thomas F.; Dorney, Daniel J.; Turner, James (Technical Monitor)

2002-01-01

Understanding the unsteady aspects of turbine rotor flow fields is critical to successful future turbine designs. A technology program was conducted at NASA's Marshall Space Flight Center to increase the understanding of unsteady environments for rocket engine turbines. The experimental program involved instrumenting turbine rotor blades with miniature surface mounted high frequency response pressure transducers. The turbine model was then tested to measure the unsteady pressures on the rotor blades. The data obtained from the experimental program is unique in two respects. First, much more unsteady data was obtained (several minutes per set point) than has been possible in the past. Also, an extensive steady performance database existed for the turbine model. This allowed an evaluation of the effect of the on-blade instrumentation on the turbine's performance. A three-dimensional unsteady Navier-Stokes analysis was also used to blindly predict the unsteady flow field in the turbine at the design operating conditions and at +15 degrees relative incidence to the first-stage rotor. The predicted time-averaged and unsteady pressure distributions show good agreement with the experimental data. This unique data set, the lessons learned for acquiring this type of data, and the improvements made to the data analysis and prediction tools are contributing significantly to current Space Launch Initiative turbine airflow test and blade surface pressure prediction efforts.

Numerical study of Reynolds stress in compressible flows

NASA Technical Reports Server (NTRS)

Vandromme, D.; Hamin, H.

1985-01-01

A second order closure has been implemented in an implicit Navier-Stokes solver to study the behavior of the Reynolds stresses under the influence of severe pressure gradients. In the boundary layer zone, the strongly sheared character of the mean flow dominates the turbulence generation mechanisms. However, the pressure gradients also play a very important role for these processes, but at different locations within the boundary layer.

Nonlinear stability of Taylor's vortex array

NASA Technical Reports Server (NTRS)

Lin, S. P.; Tobak, M.

1987-01-01

It is proved that the two-dimensional Taylor vortex array, which is an exact unsteady solution of the Navier-Stokes equation, is globally and asymptotically stable in the mean with respect to three-dimensional periodic disturbances. A time-dependent bound on the decay rate of the kinetic energy of disturbances is obtained.

Transport of Multivalent Electrolyte Mixtures in Micro- and Nanochannels

DTIC Science & Technology

2013-11-08

equations for this process are the unsteady Navier-Stokes equations along with continuity and the Poisson- Nernst -Planck system for the electro- static part...about five times the Debye screening length D (the 1/e lengthscale for the potential from the solution of the linearized Poisson- Boltzmann equation

A Modular Approach to Model Oscillating Control Surfaces Using Navier Stokes Equations

NASA Technical Reports Server (NTRS)

Guruswamy, Guru P.; Lee, Henry

2014-01-01

The use of active controls for rotorcraft is becoming more important for modern aerospace configurations. Efforts to reduce the vibrations of helicopter blades with use of active-controls are in progress. Modeling oscillating control surfaces using the linear aerodynamics theory is well established. However, higher-fidelity methods are needed to account for nonlinear effects, such as those that occur in transonic flow. The aeroelastic responses of a wing with an oscillating control surface, computed using the transonic small perturbation (TSP) theory, have been shown to cause important transonic flow effects such as a reversal of control surface effectiveness that occurs as the shock wave crosses the hinge line. In order to account for flow complexities such as blade-vortex interactions of rotor blades higher-fidelity methods based on the Navier-Stokes equations are used. Reference 6 presents a procedure that uses the Navier-Stokes equations with moving-sheared grids and demonstrates up to 8 degrees of control-surface amplitude, using a single grid. Later, this procedure was extended to accommodate larger amplitudes, based on sliding grid zones. The sheared grid method implemented in EulerlNavier-Stokes-based aeroelastic code ENS AERO was successfully applied to active control design by industry. Recently there are several papers that present results for oscillating control surface using Reynolds Averaged Navier-Stokes (RANS) equations. References 9 and 10 report 2-D cases by filling gaps with overset grids. Reference 9 compares integrated forces with the experiment at low oscillating frequencies whereas Ref. 10 reports parametric studies but with no validation. Reference II reports results for a 3D case by modeling the gap region with a deformed grid and compares force results with the experiment only at the mid-span of flap. In Ref. II grid is deformed to match the control surface deflections at the section where the measurements are made. However, there is no indication in Ref. II that the gaps are explicitly modeled as in Ref. 6. Computations using overset grids are reported in Ref. 12 for a case by adding moving control surface to an existing blade but with no validation either with an experiment or another computation.

Application of Aeroelastic Solvers Based on Navier Stokes Equations

NASA Technical Reports Server (NTRS)

Keith, Theo G., Jr.; Srivastava, Rakesh

2001-01-01

The propulsion element of the NASA Advanced Subsonic Technology (AST) initiative is directed towards increasing the overall efficiency of current aircraft engines. This effort requires an increase in the efficiency of various components, such as fans, compressors, turbines etc. Improvement in engine efficiency can be accomplished through the use of lighter materials, larger diameter fans and/or higher-pressure ratio compressors. However, each of these has the potential to result in aeroelastic problems such as flutter or forced response. To address the aeroelastic problems, the Structural Dynamics Branch of NASA Glenn has been involved in the development of numerical capabilities for analyzing the aeroelastic stability characteristics and forced response of wide chord fans, multi-stage compressors and turbines. In order to design an engine to safely perform a set of desired tasks, accurate information of the stresses on the blade during the entire cycle of blade motion is required. This requirement in turn demands that accurate knowledge of steady and unsteady blade loading is available. To obtain the steady and unsteady aerodynamic forces for the complex flows around the engine components, for the flow regimes encountered by the rotor, an advanced compressible Navier-Stokes solver is required. A finite volume based Navier-Stokes solver has been developed at Mississippi State University (MSU) for solving the flow field around multistage rotors. The focus of the current research effort, under NASA Cooperative Agreement NCC3- 596 was on developing an aeroelastic analysis code (entitled TURBO-AE) based on the Navier-Stokes solver developed by MSU. The TURBO-AE code has been developed for flutter analysis of turbomachine components and delivered to NASA and its industry partners. The code has been verified. validated and is being applied by NASA Glenn and by aircraft engine manufacturers to analyze the aeroelastic stability characteristics of modem fans, compressors and turbines.

An incremental block-line-Gauss-Seidel method for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Napolitano, M.; Walters, R. W.

1985-01-01

A block-line-Gauss-Seidel (LGS) method is developed for solving the incompressible and compressible Navier-Stokes equations in two dimensions. The method requires only one block-tridiagonal solution process per iteration and is consequently faster per step than the linearized block-ADI methods. Results are presented for both incompressible and compressible separated flows: in all cases the proposed block-LGS method is more efficient than the block-ADI methods. Furthermore, for high Reynolds number weakly separated incompressible flow in a channel, which proved to be an impossible task for a block-ADI method, solutions have been obtained very efficiently by the new scheme.

Remarks on High Reynolds Numbers Hydrodynamics and the Inviscid Limit

NASA Astrophysics Data System (ADS)

Constantin, Peter; Vicol, Vlad

2018-04-01

We prove that any weak space-time L^2 vanishing viscosity limit of a sequence of strong solutions of Navier-Stokes equations in a bounded domain of R^2 satisfies the Euler equation if the solutions' local enstrophies are uniformly bounded. We also prove that t-a.e. weak L^2 inviscid limits of solutions of 3D Navier-Stokes equations in bounded domains are weak solutions of the Euler equation if they locally satisfy a scaling property of their second-order structure function. The conditions imposed are far away from boundaries, and wild solutions of Euler equations are not a priori excluded in the limit.

A General Algorithm for Reusing Krylov Subspace Information. I. Unsteady Navier-Stokes

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Vuik, C.; Lucas, Peter; vanGijzen, Martin; Bijl, Hester

2010-01-01

A general algorithm is developed that reuses available information to accelerate the iterative convergence of linear systems with multiple right-hand sides A x = b (sup i), which are commonly encountered in steady or unsteady simulations of nonlinear equations. The algorithm is based on the classical GMRES algorithm with eigenvector enrichment but also includes a Galerkin projection preprocessing step and several novel Krylov subspace reuse strategies. The new approach is applied to a set of test problems, including an unsteady turbulent airfoil, and is shown in some cases to provide significant improvement in computational efficiency relative to baseline approaches.

Simulation of self-induced unsteady motion in the near wake of a Joukowski airfoil

NASA Technical Reports Server (NTRS)

Ghia, K. N.; Osswald, G. A.; Ghia, U.

1986-01-01

The unsteady Navier-Stokes analysis is shown to be capable of analyzing the massively separated, persistently unsteady flow in the post-stall regime of a Joukowski airfoil for an angle of attack as high as 53 degrees. The analysis has provided the detailed flow structure, showing the complex vortex interaction for this configuration. The aerodynamic coefficients for lift, drag, and moment were calculated. So far only the spatial structure of the vortex interaction was computed. It is now important to potentially use the large-scale vortex interactions, an additional energy source, to improve the aerodynamic performance.

Initial conditions and modeling for simulations of shock driven turbulent material mixing

DOE PAGES

Grinstein, Fernando F.

2016-11-17

Here, we focus on the simulation of shock-driven material mixing driven by flow instabilities and initial conditions (IC). Beyond complex multi-scale resolution issues of shocks and variable density turbulence, me must address the equally difficult problem of predicting flow transition promoted by energy deposited at the material interfacial layer during the shock interface interactions. Transition involves unsteady large-scale coherent-structure dynamics capturable by a large eddy simulation (LES) strategy, but not by an unsteady Reynolds-Averaged Navier–Stokes (URANS) approach based on developed equilibrium turbulence assumptions and single-point-closure modeling. On the engineering end of computations, such URANS with reduced 1D/2D dimensionality and coarsermore » grids, tend to be preferred for faster turnaround in full-scale configurations.« less

2-D eddy resolving simulations of flow past a circular array of cylindrical plant stems

NASA Astrophysics Data System (ADS)

Chang, Kyoungsik; Constantinescu, George; Park, Sanghyun

2018-04-01

In the present study, 2-D large eddy simulations (LES) are conducted for flow past a porous circular array with a solid volume fraction (SVF) of 8.8%, 15.4% and 21.5%. Such simulations are relevant to understanding flow in natural streams and channels containing patches of emerged vegetation. In the simulations discussed in the paper, the porous cylinder of diameter D contains a variable number of identical solid circular cylinders (rigid plant stems) of diameter d = 0.048 D. Most of the simulations are conducted at a Reynolds number of 2 100 based on the diameter D and the velocity of the steady uniform incoming flow. Though in all cases wake billows are shed in the regions where the separated shear layers (SSLs) forming on the sides of the porous cylinder interact, the effect of these wake billows on the mean drag is different. While in the high SVF case (21.5%), the total drag force oscillates quasi-regularly in time, similar to the canonical case of a large solid cylinder, in the cases with a lower SVF the shedding of the wake billows takes place sufficiently far from the cylinder such that the unsteady component of the total drag force is negligible. The mean amplitude of the oscillations of the drag force on the individual cylinders is the largest in a streamwise band centered around the center of the porous cylinder, where the wake to wake interactions are the strongest. In all cases the maximum drag force on the individual cylinders is the largest for the cylinders directly exposed to the flow, but this force is always smaller than the one induced on a small isolated cylinder and the average magnitude of the force on the cylinders directly exposed to the flow decreases monotonically with the increase in the SVF. Predictions of the global drag coefficients, Strouhal numbers associated with the wake vortex shedding and individual forces on the cylinders in the array from the present LES are in very good agreement with those of 2-D direct numerical simulations conducted on finer meshes, which suggests LES is a better option to numerically investigate flow in channels containing canopy patches, given that LES is computationally much less expensive than DNS at high Reynolds number. To prove this point, the paper also discusses results of 2-D LES conducted at a much higher Reynolds number, where the near-wake flow is strongly turbulent. For the higher Reynolds number cases, where the influence of the turbulence model is important, the effect of the sub-grid scale model and the predictive capabilities of the unsteady Reynolds averaged Navier-Stokes (RANS) approach to predict flow past porous cylinders are discussed.

Zonal PANS: evaluation of different treatments of the RANS-LES interface

NASA Astrophysics Data System (ADS)

Davidson, L.

2016-03-01

The partially Reynolds-averaged Navier-Stokes (PANS) model can be used to simulate turbulent flows either as RANS, large eddy simulation (LES) or DNS. Its main parameter is fk whose physical meaning is the ratio of the modelled to the total turbulent kinetic energy. In RANS fk = 1, in DNS fk = 0 and in LES fk takes values between 0 and 1. Three different ways of prescribing fk are evaluated for decaying grid turbulence and fully developed channel flow: fk = 0.4, fk = k3/2tot/ɛ and, from its definition, fk = k/ktot where ktot is the sum of the modelled, k, and resolved, kres, turbulent kinetic energy. It is found that the fk = 0.4 gives the best results. In Girimaji and Wallin, a method was proposed to include the effect of the gradient of fk. This approach is used at RANS- LES interface in the present study. Four different interface models are evaluated in fully developed channel flow and embedded LES of channel flow: in both cases, PANS is used as a zonal model with fk = 1 in the unsteady RANS (URANS) region and fk = 0.4 in the LES region. In fully developed channel flow, the RANS- LES interface is parallel to the wall (horizontal) and in embedded LES, it is parallel to the inlet (vertical). The importance of the location of the horizontal interface in fully developed channel flow is also investigated. It is found that the location - and the choice of the treatment at the interface - may be critical at low Reynolds number or if the interface is placed too close to the wall. The reason is that the modelled turbulent shear stress at the interface is large and hence the relative strength of the resolved turbulence is small. In RANS, the turbulent viscosity - and consequently also the modelled Reynolds shear stress - is only weakly dependent on Reynolds number. It is found in the present work that it also applies in the URANS region.

Cavitating Propeller Performance in Inclined Shaft Conditions with OpenFOAM: PPTC 2015 Test Case

NASA Astrophysics Data System (ADS)

Gaggero, Stefano; Villa, Diego

2018-05-01

In this paper, we present our analysis of the non-cavitating and cavitating unsteady performances of the Potsdam Propeller Test Case (PPTC) in oblique flow. For our calculations, we used the Reynolds-averaged Navier-Stokes equation (RANSE) solver from the open-source OpenFOAM libraries. We selected the homogeneous mixture approach to solve for multiphase flow with phase change, using the volume of fluid (VoF) approach to solve the multiphase flow and modeling the mass transfer between vapor and water with the Schnerr-Sauer model. Comparing the model results with the experimental measurements collected during the Second Workshop on Cavitation and Propeller Performance - SMP'15 enabled our assessment of the reliability of the open-source calculations. Comparisons with the numerical data collected during the workshop enabled further analysis of the reliability of different flow solvers from which we produced an overview of recommended guidelines (mesh arrangements and solver setups) for accurate numerical prediction even in off-design conditions. Lastly, we propose a number of calculations using the boundary element method developed at the University of Genoa for assessing the reliability of this dated but still widely adopted approach for design and optimization in the preliminary stages of very demanding test cases.

Verification and Validation of the k-kL Turbulence Model in FUN3D and CFL3D Codes

NASA Technical Reports Server (NTRS)

Abdol-Hamid, Khaled S.; Carlson, Jan-Renee; Rumsey, Christopher L.

2015-01-01

The implementation of the k-kL turbulence model using multiple computational uid dy- namics (CFD) codes is reported herein. The k-kL model is a two-equation turbulence model based on Abdol-Hamid's closure and Menter's modi cation to Rotta's two-equation model. Rotta shows that a reliable transport equation can be formed from the turbulent length scale L, and the turbulent kinetic energy k. Rotta's equation is well suited for term-by-term mod- eling and displays useful features compared to other two-equation models. An important di erence is that this formulation leads to the inclusion of higher-order velocity derivatives in the source terms of the scale equations. This can enhance the ability of the Reynolds- averaged Navier-Stokes (RANS) solvers to simulate unsteady ows. The present report documents the formulation of the model as implemented in the CFD codes Fun3D and CFL3D. Methodology, veri cation and validation examples are shown. Attached and sepa- rated ow cases are documented and compared with experimental data. The results show generally very good comparisons with canonical and experimental data, as well as matching results code-to-code. The results from this formulation are similar or better than results using the SST turbulence model.

Aerodynamic Analysis of a Hale Aircraft Joined-Wing Configuration

NASA Astrophysics Data System (ADS)

Sivaji, Rangarajan; Ghia, Urmila; Ghia, Karman; Thornburg, Hugh

2003-11-01

Aerodynamic analysis of a high-aspect ratio, joined wing of a High-Altitude Long Endurance (HALE) aircraft is performed. The requirement of high lift over extended flight periods for the HALE aircraft leads to high-aspect ratio wings experiencing significant deflections necessitating consideration of aeroelastic effects. The finite-volume solver COBALT, with Reynolds-averaged Navier-Stokes (RANS) and Detached Eddy Simulation (DES) capabilities, is used for the flow simulations. Calculations are performed at á = 0° and 12° for M = 0.6, at an altitude of 30,000 feet, at a Re per unit length of 5.6x106. The wing cross sections are NACA 4421 airfoils. Because of the high lift-to-drag ratio wings, an inviscid flow analysis is also performed. The inviscid surface pressure coefficient (Cp) is compared with the corresponding viscous Cp to examine the feasibility of the use of the inviscid pressure loads as an estimate of the total fluid loads on the structure. The viscous and inviscid Cp results compare reasonably only at á = 0°. The viscous flow is examined in detail via surface and field velocity vectors, vorticity, density and pressure contours. For á = 12°, the unsteady DES solutions show a weak shock at the aft-wing trailing edge. Also, the flow near the joint exhibits a region of mild separation.

Simulation of an Isolated Tiltrotor in Hover with an Unstructured Overset-Grid RANS Solver

NASA Technical Reports Server (NTRS)

Lee-Rausch, Elizabeth M.; Biedron, Robert T.

2009-01-01

An unstructured overset-grid Reynolds Averaged Navier-Stokes (RANS) solver, FUN3D, is used to simulate an isolated tiltrotor in hover. An overview of the computational method is presented as well as the details of the overset-grid systems. Steady-state computations within a noninertial reference frame define the performance trends of the rotor across a range of the experimental collective settings. Results are presented to show the effects of off-body grid refinement and blade grid refinement. The computed performance and blade loading trends show good agreement with experimental results and previously published structured overset-grid computations. Off-body flow features indicate a significant improvement in the resolution of the first perpendicular blade vortex interaction with background grid refinement across the collective range. Considering experimental data uncertainty and effects of transition, the prediction of figure of merit on the baseline and refined grid is reasonable at the higher collective range- within 3 percent of the measured values. At the lower collective settings, the computed figure of merit is approximately 6 percent lower than the experimental data. A comparison of steady and unsteady results show that with temporal refinement, the dynamic results closely match the steady-state noninertial results which gives confidence in the accuracy of the dynamic overset-grid approach.

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.

Assessments of a Turbulence Model Based on Menter's Modification to Rotta's Two-Equation Model

NASA Technical Reports Server (NTRS)

Abdol-Hamid, Khaled S.

2013-01-01

The main objective of this paper is to construct a turbulence model with a more reliable second equation simulating length scale. In the present paper, we assess the length scale equation based on Menter s modification to Rotta s two-equation model. Rotta shows that a reliable second equation can be formed in an exact transport equation from the turbulent length scale L and kinetic energy. Rotta s equation is well suited for a term-by-term modeling and shows some interesting features compared to other approaches. The most important difference is that the formulation leads to a natural inclusion of higher order velocity derivatives into the source terms of the scale equation, which has the potential to enhance the capability of Reynolds-averaged Navier-Stokes (RANS) to simulate unsteady flows. The model is implemented in the PAB3D solver with complete formulation, usage methodology, and validation examples to demonstrate its capabilities. The detailed studies include grid convergence. Near-wall and shear flows cases are documented and compared with experimental and Large Eddy Simulation (LES) data. The results from this formulation are as good or better than the well-known SST turbulence model and much better than k-epsilon results. Overall, the study provides useful insights into the model capability in predicting attached and separated flows.

Computational Study of an Axisymmetric Dual Throat Fluidic Thrust Vectoring Nozzle for a Supersonic Aircraft Application

NASA Technical Reports Server (NTRS)

Deere, Karen A.; Flamm, Jeffrey D.; Berrier, Bobby L.; Johnson, Stuart K.

2007-01-01

A computational investigation of an axisymmetric Dual Throat Nozzle concept has been conducted. This fluidic thrust-vectoring nozzle was designed with a recessed cavity to enhance the throat shifting technique for improved thrust vectoring. The structured-grid, unsteady Reynolds- Averaged Navier-Stokes flow solver PAB3D was used to guide the nozzle design and analyze performance. Nozzle design variables included extent of circumferential injection, cavity divergence angle, cavity length, and cavity convergence angle. Internal nozzle performance (wind-off conditions) and thrust vector angles were computed for several configurations over a range of nozzle pressure ratios from 1.89 to 10, with the fluidic injection flow rate equal to zero and up to 4 percent of the primary flow rate. The effect of a variable expansion ratio on nozzle performance over a range of freestream Mach numbers up to 2 was investigated. Results indicated that a 60 circumferential injection was a good compromise between large thrust vector angles and efficient internal nozzle performance. A cavity divergence angle greater than 10 was detrimental to thrust vector angle. Shortening the cavity length improved internal nozzle performance with a small penalty to thrust vector angle. Contrary to expectations, a variable expansion ratio did not improve thrust efficiency at the flight conditions investigated.

Large eddy simulation of combustion characteristics in a kerosene fueled rocket-based combined-cycle engine combustor

NASA Astrophysics Data System (ADS)

Huang, Zhi-wei; He, Guo-qiang; Qin, Fei; Cao, Dong-gang; Wei, Xiang-geng; Shi, Lei

2016-10-01

This study reports combustion characteristics of a rocket-based combined-cycle engine combustor operating at ramjet mode numerically. Compressible large eddy simulation with liquid kerosene sprayed and vaporized is used to study the intrinsic unsteadiness of combustion in such a propulsion system. Results for the pressure oscillation amplitude and frequency in the combustor as well as the wall pressure distribution along the flow-path, are validated using experimental data, and they show acceptable agreement. Coupled with reduced chemical kinetics of kerosene, results are compared with the simultaneously obtained Reynolds-Averaged Navier-Stokes results, and show significant differences. A flow field analysis is also carried out for further study of the turbulent flame structures. Mixture fraction is used to determine the most probable flame location in the combustor at stoichiometric condition. Spatial distributions of the Takeno flame index, scalar dissipation rate, and heat release rate reveal that different combustion modes, such as premixed and non-premixed modes, coexisted at different sections of the combustor. The RBCC combustor is divided into different regions characterized by their non-uniform features. Flame stabilization mechanism, i.e., flame propagation or fuel auto-ignition, and their relative importance, is also determined at different regions in the combustor.

An assessment and application of turbulence models for hypersonic flows

NASA Technical Reports Server (NTRS)

Coakley, T. J.; Viegas, J. R.; Huang, P. G.; Rubesin, M. W.

1990-01-01

The current approach to the Accurate Computation of Complex high-speed flows is to solve the Reynolds averaged Navier-Stokes equations using finite difference methods. An integral part of this approach consists of development and applications of mathematical turbulence models which are necessary in predicting the aerothermodynamic loads on the vehicle and the performance of the propulsion plant. Computations of several high speed turbulent flows using various turbulence models are described and the models are evaluated by comparing computations with the results of experimental measurements. The cases investigated include flows over insulated and cooled flat plates with Mach numbers ranging from 2 to 8 and wall temperature ratios ranging from 0.2 to 1.0. The turbulence models investigated include zero-equation, two-equation, and Reynolds-stress transport models.

Exploring Model Assumptions Through Three Dimensional Mixing Simulations Using a High-order Hydro Option in the Ares Code

NASA Astrophysics Data System (ADS)

White, Justin; Olson, Britton; Morgan, Brandon; McFarland, Jacob; Lawrence Livermore National Laboratory Team; University of Missouri-Columbia Team

2015-11-01

This work presents results from a large eddy simulation of a high Reynolds number Rayleigh-Taylor instability and Richtmyer-Meshkov instability. A tenth-order compact differencing scheme on a fixed Eulerian mesh is utilized within the Ares code developed at Lawrence Livermore National Laboratory. (LLNL) We explore the self-similar limit of the mixing layer growth in order to evaluate the k-L-a Reynolds Averaged Navier Stokes (RANS) model (Morgan and Wickett, Phys. Rev. E, 2015). Furthermore, profiles of turbulent kinetic energy, turbulent length scale, mass flux velocity, and density-specific-volume correlation are extracted in order to aid the creation a high fidelity LES data set for RANS modeling. Prepared by LLNL under Contract DE-AC52-07NA27344.

Scaling laws for homogeneous turbulent shear flows in a rotating frame

NASA Technical Reports Server (NTRS)

Speziale, Charles G.; Mhuiris, Nessan Macgiolla

1988-01-01

The scaling properties of plane homogeneous turbulent shear flows in a rotating frame are examined mathematically by a direct analysis of the Navier-Stokes equations. It is proved that two such shear flows are dynamically similar if and only if their initial dimensionless energy spectrum E star (k star, 0), initial dimensionless shear rate SK sub 0/epsilon sub 0, initial Reynolds number K squared sub 0/nu epsilon sub 0, and the ration of the rotation rate to the shear rate omega/S are identical. Consequently, if universal equilibrium states exist, at high Reynolds numbers, they will only depend on the single parameter omega/S. The commonly assumed dependence of such equilibrium states on omega/S through the Richardson number Ri=-2(omega/S)(1-2 omega/S) is proven to be inconsistent with the full Navier-Stokes equations and to constitute no more than a weak approximation. To be more specific, Richardson number similarity is shown to only rigorously apply to certain low-order truncations of the Navier-Stokes equations (i.e., to certain second-order closure models) wherein closure is achieved at the second-moment level by assuming that the higher-order moments are a small perturbation of their isotropic states. The physical dependence of rotating turbulent shear flows on omega/S is discussed in detail along with the implications for turbulence modeling.

Navier-Stokes Computations of a Wing-Flap Model With Blowing Normal to the Flap Surface

NASA Technical Reports Server (NTRS)

Boyd, D. Douglas, Jr.

2005-01-01

A computational study of a generic wing with a half span flap shows the mean flow effects of several blown flap configurations. The effort compares and contrasts the thin-layer, Reynolds averaged, Navier-Stokes solutions of a baseline wing-flap configuration with configurations that have blowing normal to the flap surface through small slits near the flap side edge. Vorticity contours reveal a dual vortex structure at the flap side edge for all cases. The dual vortex merges into a single vortex at approximately the mid-flap chord location. Upper surface blowing reduces the strength of the merged vortex and moves the vortex away from the upper edge. Lower surface blowing thickens the lower shear layer and weakens the merged vortex, but not as much as upper surface blowing. Side surface blowing forces the lower surface vortex farther outboard of the flap edge by effectively increasing the aerodynamic span of the flap. It is seen that there is no global aerodynamic penalty or benefit from the particular blowing configurations examined.

Numerical computation of viscous flow about unconventional airfoil shapes

NASA Technical Reports Server (NTRS)

Ahmed, S.; Tannehill, J. C.

1990-01-01

A new two-dimensional computer code was developed to analyze the viscous flow around unconventional airfoils at various Mach numbers and angles of attack. The Navier-Stokes equations are solved using an implicit, upwind, finite-volume scheme. Both laminar and turbulent flows can be computed. A new nonequilibrium turbulence closure model was developed for computing turbulent flows. This two-layer eddy viscosity model was motivated by the success of the Johnson-King model in separated flow regions. The influence of history effects are described by an ordinary differential equation developed from the turbulent kinetic energy equation. The performance of the present code was evaluated by solving the flow around three airfoils using the Reynolds time-averaged Navier-Stokes equations. Excellent results were obtained for both attached and separated flows about the NACA 0012 airfoil, the RAE 2822 airfoil, and the Integrated Technology A 153W airfoil. Based on the comparison of the numerical solutions with the available experimental data, it is concluded that the present code in conjunction with the new nonequilibrium turbulence model gives excellent results.

Coupled fluid-flow and magnetic-field simulation of the Riga dynamo experiment

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

Kenjeres, S.; Hanjalic, K.; Renaudier, S.

2006-12-15

Magnetic fields of planets, stars, and galaxies result from self-excitation in moving electroconducting fluids, also known as the dynamo effect. This phenomenon was recently experimentally confirmed in the Riga dynamo experiment [A. Gailitis et al., Phys. Rev. Lett. 84, 4365 (2000); A. Gailitis et al., Physics of Plasmas 11, 2838 (2004)], consisting of a helical motion of sodium in a long pipe followed by a straight backflow in a surrounding annular passage, which provided adequate conditions for magnetic-field self-excitation. In this paper, a first attempt to simulate computationally the Riga experiment is reported. The velocity and turbulence fields are modeledmore » by a finite-volume Navier-Stokes solver using a Reynolds-averaged-Navier-Stokes turbulence model. The magnetic field is computed by an Adams-Bashforth finite-difference solver. The coupling of the two computational codes, although performed sequentially, provides an improved understanding of the interaction between the fluid velocity and magnetic fields in the saturation regime of the Riga dynamo experiment under realistic working conditions.« less

FANS Simulation of Propeller Wash at Navy Harbors (ESTEP Project ER-201031)

DTIC Science & Technology

2016-08-01

this study, the Finite-Analytic Navier–Stokes code was employed to solve the Reynolds-Averaged Navier–Stokes equations in conjunction with advanced...site-specific harbor configurations, it is desirable to perform propeller wash study by solving the Navier–Stokes equations directly in conjunction ...Analytic Navier–Stokes code was employed to solve the Reynolds-Averaged Navier–Stokes equations in conjunction with advanced near-wall turbulence

Exact integration of the unsteady incompressible Navier-Stokes equations, gauge criteria, and applications

NASA Astrophysics Data System (ADS)

Scholle, M.; Gaskell, P. H.; Marner, F.

2018-04-01

An exact first integral of the full, unsteady, incompressible Navier-Stokes equations is achieved in its most general form via the introduction of a tensor potential and parallels drawn with Maxwell's theory. Subsequent to this gauge freedoms are explored, showing that when used astutely they lead to a favourable reduction in the complexity of the associated equation set and number of unknowns, following which the inviscid limit case is discussed. Finally, it is shown how a change in gauge criteria enables a variational principle for steady viscous flow to be constructed having a self-adjoint form. Use of the new formulation is demonstrated, for different gauge variants of the first integral as the starting point, through the solution of a hierarchy of classical three-dimensional flow problems, two of which are tractable analytically, the third being solved numerically. In all cases the results obtained are found to be in excellent accord with corresponding solutions available in the open literature. Concurrently, the prescription of appropriate commonly occurring physical and necessary auxiliary boundary conditions, incorporating for completeness the derivation of a first integral of the dynamic boundary condition at a free surface, is established, together with how the general approach can be advantageously reformulated for application in solving unsteady flow problems with periodic boundaries.

Development of a three-dimensional Navier-Stokes code on CDC star-100 computer

NASA Technical Reports Server (NTRS)

Vatsa, V. N.; Goglia, G. L.

1978-01-01

A three-dimensional code in body-fitted coordinates was developed using MacCormack's algorithm. The code is structured to be compatible with any general configuration, provided that the metric coefficients for the transformation are available. The governing equations are developed in primitive variables in order to facilitate the incorporation of physical boundary conditions and turbulence-closure models. MacCormack's two-step, unsplit, time-marching algorithm is used to solve the unsteady Navier-Stokes equations until steady-state solution is achieved. Cases discussed include (1) flat plate in supersonic free stream; (2) supersonic flow along an axial corner; (3) subsonic flow in an axial corner at M infinity = 0.95; and (4) supersonic flow in an axial corner at M infinity 1.5.

Wake Management Strategies for Reduction of Turbomachinery Fan Noise

NASA Technical Reports Server (NTRS)

Waitz, Ian A.

1998-01-01

The primary objective of our work was to evaluate and test several wake management schemes for the reduction of turbomachinery fan noise. Throughout the course of this work we relied on several tools. These include 1) Two-dimensional steady boundary-layer and wake analyses using MISES (a thin-shear layer Navier-Stokes code), 2) Two-dimensional unsteady wake-stator interaction simulations using UNSFLO, 3) Three-dimensional, steady Navier-Stokes rotor simulations using NEWT, 4) Internal blade passage design using quasi-one-dimensional passage flow models developed at MIT, 5) Acoustic modeling using LINSUB, 6) Acoustic modeling using VO72, 7) Experiments in a low-speed cascade wind-tunnel, and 8) ADP fan rig tests in the MIT Blowdown Compressor.

Computational study of engine external aerodynamics as a part of multidisciplinary optimization procedure

NASA Astrophysics Data System (ADS)

Savelyev, Andrey; Anisimov, Kirill; Kazhan, Egor; Kursakov, Innocentiy; Lysenkov, Alexandr

2016-10-01

The paper is devoted to the development of methodology to optimize external aerodynamics of the engine. Optimization procedure is based on numerical solution of the Reynolds-averaged Navier-Stokes equations. As a method of optimization the surrogate based method is used. As a test problem optimal shape design of turbofan nacelle is considered. The results of the first stage, which investigates classic airplane configuration with engine located under the wing, are presented. Described optimization procedure is considered in the context of multidisciplinary optimization of the 3rd generation, developed in the project AGILE.

Numerical prediction of a draft tube flow taking into account uncertain inlet conditions

NASA Astrophysics Data System (ADS)

Brugiere, O.; Balarac, G.; Corre, C.; Metais, O.; Flores, E.; Pleroy

2012-11-01

The swirling turbulent flow in a hydroturbine draft tube is computed with a non-intrusive uncertainty quantification (UQ) method coupled to Reynolds-Averaged Navier-Stokes (RANS) modelling in order to take into account in the numerical prediction the physical uncertainties existing on the inlet flow conditions. The proposed approach yields not only mean velocity fields to be compared with measured profiles, as is customary in Computational Fluid Dynamics (CFD) practice, but also variance of these quantities from which error bars can be deduced on the computed profiles, thus making more significant the comparison between experiment and computation.

Multigrid Methods for Aerodynamic Problems in Complex Geometries

NASA Technical Reports Server (NTRS)

Caughey, David A.

1995-01-01

Work has been directed at the development of efficient multigrid methods for the solution of aerodynamic problems involving complex geometries, including the development of computational methods for the solution of both inviscid and viscous transonic flow problems. The emphasis is on problems of complex, three-dimensional geometry. The methods developed are based upon finite-volume approximations to both the Euler and the Reynolds-Averaged Navier-Stokes equations. The methods are developed for use on multi-block grids using diagonalized implicit multigrid methods to achieve computational efficiency. The work is focused upon aerodynamic problems involving complex geometries, including advanced engine inlets.

CFD Methods and Tools for Multi-Element Airfoil Analysis

NASA Technical Reports Server (NTRS)

Rogers, Stuart E.; George, Michael W. (Technical Monitor)

1995-01-01

This lecture will discuss the computational tools currently available for high-lift multi-element airfoil analysis. It will present an overview of a number of different numerical approaches, their current capabilities, short-comings, and computational costs. The lecture will be limited to viscous methods, including inviscid/boundary layer coupling methods, and incompressible and compressible Reynolds-averaged Navier-Stokes methods. Both structured and unstructured grid generation approaches will be presented. Two different structured grid procedures are outlined, one which uses multi-block patched grids, the other uses overset chimera grids. Turbulence and transition modeling will be discussed.

Preliminary Computational Fluid Dynamics (CFD) Simulation of EIIB Push Barge in Shallow Water

NASA Astrophysics Data System (ADS)

Beneš, Petr; Kollárik, Róbert

2011-12-01

This study presents preliminary CFD simulation of EIIb push barge in inland conditions using CFD software Ansys Fluent. The RANSE (Reynolds Averaged Navier-Stokes Equation) methods are used for the viscosity solution of turbulent flow around the ship hull. Different RANSE methods are used for the comparison of their results in ship resistance calculations, for selecting the appropriate and removing inappropriate methods. This study further familiarizes on the creation of geometrical model which considers exact water depth to vessel draft ratio in shallow water conditions, grid generation, setting mathematical model in Fluent and evaluation of the simulations results.

LES, DNS and RANS for the analysis of high-speed turbulent reacting flows

NASA Technical Reports Server (NTRS)

Adumitroaie, V.; Colucci, P. J.; Taulbee, D. B.; Givi, P.

1995-01-01

The purpose of this research is to continue our efforts in advancing the state of knowledge in large eddy simulation (LES), direct numerical simulation (DNS), and Reynolds averaged Navier Stokes (RANS) methods for the computational analysis of high-speed reacting turbulent flows. In the second phase of this work, covering the period 1 Aug. 1994 - 31 Jul. 1995, we have focused our efforts on two programs: (1) developments of explicit algebraic moment closures for statistical descriptions of compressible reacting flows and (2) development of Monte Carlo numerical methods for LES of chemically reacting flows.

The high-energy-density counterpropagating shear experiment and turbulent self-heating

DOE PAGES

Doss, F. W.; Fincke, J. R.; Loomis, E. N.; ...

2013-12-06

The counterpropagating shear experiment has previously demonstrated the ability to create regions of shockdriven shear, balanced symmetrically in pressure and experiencing minimal net drift. This allows for the creation of a high-Mach-number high-energy-density shear environment. New data from the counterpropagating shear campaign is presented, and both hydrocode modeling and theoretical analysis in the context of a Reynolds-averaged-Navier-Stokes model suggest turbulent dissipation of energy from the supersonic flow bounding the layer is a significant driver in its expansion. A theoretical minimum shear flow Mach number threshold is suggested for substantial thermal-turbulence coupling.

Aerodynamic study of different cyclist positions: CFD analysis and full-scale wind-tunnel tests.

PubMed

Defraeye, Thijs; Blocken, Bert; Koninckx, Erwin; Hespel, Peter; Carmeliet, Jan

2010-05-07

Three different cyclist positions were evaluated with Computational Fluid Dynamics (CFD) and wind-tunnel experiments were used to provide reliable data to evaluate the accuracy of the CFD simulations. Specific features of this study are: (1) both steady Reynolds-averaged Navier-Stokes (RANS) and unsteady flow modelling, with more advanced turbulence modelling techniques (Large-Eddy Simulation - LES), were evaluated; (2) the boundary layer on the cyclist's surface was resolved entirely with low-Reynolds number modelling, instead of modelling it with wall functions; (3) apart from drag measurements, also surface pressure measurements on the cyclist's body were performed in the wind-tunnel experiment, which provided the basis for a more detailed evaluation of the predicted flow field by CFD. The results show that the simulated and measured drag areas differed about 11% (RANS) and 7% (LES), which is considered to be a close agreement in CFD studies. A fair agreement with wind-tunnel data was obtained for the predicted surface pressures, especially with LES. Despite the higher accuracy of LES, its much higher computational cost could make RANS more attractive for practical use in some situations. CFD is found to be a valuable tool to evaluate the drag of different cyclist positions and to investigate the influence of small adjustments in the cyclist's position. A strong advantage of CFD is that detailed flow field information is obtained, which cannot easily be obtained from wind-tunnel tests. This detailed information allows more insight in the causes of the drag force and provides better guidance for position improvements. Copyright 2010 Elsevier Ltd. All rights reserved.

Quantifying and reducing model-form uncertainties in Reynolds-averaged Navier-Stokes simulations: A data-driven, physics-informed Bayesian approach

NASA Astrophysics Data System (ADS)

Xiao, H.; Wu, J.-L.; Wang, J.-X.; Sun, R.; Roy, C. J.

2016-11-01

Despite their well-known limitations, Reynolds-Averaged Navier-Stokes (RANS) models are still the workhorse tools for turbulent flow simulations in today's engineering analysis, design and optimization. While the predictive capability of RANS models depends on many factors, for many practical flows the turbulence models are by far the largest source of uncertainty. As RANS models are used in the design and safety evaluation of many mission-critical systems such as airplanes and nuclear power plants, quantifying their model-form uncertainties has significant implications in enabling risk-informed decision-making. In this work we develop a data-driven, physics-informed Bayesian framework for quantifying model-form uncertainties in RANS simulations. Uncertainties are introduced directly to the Reynolds stresses and are represented with compact parameterization accounting for empirical prior knowledge and physical constraints (e.g., realizability, smoothness, and symmetry). An iterative ensemble Kalman method is used to assimilate the prior knowledge and observation data in a Bayesian framework, and to propagate them to posterior distributions of velocities and other Quantities of Interest (QoIs). We use two representative cases, the flow over periodic hills and the flow in a square duct, to evaluate the performance of the proposed framework. Both cases are challenging for standard RANS turbulence models. Simulation results suggest that, even with very sparse observations, the obtained posterior mean velocities and other QoIs have significantly better agreement with the benchmark data compared to the baseline results. At most locations the posterior distribution adequately captures the true model error within the developed model form uncertainty bounds. The framework is a major improvement over existing black-box, physics-neutral methods for model-form uncertainty quantification, where prior knowledge and details of the models are not exploited. This approach has potential implications in many fields in which the governing equations are well understood but the model uncertainty comes from unresolved physical processes.

Transition and mixing in axisymmetric jets and vortex rings

NASA Technical Reports Server (NTRS)

Allen, G. A., Jr.; Cantwell, B. J.

1986-01-01

A class of impulsively started, axisymmetric, laminar jets produced by a time dependent joint source of momentum are considered. These jets are different flows, each initially at rest in an unbounded fluid. The study is conducted at three levels of detail. First, a generalized set of analytic creeping flow solutions are derived with a method of flow classification. Second, from this set, three specific creeping flow solutions are studied in detail: the vortex ring, the round jet, and the ramp jet. This study involves derivation of vorticity, stream function, entrainment diagrams, and evolution of time lines through computer animation. From entrainment diagrams, critical points are derived and analyzed. The flow geometry is dictated by the properties and location of critical points which undergo bifurcation and topological transformation (a form of transition) with changing Reynolds number. Transition Reynolds numbers were calculated. A state space trajectory was derived describing the topological behavior of these critical points. This state space derivation yielded three states of motion which are universal for all axisymmetric jets. Third, the axisymmetric round jet is solved numerically using the unsteady laminar Navier Stokes equations. These equations were shown to be self similar for the round jet. Numerical calculations were performed up to a Reynolds number of 30 for a 60x60 point mesh. Animations generated from numerical solution showed each of the three states of motion for the round jet, including the Re = 30 case.

Effect of Rotational Speed on the Stability of Two Rotating Side-by-side Circular Cylinders at Low Reynolds Number

NASA Astrophysics Data System (ADS)

Dou, Huashu; Zhang, Shuo; Yang, Hui; Setoguchi, Toshiaki; Kinoue, Yoichi

2018-04-01

Flow around two rotating side-by-side circular cylinders of equal diameter D is numerically studied at the Reynolds number 40≤ Re ≤200 and various rotation rate θ i . The incoming flow is assumed to be two-dimensional laminar flow. The governing equations are the incompressible Navier-Stokes equations and solved by the finite volume method (FVM). The ratio of the center-to-center spacing to the cylinder diameter is T/D=2. The objective of the present work is to investigate the effect of rotational speed and Reynolds number on the stability of the flow. The simulation results are compared with the experimental data and a good agreement is achieved. The stability of the flow is analyzed by using the energy gradient theory, which produces the energy gradient function K to identify the region where the flow is the most prone to be destabilized and the degree of the destabilization. Numerical results reveal that K is the most significant at the separated shear layers of the cylinder pair. With Re increases, the length of the wake is shorter and the vortex shedding generally exhibits a symmetrical distribution for θ i < θ crit . It is also shown that the unsteady vortex shedding can be suppressed by rotating the cylinders in the counter-rotating mode.

Multiple-relaxation-time color-gradient lattice Boltzmann model for simulating two-phase flows with high density ratio

NASA Astrophysics Data System (ADS)

Ba, Yan; Liu, Haihu; Li, Qing; Kang, Qinjun; Sun, Jinju

2016-08-01

In this paper we propose a color-gradient lattice Boltzmann (LB) model for simulating two-phase flows with high density ratio and high Reynolds number. The model applies a multirelaxation-time (MRT) collision operator to enhance the stability of the simulation. A source term, which is derived by the Chapman-Enskog analysis, is added into the MRT LB equation so that the Navier-Stokes equations can be exactly recovered. Also, a form of the equilibrium density distribution function is used to simplify the source term. To validate the proposed model, steady flows of a static droplet and the layered channel flow are first simulated with density ratios up to 1000. Small values of spurious velocities and interfacial tension errors are found in the static droplet test, and improved profiles of velocity are obtained by the present model in simulating channel flows. Then, two cases of unsteady flows, Rayleigh-Taylor instability and droplet splashing on a thin film, are simulated. In the former case, the density ratio of 3 and Reynolds numbers of 256 and 2048 are considered. The interface shapes and spike and bubble positions are in good agreement with the results of previous studies. In the latter case, the droplet spreading radius is found to obey the power law proposed in previous studies for the density ratio of 100 and Reynolds number up to 500.

Numerical solutions of Navier-Stokes equations for a Butler wing

NASA Technical Reports Server (NTRS)

Abolhassani, J. S.; Tiwari, S. N.

1985-01-01

The flow field is simulated on the surface of a given delta wing (Butler wing) at zero incident in a uniform stream. The simulation is done by integrating a set of flow field equations. This set of equations governs the unsteady, viscous, compressible, heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. These equations are solved by the finite difference method, and results obtained for high-speed freestream conditions are compared with theoretical and experimental results. In this study, the Navier-Stokes equations are solved numerically. These equations are unsteady, compressible, viscous, and three-dimensional without neglecting any terms. The time dependency of the governing equations allows the solution to progress naturally for an arbitrary initial initial guess to an asymptotic steady state, if one exists. The equations are transformed from physical coordinates to the computational coordinates, allowing the solution of the governing equations in a rectangular parallel-piped domain. The equations are solved by the MacCormack time-split technique which is vectorized and programmed to run on the CDC VPS 32 computer.

Deep learning of unsteady laminar flow over a cylinder

NASA Astrophysics Data System (ADS)

Lee, Sangseung; You, Donghyun

2017-11-01

Unsteady flow over a circular cylinder is reconstructed using deep learning with a particular emphasis on elucidating the potential of learning the solution of the Navier-Stokes equations. A deep neural network (DNN) is employed for deep learning, while numerical simulations are conducted to produce training database. Instantaneous and mean flow fields which are reconstructed by deep learning are compared with the simulation results. Fourier transform of flow variables has been conducted to validate the ability of DNN to capture both amplitudes and frequencies of flow motions. Basis decomposition of learned flow is performed to understand the underlying mechanisms of learning flow through DNN. The present study suggests that a deep learning technique can be utilized for reconstruction and, potentially, for prediction of fluid flow instead of solving the Navier-Stokes equations. This work was supported by the National Research Foundation of Korea(NRF) Grant funded by the Korea government(Ministry of Science, ICT and Future Planning) (No. 2014R1A2A1A11049599, No. 2015R1A2A1A15056086, No. 2016R1E1A2A01939553).

Self-Contained Automated Methodology for Optimal Flow Control

NASA Technical Reports Server (NTRS)

Joslin, Ronald D.; Gunzburger, Max D.; Nicolaides, Roy A.; Erlebacherl, Gordon; Hussaini, M. Yousuff

1997-01-01

This paper describes a self-contained, automated methodology for active flow control which couples the time-dependent Navier-Stokes system with an adjoint Navier-Stokes system and optimality conditions from which optimal states, i.e., unsteady flow fields and controls (e.g., actuators), may be determined. The problem of boundary layer instability suppression through wave cancellation is used as the initial validation case to test the methodology. Here, the objective of control is to match the stress vector along a portion of the boundary to a given vector; instability suppression is achieved by choosing the given vector to be that of a steady base flow. Control is effected through the injection or suction of fluid through a single orifice on the boundary. The results demonstrate that instability suppression can be achieved without any a priori knowledge of the disturbance, which is significant because other control techniques have required some knowledge of the flow unsteadiness such as frequencies, instability type, etc. The present methodology has been extended to three dimensions and may potentially be applied to separation control, re-laminarization, and turbulence control applications using one to many sensors and actuators.

Group-theoretical model of developed turbulence and renormalization of the Navier-Stokes equation.

PubMed

Saveliev, V L; Gorokhovski, M A

2005-07-01

On the basis of the Euler equation and its symmetry properties, this paper proposes a model of stationary homogeneous developed turbulence. A regularized averaging formula for the product of two fields is obtained. An equation for the averaged turbulent velocity field is derived from the Navier-Stokes equation by renormalization-group transformation.

A Navier-Stokes-Based Approach for Mean Flow Perturbation Analysis

NASA Astrophysics Data System (ADS)

Bhaumik, Swagata; Gaitonde, Datta; Waindim, Mbu; The Ohio State University Team

2014-11-01

The manner in which a basic state, obtained from a time-averaged unsteady flowfield, processes perturbations can provide significant insight into the cause and evolution of instabilities. A widely used approach is based on Parabolized Stability Equations (PSE), which limits streamwise mean flow variation and is often applied to 2-D base flows. To avoid some of these issues, we advance a Navier-Stokes-based method, which can address non-trivial three-dimensional fields. The method stems from that employed by Touber and Sandham (Theor. Comput. Fluid. Dyn., 23, 79, 2009) to analyze global modes in nominally 2-D shock-wave turbulent-boundary layer interactions (STBLI). We first develop its theoretical underpinnings by examining conditions under which it degenerates to traditional methods. We then illustrate the application by considering perturbations to an entropy layer at Mach 6, a turbulent supersonic jet at Mach 1.3 and STBLI at Mach 2.3. For the entropy layer and jet cases, known linear stability and PSE results are successfully reproduced, while global modes are obtained for STBLI. The results not only validate the proposed technique, but also demonstrate its suitability in analyzing instabilities for any general 3D basic state, including impulse response. Sponsored by AFOSR.

Time-Accurate Numerical Simulations of Synthetic Jet Quiescent Air

NASA Technical Reports Server (NTRS)

Rupesh, K-A. B.; Ravi, B. R.; Mittal, R.; Raju, R.; Gallas, Q.; Cattafesta, L.

2007-01-01

The unsteady evolution of three-dimensional synthetic jet into quiescent air is studied by time-accurate numerical simulations using a second-order accurate mixed explicit-implicit fractional step scheme on Cartesian grids. Both two-dimensional and three-dimensional calculations of synthetic jet are carried out at a Reynolds number (based on average velocity during the discharge phase of the cycle V(sub j), and jet width d) of 750 and Stokes number of 17.02. The results obtained are assessed against PIV and hotwire measurements provided for the NASA LaRC workshop on CFD validation of synthetic jets.

Near-Field Noise Computation for a Supersonic Circular Jet

NASA Technical Reports Server (NTRS)

Loh, Ching Y.; Hultgren, Lennart S.

2005-01-01

A fully expanded, high-Reynolds-number, supersonic circular jet of Mach number 1.4 is simulated, using a 3-D finite-volume Navier-Stokes solver, with emphasis on the near field noise. The numerical results are generally in good agreement with existing experimental findings.

Time-asymptotic solutions of the Navier-Stokes equation for free shear flows using an alternating-direction implicit method

NASA Technical Reports Server (NTRS)

Rudy, D. H.; Morris, D. J.

1976-01-01

An uncoupled time asymptotic alternating direction implicit method for solving the Navier-Stokes equations was tested on two laminar parallel mixing flows. A constant total temperature was assumed in order to eliminate the need to solve the full energy equation; consequently, static temperature was evaluated by using algebraic relationship. For the mixing of two supersonic streams at a Reynolds number of 1,000, convergent solutions were obtained for a time step 5 times the maximum allowable size for an explicit method. The solution diverged for a time step 10 times the explicit limit. Improved convergence was obtained when upwind differencing was used for convective terms. Larger time steps were not possible with either upwind differencing or the diagonally dominant scheme. Artificial viscosity was added to the continuity equation in order to eliminate divergence for the mixing of a subsonic stream with a supersonic stream at a Reynolds number of 1,000.

Kinetically reduced local Navier-Stokes equations for simulation of incompressible viscous flows.

PubMed

Borok, S; Ansumali, S; Karlin, I V

2007-12-01

Recently, another approach to study incompressible fluid flow was suggested [S. Ansumali, I. Karlin, and H. Ottinger, Phys. Rev. Lett. 94, 080602 (2005)]-the kinetically reduced local Navier-Stokes (KRLNS) equations. We consider a simplified two-dimensional KRLNS system and compare it with Chorin's artificial compressibility method. A comparison of the two methods for steady state computation of the flow in a lid-driven cavity at various Reynolds numbers shows that the results from both methods are in good agreement with each other. However, in the transient flow, it is demonstrated that the KRLNS equations correctly describe the time evolution of the velocity and of the pressure, unlike the artificial compressibility method.

Time-accurate simulations of a shear layer forced at a single frequency

NASA Technical Reports Server (NTRS)

Claus, R. W.; Huang, P. G.; Macinnes, J. M.

1988-01-01

Calculations are presented for the forced shear layer studied experimentally by Oster and Wygnanski, and Weisbrot. Two different computational approaches are examined: Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES). The DNS approach solves the full three dimensional Navier-Stokes equations for a temporally evolving mixing layer, while the LES approach solves the two dimensional Navier-Stokes equations with a subgrid scale turbulence model. While the comparison between these calculations and experimental data was hampered by a lack of information on the inflow boundary conditions, the calculations are shown to qualitatively agree with several aspects of the experiment. The sensitivity of these calculations to factors such as mesh refinement and Reynolds number is illustrated.

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.

Buoyancy and blockage effects on transient laminar opposing mixed convection heat transfer from two horizontal confined isothermal cylinder in tandem

NASA Astrophysics Data System (ADS)

Martínez-Suástegui, Lorenzo; Salcedo, Erick; Cajas, Juan; Treviño, César

2015-11-01

Transient mixed convection in a laminar cross-flow from two isothermal cylinders in tandem arrangement confined inside a vertical channel is studied numerically using the vorticity-stream function formulation of the unsteady two-dimensional Navier-Stokes and energy equations. Numerical experiments are performed for a Reynolds number based on cylinder diameter of Re = 200, Prandtl number of Pr = 7, blockage ratio of D/H = 0.2, a pitch-to-diameter ratio of L/D = 2, and several values of buoyancy strength or Richardson number Ri = Gr/Re2. The results reported herein demonstrate how the wall confinement, interference effects and opposing buoyancy affect the flow structure and heat transfer characteristics of the cylinder array. This research was supported by the Consejo Nacional de Ciencia y Tecnología (CONACYT), Grant number 167474 and by the Secretaría de Investigación y Posgrado del IPN, Grant number SIP 20141309.

Flow on the symmetry plane of a total cavo-pulmonary connection.

PubMed

Bolzon, G; Pedrizzetti, G; Grigioni, M; Zovatto, L; Daniele, C; D'Avenio, G

2002-05-01

The flow inside a total cavo-pulmonary connection, a bypass operation of the right heart adopted in the presence of congenital malformation, is here studied for a specific geometry which has been recently introduced in clinics. The analysis has been performed by preliminary experimental observation and a novel Navier-Stokes formulation on the symmetry plane. This method, once some basic hypotheses are verified, allows to reproduce the flow on the symmetry plane of a three-dimensional field by using an extension of the two-dimensional approach. The analysis has confirmed the existence of a central vortex showing that it is not a real vortex (i.e. a place with accumulation of vorticity) but, rather, a weakly dissipative recirculating zone. It is surrounded by a shear layer that becomes spontaneously unsteady at moderately high Reynolds number. The topological changes and energy dissipation have been analysed in both cases of unbalanced and of balanced pulmonary artery and caval flows.

Numerical method for predicting flow characteristics and performance of nonaxisymmetric nozzles, theory

NASA Technical Reports Server (NTRS)

Thomas, P. D.

1979-01-01

The theoretical foundation and formulation of a numerical method for predicting the viscous flowfield in and about isolated three dimensional nozzles of geometrically complex configuration are presented. High Reynolds number turbulent flows are of primary interest for any combination of subsonic, transonic, and supersonic flow conditions inside or outside the nozzle. An alternating-direction implicit (ADI) numerical technique is employed to integrate the unsteady Navier-Stokes equations until an asymptotic steady-state solution is reached. Boundary conditions are computed with an implicit technique compatible with the ADI technique employed at interior points of the flow region. The equations are formulated and solved in a boundary-conforming curvilinear coordinate system. The curvilinear coordinate system and computational grid is generated numerically as the solution to an elliptic boundary value problem. A method is developed that automatically adjusts the elliptic system so that the interior grid spacing is controlled directly by the a priori selection of the grid spacing on the boundaries of the flow region.

Numerical simulation of magnetic nanoparticles targeting in a bifurcation vessel

NASA Astrophysics Data System (ADS)

Larimi, M. M.; Ramiar, A.; Ranjbar, A. A.

2014-08-01

Guiding magnetic iron oxide nanoparticles with the help of an external magnetic field to its target is the principle behind the development of super paramagnetic iron oxide nanoparticles (SPIONs) as novel drug delivery vehicles. The present paper is devoted to study on MDT (Magnetic Drug Targeting) technique by particle tracking in the presence of magnetic field in a bifurcation vessel. The blood flow in bifurcation is considered incompressible, unsteady and Newtonian. The flow analysis applies the time dependent, two dimensional, incompressible Navier-Stokes equations for Newtonian fluids. The Lagrangian particle tracking is performed to estimate particle behavior under influence of imposed magnetic field gradients along the bifurcation. According to the results, the magnetic field increased the volume fraction of particle in target region, but in vessels with high Reynolds number, the efficiency of MDT technique is very low. Also the results showed that in the bifurcation vessels with lower angles, wall shear stress is higher and consequently the risk of the vessel wall rupture increases.

Simulation of Nonlinear Instabilities in an Attachment-Line Boundary Layer

NASA Technical Reports Server (NTRS)

Joslin, Ronald D.

1996-01-01

The linear and the nonlinear stability of disturbances that propagate along the attachment line of a three-dimensional boundary layer is considered. The spatially evolving disturbances in the boundary layer are computed by direct numerical simulation (DNS) of the unsteady, incompressible Navier-Stokes equations. Disturbances are introduced either by forcing at the in ow or by applying suction and blowing at the wall. Quasi-parallel linear stability theory and a nonparallel theory yield notably different stability characteristics for disturbances near the critical Reynolds number; the DNS results con rm the latter theory. Previously, a weakly nonlinear theory and computations revealed a high wave-number region of subcritical disturbance growth. More recent computations have failed to achieve this subcritical growth. The present computational results indicate the presence of subcritically growing disturbances; the results support the weakly nonlinear theory. Furthermore, an explanation is provided for the previous theoretical and computational discrepancy. In addition, the present results demonstrate that steady suction can be used to stabilize disturbances that otherwise grow subcritically along the attachment line.

Numerical study of large-eddy breakup and its effect on the drag characteristics of boundary layers

NASA Technical Reports Server (NTRS)

Kinney, R. B.; Taslim, M. E.; Hung, S. C.

1985-01-01

The break-up of a field of eddies by a flat-plate obstacle embedded in a boundary layer is studied using numerical solutions to the two-dimensional Navier-Stokes equations. The flow is taken to be incompressible and unsteady. The flow field is initiated from rest. A train of eddies of predetermined size and strength are swept into the computational domain upstream of the plate. The undisturbed velocity profile is given by the Blasius solution. The disturbance vorticity generated at the plate and wall, plus that introduced with the eddies, mix with the background vorticity and is transported throughout the entire flow. All quantities are scaled by the plate length, the unidsturbed free-stream velocity, and the fluid kinematic viscosity. The Reynolds number is 1000, the Blasius boundary layer thickness is 2.0, and the plate is positioned a distance of 1.0 above the wall. The computational domain is four units high and sixteen units long.

Fluid-structure interaction of turbulent boundary layer over a compliant surface

NASA Astrophysics Data System (ADS)

Anantharamu, Sreevatsa; Mahesh, Krishnan

2016-11-01

Turbulent flows induce unsteady loads on surfaces in contact with them, which affect material stresses, surface vibrations and far-field acoustics. We are developing a numerical methodology to study the coupled interaction of a turbulent boundary layer with the underlying surface. The surface is modeled as a linear elastic solid, while the fluid follows the spatially filtered incompressible Navier-Stokes equations. An incompressible Large Eddy Simulation finite volume flow approach based on the algorithm of Mahesh et al. is used in the fluid domain. The discrete kinetic energy conserving property of the method ensures robustness at high Reynolds number. The linear elastic model in the solid domain is integrated in space using finite element method and in time using the Newmark time integration method. The fluid and solid domain solvers are coupled using both weak and strong coupling methods. Details of the algorithm, validation, and relevant results will be presented. This work is supported by NSWCCD, ONR.

On the nonlinear stability of viscous modes within the Rayleigh problem on an infinite flat plate

NASA Technical Reports Server (NTRS)

Webb, J. C.; Otto, S. R.; Lilley, G. M.

1994-01-01

The stability has been investigated of the unsteady flow past an infinite flat plate when it is moved impulsively from rest, in its own plane. For small times the instantaneous stability of the flow depends on the linearized equations of motion which reduce in this problem to the Orr-Sommerfeld equation. It is known that the flow for certain values of Reynolds number, frequency and wave number is unstable to Tollmien-Schlichting waves, as in the case of the Blasius boundary layer flow past a flat plate. With increase in time, the unstable waves only undergo growth for a finite time interval, and this growth rate is itself a function of time. The influence of finite amplitude effects is studied by solving the full Navier-Stokes equations. It is found that the stability characteristics are markedly changed both by the consideration of the time evolution of the flow, and by the introduction of finite amplitude effects.

Numerical solutions of 2-D multi-stage rotor/stator unsteady flow interactions

NASA Astrophysics Data System (ADS)

Yang, R.-J.; Lin, S.-J.

1991-01-01

The Rai method of single-stage rotor/stator flow interaction is extended to handle multistage configurations. In this study, a two-dimensional Navier-Stokes multi-zone approach was used to investigate unsteady flow interactions within two multistage axial turbines. The governing equations are solved by an iterative, factored, implicit finite-difference, upwind algorithm. Numerical accuracy is checked by investigating the effect of time step size, the effect of subiteration in the Newton-Raphson technique, and the effect of full viscous versus thin-layer approximation. Computer results compared well with experimental data. Unsteady flow interactions, wake cutting, and the associated evolution of vortical entities are discussed.

Off-Design Performance of a Multi-Stage Supersonic Turbine

NASA Technical Reports Server (NTRS)

Dorney, Daniel J.; Griffin, Lisa W.; Huber, Frank; Sondak, Douglas L.

2003-01-01

The drive towards high-work turbines has led to designs which can be compact, transonic, supersonic, counter rotating, or use a dense drive gas. These aggressive designs can lead to strong unsteady secondary flows and flow separation. The amplitude and extent of these unsteady flow phenomena can be amplified at off-design operating conditions. Pre-test off-design predictions have been performed for a new two-stage supersonic turbine design that is currently being tested in air. The simulations were performed using a three-dimensional unsteady Navier-Stokes analysis, and the predicted results have been compared with solutions from a validated meanline analysis.

Pressure loadings in a rectangular cavity with and without a captive store

DOE PAGES

Barone, Matthew; Arunajatesan, Srinivasan

2016-05-31

Simulations of the flow past a rectangular cavity containing a model captive store are performed using a hybrid Reynolds-averaged Navier–Stokes/large-eddy simulation model. Calculated pressure fluctuation spectra are validated using measurements made on the same configuration in a trisonic wind tunnel at Mach numbers of 0.60, 0.80, and 1.47. The simulation results are used to calculate unsteady integrated forces and moments acting on the store. Spectra of the forces and moments, along with correlations calculated for force/moment pairs, reveal that a complex relationship exists between the unsteady integrated forces and the measured resonant cavity modes, as indicated in the cavity wallmore » pressure measurements. As a result, the structure of identified cavity resonant tones is examined by visualization of filtered surface pressure fields.« less

Wind Tunnel and Numerical Analysis of Thick Blunt Trailing Edge Airfoils

NASA Astrophysics Data System (ADS)

McLennan, Anthony William

Two-dimensional aerodynamic characteristics of several thick blunt trailing edge airfoils are presented. These airfoils are not only directly applicable to the root section of wind turbine blades, where they provide the required structural strength at a fraction of the material and weight of an equivalent sharp trailing edge airfoil, but are also applicable to the root sections of UAVs having high aspect ratios, that also encounter heavy root bending forces. The Reynolds averaged Navier-Stokes code, ARC2D, was the primary numerical tool used to analyze each airfoil. The UCD-38-095, referred to as the Pareto B airfoil in this thesis, was also tested in the University of California, Davis Aeronautical Wind Tunnel. The Pareto B has an experimentally determined maximum lift coefficient of 1.64 at 14 degrees incidence, minimum drag coefficient of 0.0385, and maximum lift over drag ratio of 35.9 at a lift coefficient of 1.38, 10 degrees incidence at a Reynolds number of 666,000. Zig-zag tape at 2% and 5% of the chord was placed on the leading edge pressure and suction side of the Pareto B model in order to determine the aerodynamic performance characteristics at turbulent flow conditions. Experimental Pareto B wind tunnel data and previous FB-3500-0875 data is also presented and used to validate the ARC2D results obtained in this study. Additionally MBFLO, a detached eddy simulation Navier-Stokes code, was used to analyze the Pareto B airfoil for comparison and validation purposes.