Thin-layer and full Navier-Stokes calculations for turbulent supersonic flow over a cone at an angle of attack

NASA Technical Reports Server (NTRS)

Smith, Crawford F.; Podleski, Steve D.

1993-01-01

The proper use of a computational fluid dynamics code requires a good understanding of the particular code being applied. In this report the application of CFL3D, a thin-layer Navier-Stokes code, is compared with the results obtained from PARC3D, a full Navier-Stokes code. In order to gain an understanding of the use of this code, a simple problem was chosen in which several key features of the code could be exercised. The problem chosen is a cone in supersonic flow at an angle of attack. The issues of grid resolution, grid blocking, and multigridding with CFL3D are explored. The use of multigridding resulted in a significant reduction in the computational time required to solve the problem. Solutions obtained are compared with the results using the full Navier-Stokes equations solver PARC3D. The results obtained with the CFL3D code compared well with the PARC3D solutions.

PHYSICS REQUIRES A SIMPLE LOW MACH NUMBER FLOW TO BE COMPRESSIBLE

EPA Science Inventory

Radial, laminar, plane, low velocity flow represents the simplest, non-linear fluid dynamics problem. Ostensibly this apparently trivial flow could be solved using the incompressible Navier-Stokes equations, universally believed to be adequate for such problems. Most researchers ...

Finite element flow analysis; Proceedings of the Fourth International Symposium on Finite Element Methods in Flow Problems, Chuo University, Tokyo, Japan, July 26-29, 1982

NASA Astrophysics Data System (ADS)

Kawai, T.

Among the topics discussed are the application of FEM to nonlinear free surface flow, Navier-Stokes shallow water wave equations, incompressible viscous flows and weather prediction, the mathematical analysis and characteristics of FEM, penalty function FEM, convective, viscous, and high Reynolds number FEM analyses, the solution of time-dependent, three-dimensional and incompressible Navier-Stokes equations, turbulent boundary layer flow, FEM modeling of environmental problems over complex terrain, and FEM's application to thermal convection problems and to the flow of polymeric materials in injection molding processes. Also covered are FEMs for compressible flows, including boundary layer flows and transonic flows, hybrid element approaches for wave hydrodynamic loadings, FEM acoustic field analyses, and FEM treatment of free surface flow, shallow water flow, seepage flow, and sediment transport. Boundary element methods and FEM computational technique topics are also discussed. For individual items see A84-25834 to A84-25896

A compatible high-order meshless method for the Stokes equations with applications to suspension flows

NASA Astrophysics Data System (ADS)

Trask, Nathaniel; Maxey, Martin; Hu, Xiaozhe

2018-02-01

A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a discretization that couples a staggered scheme for pressure approximation with a divergence-free velocity reconstruction to obtain an adaptive, high-order, finite difference-like discretization that can be efficiently solved with conventional algebraic multigrid techniques. We use analytic benchmarks to demonstrate equal-order convergence for both velocity and pressure when solving problems with curvilinear geometries. In order to study problems in dense suspensions, we couple the solution for the flow to the equations of motion for freely suspended particles in an implicit monolithic scheme. The combination of high-order accuracy with fully-implicit schemes allows the accurate resolution of stiff lubrication forces directly from the solution of the Stokes problem without the need to introduce sub-grid lubrication models.

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).

Compressible-Incompressible Two-Phase Flows with Phase Transition: Model Problem

NASA Astrophysics Data System (ADS)

Watanabe, Keiichi

2017-12-01

We study the compressible and incompressible two-phase flows separated by a sharp interface with a phase transition and a surface tension. In particular, we consider the problem in R^N , and the Navier-Stokes-Korteweg equations is used in the upper domain and the Navier-Stokes equations is used in the lower domain. We prove the existence of R -bounded solution operator families for a resolvent problem arising from its model problem. According to Göts and Shibata (Asymptot Anal 90(3-4):207-236, 2014), the regularity of ρ _+ is W^1_q in space, but to solve the kinetic equation: u_Γ \\cdot n_t = [[ρ u

On a multigrid method for the coupled Stokes and porous media flow problem

NASA Astrophysics Data System (ADS)

Luo, P.; Rodrigo, C.; Gaspar, F. J.; Oosterlee, C. W.

2017-07-01

The multigrid solution of coupled porous media and Stokes flow problems is considered. The Darcy equation as the saturated porous medium model is coupled to the Stokes equations by means of appropriate interface conditions. We focus on an efficient multigrid solution technique for the coupled problem, which is discretized by finite volumes on staggered grids, giving rise to a saddle point linear system. Special treatment is required regarding the discretization at the interface. An Uzawa smoother is employed in multigrid, which is a decoupled procedure based on symmetric Gauss-Seidel smoothing for velocity components and a simple Richardson iteration for the pressure field. Since a relaxation parameter is part of a Richardson iteration, Local Fourier Analysis (LFA) is applied to determine the optimal parameters. Highly satisfactory multigrid convergence is reported, and, moreover, the algorithm performs well for small values of the hydraulic conductivity and fluid viscosity, that are relevant for applications.

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.

Generalized second-order slip boundary condition for nonequilibrium gas flows

NASA Astrophysics Data System (ADS)

Guo, Zhaoli; Qin, Jishun; Zheng, Chuguang

2014-01-01

It is a challenging task to model nonequilibrium gas flows within a continuum-fluid framework. Recently some extended hydrodynamic models in the Navier-Stokes formulation have been developed for such flows. A key problem in the application of such models is that suitable boundary conditions must be specified. In the present work, a generalized second-order slip boundary condition is developed in which an effective mean-free path considering the wall effect is used. By combining this slip scheme with certain extended Navier-Stokes constitutive relation models, we obtained a method for nonequilibrium gas flows with solid boundaries. The method is applied to several rarefied gas flows involving planar or curved walls, including the Kramers' problem, the planar Poiseuille flow, the cylindrical Couette flow, and the low speed flow over a sphere. The results show that the proposed method is able to give satisfied predictions, indicating the good potential of the method for nonequilibrium flows.

The Compressible Stokes Flows with No-Slip Boundary Condition on Non-Convex Polygons

NASA Astrophysics Data System (ADS)

Kweon, Jae Ryong

2017-03-01

In this paper we study the compressible Stokes equations with no-slip boundary condition on non-convex polygons and show a best regularity result that the solution can have without subtracting corner singularities. This is obtained by a suitable Helmholtz decomposition: {{{u}}={{w}}+nablaφ_R} with div w = 0 and a potential φ_R. Here w is the solution for the incompressible Stokes problem and φ_R is defined by subtracting from the solution of the Neumann problem the leading two corner singularities at non-convex vertices.

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.

Analysis of strong-interaction dynamic stall for laminar flow on airfoils

NASA Technical Reports Server (NTRS)

Gibeling, H. J.; Shamroth, S. J.; Eiseman, P. R.

1978-01-01

A compressible Navier-Stokes solution procedure is applied to the flow about an isolated airfoil. Two major problem areas were investigated. The first area is that of developing a coordinate system and an initial step in this direction has been taken. An airfoil coordinate system obtained from specification of discrete data points developed and the heat conduction equation has been solved in this system. Efforts required to allow the Navier-Stokes equations to be solved in this system are discussed. The second problem area is that of obtaining flow field solutions. Solutions for the flow about a circular cylinder and an isolated airfoil are presented. In the former case, the prediction is shown to be in good agreement with data.

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.

A reconstruction method of intra-ventricular blood flow using color flow ultrasound: a simulation study

NASA Astrophysics Data System (ADS)

Jang, Jaeseong; Ahn, Chi Young; Jeon, Kiwan; Choi, Jung-il; Lee, Changhoon; Seo, Jin Keun

2015-03-01

A reconstruction method is proposed here to quantify the distribution of blood flow velocity fields inside the left ventricle from color Doppler echocardiography measurement. From 3D incompressible Navier- Stokes equation, a 2D incompressible Navier-Stokes equation with a mass source term is derived to utilize the measurable color flow ultrasound data in a plane along with the moving boundary condition. The proposed model reflects out-of-plane blood flows on the imaging plane through the mass source term. For demonstrating a feasibility of the proposed method, we have performed numerical simulations of the forward problem and numerical analysis of the reconstruction method. First, we construct a 3D moving LV region having a specific stroke volume. To obtain synthetic intra-ventricular flows, we performed a numerical simulation of the forward problem of Navier-Stokes equation inside the 3D moving LV, computed 3D intra-ventricular velocity fields as a solution of the forward problem, projected the 3D velocity fields on the imaging plane and took the inner product of the 2D velocity fields on the imaging plane and scanline directional velocity fields for synthetic scanline directional projected velocity at each position. The proposed method utilized the 2D synthetic projected velocity data for reconstructing LV blood flow. By computing the difference between synthetic flow and reconstructed flow fields, we obtained the averaged point-wise errors of 0.06 m/s and 0.02 m/s for u- and v-components, respectively.

Towards adjoint-based inversion for rheological parameters in nonlinear viscous mantle flow

NASA Astrophysics Data System (ADS)

Worthen, Jennifer; Stadler, Georg; Petra, Noemi; Gurnis, Michael; Ghattas, Omar

2014-09-01

We address the problem of inferring mantle rheological parameter fields from surface velocity observations and instantaneous nonlinear mantle flow models. We formulate this inverse problem as an infinite-dimensional nonlinear least squares optimization problem governed by nonlinear Stokes equations. We provide expressions for the gradient of the cost functional of this optimization problem with respect to two spatially-varying rheological parameter fields: the viscosity prefactor and the exponent of the second invariant of the strain rate tensor. Adjoint (linearized) Stokes equations, which are characterized by a 4th order anisotropic viscosity tensor, facilitates efficient computation of the gradient. A quasi-Newton method for the solution of this optimization problem is presented, which requires the repeated solution of both nonlinear forward Stokes and linearized adjoint Stokes equations. For the solution of the nonlinear Stokes equations, we find that Newton’s method is significantly more efficient than a Picard fixed point method. Spectral analysis of the inverse operator given by the Hessian of the optimization problem reveals that the numerical eigenvalues collapse rapidly to zero, suggesting a high degree of ill-posedness of the inverse problem. To overcome this ill-posedness, we employ Tikhonov regularization (favoring smooth parameter fields) or total variation (TV) regularization (favoring piecewise-smooth parameter fields). Solution of two- and three-dimensional finite element-based model inverse problems show that a constant parameter in the constitutive law can be recovered well from surface velocity observations. Inverting for a spatially-varying parameter field leads to its reasonable recovery, in particular close to the surface. When inferring two spatially varying parameter fields, only an effective viscosity field and the total viscous dissipation are recoverable. Finally, a model of a subducting plate shows that a localized weak zone at the plate boundary can be partially recovered, especially with TV regularization.

A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem

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

Cortes, Adriano M.; Dalcin, Lisandro; Sarmiento, Adel F.

The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity–pressure pairs for viscous incompressible flows that are at the same time inf–sup stable and pointwise divergence-free. When applied to the discretized Stokes problem, these spaces generate a symmetric and indefinite saddle-point linear system. The iterative method of choice to solve such system is the Generalized Minimum Residual Method. This method lacks robustness, and one remedy is to use preconditioners. For linear systems of saddle-point type, a large family of preconditioners can be obtained by using a block factorization of the system. In this paper, we show howmore » the nesting of “black-box” solvers and preconditioners can be put together in a block triangular strategy to build a scalable block preconditioner for the Stokes system discretized by divergence-conforming B-splines. Lastly, besides the known cavity flow problem, we used for benchmark flows defined on complex geometries: an eccentric annulus and hollow torus of an eccentric annular cross-section.« less

A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem

DOE PAGES

Cortes, Adriano M.; Dalcin, Lisandro; Sarmiento, Adel F.; ...

2016-10-19

The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity–pressure pairs for viscous incompressible flows that are at the same time inf–sup stable and pointwise divergence-free. When applied to the discretized Stokes problem, these spaces generate a symmetric and indefinite saddle-point linear system. The iterative method of choice to solve such system is the Generalized Minimum Residual Method. This method lacks robustness, and one remedy is to use preconditioners. For linear systems of saddle-point type, a large family of preconditioners can be obtained by using a block factorization of the system. In this paper, we show howmore » the nesting of “black-box” solvers and preconditioners can be put together in a block triangular strategy to build a scalable block preconditioner for the Stokes system discretized by divergence-conforming B-splines. Lastly, besides the known cavity flow problem, we used for benchmark flows defined on complex geometries: an eccentric annulus and hollow torus of an eccentric annular cross-section.« less

Asymptotic behaviour of Stokes flow in a thin domain with a moving rough boundary

PubMed Central

Fabricius, J.; Koroleva, Y. O.; Tsandzana, A.; Wall, P.

2014-01-01

We consider a problem that models fluid flow in a thin domain bounded by two surfaces. One of the surfaces is rough and moving, whereas the other is flat and stationary. The problem involves two small parameters ϵ and μ that describe film thickness and roughness wavelength, respectively. Depending on the ratio λ=ϵ/μ, three different flow regimes are obtained in the limit as both of them tend to zero. Time-dependent equations of Reynolds type are obtained in all three cases (Stokes roughness, Reynolds roughness and high-frequency roughness regime). The derivations of the limiting equations are based on formal expansions in the parameters ϵ and μ. PMID:25002820

Aerodynamic Analyses Requiring Advanced Computers, Part 1

NASA Technical Reports Server (NTRS)

1975-01-01

Papers are presented which deal with results of theoretical research on aerodynamic flow problems requiring the use of advanced computers. Topics discussed include: viscous flows, boundary layer equations, turbulence modeling and Navier-Stokes equations, and internal flows.

A Navier-Stokes phase-field crystal model for colloidal suspensions

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

Praetorius, Simon, E-mail: simon.praetorius@tu-dresden.de; Voigt, Axel, E-mail: axel.voigt@tu-dresden.de

2015-04-21

We develop a fully continuous model for colloidal suspensions with hydrodynamic interactions. The Navier-Stokes Phase-Field Crystal model combines ideas of dynamic density functional theory with particulate flow approaches and is derived in detail and related to other dynamic density functional theory approaches with hydrodynamic interactions. The derived system is numerically solved using adaptive finite elements and is used to analyze colloidal crystallization in flowing environments demonstrating a strong coupling in both directions between the crystal shape and the flow field. We further validate the model against other computational approaches for particulate flow systems for various colloidal sedimentation problems.

A Navier-Stokes phase-field crystal model for colloidal suspensions.

PubMed

Praetorius, Simon; Voigt, Axel

2015-04-21

We develop a fully continuous model for colloidal suspensions with hydrodynamic interactions. The Navier-Stokes Phase-Field Crystal model combines ideas of dynamic density functional theory with particulate flow approaches and is derived in detail and related to other dynamic density functional theory approaches with hydrodynamic interactions. The derived system is numerically solved using adaptive finite elements and is used to analyze colloidal crystallization in flowing environments demonstrating a strong coupling in both directions between the crystal shape and the flow field. We further validate the model against other computational approaches for particulate flow systems for various colloidal sedimentation problems.

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.

Computation of multi-dimensional viscous supersonic flow

NASA Technical Reports Server (NTRS)

Buggeln, R. C.; Kim, Y. N.; Mcdonald, H.

1986-01-01

A method has been developed for two- and three-dimensional computations of viscous supersonic jet flows interacting with an external flow. The approach employs a reduced form of the Navier-Stokes equations which allows solution as an initial-boundary value problem in space, using an efficient noniterative forward marching algorithm. Numerical instability associated with forward marching algorithms for flows with embedded subsonic regions is avoided by approximation of the reduced form of the Navier-Stokes equations in the subsonic regions of the boundary layers. Supersonic and subsonic portions of the flow field are simultaneously calculated by a consistently split linearized block implicit computational algorithm. The results of computations for a series of test cases associated with supersonic jet flow is presented and compared with other calculations for axisymmetric cases. Demonstration calculations indicate that the computational technique has great promise as a tool for calculating a wide range of supersonic flow problems including jet flow. Finally, a User's Manual is presented for the computer code used to perform the calculations.

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.

Nonlinear travelling waves in rotating Hagen–Poiseuille flow

NASA Astrophysics Data System (ADS)

Pier, Benoît; Govindarajan, Rama

2018-03-01

The dynamics of viscous flow through a rotating pipe is considered. Small-amplitude stability characteristics are obtained by linearizing the Navier–Stokes equations around the base flow and solving the resulting eigenvalue problems. For linearly unstable configurations, the dynamics leads to fully developed finite-amplitude perturbations that are computed by direct numerical simulations of the complete Navier–Stokes equations. By systematically investigating all linearly unstable combinations of streamwise wave number k and azimuthal mode number m, for streamwise Reynolds numbers {{Re}}z ≤slant 500 and rotational Reynolds numbers {{Re}}{{Ω }} ≤slant 500, the complete range of nonlinear travelling waves is obtained and the associated flow fields are characterized.

Adaptive mesh refinement techniques for the immersed interface method applied to flow problems

PubMed Central

Li, Zhilin; Song, Peng

2013-01-01

In this paper, we develop an adaptive mesh refinement strategy of the Immersed Interface Method for flow problems with a moving interface. The work is built on the AMR method developed for two-dimensional elliptic interface problems in the paper [12] (CiCP, 12(2012), 515–527). The interface is captured by the zero level set of a Lipschitz continuous function φ(x, y, t). Our adaptive mesh refinement is built within a small band of |φ(x, y, t)| ≤ δ with finer Cartesian meshes. The AMR-IIM is validated for Stokes and Navier-Stokes equations with exact solutions, moving interfaces driven by the surface tension, and classical bubble deformation problems. A new simple area preserving strategy is also proposed in this paper for the level set method. PMID:23794763

Numerical Simulation of Interaction of Human Vocal Folds and Fluid Flow

NASA Astrophysics Data System (ADS)

Kosík, A.; Feistauer, M.; Horáček, J.; Sváček, P.

Our goal is to simulate airflow in human vocal folds and their flow-induced vibrations. We consider two-dimensional viscous incompressible flow in a time-dependent domain. The fluid flow is described by the Navier-Stokes equations in the arbitrary Lagrangian-Eulerian formulation. The flow problem is coupled with the elastic behaviour of the solid bodies. The developed solution of the coupled problem based on the finite element method is demonstrated by numerical experiments.

Application of CFD codes to the design and development of propulsion systems

NASA Technical Reports Server (NTRS)

Lord, W. K.; Pickett, G. F.; Sturgess, G. J.; Weingold, H. D.

1987-01-01

The internal flows of aerospace propulsion engines have certain common features that are amenable to analysis through Computational Fluid Dynamics (CFD) computer codes. Although the application of CFD to engineering problems in engines was delayed by the complexities associated with internal flows, many codes with different capabilities are now being used as routine design tools. This is illustrated by examples taken from the aircraft gas turbine engine of flows calculated with potential flow, Euler flow, parabolized Navier-Stokes, and Navier-Stokes codes. Likely future directions of CFD applied to engine flows are described, and current barriers to continued progress are highlighted. The potential importance of the Numerical Aerodynamic Simulator (NAS) to resolution of these difficulties is suggested.

Finite element computation of a viscous compressible free shear flow governed by the time dependent Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Cooke, C. H.; Blanchard, D. K.

1975-01-01

A finite element algorithm for solution of fluid flow problems characterized by the two-dimensional compressible Navier-Stokes equations was developed. The program is intended for viscous compressible high speed flow; hence, primitive variables are utilized. The physical solution was approximated by trial functions which at a fixed time are piecewise cubic on triangular elements. The Galerkin technique was employed to determine the finite-element model equations. A leapfrog time integration is used for marching asymptotically from initial to steady state, with iterated integrals evaluated by numerical quadratures. The nonsymmetric linear systems of equations governing time transition from step-to-step are solved using a rather economical block iterative triangular decomposition scheme. The concept was applied to the numerical computation of a free shear flow. Numerical results of the finite-element method are in excellent agreement with those obtained from a finite difference solution of the same problem.

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.

Energy-based operator splitting approach for the time discretization of coupled systems of partial and ordinary differential equations for fluid flows: The Stokes case

NASA Astrophysics Data System (ADS)

Carichino, Lucia; Guidoboni, Giovanna; Szopos, Marcela

2018-07-01

The goal of this work is to develop a novel splitting approach for the numerical solution of multiscale problems involving the coupling between Stokes equations and ODE systems, as often encountered in blood flow modeling applications. The proposed algorithm is based on a semi-discretization in time based on operator splitting, whose design is guided by the rationale of ensuring that the physical energy balance is maintained at the discrete level. As a result, unconditional stability with respect to the time step choice is ensured by the implicit treatment of interface conditions within the Stokes substeps, whereas the coupling between Stokes and ODE substeps is enforced via appropriate initial conditions for each substep. Notably, unconditional stability is attained without the need of subiterating between Stokes and ODE substeps. Stability and convergence properties of the proposed algorithm are tested on three specific examples for which analytical solutions are derived.

Variational method enabling simplified solutions to the linearized Boltzmann equation for oscillatory gas flows

NASA Astrophysics Data System (ADS)

Ladiges, Daniel R.; Sader, John E.

2018-05-01

Nanomechanical resonators and sensors, operated in ambient conditions, often generate low-Mach-number oscillating rarefied gas flows. Cercignani [C. Cercignani, J. Stat. Phys. 1, 297 (1969), 10.1007/BF01007482] proposed a variational principle for the linearized Boltzmann equation, which can be used to derive approximate analytical solutions of steady (time-independent) flows. Here we extend and generalize this principle to unsteady oscillatory rarefied flows and thus accommodate resonating nanomechanical devices. This includes a mathematical approach that facilitates its general use and allows for systematic improvements in accuracy. This formulation is demonstrated for two canonical flow problems: oscillatory Couette flow and Stokes' second problem. Approximate analytical formulas giving the bulk velocity and shear stress, valid for arbitrary oscillation frequency, are obtained for Couette flow. For Stokes' second problem, a simple system of ordinary differential equations is derived which may be solved to obtain the desired flow fields. Using this framework, a simple and accurate formula is provided for the shear stress at the oscillating boundary, again for arbitrary frequency, which may prove useful in application. These solutions are easily implemented on any symbolic or numerical package, such as Mathematica or matlab, facilitating the characterization of flows produced by nanomechanical devices and providing insight into the underlying flow physics.

Analytical solutions for two-dimensional Stokes flow singularities in a no-slip wedge of arbitrary angle

PubMed Central

Brzezicki, Samuel J.

2017-01-01

An analytical method to find the flow generated by the basic singularities of Stokes flow in a wedge of arbitrary angle is presented. Specifically, we solve a biharmonic equation for the stream function of the flow generated by a point stresslet singularity and satisfying no-slip boundary conditions on the two walls of the wedge. The method, which is readily adapted to any other singularity type, takes full account of any transcendental singularities arising at the corner of the wedge. The approach is also applicable to problems of plane strain/stress of an elastic solid where the biharmonic equation also governs the Airy stress function. PMID:28690412

Analytical solutions for two-dimensional Stokes flow singularities in a no-slip wedge of arbitrary angle.

PubMed

Crowdy, Darren G; Brzezicki, Samuel J

2017-06-01

An analytical method to find the flow generated by the basic singularities of Stokes flow in a wedge of arbitrary angle is presented. Specifically, we solve a biharmonic equation for the stream function of the flow generated by a point stresslet singularity and satisfying no-slip boundary conditions on the two walls of the wedge. The method, which is readily adapted to any other singularity type, takes full account of any transcendental singularities arising at the corner of the wedge. The approach is also applicable to problems of plane strain/stress of an elastic solid where the biharmonic equation also governs the Airy stress function.

Numerical simulation of three-dimensional transonic turbulent projectile aerodynamics by TVD schemes

NASA Technical Reports Server (NTRS)

Shiau, Nae-Haur; Hsu, Chen-Chi; Chyu, Wei-Jao

1989-01-01

The two-dimensional symmetric TVD scheme proposed by Yee has been extended to and investigated for three-dimensional thin-layer Navier-Stokes simulation of complex aerodynamic problems. An existing three-dimensional Navier-stokes code based on the beam and warming algorithm is modified to provide an option of using the TVD algorithm and the flow problem considered is a transonic turbulent flow past a projectile with sting at ten-degree angle of attack. Numerical experiments conducted for three flow cases, free-stream Mach numbers of 0.91, 0.96 and 1.20 show that the symmetric TVD algorithm can provide surface pressure distribution in excellent agreement with measured data; moreover, the rate of convergence to attain a steady state solution is about two times faster than the original beam and warming algorithm.

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

NASA Technical Reports Server (NTRS)

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

1985-01-01

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

Fast preconditioned multigrid solution of the Euler and Navier-Stokes equations for steady, compressible flows

NASA Astrophysics Data System (ADS)

Caughey, David A.; Jameson, Antony

2003-10-01

New versions of implicit algorithms are developed for the efficient solution of the Euler and Navier-Stokes equations of compressible flow. The methods are based on a preconditioned, lower-upper (LU) implementation of a non-linear, symmetric Gauss-Seidel (SGS) algorithm for use as a smoothing algorithm in a multigrid method. Previously, this method had been implemented for flows in quasi-one-dimensional ducts and for two-dimensional flows past airfoils on boundary-conforming O-type grids for a variety of symmetric limited positive (SLIP) spatial approximations, including the scalar dissipation and convective upwind split pressure (CUSP) schemes. Here results are presented for both inviscid and viscous (laminar) flows past airfoils on boundary-conforming C-type grids. The method is significantly faster than earlier explicit or implicit methods for inviscid problems, allowing solution of these problems to the level of truncation error in three to five multigrid cycles. Viscous solutions still require as many as twenty multigrid cycles.

Implicit solution of Navier-Stokes equations on staggered curvilinear grids using a Newton-Krylov method with a novel analytical Jacobian.

NASA Astrophysics Data System (ADS)

Borazjani, Iman; Asgharzadeh, Hafez

2015-11-01

Flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates with explicit and semi-implicit schemes. Implicit schemes can be used to overcome these restrictions. However, implementing implicit solver for nonlinear equations including Navier-Stokes is not straightforward. Newton-Krylov subspace methods (NKMs) are one of the most advanced iterative methods to solve non-linear equations such as implicit descritization of the Navier-Stokes equation. The efficiency of NKMs massively depends on the Jacobian formation method, e.g., automatic differentiation is very expensive, and matrix-free methods slow down as the mesh is refined. Analytical Jacobian is inexpensive method, but derivation of analytical Jacobian for Navier-Stokes equation on staggered grid is challenging. The NKM with a novel analytical Jacobian was developed and validated against Taylor-Green vortex and pulsatile flow in a 90 degree bend. The developed method successfully handled the complex geometries such as an intracranial aneurysm with multiple overset grids, and immersed boundaries. It is shown that the NKM with an analytical Jacobian is 3 to 25 times faster than the fixed-point implicit Runge-Kutta method, and more than 100 times faster than automatic differentiation depending on the grid (size) and the flow problem. The developed methods are fully parallelized with parallel efficiency of 80-90% on the problems tested.

Viscous flow computations using a second-order upwind differencing scheme

NASA Technical Reports Server (NTRS)

Chen, Y. S.

1988-01-01

In the present computations of a wide range of fluid flow problems by means of the primitive variables-incorporating Navier-Stokes equations, a mixed second-order upwinding scheme approximates the convective terms of the transport equations and the scheme's accuracy is verified for convection-dominated high Re number flow problems. An adaptive dissipation scheme is used as a monotonic supersonic shock flow capture mechanism. Many benchmark fluid flow problems, including the compressible and incompressible, laminar and turbulent, over a wide range of M and Re numbers, are presently studied to verify the accuracy and robustness of this numerical method.

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.

Preconditioned upwind methods to solve 3-D incompressible Navier-Stokes equations for viscous flows

NASA Technical Reports Server (NTRS)

Hsu, C.-H.; Chen, Y.-M.; Liu, C. H.

1990-01-01

A computational method for calculating low-speed viscous flowfields is developed. The method uses the implicit upwind-relaxation finite-difference algorithm with a nonsingular eigensystem to solve the preconditioned, three-dimensional, incompressible Navier-Stokes equations in curvilinear coordinates. The technique of local time stepping is incorporated to accelerate the rate of convergence to a steady-state solution. An extensive study of optimizing the preconditioned system is carried out for two viscous flow problems. Computed results are compared with analytical solutions and experimental data.

Resolvent analysis of shear flows using One-Way Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Rigas, Georgios; Schmidt, Oliver; Towne, Aaron; Colonius, Tim

2017-11-01

For three-dimensional flows, questions of stability, receptivity, secondary flows, and coherent structures require the solution of large partial-derivative eigenvalue problems. Reduced-order approximations are thus required for engineering prediction since these problems are often computationally intractable or prohibitively expensive. For spatially slowly evolving flows, such as jets and boundary layers, the One-Way Navier-Stokes (OWNS) equations permit a fast spatial marching procedure that results in a huge reduction in computational cost. Here, an adjoint-based optimization framework is proposed and demonstrated for calculating optimal boundary conditions and optimal volumetric forcing. The corresponding optimal response modes are validated against modes obtained in terms of global resolvent analysis. For laminar base flows, the optimal modes reveal modal and non-modal transition mechanisms. For turbulent base flows, they predict the evolution of coherent structures in a statistical sense. Results from the application of the method to three-dimensional laminar wall-bounded flows and turbulent jets will be presented. This research was supported by the Office of Naval Research (N00014-16-1-2445) and Boeing Company (CT-BA-GTA-1).

Impact of the inherent separation of scales in the Navier-Stokes- alphabeta equations.

PubMed

Kim, Tae-Yeon; Cassiani, Massimo; Albertson, John D; Dolbow, John E; Fried, Eliot; Gurtin, Morton E

2009-04-01

We study the effect of the length scales alpha and beta in the Navier-Stokes- alphabeta equations on the energy spectrum and the alignment between the vorticity and the eigenvectors of the stretching tensor in three-dimensional homogeneous and isotropic turbulent flows in a periodic cubic domain, including the limiting cases of the Navier-Stokes- alpha and Navier-Stokes equations. A significant increase in the accuracy of the energy spectrum at large wave numbers arises for beta

Meshfree and efficient modeling of swimming cells

NASA Astrophysics Data System (ADS)

Gallagher, Meurig T.; Smith, David J.

2018-05-01

Locomotion in Stokes flow is an intensively studied problem because it describes important biological phenomena such as the motility of many species' sperm, bacteria, algae, and protozoa. Numerical computations can be challenging, particularly in three dimensions, due to the presence of moving boundaries and complex geometries; methods which combine ease of implementation and computational efficiency are therefore needed. A recently proposed method to discretize the regularized Stokeslet boundary integral equation without the need for a connected mesh is applied to the inertialess locomotion problem in Stokes flow. The mathematical formulation and key aspects of the computational implementation in matlab® or GNU Octave are described, followed by numerical experiments with biflagellate algae and multiple uniflagellate sperm swimming between no-slip surfaces, for which both swimming trajectories and flow fields are calculated. These computational experiments required minutes of time on modest hardware; an extensible implementation is provided in a GitHub repository. The nearest-neighbor discretization dramatically improves convergence and robustness, a key challenge in extending the regularized Stokeslet method to complicated three-dimensional biological fluid problems.

RIACS

NASA Technical Reports Server (NTRS)

Oliger, Joseph

1997-01-01

Topics considered include: high-performance computing; cognitive and perceptual prostheses (computational aids designed to leverage human abilities); autonomous systems. Also included: development of a 3D unstructured grid code based on a finite volume formulation and applied to the Navier-stokes equations; Cartesian grid methods for complex geometry; multigrid methods for solving elliptic problems on unstructured grids; algebraic non-overlapping domain decomposition methods for compressible fluid flow problems on unstructured meshes; numerical methods for the compressible navier-stokes equations with application to aerodynamic flows; research in aerodynamic shape optimization; S-HARP: a parallel dynamic spectral partitioner; numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains; application of high-order shock capturing schemes to direct simulation of turbulence; multicast technology; network testbeds; supercomputer consolidation project.

Compressible bubbles in Stokes flow

NASA Astrophysics Data System (ADS)

Crowdy, Darren G.

2003-02-01

The problem of a two-dimensional inviscid compressible bubble evolving in Stokes flow is considered. By generalizing the work of Tanveer & Vasconcelos (1995) it is shown that for certain classes of initial condition the quasi-steady free boundary problem for the bubble shape evolution is reducible to a finite set of coupled nonlinear ordinary differential equations, the form of which depends on the equation of state governing the relationship between the bubble pressure and its area. Recent numerical calculations by Pozrikidis (2001) using boundary integral methods are retrieved and extended. If the ambient pressures are small enough, it is shown that bubbles can expand significantly. It is also shown that a bubble evolving adiabatically is less likely to expand than an isothermal bubble.

Rotationally symmetric viscous gas flows

NASA Astrophysics Data System (ADS)

Weigant, W.; Plotnikov, P. I.

2017-03-01

The Dirichlet boundary value problem for the Navier-Stokes equations of a barotropic viscous compressible fluid is considered. The flow region and the data of the problem are assumed to be invariant under rotations about a fixed axis. The existence of rotationally symmetric weak solutions for all adiabatic exponents from the interval (γ*,∞) with a critical exponent γ* < 4/3 is proved.

Dependence of energy characteristics of ascending swirling air flow on velocity of vertical blowing

NASA Astrophysics Data System (ADS)

Volkov, R. E.; Obukhov, A. G.; Kutrunov, V. N.

2018-05-01

In the model of a compressible continuous medium, for the complete Navier-Stokes system of equations, an initial boundary problem is proposed that corresponds to the conducted and planned experiments and describes complex three-dimensional flows of a viscous compressible heat-conducting gas in ascending swirling flows that are initiated by a vertical cold blowing. Using parallelization methods, three-dimensional nonstationary flows of a polytropic viscous compressible heat-conducting gas are constructed numerically in different scaled ascending swirling flows under the condition when gravity and Coriolis forces act. With the help of explicit difference schemes and the proposed initial boundary conditions, approximate solutions of the complete system of Navier-Stokes equations are constructed as well as the velocity and energy characteristics of three-dimensional nonstationary gas flows in ascending swirling flows are determined.

Space-Time Error Representation and Estimation in Navier-Stokes Calculations

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

2006-01-01

The mathematical framework for a-posteriori error estimation of functionals elucidated by Eriksson et al. [7] and Becker and Rannacher [3] is revisited in a space-time context. Using these theories, a hierarchy of exact and approximate error representation formulas are presented for use in error estimation and mesh adaptivity. Numerical space-time results for simple model problems as well as compressible Navier-Stokes flow at Re = 300 over a 2D circular cylinder are then presented to demonstrate elements of the error representation theory for time-dependent problems.

Final Report - High-Order Spectral Volume Method for the Navier-Stokes Equations On Unstructured Tetrahedral Grids

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

Wang, Z J

2012-12-06

The overriding objective for this project is to develop an efficient and accurate method for capturing strong discontinuities and fine smooth flow structures of disparate length scales with unstructured grids, and demonstrate its potentials for problems relevant to DOE. More specifically, we plan to achieve the following objectives: 1. Extend the SV method to three dimensions, and develop a fourth-order accurate SV scheme for tetrahedral grids. Optimize the SV partition by minimizing a form of the Lebesgue constant. Verify the order of accuracy using the scalar conservation laws with an analytical solution; 2. Extend the SV method to Navier-Stokes equationsmore » for the simulation of viscous flow problems. Two promising approaches to compute the viscous fluxes will be tested and analyzed; 3. Parallelize the 3D viscous SV flow solver using domain decomposition and message passing. Optimize the cache performance of the flow solver by designing data structures minimizing data access times; 4. Demonstrate the SV method with a wide range of flow problems including both discontinuities and complex smooth structures. The objectives remain the same as those outlines in the original proposal. We anticipate no technical obstacles in meeting these objectives.« less

The Krylov accelerated SIMPLE(R) method for flow problems in industrial furnaces

NASA Astrophysics Data System (ADS)

Vuik, C.; Saghir, A.; Boerstoel, G. P.

2000-08-01

Numerical modeling of the melting and combustion process is an important tool in gaining understanding of the physical and chemical phenomena that occur in a gas- or oil-fired glass-melting furnace. The incompressible Navier-Stokes equations are used to model the gas flow in the furnace. The discrete Navier-Stokes equations are solved by the SIMPLE(R) pressure-correction method. In these applications, many SIMPLE(R) iterations are necessary to obtain an accurate solution. In this paper, Krylov accelerated versions are proposed: GCR-SIMPLE(R). The properties of these methods are investigated for a simple two-dimensional flow. Thereafter, the efficiencies of the methods are compared for three-dimensional flows in industrial glass-melting furnaces. Copyright

A compressible solution of the Navier-Stokes equations for turbulent flow about an airfoil

NASA Technical Reports Server (NTRS)

Shamroth, S. J.; Gibeling, H. J.

1979-01-01

A compressible time dependent solution of the Navier-Stokes equations including a transition turbulence model is obtained for the isolated airfoil flow field problem. The equations are solved by a consistently split linearized block implicit scheme. A nonorthogonal body-fitted coordinate system is used which has maximum resolution near the airfoil surface and in the region of the airfoil leading edge. The transition turbulence model is based upon the turbulence kinetic energy equation and predicts regions of laminar, transitional, and turbulent flow. Mean flow field and turbulence field results are presented for an NACA 0012 airfoil at zero and nonzero incidence angles of Reynolds number up to one million and low subsonic Mach numbers.

A zonal method for modeling powered-lift aircraft flow fields

NASA Technical Reports Server (NTRS)

Roberts, D. W.

1989-01-01

A zonal method for modeling powered-lift aircraft flow fields is based on the coupling of a three-dimensional Navier-Stokes code to a potential flow code. By minimizing the extent of the viscous Navier-Stokes zones the zonal method can be a cost effective flow analysis tool. The successful coupling of the zonal solutions provides the viscous/inviscid interations that are necessary to achieve convergent and unique overall solutions. The feasibility of coupling the two vastly different codes is demonstrated. The interzone boundaries were overlapped to facilitate the passing of boundary condition information between the codes. Routines were developed to extract the normal velocity boundary conditions for the potential flow zone from the viscous zone solution. Similarly, the velocity vector direction along with the total conditions were obtained from the potential flow solution to provide boundary conditions for the Navier-Stokes solution. Studies were conducted to determine the influence of the overlap of the interzone boundaries and the convergence of the zonal solutions on the convergence of the overall solution. The zonal method was applied to a jet impingement problem to model the suckdown effect that results from the entrainment of the inviscid zone flow by the viscous zone jet. The resultant potential flow solution created a lower pressure on the base of the vehicle which produces the suckdown load. The feasibility of the zonal method was demonstrated. By enhancing the Navier-Stokes code for powered-lift flow fields and optimizing the convergence of the coupled analysis a practical flow analysis tool will result.

Comparison of continuum and particle simulations of expanding rarefied flows

NASA Technical Reports Server (NTRS)

Lumpkin, Forrest E., III; Boyd, Iain D.; Venkatapathy, Ethiraj

1993-01-01

Comparisons of Navier-Stokes solutions and particle simulations for a simple two-dimensional model problem at a succession of altitudes are performed in order to assess the importance of rarefaction effects on the base flow region. In addition, an attempt is made to include 'Burnett-type' extensions to the Navier-Stokes constitutive relations. The model geometry consists of a simple blunted wedge with a 0.425 meter nose radius, a 70 deg cone half angle, a 1.7 meter base length, and a rounded shoulder. The working gas is monatomic with a molecular weight and viscosity similar to air and was chosen to focus the study on the continuum and particle methodologies rather than the implementation of thermo-chemical modeling. Three cases are investigated, all at Mach 29, with densities corresponding to altitudes of 92 km, 99 km, and 105 km. At the lowest altitude, Navier-Stokes solutions agree well with particle simulations. At the higher altitudes, the Navier-Stokes equations become less accurate. In particular, the Navier-Stokes equations and particle method predict substantially different flow turning angle in the wake near the after body. Attempts to achieve steady continuum solutions including 'Burnett-type' terms failed. Further research is required to determine whether the boundary conditions, the equations themselves, or other unknown causes led to this failure.

Solutions to Three-Dimensional Thin-Layer Navier-Stokes Equations in Rotating Coordinates for Flow Through Turbomachinery

NASA Technical Reports Server (NTRS)

Ghosh, Amrit Raj

1996-01-01

The viscous, Navier-Stokes solver for turbomachinery applications, MSUTC has been modified to include the rotating frame formulation. The three-dimensional thin-layer Navier-Stokes equations have been cast in a rotating Cartesian frame enabling the freezing of grid motion. This also allows the flow-field associated with an isolated rotor to be viewed as a steady-state problem. Consequently, local time stepping can be used to accelerate convergence. The formulation is validated by running NASA's Rotor 67 as the test case. results are compared between the rotating frame code and the absolute frame code. The use of the rotating frame approach greatly enhances the performance of the code with respect to savings in computing time, without degradation of the solution.

Reliability enhancement of Navier-Stokes codes through convergence acceleration

NASA Technical Reports Server (NTRS)

Merkle, Charles L.; Dulikravich, George S.

1995-01-01

Methods for enhancing the reliability of Navier-Stokes computer codes through improving convergence characteristics are presented. The improving of these characteristics decreases the likelihood of code unreliability and user interventions in a design environment. The problem referred to as a 'stiffness' in the governing equations for propulsion-related flowfields is investigated, particularly in regard to common sources of equation stiffness that lead to convergence degradation of CFD algorithms. Von Neumann stability theory is employed as a tool to study the convergence difficulties involved. Based on the stability results, improved algorithms are devised to ensure efficient convergence in different situations. A number of test cases are considered to confirm a correlation between stability theory and numerical convergence. The examples of turbulent and reacting flow are presented, and a generalized form of the preconditioning matrix is derived to handle these problems, i.e., the problems involving additional differential equations for describing the transport of turbulent kinetic energy, dissipation rate and chemical species. Algorithms for unsteady computations are considered. The extension of the preconditioning techniques and algorithms derived for Navier-Stokes computations to three-dimensional flow problems is discussed. New methods to accelerate the convergence of iterative schemes for the numerical integration of systems of partial differential equtions are developed, with a special emphasis on the acceleration of convergence on highly clustered grids.

Numerical solution of the incompressible Navier-Stokes equations. Ph.D. Thesis - Stanford Univ., Mar. 1989

NASA Technical Reports Server (NTRS)

Rogers, Stuart E.

1990-01-01

The current work is initiated in an effort to obtain an efficient, accurate, and robust algorithm for the numerical solution of the incompressible Navier-Stokes equations in two- and three-dimensional generalized curvilinear coordinates for both steady-state and time-dependent flow problems. This is accomplished with the use of the method of artificial compressibility and a high-order flux-difference splitting technique for the differencing of the convective terms. Time accuracy is obtained in the numerical solutions by subiterating the equations in psuedo-time for each physical time step. The system of equations is solved with a line-relaxation scheme which allows the use of very large pseudo-time steps leading to fast convergence for steady-state problems as well as for the subiterations of time-dependent problems. Numerous laminar test flow problems are computed and presented with a comparison against analytically known solutions or experimental results. These include the flow in a driven cavity, the flow over a backward-facing step, the steady and unsteady flow over a circular cylinder, flow over an oscillating plate, flow through a one-dimensional inviscid channel with oscillating back pressure, the steady-state flow through a square duct with a 90 degree bend, and the flow through an artificial heart configuration with moving boundaries. An adequate comparison with the analytical or experimental results is obtained in all cases. Numerical comparisons of the upwind differencing with central differencing plus artificial dissipation indicates that the upwind differencing provides a much more robust algorithm, which requires significantly less computing time. The time-dependent problems require on the order of 10 to 20 subiterations, indicating that the elliptical nature of the problem does require a substantial amount of computing effort.

Capabilities and performance of Elmer/Ice, a new-generation ice sheet model

NASA Astrophysics Data System (ADS)

Gagliardini, O.; Zwinger, T.; Gillet-Chaulet, F.; Durand, G.; Favier, L.; de Fleurian, B.; Greve, R.; Malinen, M.; Martín, C.; Råback, P.; Ruokolainen, J.; Sacchettini, M.; Schäfer, M.; Seddik, H.; Thies, J.

2013-08-01

The Fourth IPCC Assessment Report concluded that ice sheet flow models, in their current state, were unable to provide accurate forecast for the increase of polar ice sheet discharge and the associated contribution to sea level rise. Since then, the glaciological community has undertaken a huge effort to develop and improve a new generation of ice flow models, and as a result a significant number of new ice sheet models have emerged. Among them is the parallel finite-element model Elmer/Ice, based on the open-source multi-physics code Elmer. It was one of the first full-Stokes models used to make projections for the evolution of the whole Greenland ice sheet for the coming two centuries. Originally developed to solve local ice flow problems of high mechanical and physical complexity, Elmer/Ice has today reached the maturity to solve larger-scale problems, earning the status of an ice sheet model. Here, we summarise almost 10 yr of development performed by different groups. Elmer/Ice solves the full-Stokes equations, for isotropic but also anisotropic ice rheology, resolves the grounding line dynamics as a contact problem, and contains various basal friction laws. Derived fields, like the age of the ice, the strain rate or stress, can also be computed. Elmer/Ice includes two recently proposed inverse methods to infer badly known parameters. Elmer is a highly parallelised code thanks to recent developments and the implementation of a block preconditioned solver for the Stokes system. In this paper, all these components are presented in detail, as well as the numerical performance of the Stokes solver and developments planned for the future.

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.

Parametric Study of a YAV-8B Harrier in Ground Effect Using Time-Dependent Navier-Stokes Computations

NASA Technical Reports Server (NTRS)

Shishir, Pandya; Chaderjian, Neal; Ahmad, Jsaim; Kwak, Dochan (Technical Monitor)

2001-01-01

Flow simulations using the time-dependent Navier-Stokes equations remain a challenge for several reasons. Principal among them are the difficulty to accurately model complex flows, and the time needed to perform the computations. A parametric study of such complex problems is not considered practical due to the large cost associated with computing many time-dependent solutions. The computation time for each solution must be reduced in order to make a parametric study possible. With successful reduction of computation time, the issue of accuracy, and appropriateness of turbulence models will become more tractable.

High-Order Methods for Incompressible Fluid Flow

NASA Astrophysics Data System (ADS)

Deville, M. O.; Fischer, P. F.; Mund, E. H.

2002-08-01

High-order numerical methods provide an efficient approach to simulating many physical problems. This book considers the range of mathematical, engineering, and computer science topics that form the foundation of high-order numerical methods for the simulation of incompressible fluid flows in complex domains. Introductory chapters present high-order spatial and temporal discretizations for one-dimensional problems. These are extended to multiple space dimensions with a detailed discussion of tensor-product forms, multi-domain methods, and preconditioners for iterative solution techniques. Numerous discretizations of the steady and unsteady Stokes and Navier-Stokes equations are presented, with particular sttention given to enforcement of imcompressibility. Advanced discretizations. implementation issues, and parallel and vector performance are considered in the closing sections. Numerous examples are provided throughout to illustrate the capabilities of high-order methods in actual applications.

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.

New Finite Difference Methods Based on IIM for Inextensible Interfaces in Incompressible Flows

PubMed Central

Li, Zhilin; Lai, Ming-Chih

2012-01-01

In this paper, new finite difference methods based on the augmented immersed interface method (IIM) are proposed for simulating an inextensible moving interface in an incompressible two-dimensional flow. The mathematical models arise from studying the deformation of red blood cells in mathematical biology. The governing equations are incompressible Stokes or Navier-Stokes equations with an unknown surface tension, which should be determined in such a way that the surface divergence of the velocity is zero along the interface. Thus, the area enclosed by the interface and the total length of the interface should be conserved during the evolution process. Because of the nonlinear and coupling nature of the problem, direct discretization by applying the immersed boundary or immersed interface method yields complex nonlinear systems to be solved. In our new methods, we treat the unknown surface tension as an augmented variable so that the augmented IIM can be applied. Since finding the unknown surface tension is essentially an inverse problem that is sensitive to perturbations, our regularization strategy is to introduce a controlled tangential force along the interface, which leads to a least squares problem. For Stokes equations, the forward solver at one time level involves solving three Poisson equations with an interface. For Navier-Stokes equations, we propose a modified projection method that can enforce the pressure jump condition corresponding directly to the unknown surface tension. Several numerical experiments show good agreement with other results in the literature and reveal some interesting phenomena. PMID:23795308

Non-linear instability analysis of the two-dimensional Navier-Stokes equation: The Taylor-Green vortex problem

NASA Astrophysics Data System (ADS)

Sengupta, Tapan K.; Sharma, Nidhi; Sengupta, Aditi

2018-05-01

An enstrophy-based non-linear instability analysis of the Navier-Stokes equation for two-dimensional (2D) flows is presented here, using the Taylor-Green vortex (TGV) problem as an example. This problem admits a time-dependent analytical solution as the base flow, whose instability is traced here. The numerical study of the evolution of the Taylor-Green vortices shows that the flow becomes turbulent, but an explanation for this transition has not been advanced so far. The deviation of the numerical solution from the analytical solution is studied here using a high accuracy compact scheme on a non-uniform grid (NUC6), with the fourth-order Runge-Kutta method. The stream function-vorticity (ψ, ω) formulation of the governing equations is solved here in a periodic square domain with four vortices at t = 0. Simulations performed at different Reynolds numbers reveal that numerical errors in computations induce a breakdown of symmetry and simultaneous fragmentation of vortices. It is shown that the actual physical instability is triggered by the growth of disturbances and is explained by the evolution of disturbance mechanical energy and enstrophy. The disturbance evolution equations have been traced by looking at (a) disturbance mechanical energy of the Navier-Stokes equation, as described in the work of Sengupta et al., "Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003), and (b) the creation of rotationality via the enstrophy transport equation in the work of Sengupta et al., "Diffusion in inhomogeneous flows: Unique equilibrium state in an internal flow," Comput. Fluids 88, 440-451 (2013).

What's Cooler Than Being Cool? Ice-Sheet Models Using a Fluidity-Based FOSLS Approach to Nonlinear-Stokes Flow

NASA Astrophysics Data System (ADS)

Allen, Jeffery M.

This research involves a few First-Order System Least Squares (FOSLS) formulations of a nonlinear-Stokes flow model for ice sheets. In Glen's flow law, a commonly used constitutive equation for ice rheology, the viscosity becomes infinite as the velocity gradients approach zero. This typically occurs near the ice surface or where there is basal sliding. The computational difficulties associated with the infinite viscosity are often overcome by an arbitrary modification of Glen's law that bounds the maximum viscosity. The FOSLS formulations developed in this thesis are designed to overcome this difficulty. The first FOSLS formulation is just the first-order representation of the standard nonlinear, full-Stokes and is known as the viscosity formulation and suffers from the problem above. To overcome the problem of infinite viscosity, two new formulation exploit the fact that the deviatoric stress, the product of viscosity and strain-rate, approaches zero as the viscosity goes to infinity. Using the deviatoric stress as the basis for a first-order system results in the the basic fluidity system. Augmenting the basic fluidity system with a curl-type equation results in the augmented fluidity system, which is more amenable to the iterative solver, Algebraic MultiGrid (AMG). A Nested Iteration (NI) Newton-FOSLS-AMG approach is used to solve the nonlinear-Stokes problems. Several test problems from the ISMIP set of benchmarks is examined to test the effectiveness of the various formulations. These test show that the viscosity based method is more expensive and less accurate. The basic fluidity system shows optimal finite-element convergence. However, there is not yet an efficient iterative solver for this type of system and this is the topic of future research. Alternatively, AMG performs better on the augmented fluidity system when using specific scaling. Unfortunately, this scaling results in reduced finite-element convergence.

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.

Hypersonic low-density solutions of the Navier-Stokes equations with chemical nonequilibrium and multicomponent surface slip

NASA Technical Reports Server (NTRS)

Gupta, R. N.; Simmonds, A. L.

1986-01-01

Solutions of the Navier-Stokes equations with chemical nonequilibrium and multicomponent surface slip are presented along the stagnation streamline under low-density hypersonic flight conditions. The conditions analyzed are those encountered by the nose region of the Space Shuttle Orbiter during reentry. A detailed comparison of the Navier-Stokes (NS) results is made with the viscous shock-layer (VSL) and Direct Simulation Monte Carlo (DSMC) predictions. With the inclusion of surface-slip boundary conditions in NS calculations, the surface heat transfer and other flow field quantities adjacent to the surface are predicted favorably with the DSMC calculations from 75 km to 115 km in altitude. Therefore, the practical range for the applicability of Navier-Stokes solutions is much wider than previously thought. This is appealing because the continuum (NS and VSL) methods are commonly used to solve the fluid flow problems and are less demanding in terms of computer resource requirements than the noncontinuum (DSMC) methods. The NS solutions agree well with the VSL results for altitudes less than 92 km. An assessment is made of the frozen flow approximation employed in the VSL calculations.

On non-symmetric axial corner-layer flow

NASA Astrophysics Data System (ADS)

Boiko, A. V.; Kirilovskiy, S. V.; Nechepurenko, Y. M.; Poplavskaya, T. V.

2017-10-01

The problem of asymmetric incompressible axial flow in a corner formed of two intersecting plates at a right angle is considered. The asymptotic behaviour of the flow far away from the corner is analysed. Two types of asymptotic behaviour are found. It is shown that the flow is very sensitive to the asymmetry parameter. A comparison of the results with computations of full Navier-Stokes equations was performed.

An Evaluation of the NEKTON Program

DTIC Science & Technology

1990-09-01

features could be studied. Test cases were chosen for which experimental data or analytic solutions exist. These test cases verify NEKTON’s unsteady flow ...including steady and unsteady incompressible flow problems in two or three spatial dimensions. NEKTON version 2.6, which was evaluated for this... unsteady flow decay of a free surface moderate [7] 2-D laminar flow flow past a cylinder 100 [7] 3-D Stokes flow spiral groove thrust bearing < 1 [8

Iterative spectral methods and spectral solutions to compressible flows

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Zang, T. A.

1982-01-01

A spectral multigrid scheme is described which can solve pseudospectral discretizations of self-adjoint elliptic problems in O(N log N) operations. An iterative technique for efficiently implementing semi-implicit time-stepping for pseudospectral discretizations of Navier-Stokes equations is discussed. This approach can handle variable coefficient terms in an effective manner. Pseudospectral solutions of compressible flow problems are presented. These include one dimensional problems and two dimensional Euler solutions. Results are given both for shock-capturing approaches and for shock-fitting ones.

Strong solutions for an incompressible Navier-Stokes/Allen-Cahn system with different densities

NASA Astrophysics Data System (ADS)

Li, Yinghua; Huang, Mingxia

2018-06-01

In this paper, we investigate a coupled Navier-Stokes/Allen-Cahn system describing a diffuse interface model for two-phase flow of viscous incompressible fluids with different densities in a bounded domain Ω \\subset R^N(N=2,3). We prove the existence and uniqueness of local strong solutions to the initial boundary value problem when the initial density function ρ _0 has a positive lower bound.

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.

Flow of “stress power-law” fluids between parallel rotating discs with distinct axes

DOE PAGES

Srinivasan, Shriram; Karra, Satish

2015-04-16

The problem of flow between parallel rotating discs with distinct axes corresponds to the case of flow in an orthogonal rheometer and has been studied extensively for different fluids since the instrument's inception. All the prior studies presume a constitutive prescription of the fluid stress in terms of the kinematical variables. In this paper, we approach the problem from a different perspective, i.e., a constitutive specification of the symmetric part of the velocity gradient in terms of the Cauchy stress. Such an approach ensures that the boundary conditions can be incorporated in a manner quite faithful to real world experimentsmore » with the instrument. Interestingly, the choice of the boundary condition is critical to the solvability of the problem for the case of creeping/Stokes flow. Furthermore, when the no-slip condition is enforced at the boundaries, depending on the model parameters and axes offset, the fluid response can show non-uniqueness or unsolvability, features which are absent in a conventional constitutive specification. In case of creeping/Stokes flow with prescribed values of the stress, the fluid response is indeterminate. We also record the response of a particular case of the given “stress power-law” fluid; one that cannot be attained by the conventional power-law fluids.« less

An adjoint view on flux consistency and strong wall boundary conditions to the Navier–Stokes equations

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

Stück, Arthur, E-mail: arthur.stueck@dlr.de

2015-11-15

Inconsistent discrete expressions in the boundary treatment of Navier–Stokes solvers and in the definition of force objective functionals can lead to discrete-adjoint boundary treatments that are not a valid representation of the boundary conditions to the corresponding adjoint partial differential equations. The underlying problem is studied for an elementary 1D advection–diffusion problem first using a node-centred finite-volume discretisation. The defect of the boundary operators in the inconsistently defined discrete-adjoint problem leads to oscillations and becomes evident with the additional insight of the continuous-adjoint approach. A homogenisation of the discretisations for the primal boundary treatment and the force objective functional yieldsmore » second-order functional accuracy and eliminates the defect in the discrete-adjoint boundary treatment. Subsequently, the issue is studied for aerodynamic Reynolds-averaged Navier–Stokes problems in conjunction with a standard finite-volume discretisation on median-dual grids and a strong implementation of noslip walls, found in many unstructured general-purpose flow solvers. Going out from a base-line discretisation of force objective functionals which is independent of the boundary treatment in the flow solver, two improved flux-consistent schemes are presented; based on either body wall-defined or farfield-defined control-volumes they resolve the dual inconsistency. The behaviour of the schemes is investigated on a sequence of grids in 2D and 3D.« less

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1976-01-01

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C deg-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1,000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and asymptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

A Discontinuous Petrov-Galerkin Methodology for Adaptive Solutions to the Incompressible Navier-Stokes Equations

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

Roberts, Nathan V.; Demkowiz, Leszek; Moser, Robert

2015-11-15

The discontinuous Petrov-Galerkin methodology with optimal test functions (DPG) of Demkowicz and Gopalakrishnan [18, 20] guarantees the optimality of the solution in an energy norm, and provides several features facilitating adaptive schemes. Whereas Bubnov-Galerkin methods use identical trial and test spaces, Petrov-Galerkin methods allow these function spaces to differ. In DPG, test functions are computed on the fly and are chosen to realize the supremum in the inf-sup condition; the method is equivalent to a minimum residual method. For well-posed problems with sufficiently regular solutions, DPG can be shown to converge at optimal rates—the inf-sup constants governing the convergence aremore » mesh-independent, and of the same order as those governing the continuous problem [48]. DPG also provides an accurate mechanism for measuring the error, and this can be used to drive adaptive mesh refinements. We employ DPG to solve the steady incompressible Navier-Stokes equations in two dimensions, building on previous work on the Stokes equations, and focusing particularly on the usefulness of the approach for automatic adaptivity starting from a coarse mesh. We apply our approach to a manufactured solution due to Kovasznay as well as the lid-driven cavity flow, backward-facing step, and flow past a cylinder problems.« less

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

NASA Technical Reports Server (NTRS)

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

1995-01-01

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

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.

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

NASA Technical Reports Server (NTRS)

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

1994-01-01

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

Application of the method of lines for solutions of the Navier-Stokes equations using a nonuniform grid distribution

NASA Technical Reports Server (NTRS)

Abolhassani, J. S.; Tiwari, S. N.

1983-01-01

The feasibility of the method of lines for solutions of physical problems requiring nonuniform grid distributions is investigated. To attain this, it is also necessary to investigate the stiffness characteristics of the pertinent equations. For specific applications, the governing equations considered are those for viscous, incompressible, two dimensional and axisymmetric flows. These equations are transformed from the physical domain having a variable mesh to a computational domain with a uniform mesh. The two governing partial differential equations are the vorticity and stream function equations. The method of lines is used to solve the vorticity equation and the successive over relaxation technique is used to solve the stream function equation. The method is applied to three laminar flow problems: the flow in ducts, curved-wall diffusers, and a driven cavity. Results obtained for different flow conditions are in good agreement with available analytical and numerical solutions. The viability and validity of the method of lines are demonstrated by its application to Navier-Stokes equations in the physical domain having a variable mesh.

Numerical solution of 3D Navier-Stokes equations with upwind implicit schemes

NASA Technical Reports Server (NTRS)

Marx, Yves P.

1990-01-01

An upwind MUSCL type implicit scheme for the three-dimensional Navier-Stokes equations is presented. Comparison between different approximate Riemann solvers (Roe and Osher) are performed and the influence of the reconstructions schemes on the accuracy of the solution as well as on the convergence of the method is studied. A new limiter is introduced in order to remove the problems usually associated with non-linear upwind schemes. The implementation of a diagonal upwind implicit operator for the three-dimensional Navier-Stokes equations is also discussed. Finally the turbulence modeling is assessed. Good prediction of separated flows are demonstrated if a non-equilibrium turbulence model is used.

Boundary layer transition: A review of theory, experiment and related phenomena

NASA Technical Reports Server (NTRS)

Kistler, E. L.

1971-01-01

The overall problem of boundary layer flow transition is reviewed. Evidence indicates a need for new, basic physical hypotheses in classical fluid mechanics math models based on the Navier-Stokes equations. The Navier-Stokes equations are challenged as inadequate for the investigation of fluid transition, since they are based on several assumptions which should be expected to alter significantly the stability characteristics of the resulting math model. Strong prima facie evidence is presented to this effect.

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.

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.

Modeling of high speed chemically reacting flow-fields

NASA Technical Reports Server (NTRS)

Drummond, J. P.; Carpenter, Mark H.; Kamath, H.

1989-01-01

The SPARK3D and SPARK3D-PNS computer programs were developed to model 3-D supersonic, chemically reacting flow-fields. The SPARK3D code is a full Navier-Stokes solver, and is suitable for use in scramjet combustors and other regions where recirculation may be present. The SPARK3D-PNS is a parabolized Navier-Stokes solver and provides an efficient means of calculating steady-state combustor far-fields and nozzles. Each code has a generalized chemistry package, making modeling of any chemically reacting flow possible. Research activities by the Langley group range from addressing fundamental theoretical issues to simulating problems of practical importance. Algorithmic development includes work on higher order and upwind spatial difference schemes. Direct numerical simulations employ these algorithms to address the fundamental issues of flow stability and transition, and the chemical reaction of supersonic mixing layers and jets. It is believed that this work will lend greater insight into phenomenological model development for simulating supersonic chemically reacting flows in practical combustors. Currently, the SPARK3D and SPARK3D-PNS codes are used to study problems of engineering interest, including various injector designs and 3-D combustor-nozzle configurations. Examples, which demonstrate the capabilities of each code are presented.

A Navier-Stokes solution of the three-dimensional viscous compressible flow in a centrifugal compressor impeller

NASA Technical Reports Server (NTRS)

Harp, J. L., Jr.

1977-01-01

A two-dimensional time-dependent computer code was utilized to calculate the three-dimensional steady flow within the impeller blading. The numerical method is an explicit time marching scheme in two spatial dimensions. Initially, an inviscid solution is generated on the hub blade-to-blade surface by the method of Katsanis and McNally (1973). Starting with the known inviscid solution, the viscous effects are calculated through iteration. The approach makes it possible to take into account principal impeller fluid-mechanical effects. It is pointed out that the second iterate provides a complete solution to the three-dimensional, compressible, Navier-Stokes equations for flow in a centrifugal impeller. The problems investigated are related to the study of a radial impeller and a backswept impeller.

Incompressible Navier-Stokes Computations with Heat Transfer

NASA Technical Reports Server (NTRS)

Kiris, Cetin; Kwak, Dochan; Rogers, Stuart; Kutler, Paul (Technical Monitor)

1994-01-01

The existing pseudocompressibility method for the system of incompressible Navier-Stokes equations is extended to heat transfer problems by including the energy equation. The solution method is based on the pseudo compressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. Current computations use one-equation Baldwin-Barth turbulence model which is derived from a simplified form of the standard k-epsilon model equations. Both forced and natural convection problems are examined. Numerical results from turbulent reattaching flow behind a backward-facing step will be compared against experimental measurements for the forced convection case. The validity of Boussinesq approximation to simplify the buoyancy force term will be investigated. The natural convective flow structure generated by heat transfer in a vertical rectangular cavity will be studied. The numerical results will be compared by experimental measurements by Morrison and Tran.

Navier-Stokes simulation of the crossflow instability in swept-wing flows

NASA Technical Reports Server (NTRS)

Reed, Helen L.

1989-01-01

The computational modeling of the transition process characteristic of flows over swept wings are described. Specifically, the crossflow instability and crossflow/T-S wave interactions are analyzed through the numerical solution of the full three-dimensional Navier-Stokes equations including unsteadiness, curvature, and sweep. This approach is chosen because of the complexity of the problem and because it appears that linear stability theory is insufficient to explain the discrepancies between different experiments and between theory and experiments. The leading edge region of a swept wing is considered in a three-dimensional spatial simulation with random disturbances as the initial conditions. The work has been closely coordinated with the experimental program of Professor William Saric, examining the same problem. Comparisons with NASA flight test data and the experiments at Arizona State University were a necessary and an important integral part of this work.

Two-dimensional CFD modeling of wave rotor flow dynamics

NASA Technical Reports Server (NTRS)

Welch, Gerard E.; Chima, Rodrick V.

1994-01-01

A two-dimensional Navier-Stokes solver developed for detailed study of wave rotor flow dynamics is described. The CFD model is helping characterize important loss mechanisms within the wave rotor. The wave rotor stationary ports and the moving rotor passages are resolved on multiple computational grid blocks. The finite-volume form of the thin-layer Navier-Stokes equations with laminar viscosity are integrated in time using a four-stage Runge-Kutta scheme. Roe's approximate Riemann solution scheme or the computationally less expensive advection upstream splitting method (AUSM) flux-splitting scheme is used to effect upwind-differencing of the inviscid flux terms, using cell interface primitive variables set by MUSCL-type interpolation. The diffusion terms are central-differenced. The solver is validated using a steady shock/laminar boundary layer interaction problem and an unsteady, inviscid wave rotor passage gradual opening problem. A model inlet port/passage charging problem is simulated and key features of the unsteady wave rotor flow field are identified. Lastly, the medium pressure inlet port and high pressure outlet port portion of the NASA Lewis Research Center experimental divider cycle is simulated and computed results are compared with experimental measurements. The model accurately predicts the wave timing within the rotor passages and the distribution of flow variables in the stationary inlet port region.

Two-dimensional CFD modeling of wave rotor flow dynamics

NASA Technical Reports Server (NTRS)

Welch, Gerard E.; Chima, Rodrick V.

1993-01-01

A two-dimensional Navier-Stokes solver developed for detailed study of wave rotor flow dynamics is described. The CFD model is helping characterize important loss mechanisms within the wave rotor. The wave rotor stationary ports and the moving rotor passages are resolved on multiple computational grid blocks. The finite-volume form of the thin-layer Navier-Stokes equations with laminar viscosity are integrated in time using a four-stage Runge-Kutta scheme. The Roe approximate Riemann solution scheme or the computationally less expensive Advection Upstream Splitting Method (AUSM) flux-splitting scheme are used to effect upwind-differencing of the inviscid flux terms, using cell interface primitive variables set by MUSCL-type interpolation. The diffusion terms are central-differenced. The solver is validated using a steady shock/laminar boundary layer interaction problem and an unsteady, inviscid wave rotor passage gradual opening problem. A model inlet port/passage charging problem is simulated and key features of the unsteady wave rotor flow field are identified. Lastly, the medium pressure inlet port and high pressure outlet port portion of the NASA Lewis Research Center experimental divider cycle is simulated and computed results are compared with experimental measurements. The model accurately predicts the wave timing within the rotor passage and the distribution of flow variables in the stationary inlet port region.

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.

Newton-like methods for Navier-Stokes solution

NASA Astrophysics Data System (ADS)

Qin, N.; Xu, X.; Richards, B. E.

1992-12-01

The paper reports on Newton-like methods called SFDN-alpha-GMRES and SQN-alpha-GMRES methods that have been devised and proven as powerful schemes for large nonlinear problems typical of viscous compressible Navier-Stokes solutions. They can be applied using a partially converged solution from a conventional explicit or approximate implicit method. Developments have included the efficient parallelization of the schemes on a distributed memory parallel computer. The methods are illustrated using a RISC workstation and a transputer parallel system respectively to solve a hypersonic vortical flow.

Some observations on a new numerical method for solving Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Kumar, A.

1981-01-01

An explicit-implicit technique for solving Navier-Stokes equations is described which, is much less complex than other implicit methods. It is used to solve a complex, two-dimensional, steady-state, supersonic-flow problem. The computational efficiency of the method and the quality of the solution obtained from it at high Courant-Friedrich-Lewy (CFL) numbers are discussed. Modifications are discussed and certain observations are made about the method which may be helpful in using it successfully.

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

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

Zhu, Hongyu; Petra, Noemi; Stadler, Georg

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations andmore » model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.« less

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

DOE PAGES

Zhu, Hongyu; Petra, Noemi; Stadler, Georg; ...

2016-07-13

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations andmore » model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.« less

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

NASA Astrophysics Data System (ADS)

Zhu, Hongyu; Petra, Noemi; Stadler, Georg; Isaac, Tobin; Hughes, Thomas J. R.; Ghattas, Omar

2016-07-01

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection-diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov-Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems - i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian - we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. We show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.

A boundary element method for Stokes flows with interfaces

NASA Astrophysics Data System (ADS)

Alinovi, Edoardo; Bottaro, Alessandro

2018-03-01

The boundary element method is a widely used and powerful technique to numerically describe multiphase flows with interfaces, satisfying Stokes' approximation. However, low viscosity ratios between immiscible fluids in contact at an interface and large surface tensions may lead to consistency issues as far as mass conservation is concerned. A simple and effective approach is described to ensure mass conservation at all viscosity ratios and capillary numbers within a standard boundary element framework. Benchmark cases are initially considered demonstrating the efficacy of the proposed technique in satisfying mass conservation, comparing with approaches and other solutions present in the literature. The methodology developed is finally applied to the problem of slippage over superhydrophobic surfaces.

Least-squares solution of incompressible Navier-Stokes equations with the p-version of finite elements

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Sonnad, Vijay

1991-01-01

A p-version of the least squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady state incompressible viscous flow problems. The resulting system of symmetric and positive definite linear equations can be solved satisfactorily with the conjugate gradient method. In conjunction with the use of rapid operator application which avoids the formation of either element of global matrices, it is possible to achieve a highly compact and efficient solution scheme for the incompressible Navier-Stokes equations. Numerical results are presented for two-dimensional flow over a backward facing step. The effectiveness of simple outflow boundary conditions is also demonstrated.

Direct numerical simulation of sheared turbulent flow

NASA Technical Reports Server (NTRS)

Harris, Vascar G.

1994-01-01

The summer assignment to study sheared turbulent flow was divided into three phases which were: (1) literature survey, (2) computational familiarization, and (3) pilot computational studies. The governing equations of fluid dynamics or Navier-Stokes equations describe the velocity, pressure, and density as functions of position and time. In principle, when combined with conservation equations for mass, energy, and thermodynamic state of the fluid a determinate system could be obtained. In practice the Navier-Stokes equations have not been solved due to the nonlinear nature and complexity of these equations. Consequently, the importance of experiments in gaining insight for understanding the physics of the problem has been an ongoing process. Reasonable computer simulations of the problem have occured as the computational speed and storage of computers has evolved. The importance of the microstructure of the turbulence dictates the need for high resolution grids in extracting solutions which contain the physical mechanisms which are essential to a successful simulation. The recognized breakthrough occurred as a result of the pioneering work of Orzag and Patterson in which the Navier-Stokes equations were solved numerically utilizing a time saving toggling technique between physical and wave space, known as a spectral method. An equally analytically unsolvable problem, containing the same quasi-chaotic nature as turbulence, is known as the three body problem which was studied computationally as a first step this summer. This study was followed by computations of a two dimensional (2D) free shear layer.

Computation of multi-dimensional viscous supersonic jet flow

NASA Technical Reports Server (NTRS)

Kim, Y. N.; Buggeln, R. C.; Mcdonald, H.

1986-01-01

A new method has been developed for two- and three-dimensional computations of viscous supersonic flows with embedded subsonic regions adjacent to solid boundaries. The approach employs a reduced form of the Navier-Stokes equations which allows solution as an initial-boundary value problem in space, using an efficient noniterative forward marching algorithm. Numerical instability associated with forward marching algorithms for flows with embedded subsonic regions is avoided by approximation of the reduced form of the Navier-Stokes equations in the subsonic regions of the boundary layers. Supersonic and subsonic portions of the flow field are simultaneously calculated by a consistently split linearized block implicit computational algorithm. The results of computations for a series of test cases relevant to internal supersonic flow is presented and compared with data. Comparison between data and computation are in general excellent thus indicating that the computational technique has great promise as a tool for calculating supersonic flow with embedded subsonic regions. Finally, a User's Manual is presented for the computer code used to perform the calculations.

Entropy Stable Staggered Grid Spectral Collocation for the Burgers' and Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Parsani, Matteo; Fisher, Travis C.; Nielsen, Eric J.

2015-01-01

Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for Burgers' and the compressible Navier-Stokes equations on unstructured hexahedral elements. This generalization of previous entropy stable spectral collocation work [1, 2], extends the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to a combination of tensor product Legendre-Gauss (LG) and LGL points. The new semi-discrete operators discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality for both Burgers' and the compressible Navier-Stokes equations in three spatial dimensions. They are valid for smooth as well as discontinuous flows. The staggered LG and conventional LGL point formulations are compared on several challenging test problems. The staggered LG operators are significantly more accurate, although more costly to implement. The LG and LGL operators exhibit similar robustness, as is demonstrated using test problems known to be problematic for operators that lack a nonlinearly stability proof for the compressible Navier-Stokes equations (e.g., discontinuous Galerkin, spectral difference, or flux reconstruction operators).

Toward a CFD nose-to-tail capability - Hypersonic unsteady Navier-Stokes code validation

NASA Technical Reports Server (NTRS)

Edwards, Thomas A.; Flores, Jolen

1989-01-01

Computational fluid dynamics (CFD) research for hypersonic flows presents new problems in code validation because of the added complexity of the physical models. This paper surveys code validation procedures applicable to hypersonic flow models that include real gas effects. The current status of hypersonic CFD flow analysis is assessed with the Compressible Navier-Stokes (CNS) code as a case study. The methods of code validation discussed to beyond comparison with experimental data to include comparisons with other codes and formulations, component analyses, and estimation of numerical errors. Current results indicate that predicting hypersonic flows of perfect gases and equilibrium air are well in hand. Pressure, shock location, and integrated quantities are relatively easy to predict accurately, while surface quantities such as heat transfer are more sensitive to the solution procedure. Modeling transition to turbulence needs refinement, though preliminary results are promising.

Application of the Galerkin/least-squares formulation to the analysis of hypersonic flows. II - Flow past a double ellipse

NASA Technical Reports Server (NTRS)

Chalot, F.; Hughes, T. J. R.; Johan, Z.; Shakib, F.

1991-01-01

A finite element method for the compressible Navier-Stokes equations is introduced. The discretization is based on entropy variables. The methodology is developed within the framework of a Galerkin/least-squares formulation to which a discontinuity-capturing operator is added. Results for four test cases selected among those of the Workshop on Hypersonic Flows for Reentry Problems are presented.

Application of the Galerkin/least-squares formulation to the analysis of hypersonic flows. I - Flow over a two-dimensional ramp

NASA Technical Reports Server (NTRS)

Chalot, F.; Hughes, T. J. R.; Johan, Z.; Shakib, F.

1991-01-01

An FEM for the compressible Navier-Stokes equations is introduced. The discretization is based on entropy variables. The methodology is developed within the framework of a Galerkin/least-squares formulation to which a discontinuity-capturing operator is added. Results for three test cases selected among those of the Workshop on Hypersonic Flows for Reentry Problems are presented.

Application of multi-grid methods for solving the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Demuren, A. O.

1989-01-01

The application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems is discussed. The methods consist of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line-, or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to that of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.

Application of multi-grid methods for solving the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Demuren, A. O.

1989-01-01

This paper presents the application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems. The methods consists of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line- or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to those of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.

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.

Receptivity of the Boundary Layer to Vibrations of the Wing Surface

NASA Astrophysics Data System (ADS)

Bernots, Tomass; Ruban, Anatoly; Pryce, David; Laminar Flow Control UK Group Team

2014-11-01

In this work we study generation of Tollmien-Schlichting (T-S) waves in the boundary layer due to elastic vibrations of the wing surface. The flow is investigated based on the asymptotic analysis of the Navier-Stokes equations at large values of the Reynolds number. It is assumed that in the spectrum of the wing vibrations there is a harmonic which comes in resonance with the T-S wave on the lower branch of the stability curve. It was found that the vibrations of the wing surface produce pressure perturbations in the flow outside the boundary layer which can be calculated with the help of the piston theory. As the pressure perturbations penetrate into the boundary layer, a Stokes layer forms on the wing surface which appears to be influenced significantly by the compressibility of the flow, and is incapable of producing the T-S waves. The situation changes when the Stokes layer encounters an roughness; near which the flow is described using the triple-deck theory. The solution of the triple-deck problem can be found in an analytic form. Our main concern is with the flow behaviour downstream of the roughness and, in particular, with the amplitude of the generated Tollmien-Schlichting waves. This research was performed in the Laminar Flow Control Centre (LFC-UK) at Imperial College London. The centre is supported by EPSRC, Airbus UK and EADS Innovation Works.

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.

Navier-Stokes and Euler solutions for lee-side flows over supersonic delta wings. A correlation with experiment

NASA Technical Reports Server (NTRS)

Mcmillin, S. Naomi; Thomas, James L.; Murman, Earll M.

1990-01-01

An Euler flow solver and a thin layer Navier-Stokes flow solver were used to numerically simulate the supersonic leeside flow fields over delta wings which were observed experimentally. Three delta wings with 75, 67.5, and 60 deg leading edge sweeps were computed over an angle-of-attack range of 4 to 20 deg at a Mach number 2.8. The Euler code and Navier-Stokes code predict equally well the primary flow structure where the flow is expected to be separated or attached at the leading edge based on the Stanbrook-Squire boundary. The Navier-Stokes code is capable of predicting both the primary and the secondary flow features for the parameter range investigated. For those flow conditions where the Euler code did not predict the correct type of primary flow structure, the Navier-Stokes code illustrated that the flow structure is sensitive to boundary layer model. In general, the laminar Navier-Stokes solutions agreed better with the experimental data, especially for the lower sweep delta wings. The computational results and a detailed re-examination of the experimental data resulted in a refinement of the flow classifications. This refinement in the flow classification results in the separation bubble with the shock flow type as the intermediate flow pattern between separated and attached flows.

Comparison of Implicit Schemes for the Incompressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Rogers, Stuart E.

1995-01-01

For a computational flow simulation tool to be useful in a design environment, it must be very robust and efficient. To develop such a tool for incompressible flow applications, a number of different implicit schemes are compared for several two-dimensional flow problems in the current study. The schemes include Point-Jacobi relaxation, Gauss-Seidel line relaxation, incomplete lower-upper decomposition, and the generalized minimum residual method preconditioned with each of the three other schemes. The efficiency of the schemes is measured in terms of the computing time required to obtain a steady-state solution for the laminar flow over a backward-facing step, the flow over a NACA 4412 airfoil, and the flow over a three-element airfoil using overset grids. The flow solver used in the study is the INS2D code that solves the incompressible Navier-Stokes equations using the method of artificial compressibility and upwind differencing of the convective terms. The results show that the generalized minimum residual method preconditioned with the incomplete lower-upper factorization outperforms all other methods by at least a factor of 2.

Existence of Optimal Controls for Compressible Viscous Flow

NASA Astrophysics Data System (ADS)

Doboszczak, Stefan; Mohan, Manil T.; Sritharan, Sivaguru S.

2018-03-01

We formulate a control problem for a distributed parameter system where the state is governed by the compressible Navier-Stokes equations. Introducing a suitable cost functional, the existence of an optimal control is established within the framework of strong solutions in three dimensions.

Numerical modelling of single-phase flow in rough fractures with contacts

NASA Astrophysics Data System (ADS)

Olkiewicz, Piotr; Dabrowski, Marcin

2017-04-01

Fracture flow may dominate in rocks with low porosity and it can accompany both industrial and natural processes. Typical examples of such processes are natural flows in crystalline rocks and industrial flows in oil and gas production systems or hydraulic fracturing. Fracture flow provides an important mechanism for transporting mass and energy. The distribution of the apertures of fracture and contact area are the key parameters with regard to the fracture transmissivity. We use the method of correlated random fields [Mourzenko, 1996] to generate synthetic fracture geometry in 3D. The flow of an incompressible Newtonian viscous fluid in geological formation can be approximated by the Stokes, the Stokes-Brinkman or the Reynolds models. We use our own implementation of the finite element method based on MILAMIN [Dabrowski, 2008] to solve governing partial differential equation over domain. We compare the Stokes, the Stokes-Brinkamn and the Reynolds models for fracture flow based on systematic numerical simulations for a wide range of geometric parameters. Mismatch between the Reynolds and the Stokes models becomes significant with increasing fracture roughness or contact area. The Stokes-Brinkman model is more accurate than Reynolds models due to additional Laplacian term, which allows to fulfil no-slip boundary condition. We present condition when the Reynolds and the Stokes-Brinkman models are valid. In the last three decades many authors used the Reynolds equation for studying fracture flow because of its simplicity. We recommend using the Stokes-Brinkman model for fracture flow, which allows to fulfil no-slip boundary condition on asperities boundary and is more accurate for rough fractures than the Reynolds model.

PetIGA-MF: A multi-field high-performance toolbox for structure-preserving B-splines spaces

DOE PAGES

Sarmiento, Adel; Cortes, Adriano; Garcia, Daniel; ...

2016-10-07

We describe the development of a high-performance solution framework for isogeometric discrete differential forms based on B-splines: PetIGA-MF. Built on top of PetIGA, PetIGA-MF is a general multi-field discretization tool. To test the capabilities of our implementation, we solve different viscous flow problems such as Darcy, Stokes, Brinkman, and Navier-Stokes equations. Several convergence benchmarks based on manufactured solutions are presented assuring optimal convergence rates of the approximations, showing the accuracy and robustness of our solver.

On the convergence of a fully discrete scheme of LES type to physically relevant solutions of the incompressible Navier-Stokes

NASA Astrophysics Data System (ADS)

Berselli, Luigi C.; Spirito, Stefano

2018-06-01

Obtaining reliable numerical simulations of turbulent fluids is a challenging problem in computational fluid mechanics. The large eddy simulation (LES) models are efficient tools to approximate turbulent fluids, and an important step in the validation of these models is the ability to reproduce relevant properties of the flow. In this paper, we consider a fully discrete approximation of the Navier-Stokes-Voigt model by an implicit Euler algorithm (with respect to the time variable) and a Fourier-Galerkin method (in the space variables). We prove the convergence to weak solutions of the incompressible Navier-Stokes equations satisfying the natural local entropy condition, hence selecting the so-called physically relevant solutions.

Stability of mixing layers

NASA Technical Reports Server (NTRS)

Tam, Christopher; Krothapalli, A

1993-01-01

The research program for the first year of this project (see the original research proposal) consists of developing an explicit marching scheme for solving the parabolized stability equations (PSE). Performing mathematical analysis of the computational algorithm including numerical stability analysis and the determination of the proper boundary conditions needed at the boundary of the computation domain are implicit in the task. Before one can solve the parabolized stability equations for high-speed mixing layers, the mean flow must first be found. In the past, instability analysis of high-speed mixing layer has mostly been performed on mean flow profiles calculated by the boundary layer equations. In carrying out this project, it is believed that the boundary layer equations might not give an accurate enough nonparallel, nonlinear mean flow needed for parabolized stability analysis. A more accurate mean flow can, however, be found by solving the parabolized Navier-Stokes equations. The advantage of the parabolized Navier-Stokes equations is that its accuracy is consistent with the PSE method. Furthermore, the method of solution is similar. Hence, the major part of the effort of the work of this year has been devoted to the development of an explicit numerical marching scheme for the solution of the Parabolized Navier-Stokes equation as applied to the high-seed mixing layer problem.

Shock/vortex interaction and vortex-breakdown modes

NASA Technical Reports Server (NTRS)

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

1992-01-01

Computational simulation and study of shock/vortex interaction and vortex-breakdown modes are considered for bound (internal) and unbound (external) flow domains. The problem is formulated using the unsteady, compressible, full Navier-Stokes (NS) equations which are solved using an implicit, flux-difference splitting, finite-volume scheme. For the bound flow domain, a supersonic swirling flow is considered in a configured circular duct and the problem is solved for quasi-axisymmetric and three-dimensional flows. For the unbound domain, a supersonic swirling flow issued from a nozzle into a uniform supersonic flow of lower Mach number is considered for quasi-axisymmetric and three-dimensional flows. The results show several modes of breakdown; e.g., no-breakdown, transient single-bubble breakdown, transient multi-bubble breakdown, periodic multi-bubble multi-frequency breakdown and helical breakdown.

Implementation of Finite Volume based Navier Stokes Algorithm Within General Purpose Flow Network Code

NASA Technical Reports Server (NTRS)

Schallhorn, Paul; Majumdar, Alok

2012-01-01

This paper describes a finite volume based numerical algorithm that allows multi-dimensional computation of fluid flow within a system level network flow analysis. There are several thermo-fluid engineering problems where higher fidelity solutions are needed that are not within the capacity of system level codes. The proposed algorithm will allow NASA's Generalized Fluid System Simulation Program (GFSSP) to perform multi-dimensional flow calculation within the framework of GFSSP s typical system level flow network consisting of fluid nodes and branches. The paper presents several classical two-dimensional fluid dynamics problems that have been solved by GFSSP's multi-dimensional flow solver. The numerical solutions are compared with the analytical and benchmark solution of Poiseulle, Couette and flow in a driven cavity.

A semi-implicit augmented IIM for Navier–Stokes equations with open, traction, or free boundary conditions

PubMed Central

Li, Zhilin; Xiao, Li; Cai, Qin; Zhao, Hongkai; Luo, Ray

2016-01-01

In this paper, a new Navier–Stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open, traction, and free boundary conditions, which can be applied to simulations of fluid structure interaction, implicit solvent model for biomolecular applications and other free boundary or interface problems. For some problems of this type, the projection method and the augmented immersed interface method (IIM) do not work well or does not work at all. The proposed new Navier–Stokes solver is based on the local pressure boundary method, and a semi-implicit augmented IIM. A fast Poisson solver can be used in our algorithm which gives us the potential for developing fast overall solvers in the future. The time discretization is based on a second order multi-step method. Numerical tests with exact solutions are presented to validate the accuracy of the method. Application to fluid structure interaction between an incompressible fluid and a compressible gas bubble is also presented. PMID:27087702

A semi-implicit augmented IIM for Navier-Stokes equations with open, traction, or free boundary conditions.

PubMed

Li, Zhilin; Xiao, Li; Cai, Qin; Zhao, Hongkai; Luo, Ray

2015-08-15

In this paper, a new Navier-Stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open, traction, and free boundary conditions, which can be applied to simulations of fluid structure interaction, implicit solvent model for biomolecular applications and other free boundary or interface problems. For some problems of this type, the projection method and the augmented immersed interface method (IIM) do not work well or does not work at all. The proposed new Navier-Stokes solver is based on the local pressure boundary method, and a semi-implicit augmented IIM. A fast Poisson solver can be used in our algorithm which gives us the potential for developing fast overall solvers in the future. The time discretization is based on a second order multi-step method. Numerical tests with exact solutions are presented to validate the accuracy of the method. Application to fluid structure interaction between an incompressible fluid and a compressible gas bubble is also presented.

A fictitious domain approach for the Stokes problem based on the extended finite element method

NASA Astrophysics Data System (ADS)

Court, Sébastien; Fournié, Michel; Lozinski, Alexei

2014-01-01

In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by eXtended Finite Element Method and studied for Poisson problem in [Renard]. The method allows computations in domains whose boundaries do not match. A mixed finite element method is used for fluid flow. The interface between the fluid and the structure is localized by a level-set function. Dirichlet boundary conditions are taken into account using Lagrange multiplier. A stabilization term is introduced to improve the approximation of the normal trace of the Cauchy stress tensor at the interface and avoid the inf-sup condition between the spaces for velocity and the Lagrange multiplier. Convergence analysis is given and several numerical tests are performed to illustrate the capabilities of the method.

CAN-DO, CFD-based Aerodynamic Nozzle Design and Optimization program for supersonic/hypersonic wind tunnels

NASA Technical Reports Server (NTRS)

Korte, John J.; Kumar, Ajay; Singh, D. J.; White, J. A.

1992-01-01

A design program is developed which incorporates a modern approach to the design of supersonic/hypersonic wind-tunnel nozzles. The approach is obtained by the coupling of computational fluid dynamics (CFD) with design optimization. The program can be used to design a 2D or axisymmetric, supersonic or hypersonic, wind-tunnel nozzles that can be modeled with a calorically perfect gas. The nozzle design is obtained by solving a nonlinear least-squares optimization problem (LSOP). The LSOP is solved using an iterative procedure which requires intermediate flowfield solutions. The nozzle flowfield is simulated by solving the Navier-Stokes equations for the subsonic and transonic flow regions and the parabolized Navier-Stokes equations for the supersonic flow regions. The advantages of this method are that the design is based on the solution of the viscous equations eliminating the need to make separate corrections to a design contour, and the flexibility of applying the procedure to different types of nozzle design problems.

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

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

Xia, Yidong; Liu, Xiaodong; Luo, Hong

2015-06-01

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

New discretization and solution techniques for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.

1983-01-01

Several topics arising in the finite element solution of the incompressible Navier-Stokes equations are considered. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. The role of artificial viscosity in viscous flow calculations is studied, emphasizing work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some modifications are mentioned.

Model Order Reduction for the fast solution of 3D Stokes problems and its application in geophysical inversion

NASA Astrophysics Data System (ADS)

Ortega Gelabert, Olga; Zlotnik, Sergio; Afonso, Juan Carlos; Díez, Pedro

2017-04-01

The determination of the present-day physical state of the thermal and compositional structure of the Earth's lithosphere and sub-lithospheric mantle is one of the main goals in modern lithospheric research. All this data is essential to build Earth's evolution models and to reproduce many geophysical observables (e.g. elevation, gravity anomalies, travel time data, heat flow, etc) together with understanding the relationship between them. Determining the lithospheric state involves the solution of high-resolution inverse problems and, consequently, the solution of many direct models is required. The main objective of this work is to contribute to the existing inversion techniques in terms of improving the estimation of the elevation (topography) by including a dynamic component arising from sub-lithospheric mantle flow. In order to do so, we implement an efficient Reduced Order Method (ROM) built upon classic Finite Elements. ROM allows to reduce significantly the computational cost of solving a family of problems, for example all the direct models that are required in the solution of the inverse problem. The strategy of the method consists in creating a (reduced) basis of solutions, so that when a new problem has to be solved, its solution is sought within the basis instead of attempting to solve the problem itself. In order to check the Reduced Basis approach, we implemented the method in a 3D domain reproducing a portion of Earth that covers up to 400 km depth. Within the domain the Stokes equation is solved with realistic viscosities and densities. The different realizations (the family of problems) is created by varying viscosities and densities in a similar way as it would happen in an inversion problem. The Reduced Basis method is shown to be an extremely efficiently solver for the Stokes equation in this context.

A non-conventional discontinuous Lagrangian for viscous flow

PubMed Central

Marner, F.

2017-01-01

Drawing an analogy with quantum mechanics, a new Lagrangian is proposed for a variational formulation of the Navier–Stokes equations which to-date has remained elusive. A key feature is that the resulting Lagrangian is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier–Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided. PMID:28386415

A non-conventional discontinuous Lagrangian for viscous flow.

PubMed

Scholle, M; Marner, F

2017-02-01

Drawing an analogy with quantum mechanics, a new Lagrangian is proposed for a variational formulation of the Navier-Stokes equations which to-date has remained elusive. A key feature is that the resulting Lagrangian is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier-Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided.

A paradigm for modeling and computation of gas dynamics

NASA Astrophysics Data System (ADS)

Xu, Kun; Liu, Chang

2017-02-01

In the continuum flow regime, the Navier-Stokes (NS) equations are usually used for the description of gas dynamics. On the other hand, the Boltzmann equation is applied for the rarefied flow. These two equations are based on distinguishable modeling scales for flow physics. Fortunately, due to the scale separation, i.e., the hydrodynamic and kinetic ones, both the Navier-Stokes equations and the Boltzmann equation are applicable in their respective domains. However, in real science and engineering applications, they may not have such a distinctive scale separation. For example, around a hypersonic flying vehicle, the flow physics at different regions may correspond to different regimes, where the local Knudsen number can be changed significantly in several orders of magnitude. With a variation of flow physics, theoretically a continuous governing equation from the kinetic Boltzmann modeling to the hydrodynamic Navier-Stokes dynamics should be used for its efficient description. However, due to the difficulties of a direct modeling of flow physics in the scale between the kinetic and hydrodynamic ones, there is basically no reliable theory or valid governing equations to cover the whole transition regime, except resolving flow physics always down to the mean free path scale, such as the direct Boltzmann solver and the Direct Simulation Monte Carlo (DSMC) method. In fact, it is an unresolved problem about the exact scale for the validity of the NS equations, especially in the small Reynolds number cases. The computational fluid dynamics (CFD) is usually based on the numerical solution of partial differential equations (PDEs), and it targets on the recovering of the exact solution of the PDEs as mesh size and time step converging to zero. This methodology can be hardly applied to solve the multiple scale problem efficiently because there is no such a complete PDE for flow physics through a continuous variation of scales. For the non-equilibrium flow study, the direct modeling methods, such as DSMC, particle in cell, and smooth particle hydrodynamics, play a dominant role to incorporate the flow physics into the algorithm construction directly. It is fully legitimate to combine the modeling and computation together without going through the process of constructing PDEs. In other words, the CFD research is not only to obtain the numerical solution of governing equations but to model flow dynamics as well. This methodology leads to the unified gas-kinetic scheme (UGKS) for flow simulation in all flow regimes. Based on UGKS, the boundary for the validation of the Navier-Stokes equations can be quantitatively evaluated. The combination of modeling and computation provides a paradigm for the description of multiscale transport process.

Calculations of High-Temperature Jet Flow Using Hybrid Reynolds-Average Navier-Stokes Formulations

NASA Technical Reports Server (NTRS)

Abdol-Hamid, Khaled S.; Elmiligui, Alaa; Giriamaji, Sharath S.

2008-01-01

Two multiscale-type turbulence models are implemented in the PAB3D solver. The models are based on modifying the Reynolds-averaged Navier Stokes equations. The first scheme is a hybrid Reynolds-averaged- Navier Stokes/large-eddy-simulation model using the two-equation k(epsilon) model with a Reynolds-averaged-Navier Stokes/large-eddy-simulation 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 model in which the unresolved kinetic energy parameter f(sub k) is allowed to vary as a function of grid spacing and the turbulence length scale. This parameter is estimated based on a novel two-stage procedure to efficiently estimate the level of scale resolution possible for a given flow on a given grid for partially averaged Navier Stokes. It has been found that the prescribed scale resolution can play a major role in obtaining accurate flow solutions. The parameter f(sub k) varies between zero and one and is equal to one in the viscous sublayer and when the Reynolds-averaged Navier Stokes turbulent viscosity becomes smaller than the large-eddy-simulation viscosity. The formulation, usage methodology, and validation examples are presented to demonstrate the enhancement of PAB3D's time-accurate turbulence modeling capabilities. The accurate simulations of flow and turbulent quantities will provide a valuable tool for accurate jet noise predictions. Solutions from these models are compared with Reynolds-averaged Navier Stokes results and experimental data for high-temperature jet flows. The current results show promise for the capability of hybrid Reynolds-averaged Navier Stokes and large eddy simulation and partially averaged Navier Stokes in simulating such flow phenomena.

A comparative study of computational solutions to flow over a backward-facing step

NASA Technical Reports Server (NTRS)

Mizukami, M.; Georgiadis, N. J.; Cannon, M. R.

1993-01-01

A comparative study was conducted for computational fluid dynamic solutions to flow over a backward-facing step. This flow is a benchmark problem, with a simple geometry, but involves complicated flow physics such as free shear layers, reattaching flow, recirculation, and high turbulence intensities. Three Reynolds-averaged Navier-Stokes flow solvers with k-epsilon turbulence models were used, each using a different solution algorithm: finite difference, finite element, and hybrid finite element - finite difference. Comparisons were made with existing experimental data. Results showed that velocity profiles and reattachment lengths were predicted reasonably well by all three methods, while the skin friction coefficients were more difficult to predict accurately. It was noted that, in general, selecting an appropriate solver for each problem to be considered is important.

Current problems in applied mathematics and mathematical physics

NASA Astrophysics Data System (ADS)

Samarskii, A. A.

Papers are presented on such topics as mathematical models in immunology, mathematical problems of medical computer tomography, classical orthogonal polynomials depending on a discrete variable, and boundary layer methods for singular perturbation problems in partial derivatives. Consideration is also given to the computer simulation of supernova explosion, nonstationary internal waves in a stratified fluid, the description of turbulent flows by unsteady solutions of the Navier-Stokes equations, and the reduced Galerkin method for external diffraction problems using the spline approximation of fields.

Numerical analysis of exhaust jet secondary combustion in hypersonic flow field

NASA Astrophysics Data System (ADS)

Yang, Tian-Peng; Wang, Jiang-Feng; Zhao, Fa-Ming; Fan, Xiao-Feng; Wang, Yu-Han

2018-05-01

The interaction effect between jet and control surface in supersonic and hypersonic flow is one of the key problems for advanced flight control system. The flow properties of exhaust jet secondary combustion in a hypersonic compression ramp flow field were studied numerically by solving the Navier-Stokes equations with multi-species and combustion reaction effects. The analysis was focused on the flow field structure and the force amplification factor under different jet conditions. Numerical results show that a series of different secondary combustion makes the flow field structure change regularly, and the temperature increases rapidly near the jet exit.

Flux-vector splitting algorithm for chain-rule conservation-law form

NASA Technical Reports Server (NTRS)

Shih, T. I.-P.; Nguyen, H. L.; Willis, E. A.; Steinthorsson, E.; Li, Z.

1991-01-01

A flux-vector splitting algorithm with Newton-Raphson iteration was developed for the 'full compressible' Navier-Stokes equations cast in chain-rule conservation-law form. The algorithm is intended for problems with deforming spatial domains and for problems whose governing equations cannot be cast in strong conservation-law form. The usefulness of the algorithm for such problems was demonstrated by applying it to analyze the unsteady, two- and three-dimensional flows inside one combustion chamber of a Wankel engine under nonfiring conditions. Solutions were obtained to examine the algorithm in terms of conservation error, robustness, and ability to handle complex flows on time-dependent grid systems.

Compressible Navier-Stokes Equations in a Polyhedral Cylinder with Inflow Boundary Condition

NASA Astrophysics Data System (ADS)

Kwon, Ohsung; Kweon, Jae Ryong

2018-06-01

In this paper our concern is with singularity and regularity of the compressible flows through a non-convex edge in R^3. The flows are governed by the compressible Navies-Stokes equations on the infinite cylinder that has the non-convex edge on the inflow boundary. We split the edge singularity by the Poisson problem from the velocity vector and show that the remainder is twice differentiable while the edge singularity is observed to be propagated into the interior of the cylinder by the transport character of the continuity equation. An interior surface layer starting at the edge is generated and not Lipshitz continuous due to the singularity. The density function shows a very steep change near the interface and its normal derivative has a jump discontinuity across there.

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.

A perspective on unstructured grid flow solvers

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.

1995-01-01

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

Numerical solution of a flow inside a labyrinth seal

NASA Astrophysics Data System (ADS)

Šimák, Jan; Straka, Petr; Pelant, Jaroslav

2012-04-01

The aim of this study is a behaviour of a flow inside a labyrinth seal on a rotating shaft. The labyrinth seal is a type of a non-contact seal where a leakage of a fluid is prevented by a rather complicated path, which the fluid has to overcome. In the presented case the sealed medium is the air and the seal is made by a system of 20 teeth on a rotating shaft situated against a smooth static surface. Centrifugal forces present due to the rotation of the shaft create vortices in each chamber and thus dissipate the axial velocity of the escaping air.The structure of the flow field inside the seal is studied through the use of numerical methods. Three-dimensional solution of the Navier-Stokes equations for turbulent flow is very time consuming. In order to reduce the computational time we can simplify our problem and solve it as an axisymmetric problem in a two-dimensional meridian plane. For this case we use a transformation of the Navier-Stokes equations and of the standard k-omega turbulence model into a cylindrical coordinate system. A finite volume method is used for the solution of the resulting problem. A one-side modification of the Riemann problem for boundary conditions is used at the inlet and at the outlet of the axisymmetric channel. The total pressure and total density (temperature) are to be used preferably at the inlet whereas the static pressure is used at the outlet for the compatibility. This idea yields physically relevant boundary conditions. The important characteristics such as a mass flow rate and a power loss, depending on a pressure ratio (1.1 - 4) and an angular velocity (1000 - 15000 rpm) are evaluated.

Scalable High Performance Computing: Direct and Large-Eddy Turbulent Flow Simulations Using Massively Parallel Computers

NASA Technical Reports Server (NTRS)

Morgan, Philip E.

2004-01-01

This final report contains reports of research related to the tasks "Scalable High Performance Computing: Direct and Lark-Eddy Turbulent FLow Simulations Using Massively Parallel Computers" and "Devleop High-Performance Time-Domain Computational Electromagnetics Capability for RCS Prediction, Wave Propagation in Dispersive Media, and Dual-Use Applications. The discussion of Scalable High Performance Computing reports on three objectives: validate, access scalability, and apply two parallel flow solvers for three-dimensional Navier-Stokes flows; develop and validate a high-order parallel solver for Direct Numerical Simulations (DNS) and Large Eddy Simulation (LES) problems; and Investigate and develop a high-order Reynolds averaged Navier-Stokes turbulence model. The discussion of High-Performance Time-Domain Computational Electromagnetics reports on five objectives: enhancement of an electromagnetics code (CHARGE) to be able to effectively model antenna problems; utilize lessons learned in high-order/spectral solution of swirling 3D jets to apply to solving electromagnetics project; transition a high-order fluids code, FDL3DI, to be able to solve Maxwell's Equations using compact-differencing; develop and demonstrate improved radiation absorbing boundary conditions for high-order CEM; and extend high-order CEM solver to address variable material properties. The report also contains a review of work done by the systems engineer.

Mixed mimetic spectral element method for Stokes flow: A pointwise divergence-free solution

NASA Astrophysics Data System (ADS)

Kreeft, Jasper; Gerritsma, Marc

2013-05-01

In this paper we apply the recently developed mimetic discretization method to the mixed formulation of the Stokes problem in terms of vorticity, velocity and pressure. The mimetic discretization presented in this paper and in Kreeft et al. [51] is a higher-order method for curvilinear quadrilaterals and hexahedrals. Fundamental is the underlying structure of oriented geometric objects, the relation between these objects through the boundary operator and how this defines the exterior derivative, representing the grad, curl and div, through the generalized Stokes theorem. The mimetic method presented here uses the language of differential k-forms with k-cochains as their discrete counterpart, and the relations between them in terms of the mimetic operators: reduction, reconstruction and projection. The reconstruction consists of the recently developed mimetic spectral interpolation functions. The most important result of the mimetic framework is the commutation between differentiation at the continuous level with that on the finite dimensional and discrete level. As a result operators like gradient, curl and divergence are discretized exactly. For Stokes flow, this implies a pointwise divergence-free solution. This is confirmed using a set of test cases on both Cartesian and curvilinear meshes. It will be shown that the method converges optimally for all admissible boundary conditions.

A model problem for estimation of moving-film time relaxation at sudden change of boundary conditions

NASA Astrophysics Data System (ADS)

Smirnovsky, Alexander A.; Eliseeva, Viktoria O.

2018-05-01

The study of the film flow occurred under the influence of a gas slug flow is of definite interest in heat and mass transfer during the motion of a coolant in the second circuit of a nuclear water-water reactor. Thermohydraulic codes are usually used for analysis of the such problems in which the motion of the liquid film and the vapor is modeled on the basis of a one-dimensional balance equations. Due to a greater inertia of the liquid film motion, film flow parameters changes with a relaxation compared with gas flow. We consider a model problem of film flow under the influence of friction from gas slug flow neglecting such effects as wave formation, droplet breakage and deposition on the film surface, evaporation and condensation. Such a problem is analogous to the well-known problems of Couette and Stokes flows. An analytical solution has been obtained for laminar flow. Numerical RANS-based simulation of turbulent flow was performed using OpenFOAM. It is established that the relaxation process is almost self-similar. This fact opens a possibility of obtaining valuable correlations for the relaxation time.

Méthode du second membre modifié pour la gestion de rapports de viscosité importants dans le problème de Stokes bifluide

NASA Astrophysics Data System (ADS)

Bui, Thi Thu Cuc; Frey, Pascal; Maury, Bertrand

2008-06-01

In this Note, we present a method to solve numerically the Stokes equation for the incompressible flow between two immiscible fluids presenting very different viscosities. The resolution of the finite element systems of equations is performed using Uzawa's method. The stiffness matrix conditioning problems related to the very important viscosity ratios are circumvented using an new iterative scheme. A numerical example is proposed to show the efficiency of this approach. To cite this article: T.T.C. Bui et al., C. R. Mecanique 336 (2008).

Direct Coupling Method for Time-Accurate Solution of Incompressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Soh, Woo Y.

1992-01-01

A noniterative finite difference numerical method is presented for the solution of the incompressible Navier-Stokes equations with second order accuracy in time and space. Explicit treatment of convection and diffusion terms and implicit treatment of the pressure gradient give a single pressure Poisson equation when the discretized momentum and continuity equations are combined. A pressure boundary condition is not needed on solid boundaries in the staggered mesh system. The solution of the pressure Poisson equation is obtained directly by Gaussian elimination. This method is tested on flow problems in a driven cavity and a curved duct.

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.

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.

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

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

Kinetically reduced local Navier-Stokes equations: an alternative approach to hydrodynamics.

PubMed

Karlin, Iliya V; Tomboulides, Ananias G; Frouzakis, Christos E; Ansumali, Santosh

2006-09-01

An alternative approach, the kinetically reduced local Navier-Stokes (KRLNS) equations for the grand potential and the momentum, is proposed for the simulation of low Mach number flows. The Taylor-Green vortex flow is considered in the KRLNS framework, and compared to the results of the direct numerical simulation of the incompressible Navier-Stokes equations. The excellent agreement between the KRLNS equations and the incompressible nonlocal Navier-Stokes equations for this nontrivial time-dependent flow indicates that the former is a viable alternative for computational fluid dynamics at low Mach numbers.

Application of boundary element method to Stokes flows over a striped superhydrophobic surface with trapped gas bubbles

NASA Astrophysics Data System (ADS)

Ageev, A. I.; Golubkina, I. V.; Osiptsov, A. N.

2018-01-01

A slow steady flow of a viscous fluid over a superhydrophobic surface with a periodic striped system of 2D rectangular microcavities is considered. The microcavities contain small gas bubbles on the curved surface of which the shear stress vanishes. The general case is analyzed when the bubble occupies only a part of the cavity, and the flow velocity far from the surface is directed at an arbitrary angle to the cavity edge. Due to the linearity of the Stokes flow problem, the solution is split into two parts, corresponding to the flows perpendicular and along the cavities. Two variants of a boundary element method are developed and used to construct numerical solutions on the scale of a single cavity with periodic boundary conditions. By averaging these solutions, the average slip velocity and the slip length tensor components are calculated over a wide range of variation of governing parameters for the cases of a shear-driven flow and a pressure-driven channel flow. For a sufficiently high pressure drop in a microchannel of finite length, the variation of the bubble surface shift into the cavities induced by the streamwise pressure variation is estimated from numerical calculations.

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

NASA Technical Reports Server (NTRS)

Frink, Neal T.; Pirzadeh, Shahyar Z.

1998-01-01

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

Dual Dynamically Orthogonal approximation of incompressible Navier Stokes equations with random boundary conditions

NASA Astrophysics Data System (ADS)

Musharbash, Eleonora; Nobile, Fabio

2018-02-01

In this paper we propose a method for the strong imposition of random Dirichlet boundary conditions in the Dynamical Low Rank (DLR) approximation of parabolic PDEs and, in particular, incompressible Navier Stokes equations. We show that the DLR variational principle can be set in the constrained manifold of all S rank random fields with a prescribed value on the boundary, expressed in low rank format, with rank smaller then S. We characterize the tangent space to the constrained manifold by means of a Dual Dynamically Orthogonal (Dual DO) formulation, in which the stochastic modes are kept orthonormal and the deterministic modes satisfy suitable boundary conditions, consistent with the original problem. The Dual DO formulation is also convenient to include the incompressibility constraint, when dealing with incompressible Navier Stokes equations. We show the performance of the proposed Dual DO approximation on two numerical test cases: the classical benchmark of a laminar flow around a cylinder with random inflow velocity, and a biomedical application for simulating blood flow in realistic carotid artery reconstructed from MRI data with random inflow conditions coming from Doppler measurements.

Computation of rotor-stator interaction using the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Whitfield, David L.; Chen, Jen-Ping

1995-01-01

The numerical scheme presented belongs to a family of codes known as UNCLE (UNsteady Computation of fieLd Equations) as reported by Whitfield (1995), that is being used to solve problems in a variety of areas including compressible and incompressible flows. This derivation is specifically developed for general unsteady multi-blade-row turbomachinery problems. The scheme solves the Reynolds-averaged N-S equations with the Baldwin-Lomax turbulence model.

The Navier-Stokes Stress Principle for Viscous Fluids

NASA Technical Reports Server (NTRS)

Mohr, Ernst

1942-01-01

The Navier-Stokes stress principle is checked in the light of Maxwell's mechanism of friction and in connection herewith the possibility of another theorem is indicated. The Navier-Stokes stress principle is in general predicated upon the conception of the plastic body. Hence the process is a purely phenomenological one, which Newton himself followed with his special theorem for one-dimensional flows. It remained for Maxwell to discover the physical mechanism by which the shear inflow direction is developed: According to it, this shear is only 'fictitious' as it merely represents the substitute for a certain transport on macroscopic motion quantity, as conditioned by Brown's moiecular motion and the diffusion, respectively. It is clear that this mechanism is not bound to the special case of the one-dimensioilal flows, but holds for any flow as expression of the diffusion, by which a fluid differs sharply from a plastic body. If it is remembered, on the other hand, that the cause of the stresses on the plastic body lies in a certain cohesion of the molecules, it appears by no means self evident that this difference in the mechanism of friction between fluid and plastic body should not prevail in the stress principle as well, although it certainly is desirable in any case, at least subsequently, to establish the general theorem in the sense of Maxwell. Actually, a different theorem is suggested which, in contrast to that by Navier-Stokes, has the form of an unsymmetrical matrix. Without anticipating a final decision several reasons are advanced by way of a special flow which seem to affirm this new theorem. To make it clear that the problem involved here still awaits its final solution, is the real purpose behind the present article.

New discretization and solution techniques for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.

1983-01-01

This paper considers several topics arising in the finite element solution of the incompressible Navier-Stokes equations. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. Following this, the role of artificial viscosity in viscous flow calculations is studied, emphasizing recent work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some recent modifications are mentioned.

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.

Higher-order differencing method with a multigrid approach for the solution of the incompressible flow equations at high Reynolds numbers

NASA Astrophysics Data System (ADS)

Tzanos, Constantine P.

1992-10-01

A higher-order differencing scheme (Tzanos, 1990) is used in conjunction with a multigrid approach to obtain accurate solutions of the Navier-Stokes convection-diffusion equations at high Re numbers. Flow in a square cavity with a moving lid is used as a test problem. a multigrid approach based on the additive correction method (Settari and Aziz) and an iterative incomplete lower and upper solver demonstrated good performance for the whole range of Re number under consideration (from 1000 to 10,000) and for both uniform and nonuniform grids. It is concluded that the combination of the higher-order differencing scheme with a multigrid approach proved to be an effective technique for giving accurate solutions of the Navier-Stokes equations at high Re numbers.

An unstructured-grid software system for solving complex aerodynamic problems

NASA Technical Reports Server (NTRS)

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

1995-01-01

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

Turbulence coefficients and stability studies for the coaxial flow or dissimiliar fluids. [gaseous core nuclear reactors

NASA Technical Reports Server (NTRS)

Weinstein, H.; Lavan, Z.

1975-01-01

Analytical investigations of fluid dynamics problems of relevance to the gaseous core nuclear reactor program are presented. The vortex type flow which appears in the nuclear light bulb concept is analyzed along with the fluid flow in the fuel inlet region for the coaxial flow gaseous core nuclear reactor concept. The development of numerical methods for the solution of the Navier-Stokes equations for appropriate geometries is extended to the case of rotating flows and almost completes the gas core program requirements in this area. The investigations demonstrate that the conceptual design of the coaxial flow reactor needs further development.

Space-time asymptotics of the two dimensional Navier-Stokes flow in the whole plane

NASA Astrophysics Data System (ADS)

Okabe, Takahiro

2018-01-01

We consider the space-time behavior of the two dimensional Navier-Stokes flow. Introducing some qualitative structure of initial data, we succeed to derive the first order asymptotic expansion of the Navier-Stokes flow without moment condition on initial data in L1 (R2) ∩ Lσ2 (R2). Moreover, we characterize the necessary and sufficient condition for the rapid energy decay ‖ u (t) ‖ 2 = o (t-1) as t → ∞ motivated by Miyakawa-Schonbek [21]. By weighted estimated in Hardy spaces, we discuss the possibility of the second order asymptotic expansion of the Navier-Stokes flow assuming the first order moment condition on initial data. Moreover, observing that the Navier-Stokes flow u (t) lies in the Hardy space H1 (R2) for t > 0, we consider the asymptotic expansions in terms of Hardy-norm. Finally we consider the rapid time decay ‖ u (t) ‖ 2 = o (t - 3/2 ) as t → ∞ with cyclic symmetry introduced by Brandolese [2].

Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations.

PubMed

Li, Q; He, Y L; Wang, Y; Tao, W Q

2007-11-01

A coupled double-distribution-function lattice Boltzmann method is developed for the compressible Navier-Stokes equations. Different from existing thermal lattice Boltzmann methods, this method can recover the compressible Navier-Stokes equations with a flexible specific-heat ratio and Prandtl number. In the method, a density distribution function based on a multispeed lattice is used to recover the compressible continuity and momentum equations, while the compressible energy equation is recovered by an energy distribution function. The energy distribution function is then coupled to the density distribution function via the thermal equation of state. In order to obtain an adjustable specific-heat ratio, a constant related to the specific-heat ratio is introduced into the equilibrium energy distribution function. Two different coupled double-distribution-function lattice Boltzmann models are also proposed in the paper. Numerical simulations are performed for the Riemann problem, the double-Mach-reflection problem, and the Couette flow with a range of specific-heat ratios and Prandtl numbers. The numerical results are found to be in excellent agreement with analytical and/or other solutions.

Acceleration methods for multi-physics compressible flow

NASA Astrophysics Data System (ADS)

Peles, Oren; Turkel, Eli

2018-04-01

In this work we investigate the Runge-Kutta (RK)/Implicit smoother scheme as a convergence accelerator for complex multi-physics flow problems including turbulent, reactive and also two-phase flows. The flows considered are subsonic, transonic and supersonic flows in complex geometries, and also can be either steady or unsteady flows. All of these problems are considered to be a very stiff. We then introduce an acceleration method for the compressible Navier-Stokes equations. We start with the multigrid method for pure subsonic flow, including reactive flows. We then add the Rossow-Swanson-Turkel RK/Implicit smoother that enables performing all these complex flow simulations with a reasonable CFL number. We next discuss the RK/Implicit smoother for time dependent problem and also for low Mach numbers. The preconditioner includes an intrinsic low Mach number treatment inside the smoother operator. We also develop a modified Roe scheme with a corresponding flux Jacobian matrix. We then give the extension of the method for real gas and reactive flow. Reactive flows are governed by a system of inhomogeneous Navier-Stokes equations with very stiff source terms. The extension of the RK/Implicit smoother requires an approximation of the source term Jacobian. The properties of the Jacobian are very important for the stability of the method. We discuss what the chemical physics theory of chemical kinetics tells about the mathematical properties of the Jacobian matrix. We focus on the implication of the Le-Chatelier's principle on the sign of the diagonal entries of the Jacobian. We present the implementation of the method for turbulent flow. We use a two RANS turbulent model - one equation model - Spalart-Allmaras and a two-equation model - k-ω SST model. The last extension is for two-phase flows with a gas as a main phase and Eulerian representation of a dispersed particles phase (EDP). We present some examples for such flow computations inside a ballistic evaluation rocket motor. The numerical examples in this work include transonic flow about a RAE2822 airfoil, about a M6 Onera wing, NACA0012 airfoil at very low Mach number, two-phase flow inside a Ballistic evaluation motor (BEM), a turbulent reactive shear layer and a time dependent Sod's tube problem.

A dual potential formulation of the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

Numerical methods for incompressible viscous flows with engineering applications

NASA Technical Reports Server (NTRS)

Rose, M. E.; Ash, R. L.

1988-01-01

A numerical scheme has been developed to solve the incompressible, 3-D Navier-Stokes equations using velocity-vorticity variables. This report summarizes the development of the numerical approximation schemes for the divergence and curl of the velocity vector fields and the development of compact schemes for handling boundary and initial boundary value problems.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

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.

Cell-Averaged discretization for incompressible Navier-Stokes with embedded boundaries and locally refined Cartesian meshes: a high-order finite volume approach

NASA Astrophysics Data System (ADS)

Bhalla, Amneet Pal Singh; Johansen, Hans; Graves, Dan; Martin, Dan; Colella, Phillip; Applied Numerical Algorithms Group Team

2017-11-01

We present a consistent cell-averaged discretization for incompressible Navier-Stokes equations on complex domains using embedded boundaries. The embedded boundary is allowed to freely cut the locally-refined background Cartesian grid. Implicit-function representation is used for the embedded boundary, which allows us to convert the required geometric moments in the Taylor series expansion (upto arbitrary order) of polynomials into an algebraic problem in lower dimensions. The computed geometric moments are then used to construct stencils for various operators like the Laplacian, divergence, gradient, etc., by solving a least-squares system locally. We also construct the inter-level data-transfer operators like prolongation and restriction for multi grid solvers using the same least-squares system approach. This allows us to retain high-order of accuracy near coarse-fine interface and near embedded boundaries. Canonical problems like Taylor-Green vortex flow and flow past bluff bodies will be presented to demonstrate the proposed method. U.S. Department of Energy, Office of Science, ASCR (Award Number DE-AC02-05CH11231).

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.

Advances in modelling of biomimetic fluid flow at different scales

PubMed Central

2011-01-01

The biomimetic flow at different scales has been discussed at length. The need of looking into the biological surfaces and morphologies and both geometrical and physical similarities to imitate the technological products and processes has been emphasized. The complex fluid flow and heat transfer problems, the fluid-interface and the physics involved at multiscale and macro-, meso-, micro- and nano-scales have been discussed. The flow and heat transfer simulation is done by various CFD solvers including Navier-Stokes and energy equations, lattice Boltzmann method and molecular dynamics method. Combined continuum-molecular dynamics method is also reviewed. PMID:21711847

Stratified Shear Flows In Pipe Geometries

NASA Astrophysics Data System (ADS)

Harabin, George; Camassa, Roberto; McLaughlin, Richard; UNC Joint Fluids Lab Team Team

2015-11-01

Exact and series solutions to the full Navier-Stokes equations coupled to the advection diffusion equation are investigated in tilted three-dimensional pipe geometries. Analytic techniques for studying the three-dimensional problem provide a means for tackling interesting questions such as the optimal domain for mass transport, and provide new avenues for experimental investigation of diffusion driven flows. Both static and time dependent solutions will be discussed. NSF RTG DMS-0943851, NSF RTG ARC-1025523, NSF DMS-1009750.

Three dimensional PNS solutions of hypersonic internal flows with equilibrium chemistry

NASA Technical Reports Server (NTRS)

Liou, May-Fun

1989-01-01

An implicit procedure for solving parabolized Navier-Stokes equations under the assumption of a general equation of state for a gas in chemical equilibrium is given. A general and consistent approach for the evaluation of Jacobian matrices in the implicit operator avoids the use of unnecessary auxiliary quantities and approximations, and leads to a simple expression. Applications to two- and three-dimensional flow problems show efficiency in computer time and economy in storage.

Boundary conditions for the solution of compressible Navier-Stokes equations by an implicit factored method

NASA Technical Reports Server (NTRS)

Shih, T. I.-P.; Smith, G. E.; Springer, G. S.; Rimon, Y.

1983-01-01

A method is presented for formulating the boundary conditions in implicit finite-difference form needed for obtaining solutions to the compressible Navier-Stokes equations by the Beam and Warming implicit factored method. The usefulness of the method was demonstrated (a) by establishing the boundary conditions applicable to the analysis of the flow inside an axisymmetric piston-cylinder configuration and (b) by calculating velocities and mass fractions inside the cylinder for different geometries and different operating conditions. Stability, selection of time step and grid sizes, and computer time requirements are discussed in reference to the piston-cylinder problem analyzed.

Large eddy simulation in a rotary blood pump: Viscous shear stress computation and comparison with unsteady Reynolds-averaged Navier-Stokes simulation.

PubMed

Torner, Benjamin; Konnigk, Lucas; Hallier, Sebastian; Kumar, Jitendra; Witte, Matthias; Wurm, Frank-Hendrik

2018-06-01

Numerical flow analysis (computational fluid dynamics) in combination with the prediction of blood damage is an important procedure to investigate the hemocompatibility of a blood pump, since blood trauma due to shear stresses remains a problem in these devices. Today, the numerical damage prediction is conducted using unsteady Reynolds-averaged Navier-Stokes simulations. Investigations with large eddy simulations are rarely being performed for blood pumps. Hence, the aim of the study is to examine the viscous shear stresses of a large eddy simulation in a blood pump and compare the results with an unsteady Reynolds-averaged Navier-Stokes simulation. The simulations were carried out at two operation points of a blood pump. The flow was simulated on a 100M element mesh for the large eddy simulation and a 20M element mesh for the unsteady Reynolds-averaged Navier-Stokes simulation. As a first step, the large eddy simulation was verified by analyzing internal dissipative losses within the pump. Then, the pump characteristics and mean and turbulent viscous shear stresses were compared between the two simulation methods. The verification showed that the large eddy simulation is able to reproduce the significant portion of dissipative losses, which is a global indication that the equivalent viscous shear stresses are adequately resolved. The comparison with the unsteady Reynolds-averaged Navier-Stokes simulation revealed that the hydraulic parameters were in agreement, but differences for the shear stresses were found. The results show the potential of the large eddy simulation as a high-quality comparative case to check the suitability of a chosen Reynolds-averaged Navier-Stokes setup and turbulence model. Furthermore, the results lead to suggest that large eddy simulations are superior to unsteady Reynolds-averaged Navier-Stokes simulations when instantaneous stresses are applied for the blood damage prediction.

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.

Numerical Study of Pressure Field in Laterally Closed Industrial Buildings with Curved Metallic Roofs due to the Wind Effect by FEM and European Rule Comparison

NASA Astrophysics Data System (ADS)

Nieto, P. J. García; del Coz Díaz, J. J.; Vilán, J. A. Vilán; Placer, C. Casqueiro

2009-08-01

In this paper, an evaluation of distribution of the air pressure is determined throughout the laterally closed industrial buildings with curved metallic roofs due to the wind effect by the finite element method (FEM). The non-linearity is due to Reynolds-averaged Navier-Stokes (RANS) equations that govern the turbulent flow. The Navier-Stokes equations are non-linear partial differential equations and this non-linearity makes most problems difficult to solve and is part of the cause of turbulence. The RANS equations are time-averaged equations of motion for fluid flow. They are primarily used while dealing with turbulent flows. Turbulence is a highly complex physical phenomenon that is pervasive in flow problems of scientific and engineering concern like this one. In order to solve the RANS equations a two-equation model is used: the standard k-ɛ model. The calculation has been carried out keeping in mind the following assumptions: turbulent flow, an exponential-like wind speed profile with a maximum velocity of 40 m/s at 10 m reference height, and different heights of the building ranging from 6 to 10 meters. Finally, the forces and moments are determined on the cover, as well as the distribution of pressures on the same one, comparing the numerical results obtained with the Spanish CTE DB SE-AE, Spanish NBE AE-88 and European standard rules, giving place to the conclusions that are exposed in the study.

User's guide for NASCRIN: A vectorized code for calculating two-dimensional supersonic internal flow fields

NASA Technical Reports Server (NTRS)

Kumar, A.

1984-01-01

A computer program NASCRIN has been developed for analyzing two-dimensional flow fields in high-speed inlets. It solves the two-dimensional Euler or Navier-Stokes equations in conservation form by an explicit, two-step finite-difference method. An explicit-implicit method can also be used at the user's discretion for viscous flow calculations. For turbulent flow, an algebraic, two-layer eddy-viscosity model is used. The code is operational on the CDC CYBER 203 computer system and is highly vectorized to take full advantage of the vector-processing capability of the system. It is highly user oriented and is structured in such a way that for most supersonic flow problems, the user has to make only a few changes. Although the code is primarily written for supersonic internal flow, it can be used with suitable changes in the boundary conditions for a variety of other problems.

Numerical techniques for the solution of the compressible Navier-Stokes equations and implementation of turbulence models. [separated turbulent boundary layer flow problems

NASA Technical Reports Server (NTRS)

Baldwin, B. S.; Maccormack, R. W.; Deiwert, G. S.

1975-01-01

The time-splitting explicit numerical method of MacCormack is applied to separated turbulent boundary layer flow problems. Modifications of this basic method are developed to counter difficulties associated with complicated geometry and severe numerical resolution requirements of turbulence model equations. The accuracy of solutions is investigated by comparison with exact solutions for several simple cases. Procedures are developed for modifying the basic method to improve the accuracy. Numerical solutions of high-Reynolds-number separated flows over an airfoil and shock-separated flows over a flat plate are obtained. A simple mixing length model of turbulence is used for the transonic flow past an airfoil. A nonorthogonal mesh of arbitrary configuration facilitates the description of the flow field. For the simpler geometry associated with the flat plate, a rectangular mesh is used, and solutions are obtained based on a two-equation differential model of turbulence.

Influence of magnetic field on chemically reactive blood flow through stenosed bifurcated arteries

NASA Astrophysics Data System (ADS)

Hossain, Khan Enaet; Haque, Md. Mohidul

2017-06-01

Dynamic response of mass transfer in chemically reactive blood flow through bifurcated arteries under the stenotic condition is numerically studied in the present of a uniform magnetic field. The blood flowing through the artery is assumed an incompressible, fully developed and Newtonian. The nonlinear unsteady flow phenomena are governed by the Navier-Stokes and concentration equations. All these equations together with the appropriate boundary conditions describing the present biomechanical problem are transformed by using a radial transformation and the numerical results are obtained using a finite difference technique. Effects of stenosed bifurcation and externally applied magnetic field on the blood flow with chemical reaction are discussed with the help of graph. All the flow characteristics are found to be affected by the presence of chemical reaction and exposure of magnetic field of different intensities. Finally some important findings of the problem are concluded in this work.

Investigation of Navier-Stokes Code Verification and Design Optimization

NASA Technical Reports Server (NTRS)

Vaidyanathan, Rajkumar

2004-01-01

With rapid progress made in employing computational techniques for various complex Navier-Stokes fluid flow problems, design optimization problems traditionally based on empirical formulations and experiments are now being addressed with the aid of computational fluid dynamics (CFD). To be able to carry out an effective CFD-based optimization study, it is essential that the uncertainty and appropriate confidence limits of the CFD solutions be quantified over the chosen design space. The present dissertation investigates the issues related to code verification, surrogate model-based optimization and sensitivity evaluation. For Navier-Stokes (NS) CFD code verification a least square extrapolation (LSE) method is assessed. This method projects numerically computed NS solutions from multiple, coarser base grids onto a freer grid and improves solution accuracy by minimizing the residual of the discretized NS equations over the projected grid. In this dissertation, the finite volume (FV) formulation is focused on. The interplay between the xi concepts and the outcome of LSE, and the effects of solution gradients and singularities, nonlinear physics, and coupling of flow variables on the effectiveness of LSE are investigated. A CFD-based design optimization of a single element liquid rocket injector is conducted with surrogate models developed using response surface methodology (RSM) based on CFD solutions. The computational model consists of the NS equations, finite rate chemistry, and the k-6 turbulence closure. With the aid of these surrogate models, sensitivity and trade-off analyses are carried out for the injector design whose geometry (hydrogen flow angle, hydrogen and oxygen flow areas and oxygen post tip thickness) is optimized to attain desirable goals in performance (combustion length) and life/survivability (the maximum temperatures on the oxidizer post tip and injector face and a combustion chamber wall temperature). A preliminary multi-objective optimization study is carried out using a geometric mean approach. Following this, sensitivity analyses with the aid of variance-based non-parametric approach and partial correlation coefficients are conducted using data available from surrogate models of the objectives and the multi-objective optima to identify the contribution of the design variables to the objective variability and to analyze the variability of the design variables and the objectives. In summary the present dissertation offers insight into an improved coarse to fine grid extrapolation technique for Navier-Stokes computations and also suggests tools for a designer to conduct design optimization study and related sensitivity analyses for a given design problem.

Least-squares finite element solution of 3D incompressible Navier-Stokes problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Lin, Tsung-Liang; Povinelli, Louis A.

1992-01-01

Although significant progress has been made in the finite element solution of incompressible viscous flow problems. Development of more efficient methods is still needed before large-scale computation of 3D problems becomes feasible. This paper presents such a development. The most popular finite element method for the solution of incompressible Navier-Stokes equations is the classic Galerkin mixed method based on the velocity-pressure formulation. The mixed method requires the use of different elements to interpolate the velocity and the pressure in order to satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition for the existence of the solution. On the other hand, due to the lack of symmetry and positive definiteness of the linear equations arising from the mixed method, iterative methods for the solution of linear systems have been hard to come by. Therefore, direct Gaussian elimination has been considered the only viable method for solving the systems. But, for three-dimensional problems, the computer resources required by a direct method become prohibitively large. In order to overcome these difficulties, a least-squares finite element method (LSFEM) has been developed. This method is based on the first-order velocity-pressure-vorticity formulation. In this paper the LSFEM is extended for the solution of three-dimensional incompressible Navier-Stokes equations written in the following first-order quasi-linear velocity-pressure-vorticity formulation.

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.

Numerical study of hydrogen-air supersonic combustion by using elliptic and parabolized equations

NASA Technical Reports Server (NTRS)

Chitsomboon, T.; Tiwari, S. N.

1986-01-01

The two-dimensional Navier-Stokes and species continuity equations are used to investigate supersonic chemically reacting flow problems which are related to scramjet-engine configurations. A global two-step finite-rate chemistry model is employed to represent the hydrogen-air combustion in the flow. An algebraic turbulent model is adopted for turbulent flow calculations. The explicit unsplit MacCormack finite-difference algorithm is used to develop a computer program suitable for a vector processing computer. The computer program developed is then used to integrate the system of the governing equations in time until convergence is attained. The chemistry source terms in the species continuity equations are evaluated implicitly to alleviate stiffness associated with fast chemical reactions. The problems solved by the elliptic code are re-investigated by using a set of two-dimensional parabolized Navier-Stokes and species equations. A linearized fully-coupled fully-implicit finite difference algorithm is used to develop a second computer code which solves the governing equations by marching in spce rather than time, resulting in a considerable saving in computer resources. Results obtained by using the parabolized formulation are compared with the results obtained by using the fully-elliptic equations. The comparisons indicate fairly good agreement of the results of the two formulations.

Topics in viscous potential flow of two-phase systems

NASA Astrophysics Data System (ADS)

Padrino Inciarte, Juan Carlos

Two-phase flows are ubiquitous, from natural and domestic environments to industrial settings. However, due to their complexity, modeling these fluid systems remains a challenge from both the perspective of fundamental questions on the dynamics of an individual, smooth interface, and the perspective of integral analyses, which involve averaging of the conservation laws over large domains, thereby missing local details of the flow. In this work, we consider a set of five problems concerning the linear and non-linear dynamics of an interface or free surface and the study of cavitation inception. Analyses are carried out by assuming the fluid motion to be irrotational, that is, with zero vorticity, and the fluids to be viscous, although results from rotational analyses are presented for the purpose of comparison. The problems considered here are the following: First, we analyze the non-linear deformation and break-up of a bubble or drop immersed in a uniaxial extensional flow of an incompressible viscous fluid. The method of viscous potential flow, in which the flow field is irrotational and viscosity enters through the balance of normal stresses at the interface, is used in the analysis. The governing equations are solved numerically to track the motion of the interface by coupling a boundary element method with a time-integration routine. When break-up occurs, the break-up time computed here is compared with results obtained elsewhere from numerical simulations of the Navier.Stokes equations, which thus keeps vorticity in the analysis, for several combinations of the relevant dimensionless parameters of the problem. For the bubble, for Weber numbers 3 ≤ We ≤ 6, predictions from viscous potential flow shows good agreement with the results from the Navier.Stokes equations for the bubble break-up time, whereas for larger We, the former underpredicts the results given by the latter. Including viscosity increases the break-up time with respect to the inviscid case. For the drop, as expected, increasing the viscous effects of the irrotational motion produces large, elongated drops that take longer to break up in comparison with results for inviscid fluids. In the second problem, we compute the force acting on a spherical bubble of variable radius moving within a liquid with an outer spherical boundary. Viscous potential flow and the dissipation method, which is another purely irrotational approach stemming from the mechanical energy equation, are both systematically implemented. This exposes the role of the choice of the outer boundary condition for the stress on the drag, an issue not explained in the literature known to us. By means of the well-known "cell-model" analysis, the results for the drag are then applied to the case of a swarm of rising bubbles having a certain void fraction. Computations from the dissipation method for the drag coefficient and rise velocity for a bubble swarm agree with numerical solutions; evaluation against experimental data for high Reynolds and low Weber numbers shows that all the models considered, including those given in the literature, overpredict the bubble swarm rise velocity. In the next two problems, we apply the analysis of viscous potential flow and the dissipation method to study the linear dynamics of waves of "small" amplitude acting either on a plane or on a spherical interface separating a liquid from a dynamically inactive fluid. It is shown that the viscous irrational theories exhibit the features of the wave dynamics by comparing with the exact solution. The range of parameters for which good agreement with the exact solution exists is presented. The general trend shows that for long waves the dissipation method results in the best approximation, whereas for short waves, even for very viscous liquids, viscous potential flow demonstrates better agreement. Finally, the problem of cavitation inception for the flow of a viscous liquid past a stationary sphere is studied by means of the theory of stress-induced cavitation. The flow field for a single phase needed in the analysis is found from three different methods, namely, the numerical solution of the Navier--Stokes equations, the irrotational motion of a viscous fluid, and, in the limit of no inertia, the Stokes flow formulation. The new predictions are then compared with those obtained from the classical pressure criterion. The main finding is that at a fixed cavitation number more viscous liquids are at greater risk to cavitation.

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

NASA Technical Reports Server (NTRS)

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

1994-01-01

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

Frequency-dependent laminar electroosmotic flow in a closed-end rectangular microchannel.

PubMed

Marcos; Yang, C; Ooi, K T; Wong, T N; Masliyah, J H

2004-07-15

This article presents an analysis of the frequency- and time-dependent electroosmotic flow in a closed-end rectangular microchannel. An exact solution to the modified Navier-Stokes equation governing the ac electroosmotic flow field is obtained by using the Green's function formulation in combination with a complex variable approach. An analytical expression for the induced backpressure gradient is derived. With the Debye-Hückel approximation, the electrical double-layer potential distribution in the channel is obtained by analytically solving the linearized two-dimensional Poisson-Boltzmann equation. Since the counterparts of the flow rate and the electrical current are shown to be linearly proportional to the applied electric field and the pressure gradient, Onsager's principle of reciprocity is demonstrated for transient and ac electroosmotic flows. The time evolution of the electroosmotic flow and the effect of a frequency-dependent ac electric field on the oscillating electroosmotic flow in a closed-end rectangular microchannel are examined. Specifically, the induced pressure gradient is analyzed under effects of the channel dimension and the frequency of electric field. In addition, based on the Stokes second problem, the solution of the slip velocity approximation is presented for comparison with the results obtained from the analytical scheme developed in this study. Copyright 2004 Elsevier Inc.

A Comparison of Three Navier-Stokes Solvers for Exhaust Nozzle Flowfields

NASA Technical Reports Server (NTRS)

Georgiadis, Nicholas J.; Yoder, Dennis A.; Debonis, James R.

1999-01-01

A comparison of the NPARC, PAB, and WIND (previously known as NASTD) Navier-Stokes solvers is made for two flow cases with turbulent mixing as the dominant flow characteristic, a two-dimensional ejector nozzle and a Mach 1.5 elliptic jet. The objective of the work is to determine if comparable predictions of nozzle flows can be obtained from different Navier-Stokes codes employed in a multiple site research program. A single computational grid was constructed for each of the two flows and used for all of the Navier-Stokes solvers. In addition, similar k-e based turbulence models were employed in each code, and boundary conditions were specified as similarly as possible across the codes. Comparisons of mass flow rates, velocity profiles, and turbulence model quantities are made between the computations and experimental data. The computational cost of obtaining converged solutions with each of the codes is also documented. Results indicate that all of the codes provided similar predictions for the two nozzle flows. Agreement of the Navier-Stokes calculations with experimental data was good for the ejector nozzle. However, for the Mach 1.5 elliptic jet, the calculations were unable to accurately capture the development of the three dimensional elliptic mixing layer.

Quantification of topological changes of vorticity contours in two-dimensional Navier-Stokes flow.

PubMed

Ohkitani, Koji; Al Sulti, Fayeza

2010-06-01

A characterization of reconnection of vorticity contours is made by direct numerical simulations of the two-dimensional Navier-Stokes flow at a relatively low Reynolds number. We identify all the critical points of the vorticity field and classify them by solving an eigenvalue problem of its Hessian matrix on the basis of critical-point theory. The numbers of hyperbolic (saddles) and elliptic (minima and maxima) points are confirmed to satisfy Euler's index theorem numerically. Time evolution of these indices is studied for a simple initial condition. Generally speaking, we have found that the indices are found to decrease in number with time. This result is discussed in connection with related works on streamline topology, in particular, the relationship between stagnation points and the dissipation. Associated elementary procedures in physical space, the merging of vortices, are studied in detail for a number of snapshots. A similar analysis is also done using the stream function.

Application of CFD to a generic hypersonic flight research study

NASA Technical Reports Server (NTRS)

Green, Michael J.; Lawrence, Scott L.; Dilley, Arthur D.; Hawkins, Richard W.; Walker, Mary M.; Oberkampf, William L.

1993-01-01

Computational analyses have been performed for the initial assessment of flight research vehicle concepts that satisfy requirements for potential hypersonic experiments. Results were obtained from independent analyses at NASA Ames, NASA Langley, and Sandia National Labs, using sophisticated time-dependent Navier-Stokes and parabolized Navier-Stokes methods. Careful study of a common problem consisting of hypersonic flow past a slightly blunted conical forebody was undertaken to estimate the level of uncertainty in the computed results, and to assess the capabilities of current computational methods for predicting boundary-layer transition onset. Results of this study in terms of surface pressure and heat transfer comparisons, as well as comparisons of boundary-layer edge quantities and flow-field profiles are presented here. Sensitivities to grid and gas model are discussed. Finally, representative results are presented relating to the use of Computational Fluid Dynamics in the vehicle design and the integration/support of potential experiments.

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

NASA Technical Reports Server (NTRS)

Mineck, Raymond E.

1999-01-01

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

Numerical simulation of electrophoresis separation processes

NASA Technical Reports Server (NTRS)

Ganjoo, D. K.; Tezduyar, T. E.

1986-01-01

A new Petrov-Galerkin finite element formulation has been proposed for transient convection-diffusion problems. Most Petrov-Galerkin formulations take into account the spatial discretization, and the weighting functions so developed give satisfactory solutions for steady state problems. Though these schemes can be used for transient problems, there is scope for improvement. The schemes proposed here, which consider temporal as well as spatial discretization, provide improved solutions. Electrophoresis, which involves the motion of charged entities under the influence of an applied electric field, is governed by equations similiar to those encountered in fluid flow problems, i.e., transient convection-diffusion equations. Test problems are solved in electrophoresis and fluid flow. The results obtained are satisfactory. It is also expected that these schemes, suitably adapted, will improve the numerical solutions of the compressible Euler and the Navier-Stokes equations.

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.

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

NASA Technical Reports Server (NTRS)

Obayashi, Shigeru; Guruswamy, Guru P.

1995-01-01

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

Numerical solution for the interaction of shock wave with laminar boundary layer in two-dimensional flow on a flat plate. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Landau, U.

1984-01-01

The finite difference computation method was investigated for solving problems of interaction between a shock wave and a laminar boundary layer, through solution of the complete Navier-Stokes equations. This method provided excellent solutions, was simple to perform and needed a relatively short solution time. A large number of runs for various flow conditions could be carried out from which the interaction characteristics and principal factors that influence interaction could be studied.

Fully-Implicit Navier-Stokes (FIN-S)

NASA Technical Reports Server (NTRS)

Kirk, Benjamin S.

2010-01-01

FIN-S is a SUPG finite element code for flow problems under active development at NASA Lyndon B. Johnson Space Center and within PECOS: a) The code is built on top of the libMesh parallel, adaptive finite element library. b) The initial implementation of the code targeted supersonic/hypersonic laminar calorically perfect gas flows & conjugate heat transfer. c) Initial extension to thermochemical nonequilibrium about 9 months ago. d) The technologies in FIN-S have been enhanced through a strongly collaborative research effort with Sandia National Labs.

Development of numerical methods for overset grids with applications for the integrated Space Shuttle vehicle

NASA Technical Reports Server (NTRS)

Chan, William M.

1995-01-01

Algorithms and computer code developments were performed for the overset grid approach to solving computational fluid dynamics problems. The techniques developed are applicable to compressible Navier-Stokes flow for any general complex configurations. The computer codes developed were tested on different complex configurations with the Space Shuttle launch vehicle configuration as the primary test bed. General, efficient and user-friendly codes were produced for grid generation, flow solution and force and moment computation.

Numerical studies of incompressible flow around delta and double-delta wings

NASA Technical Reports Server (NTRS)

Krause, E.; Liu, C. H.

1989-01-01

The subject has been jointly investigated at NASA Langley Research Center and the Aerodynamisches Institut of the RWTH Aachen over a substantial period. The aim of this investigation has been to develop numerical integration procedures for the Navier-Stokes equations - particularly for incompressible three-dimensional viscous flows about simple and double delta wings - and to study the low speed flow behavior, with its complex vortex structures on the leeward side of the wing. The low speed flight regime poses unusual problems because high incidence flight conditions may, for example, encounter symmetric and asymmetric vortex breakdown. Because of the many difficulties to be expected in solving the problem, it was divided into two - analysis of the flow without vortex breakdown and analysis of the breakdown of isolated vortices. The major results obtained so far on the two topics are briefly described.

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.

A numerical analysis of high-temperature heat pipe startup from the frozen state

NASA Technical Reports Server (NTRS)

Cao, Y.; Faghri, A.

1993-01-01

Continuum and rarefied vapor flows co-exist along the heat pipe length for most of the startup period. A two-region model is proposed in which the vapor flow in the continuum region is modeled by the compressible Navier-Stokes equations, and the vapor flow in the rarefied region is simulated by a self-diffusion model. The two vapor regions are linked with appropriate boundary conditions, and heat pipe wail, wick, and vapor flow are solved as a conjugate problem. The numerical solutions for the entire heat pipe startup process from the frozen state are compared with the corresponding experimental data with good agreement.

Lattice Boltzmann and Navier-Stokes Cartesian CFD Approaches for Airframe Noise Predictions

NASA Technical Reports Server (NTRS)

Barad, Michael F.; Kocheemoolayil, Joseph G.; Kiris, Cetin C.

2017-01-01

Lattice Boltzmann (LB) and compressible Navier-Stokes (NS) equations based computational fluid dynamics (CFD) approaches are compared for simulating airframe noise. Both LB and NS CFD approaches are implemented within the Launch Ascent and Vehicle Aerodynamics (LAVA) framework. Both schemes utilize the same underlying Cartesian structured mesh paradigm with provision for local adaptive grid refinement and sub-cycling in time. We choose a prototypical massively separated, wake-dominated flow ideally suited for Cartesian-grid based approaches in this study - The partially-dressed, cavity-closed nose landing gear (PDCC-NLG) noise problem from AIAA's Benchmark problems for Airframe Noise Computations (BANC) series of workshops. The relative accuracy and computational efficiency of the two approaches are systematically compared. Detailed comments are made on the potential held by LB to significantly reduce time-to-solution for a desired level of accuracy within the context of modeling airframes noise from first principles.

Stability of Contact Lines in Fluids: 2D Stokes Flow

NASA Astrophysics Data System (ADS)

Guo, Yan; Tice, Ian

2018-02-01

In an effort to study the stability of contact lines in fluids, we consider the dynamics of an incompressible viscous Stokes fluid evolving in a two-dimensional open-top vessel under the influence of gravity. This is a free boundary problem: the interface between the fluid in the vessel and the air above (modeled by a trivial fluid) is free to move and experiences capillary forces. The three-phase interface where the fluid, air, and solid vessel wall meet is known as a contact point, and the angle formed between the free interface and the vessel is called the contact angle. We consider a model of this problem that allows for fully dynamic contact points and angles. We develop a scheme of a priori estimates for the model, which then allow us to show that for initial data sufficiently close to equilibrium, the model admits global solutions that decay to equilibrium exponentially quickly.

On Bifurcating Time-Periodic Flow of a Navier-Stokes Liquid Past a Cylinder

NASA Astrophysics Data System (ADS)

Galdi, Giovanni P.

2016-10-01

We provide general sufficient conditions for the existence and uniqueness of branching out of a time-periodic family of solutions from steady-state solutions to the two-dimensional Navier-Stokes equations in the exterior of a cylinder. By separating the time-independent averaged component of the velocity field from its oscillatory one, we show that the problem can be formulated as a coupled elliptic-parabolic nonlinear system in appropriate and distinct function spaces, with the property that the relevant linearized operators become Fredholm of index 0. In this functional setting, the notorious difficulty of 0 being in the essential spectrum entirely disappears and, in fact, it is even meaningless. Our approach is different and, we believe, more natural and simpler than those proposed by previous authors discussing similar questions. Moreover, the latter all fail, when applied to the problem studied here.

Separated flows near the nose of a body of revolution

NASA Technical Reports Server (NTRS)

Lin, S. P.

1986-01-01

The solution of the Navier-Stokes equations for the problem of cross-flow separataion about a deforming cylinder was achieved by iteration. It was shown that the separation starts at the rear stagnation point and the point of primary separation moves upstram along the cylinder surface. A general method of linear stability analysis for nonparallel external flows was constructed, which consists of representing the eigenfunctions with complete orthogonal sets and forms characteristic equations with the Galerkin method. The method was applied to the Kovasznay flow which is an exact solution of the Navier-Stokes equation. The results show that when the critical parameter is exceeded, there are only a few isolated unstable eigen-frequencies. Another exact solution is shown to be absolutely and monotonically stable with respect to infinitesimal disturbances of all frequencies. The flow is also globally, asymptotically, and monotonically stable in the mean with respect o three-dimensional disturbances. This result forms the sound foundation of rigorous stability analysis for nonparallel flows, and provides an invaluable test ground for future studies of nonparallel flows in which the basic states do not posses exact solutions. The application of this method to the study of the formation of spiral vorticies near the nose of a rotating body of revolution is underway. The same method will be applied to the stability analysis of reversed flow over a plate with suction.

Navier-Stokes and viscous-inviscid interaction

NASA Technical Reports Server (NTRS)

Steger, Joseph L.; Vandalsem, William R.

1989-01-01

Some considerations toward developing numerical procedures for simulating viscous compressible flows are discussed. Both Navier-Stokes and boundary layer field methods are considered. Because efficient viscous-inviscid interaction methods have been difficult to extend to complex 3-D flow simulations, Navier-Stokes procedures are more frequently being utilized even though they require considerably more work per grid point. It would seem a mistake, however, not to make use of the more efficient approximate methods in those regions in which they are clearly valid. Ideally, a general purpose compressible flow solver that can optionally take advantage of approximate solution methods would suffice, both to improve accuracy and efficiency. Some potentially useful steps toward this goal are described: a generalized 3-D boundary layer formulation and the fortified Navier-Stokes procedure.

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.

Higher-Order Compact Schemes for Numerical Simulation of Incompressible Flows

NASA Technical Reports Server (NTRS)

Wilson, Robert V.; Demuren, Ayodeji O.; Carpenter, Mark

1998-01-01

A higher order accurate numerical procedure has been developed for solving incompressible Navier-Stokes equations for 2D or 3D fluid flow problems. It is based on low-storage Runge-Kutta schemes for temporal discretization and fourth and sixth order compact finite-difference schemes for spatial discretization. The particular difficulty of satisfying the divergence-free velocity field required in incompressible fluid flow is resolved by solving a Poisson equation for pressure. It is demonstrated that for consistent global accuracy, it is necessary to employ the same order of accuracy in the discretization of the Poisson equation. Special care is also required to achieve the formal temporal accuracy of the Runge-Kutta schemes. The accuracy of the present procedure is demonstrated by application to several pertinent benchmark problems.

A numerical investigation of viscous, incompressible flow past an axisymmetric body with and without spin

NASA Astrophysics Data System (ADS)

Weber, K. F.

1985-12-01

This study deals with a preliminary investigation of the effects of spin on the axisymmetric flow past a body of revolution. The study has its genesis larger problem of Magnus forces on spinning bodies at angle of attack. However, the fundamental behavior that arises when a spinning body is placed in a uniform stream is still not well understood; therefore, the problem of axisymmetric flow with spin was undertaken. The body consists of a 3-caliber cant-ogive blunted by a spherical nosecap, a 2-caliber cylindrical section, and a 1-caliber boattail. Numerical solutions of the compressible laminar Navier-Stokes equations are obtained using a modified version of the implicit-explicit method developed by MacCormack in 1981. The benchmark problem is the nonspinning body in uniform flow at a Reynolds number of 1.14. The results show that the modified method performs well and allows time steps that are in order of magnitude greater than those permitted by explicit stability criteria.

Two-dimensional nonsteady viscous flow simulation on the Navier-Stokes computer miniNode

NASA Technical Reports Server (NTRS)

Nosenchuck, Daniel M.; Littman, Michael G.; Flannery, William

1986-01-01

The needs of large-scale scientific computation are outpacing the growth in performance of mainframe supercomputers. In particular, problems in fluid mechanics involving complex flow simulations require far more speed and capacity than that provided by current and proposed Class VI supercomputers. To address this concern, the Navier-Stokes Computer (NSC) was developed. The NSC is a parallel-processing machine, comprised of individual Nodes, each comparable in performance to current supercomputers. The global architecture is that of a hypercube, and a 128-Node NSC has been designed. New architectural features, such as a reconfigurable many-function ALU pipeline and a multifunction memory-ALU switch, have provided the capability to efficiently implement a wide range of algorithms. Efficient algorithms typically involve numerically intensive tasks, which often include conditional operations. These operations may be efficiently implemented on the NSC without, in general, sacrificing vector-processing speed. To illustrate the architecture, programming, and several of the capabilities of the NSC, the simulation of two-dimensional, nonsteady viscous flows on a prototype Node, called the miniNode, is presented.

Glottal flow through a two-mass model: comparison of Navier-Stokes solutions with simplified models.

PubMed

de Vries, M P; Schutte, H K; Veldman, A E P; Verkerke, G J

2002-04-01

A new numerical model of the vocal folds is presented based on the well-known two-mass models of the vocal folds. The two-mass model is coupled to a model of glottal airflow based on the incompressible Navier-Stokes equations. Glottal waves are produced using different initial glottal gaps and different subglottal pressures. Fundamental frequency, glottal peak flow, and closed phase of the glottal waves have been compared with values known from the literature. The phonation threshold pressure was determined for different initial glottal gaps. The phonation threshold pressure obtained using the flow model with Navier-Stokes equations corresponds better to values determined in normal phonation than the phonation threshold pressure obtained using the flow model based on the Bernoulli equation. Using the Navier-Stokes equations, an increase of the subglottal pressure causes the fundamental frequency and the glottal peak flow to increase, whereas the fundamental frequency in the Bernoulli-based model does not change with increasing pressure.

Ground and flight test program of a Stokes-flow parachute: Packaging, deployment, and sounding rocket integration

NASA Technical Reports Server (NTRS)

Niederer, P. G.; Mihora, D. J.

1972-01-01

The current design and hardware components of the patented 14 sqm Stokes flow parachute are described. The Stokes-flow parachute is a canopy of open mesh material, which is kept deployed by braces. Because of the light weight of its mesh material, and the high drag on its mesh elements when they operate in the Stokes-flow flight regime, this parachute has an extremely low ballistic coefficient. It provides a stable aerodynamic platform superior to conventional nonporous billowed parachutes, is exceptionally packable, and is easily contained within the canister of the Sidewinder Arcas or the RDT and E rockets. Thus, it offers the potential for gathering more meteorological data, especially at high altitudes, than conventional billowed parachutes. Methods for packaging the parachute are also recommended. These methods include schemes for folding the canopy and for automatically releasing the pressurizing fluid as the packaged parachute unfolds.

Notes on the space-time decay rate of the Stokes flows in the half space

NASA Astrophysics Data System (ADS)

Chang, Tongkeun; Jin, Bum Ja

2017-07-01

In this paper, a Stokes equations in the half space R+n, n ≥ 2 has been considered. We derive a rapid decay rate of the Stokes flow in space and time when the initial data decreases fast enough and satisfies some additional condition. Initial data decreasing too slowly to be | x | h ∈L1 (R+n) are also considered.

Progress on a Taylor weak statement finite element algorithm for high-speed aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Freels, J. D.

1989-01-01

A new finite element numerical Computational Fluid Dynamics (CFD) algorithm has matured to the point of efficiently solving two-dimensional high speed real-gas compressible flow problems in generalized coordinates on modern vector computer systems. The algorithm employs a Taylor Weak Statement classical Galerkin formulation, a variably implicit Newton iteration, and a tensor matrix product factorization of the linear algebra Jacobian under a generalized coordinate transformation. Allowing for a general two-dimensional conservation law system, the algorithm has been exercised on the Euler and laminar forms of the Navier-Stokes equations. Real-gas fluid properties are admitted, and numerical results verify solution accuracy, efficiency, and stability over a range of test problem parameters.

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.

Experiences with explicit finite-difference schemes for complex fluid dynamics problems on STAR-100 and CYBER-203 computers

NASA Technical Reports Server (NTRS)

Kumar, A.; Rudy, D. H.; Drummond, J. P.; Harris, J. E.

1982-01-01

Several two- and three-dimensional external and internal flow problems solved on the STAR-100 and CYBER-203 vector processing computers are described. The flow field was described by the full Navier-Stokes equations which were then solved by explicit finite-difference algorithms. Problem results and computer system requirements are presented. Program organization and data base structure for three-dimensional computer codes which will eliminate or improve on page faulting, are discussed. Storage requirements for three-dimensional codes are reduced by calculating transformation metric data in each step. As a result, in-core grid points were increased in number by 50% to 150,000, with a 10% execution time increase. An assessment of current and future machine requirements shows that even on the CYBER-205 computer only a few problems can be solved realistically. Estimates reveal that the present situation is more storage limited than compute rate limited, but advancements in both storage and speed are essential to realistically calculate three-dimensional flow.

New class of turbulence in active fluids.

PubMed

Bratanov, Vasil; Jenko, Frank; Frey, Erwin

2015-12-08

Turbulence is a fundamental and ubiquitous phenomenon in nature, occurring from astrophysical to biophysical scales. At the same time, it is widely recognized as one of the key unsolved problems in modern physics, representing a paradigmatic example of nonlinear dynamics far from thermodynamic equilibrium. Whereas in the past, most theoretical work in this area has been devoted to Navier-Stokes flows, there is now a growing awareness of the need to extend the research focus to systems with more general patterns of energy injection and dissipation. These include various types of complex fluids and plasmas, as well as active systems consisting of self-propelled particles, like dense bacterial suspensions. Recently, a continuum model has been proposed for such "living fluids" that is based on the Navier-Stokes equations, but extends them to include some of the most general terms admitted by the symmetry of the problem [Wensink HH, et al. (2012) Proc Natl Acad Sci USA 109:14308-14313]. This introduces a cubic nonlinearity, related to the Toner-Tu theory of flocking, which can interact with the quadratic Navier-Stokes nonlinearity. We show that as a result of the subtle interaction between these two terms, the energy spectra at large spatial scales exhibit power laws that are not universal, but depend on both finite-size effects and physical parameters. Our combined numerical and analytical analysis reveals the origin of this effect and even provides a way to understand it quantitatively. Turbulence in active fluids, characterized by this kind of nonlinear self-organization, defines a new class of turbulent flows.

New class of turbulence in active fluids

PubMed Central

Bratanov, Vasil; Frey, Erwin

2015-01-01

Turbulence is a fundamental and ubiquitous phenomenon in nature, occurring from astrophysical to biophysical scales. At the same time, it is widely recognized as one of the key unsolved problems in modern physics, representing a paradigmatic example of nonlinear dynamics far from thermodynamic equilibrium. Whereas in the past, most theoretical work in this area has been devoted to Navier–Stokes flows, there is now a growing awareness of the need to extend the research focus to systems with more general patterns of energy injection and dissipation. These include various types of complex fluids and plasmas, as well as active systems consisting of self-propelled particles, like dense bacterial suspensions. Recently, a continuum model has been proposed for such “living fluids” that is based on the Navier–Stokes equations, but extends them to include some of the most general terms admitted by the symmetry of the problem [Wensink HH, et al. (2012) Proc Natl Acad Sci USA 109:14308–14313]. This introduces a cubic nonlinearity, related to the Toner–Tu theory of flocking, which can interact with the quadratic Navier–Stokes nonlinearity. We show that as a result of the subtle interaction between these two terms, the energy spectra at large spatial scales exhibit power laws that are not universal, but depend on both finite-size effects and physical parameters. Our combined numerical and analytical analysis reveals the origin of this effect and even provides a way to understand it quantitatively. Turbulence in active fluids, characterized by this kind of nonlinear self-organization, defines a new class of turbulent flows. PMID:26598708

Stokes flow inside an evaporating liquid line for any contact angle

NASA Astrophysics Data System (ADS)

Petsi, A. J.; Burganos, V. N.

2008-09-01

Evaporation of droplets or liquid films lying on a substrate induces internal viscous flow, which affects the transport of suspended particles and, thus, the final deposit profile in numerous applications. In this work, the problem of Stokes flow inside a two-dimensional droplet, representing the cross section of an evaporating liquid line lying on a flat surface, is considered. The stream function formulation is adopted, leading to the biharmonic equation in bipolar coordinates. A solution in closed form is obtained for any contact angle in (0,π) and is, thus, valid for both hydrophilic and hydrophobic substrates. The solution can be used with any type of evaporation mechanism, including diffusion, convection, or kinetically controlled modes. Both pinned and depinned contact lines are considered. For the boundary conditions to be compatible at the contact lines, the Navier slip boundary condition is applied on the substrate. Numerical results are presented for kinetically and diffusion controlled evaporation. For pinned contact lines, the flow inside the evaporating liquid line is directed towards the edges, thus, promoting the coffee stain phenomenon. In the case of depinned contact lines and contact angle less than π/2 , the flow is directed towards the center of the droplet, whereas, for strongly hydrophobic substrates it is directed outwards.

Numerical investigations in the backflow region of a vacuum plume

NASA Technical Reports Server (NTRS)

Liaw, Goang-Shin

1992-01-01

The objective of this research is to numerically simulate the vacuum plume flow field in the backflow region of a low thrust nozzle exit. In space applications, the low thrust nozzles are used as a propulsion device to control the vehicle attitude, or to maneuver the vehicle flight trajectory. When the spacecraft is deployed in the orbit or cruising in a planetary mission, the vacuum plume is created behind the nozzle exit (so called backflow region), by the exhausting gas of the propulsion system or by venting internal gas to the extremely low density ambient. The low density vacuum plume flow regions cover the continuum, transitional and free molecular flow regimes, which were characterized by the Knudsen number K(sub n), K(sub n) = lambda(sub m)/L where lambda(sub m) is the mean free path of the gas molecules and L is the characteristic length of the flow field. The transitional regime is defined by 0.01 is less than or equal to K(sub n) is less than or equal to 10. The conventional Navier-Stokes equations are valid only in the flow region close to the nozzle exit since the validity of the Navier-Stokes equations fails asymptotically as the Knudsen number increases. The vacuum plume characteristics prediction is primarily a problem of transitional aerodynamics.

Sensitivity analysis, approximate analysis, and design optimization for internal and external viscous flows

NASA Technical Reports Server (NTRS)

Taylor, Arthur C., III; Hou, Gene W.; Korivi, Vamshi M.

1991-01-01

A gradient-based design optimization strategy for practical aerodynamic design applications is presented, which uses the 2D thin-layer Navier-Stokes equations. The strategy is based on the classic idea of constructing different modules for performing the major tasks such as function evaluation, function approximation and sensitivity analysis, mesh regeneration, and grid sensitivity analysis, all driven and controlled by a general-purpose design optimization program. The accuracy of aerodynamic shape sensitivity derivatives is validated on two viscous test problems: internal flow through a double-throat nozzle and external flow over a NACA 4-digit airfoil. A significant improvement in aerodynamic performance has been achieved in both cases. Particular attention is given to a consistent treatment of the boundary conditions in the calculation of the aerodynamic sensitivity derivatives for the classic problems of external flow over an isolated lifting airfoil on 'C' or 'O' meshes.

The Stokes problem for the ellipsoid using ellipsoidal kernels

NASA Technical Reports Server (NTRS)

Zhu, Z.

1981-01-01

A brief review of Stokes' problem for the ellipsoid as a reference surface is given. Another solution of the problem using an ellipsoidal kernel, which represents an iterative form of Stokes' integral, is suggested with a relative error of the order of the flattening. On studying of Rapp's method in detail the procedures of improving its convergence are discussed.

Numerical aerodynamic simulation facility. [for flows about three-dimensional configurations

NASA Technical Reports Server (NTRS)

Bailey, F. R.; Hathaway, A. W.

1978-01-01

Critical to the advancement of computational aerodynamics capability is the ability to simulate flows about three-dimensional configurations that contain both compressible and viscous effects, including turbulence and flow separation at high Reynolds numbers. Analyses were conducted of two solution techniques for solving the Reynolds averaged Navier-Stokes equations describing the mean motion of a turbulent flow with certain terms involving the transport of turbulent momentum and energy modeled by auxiliary equations. The first solution technique is an implicit approximate factorization finite-difference scheme applied to three-dimensional flows that avoids the restrictive stability conditions when small grid spacing is used. The approximate factorization reduces the solution process to a sequence of three one-dimensional problems with easily inverted matrices. The second technique is a hybrid explicit/implicit finite-difference scheme which is also factored and applied to three-dimensional flows. Both methods are applicable to problems with highly distorted grids and a variety of boundary conditions and turbulence models.

Multi-GPU three dimensional Stokes solver for simulating glacier flow

NASA Astrophysics Data System (ADS)

Licul, Aleksandar; Herman, Frédéric; Podladchikov, Yuri; Räss, Ludovic; Omlin, Samuel

2016-04-01

Here we present how we have recently developed a three-dimensional Stokes solver on the GPUs and apply it to a glacier flow. We numerically solve the Stokes momentum balance equations together with the incompressibility equation, while also taking into account strong nonlinearities for ice rheology. We have developed a fully three-dimensional numerical MATLAB application based on an iterative finite difference scheme with preconditioning of residuals. Differential equations are discretized on a regular staggered grid. We have ported it to C-CUDA to run it on GPU's in parallel, using MPI. We demonstrate the accuracy and efficiency of our developed model by manufactured analytical solution test for three-dimensional Stokes ice sheet models (Leng et al.,2013) and by comparison with other well-established ice sheet models on diagnostic ISMIP-HOM benchmark experiments (Pattyn et al., 2008). The results show that our developed model is capable to accurately and efficiently solve Stokes system of equations in a variety of different test scenarios, while preserving good parallel efficiency on up to 80 GPU's. For example, in 3D test scenarios with 250000 grid points our solver converges in around 3 minutes for single precision computations and around 10 minutes for double precision computations. We have also optimized the developed code to efficiently run on our newly acquired state-of-the-art GPU cluster octopus. This allows us to solve our problem on more than 20 million grid points, by just increasing the number of GPU used, while keeping the computation time the same. In future work we will apply our solver to real world applications and implement the free surface evolution capabilities. REFERENCES Leng,W.,Ju,L.,Gunzburger,M. & Price,S., 2013. Manufactured solutions and the verification of three-dimensional stokes ice-sheet models. Cryosphere 7,19-29. Pattyn, F., Perichon, L., Aschwanden, A., Breuer, B., de Smedt, B., Gagliardini, O., Gudmundsson,G.H., Hindmarsh, R.C.A., Hubbard, A., Johnson, J.V., Kleiner, T., Konovalov,Y., Martin, C., Payne, A.J., Pollard, D., Price, S., Rckamp, M., Saito, F., Souk, O.,Sugiyama, S. & Zwinger, T., 2008. Benchmark experiments for higher-order and full-stokes ice sheet models (ismiphom). The Cryosphere 2, 95-108.

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.

Advances in the computation of transonic separated flows over finite wings

NASA Technical Reports Server (NTRS)

Kaynak, Unver; Flores, Jolen

1989-01-01

Problems encountered in numerical simulations of transonic wind-tunnel experiments with low-aspect-ratio wings are surveyed and illustrated. The focus is on the zonal Euler/Navier-Stokes program developed by Holst et al. (1985) and its application to shock-induced separation. The physical basis and numerical implementation of the method are reviewed, and results are presented from studies of the effects of artificial dissipation, boundary conditions, grid refinement, the turbulence model, and geometry representation on the simulation accuracy. Extensive graphs and diagrams and typical flow visualizations are provided.

A High Order Element Based Method for the Simulation of Velocity Damping in the Hyporheic Zone of a High Mountain River

NASA Astrophysics Data System (ADS)

Preziosi-Ribero, Antonio; Peñaloza-Giraldo, Jorge; Escobar-Vargas, Jorge; Donado-Garzón, Leonardo

2016-04-01

Groundwater - Surface water interaction is a topic that has gained relevance among the scientific community over the past decades. However, several questions remain unsolved inside this topic, and almost all the research that has been done in the past regards the transport phenomena and has little to do with understanding the dynamics of the flow patterns of the above mentioned interactions. The aim of this research is to verify the attenuation of the water velocity that comes from the free surface and enters the porous media under the bed of a high mountain river. The understanding of this process is a key feature in order to characterize and quantify the interactions between groundwater and surface water. However, the lack of information and the difficulties that arise when measuring groundwater flows under streams make the physical quantification non reliable for scientific purposes. These issues suggest that numerical simulations and in-stream velocity measurements can be used in order to characterize these flows. Previous studies have simulated the attenuation of a sinusoidal pulse of vertical velocity that comes from a stream and goes into a porous medium. These studies used the Burgers equation and the 1-D Navier-Stokes equations as governing equations. However, the boundary conditions of the problem, and the results when varying the different parameters of the equations show that the understanding of the process is not complete yet. To begin with, a Spectral Multi Domain Penalty Method (SMPM) was proposed for quantifying the velocity damping solving the Navier - Stokes equations in 1D. The main assumptions are incompressibility and a hydrostatic approximation for the pressure distributions. This method was tested with theoretical signals that are mainly trigonometric pulses or functions. Afterwards, in order to test the results with real signals, velocity profiles were captured near the Gualí River bed (Honda, Colombia), with an Acoustic Doppler Velocimeter (ADV). These profiles were filtered, treated and set up to feed the SMPM that solves the Navier - Stokes equations for the theoretical case. Besides, the velocity fluctuations along the river bed were calculated according to the mesh that was proposed to solve the numerical problem. This mesh required more refinement near the boundary conditions in order to calculate all the turbulent flow scales near the boundary. As a result, the velocity damping inside the porous media with real velocity pulses behaves similarly to the damping of the theoretical signals. However, there is still doubt about the use of the Navier - Stokes equations with the assumptions of incompressibility and hydrostatic approximation for the pressure distributions. Furthermore, the boundary conditions of the model suggest a great theme of discussion because of their nature. To sum up, the quantification of the interactions of groundwater and surface water have to be studied using numerical models in order to observe the behavior of the flow. Our research suggests that the velocity damping of water when entering the porous media goes beyond the approximations used for the Navier-Stokes equations and that this is a pressure driven flow that does not hold the hydrostatic simplification.

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.

Vortical Flow Prediction Using an Adaptive Unstructured Grid Method

NASA Technical Reports Server (NTRS)

Pirzadeh, Shahyar Z.

2001-01-01

A computational fluid dynamics (CFD) method has been employed to compute vortical flows around slender wing/body configurations. The emphasis of the paper is on the effectiveness of an adaptive grid procedure in "capturing" concentrated vortices generated at sharp edges or flow separation lines of lifting surfaces flying at high angles of attack. The method is based on a tetrahedral unstructured grid technology developed at the NASA Langley Research Center. Two steady-state, subsonic, inviscid and Navier-Stokes flow test cases are presented to demonstrate the applicability of the method for solving practical vortical flow problems. The first test case concerns vortex flow over a simple 65deg delta wing with different values of leading-edge bluntness, and the second case is that of a more complex fighter configuration. The superiority of the adapted solutions in capturing the vortex flow structure over the conventional unadapted results is demonstrated by comparisons with the windtunnel experimental data. The study shows that numerical prediction of vortical flows is highly sensitive to the local grid resolution and that the implementation of grid adaptation is essential when applying CFD methods to such complicated flow problems.

Investigation of radiative interactions in supersonic internal flows

NASA Technical Reports Server (NTRS)

Tiwari, Surendra N.; Thomas, A. M.

1991-01-01

Analyses and numerical procedures are presented to study the radiative interactions of absorbing emitting species in chemically reacting supersonic flow in various ducts. The 2-D time dependent Navier-Stokes equations in conjunction with radiative flux equation are used to study supersonic flows undergoing finite rate chemical reaction in a hydrogen air system. The specific problem considered is the flow of premixed radiating gas between parallel plates. Specific attention was directed toward studying the radiative contribution of H2O, OH, and NO under realistic physical and flow conditions. Results are presented for the radiative flux obtained for different gases and for various combination of these gases. The problem of chemically reacting and radiating flows was solved for the flow of premixed hydrogen-air through a 10 deg compression ramp. Results demonstrate that the radiative interaction increases with an increase in pressure, temperature, amount of participating species, plate spacing, and Mach number. Most of the energy, however, is transferred by convection in the flow direction. In general the results indicate that radiation can have a significant effect on the entire flow field.

A Reduced Order Model of the Linearized Incompressible Navier-Strokes Equations for the Sensor/Actuator Placement Problem

NASA Technical Reports Server (NTRS)

Allan, Brian G.

2000-01-01

A reduced order modeling approach of the Navier-Stokes equations is presented for the design of a distributed optimal feedback kernel. This approach is based oil a Krylov subspace method where significant modes of the flow are captured in the model This model is then used in all optimal feedback control design where sensing and actuation is performed oil tile entire flow field. This control design approach yields all optimal feedback kernel which provides insight into the placement of sensors and actuators in the flow field. As all evaluation of this approach, a two-dimensional shear layer and driven cavity flow are investigated.

CFD code evaluation for internal flow modeling

NASA Technical Reports Server (NTRS)

Chung, T. J.

1990-01-01

Research on the computational fluid dynamics (CFD) code evaluation with emphasis on supercomputing in reacting flows is discussed. Advantages of unstructured grids, multigrids, adaptive methods, improved flow solvers, vector processing, parallel processing, and reduction of memory requirements are discussed. As examples, researchers include applications of supercomputing to reacting flow Navier-Stokes equations including shock waves and turbulence and combustion instability problems associated with solid and liquid propellants. Evaluation of codes developed by other organizations are not included. Instead, the basic criteria for accuracy and efficiency have been established, and some applications on rocket combustion have been made. Research toward an ultimate goal, the most accurate and efficient CFD code, is in progress and will continue for years to come.

Flux splitting algorithms for two-dimensional viscous flows with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Shuen, Jian-Shun; Liou, Meng-Sing

1989-01-01

The Roe flux difference splitting method was extended to treat 2-D viscous flows with nonequilibrium chemistry. The derivations have avoided unnecessary assumptions or approximations. For spatial discretization, the second-order Roe upwind differencing is used for the convective terms and central differencing for the viscous terms. An upwind-based TVD scheme is applied to eliminate oscillations and obtain a sharp representation of discontinuities. A two-state Runge-Kutta method is used to time integrate the discretized Navier-Stokes and species transport equations for the asymptotic steady solutions. The present method is then applied to two types of flows: the shock wave/boundary layer interaction problems and the jet in cross flows.

Flux splitting algorithms for two-dimensional viscous flows with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Shuen, Jian-Shun; Liou, Meng-Sing

1989-01-01

The Roe flux-difference splitting method has been extended to treat two-dimensional viscous flows with nonequilibrium chemistry. The derivations have avoided unnecessary assumptions or approximations. For spatial discretization, the second-order Roe upwind differencing is used for the convective terms and central differencing for the viscous terms. An upwind-based TVD scheme is applied to eliminate oscillations and obtain a sharp representation of discontinuities. A two-stage Runge-Kutta method is used to time integrate the discretized Navier-Stokes and species transport equations for the asymptotic steady solutions. The present method is then applied to two types of flows: the shock wave/boundary layer interaction problems and the jet in cross flows.

CUDA GPU based full-Stokes finite difference modelling of glaciers

NASA Astrophysics Data System (ADS)

Brædstrup, C. F.; Egholm, D. L.

2012-04-01

Many have stressed the limitations of using the shallow shelf and shallow ice approximations when modelling ice streams or surging glaciers. Using a full-stokes approach requires either large amounts of computer power or time and is therefore seldom an option for most glaciologists. Recent advances in graphics card (GPU) technology for high performance computing have proven extremely efficient in accelerating many large scale scientific computations. The general purpose GPU (GPGPU) technology is cheap, has a low power consumption and fits into a normal desktop computer. It could therefore provide a powerful tool for many glaciologists. Our full-stokes ice sheet model implements a Red-Black Gauss-Seidel iterative linear solver to solve the full stokes equations. This technique has proven very effective when applied to the stokes equation in geodynamics problems, and should therefore also preform well in glaciological flow probems. The Gauss-Seidel iterator is known to be robust but several other linear solvers have a much faster convergence. To aid convergence, the solver uses a multigrid approach where values are interpolated and extrapolated between different grid resolutions to minimize the short wavelength errors efficiently. This reduces the iteration count by several orders of magnitude. The run-time is further reduced by using the GPGPU technology where each card has up to 448 cores. Researchers utilizing the GPGPU technique in other areas have reported between 2 - 11 times speedup compared to multicore CPU implementations on similar problems. The goal of these initial investigations into the possible usage of GPGPU technology in glacial modelling is to apply the enhanced resolution of a full-stokes solver to ice streams and surging glaciers. This is a area of growing interest because ice streams are the main drainage conjugates for large ice sheets. It is therefore crucial to understand this streaming behavior and it's impact up-ice.

Numerical studies of laminar and turbulent drag reduction, part 2

NASA Technical Reports Server (NTRS)

Balasubramanian, R.; Orszag, S. A.

1983-01-01

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

A Numerical Method for Incompressible Flow with Heat Transfer

NASA Technical Reports Server (NTRS)

Sa, Jong-Youb; Kwak, Dochan

1997-01-01

A numerical method for the convective heat transfer problem is developed for low speed flow at mild temperatures. A simplified energy equation is added to the incompressible Navier-Stokes formulation by using Boussinesq approximation to account for the buoyancy force. A pseudocompressibility method is used to solve the resulting set of equations for steady-state solutions in conjunction with an approximate factorization scheme. A Neumann-type pressure boundary condition is devised to account for the interaction between pressure and temperature terms, especially near a heated or cooled solid boundary. It is shown that the present method is capable of predicting the temperature field in an incompressible flow.

Aerodynamic Design on Unstructured Grids for Turbulent Flows

NASA Technical Reports Server (NTRS)

Anderson, W. Kyle; Bonhaus, Daryl L.

1997-01-01

An aerodynamic design algorithm for turbulent flows using unstructured grids is described. The current approach uses adjoint (costate) variables for obtaining derivatives of the cost function. The solution of the adjoint equations is obtained using an implicit formulation in which the turbulence model is fully coupled with the flow equations when solving for the costate variables. The accuracy of the derivatives is demonstrated by comparison with finite-difference gradients and a few example computations are shown. In addition, a user interface is described which significantly reduces the time required for setting up the design problems. Recommendations on directions of further research into the Navier Stokes design process are made.

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.

A continuum analysis of chemical nonequilibrium under hypersonic low-density flight conditions

NASA Technical Reports Server (NTRS)

Gupta, R. N.

1986-01-01

Results of employing the continuum model of Navier-Stokes equations under the low-density flight conditions are presented. These results are obtained with chemical nonequilibrium and multicomponent surface slip boundary conditions. The conditions analyzed are those encountered by the nose region of the Space Shuttle Orbiter during reentry. A detailed comparison of the Navier-Stokes (NS) results is made with the viscous shock-layer (VSL) and direct simulation Monte Carlo (DSMC) predictions. With the inclusion of new surface-slip boundary conditions in NS calculations, the surface heat transfer and other flowfield quantities adjacent to the surface are predicted favorably with the DSMC calculations from 75 km to 115 km in altitude. This suggests a much wider practical range for the applicability of Navier-Stokes solutions than previously thought. This is appealing because the continuum (NS and VSL) methods are commonly used to solve the fluid flow problems and are less demanding in terms of computer resource requirements than the noncontinuum (DSMC) methods.

Heat Transfer Computations of Internal Duct Flows With Combined Hydraulic and Thermal Developing Length

NASA Technical Reports Server (NTRS)

Wang, C. R.; Towne, C. E.; Hippensteele, S. A.; Poinsatte, P. E.

1997-01-01

This study investigated the Navier-Stokes computations of the surface heat transfer coefficients of a transition duct flow. A transition duct from an axisymmetric cross section to a non-axisymmetric cross section, is usually used to connect the turbine exit to the nozzle. As the gas turbine inlet temperature increases, the transition duct is subjected to the high temperature at the gas turbine exit. The transition duct flow has combined development of hydraulic and thermal entry length. The design of the transition duct required accurate surface heat transfer coefficients. The Navier-Stokes computational method could be used to predict the surface heat transfer coefficients of a transition duct flow. The Proteus three-dimensional Navier-Stokes numerical computational code was used in this study. The code was first studied for the computations of the turbulent developing flow properties within a circular duct and a square duct. The code was then used to compute the turbulent flow properties of a transition duct flow. The computational results of the surface pressure, the skin friction factor, and the surface heat transfer coefficient were described and compared with their values obtained from theoretical analyses or experiments. The comparison showed that the Navier-Stokes computation could predict approximately the surface heat transfer coefficients of a transition duct flow.

Time evolution of the eddy viscosity in two-dimensional navier-stokes flow

PubMed

Chaves; Gama

2000-02-01

The time evolution of the eddy viscosity associated with an unforced two-dimensional incompressible Navier-Stokes flow is analyzed by direct numerical simulation. The initial condition is such that the eddy viscosity is isotropic and negative. It is shown by concrete examples that the Navier-Stokes dynamics stabilizes negative eddy viscosity effects. In other words, this dynamics moves monotonically the initial negative eddy viscosity to positive values before relaxation due to viscous term occurs.

On Bi-Grid Local Mode Analysis of Solution Techniques for 3-D Euler and Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Ibraheem, S. O.; Demuren, A. O.

1994-01-01

A procedure is presented for utilizing a bi-grid stability analysis as a practical tool for predicting multigrid performance in a range of numerical methods for solving Euler and Navier-Stokes equations. Model problems based on the convection, diffusion and Burger's equation are used to illustrate the superiority of the bi-grid analysis as a predictive tool for multigrid performance in comparison to the smoothing factor derived from conventional von Neumann analysis. For the Euler equations, bi-grid analysis is presented for three upwind difference based factorizations, namely Spatial, Eigenvalue and Combination splits, and two central difference based factorizations, namely LU and ADI methods. In the former, both the Steger-Warming and van Leer flux-vector splitting methods are considered. For the Navier-Stokes equations, only the Beam-Warming (ADI) central difference scheme is considered. In each case, estimates of multigrid convergence rates from the bi-grid analysis are compared to smoothing factors obtained from single-grid stability analysis. Effects of grid aspect ratio and flow skewness are examined. Both predictions are compared with practical multigrid convergence rates for 2-D Euler and Navier-Stokes solutions based on the Beam-Warming central scheme.

Stark problem in terms of the Stokes multipliers for the triconfluent Heun equation

NASA Astrophysics Data System (ADS)

Osherov, V. I.; Ushakov, V. G.

2013-11-01

The solution of the Stark problem is obtained in terms of the Stokes multipliers for the triconfluent Heun equation (the quartic oscillator equation). The Stokes multipliers are found in an analytical form at positive energies. For negative energies, the Stokes parameters are calculated in frames of a consistent asymptotic approach. The scattering phase, positions, and widths of the Stark resonances are determined as solutions of an implicit equation.

An integrated Navier-Stokes - full potential - free wake method for rotor flows

NASA Astrophysics Data System (ADS)

Berkman, Mert Enis

1998-12-01

The strong wake shed from rotary wings interacts with almost all components of the aircraft, and alters the flow field thus causing performance and noise problems. Understanding and modeling the behavior of this wake, and its effect on the aerodynamics and acoustics of helicopters have remained as challenges. This vortex wake and its effect should be accurately accounted for in any technique that aims to predict rotor flow field and performance. In this study, an advanced and efficient computational technique for predicting three-dimensional unsteady viscous flows over isolated helicopter rotors in hover and in forward flight is developed. In this hybrid technique, the advantages of various existing methods have been combined to accurately and efficiently study rotor flows with a single numerical method. The flow field is viewed in three parts: (i) an inner zone surrounding each blade where the wake and viscous effects are numerically captured, (ii) an outer zone away from the blades where wake is modeled, and (iii) a Lagrangean wake which induces wake effects in the outer zone. This technique was coded in a flow solver and compared with experimental data for hovering and advancing rotors including a two-bladed rotor, the UH-60A rotor and a tapered tip rotor. Detailed surface pressure, integrated thrust and torque, sectional thrust, and tip vortex position predictions compared favorably against experimental data. Results indicated that the hybrid solver provided accurate flow details and performance information typically in one-half to one-eighth cost of complete Navier-Stokes methods.

A computer code for multiphase all-speed transient flows in complex geometries. MAST version 1.0

NASA Technical Reports Server (NTRS)

Chen, C. P.; Jiang, Y.; Kim, Y. M.; Shang, H. M.

1991-01-01

The operation of the MAST code, which computes transient solutions to the multiphase flow equations applicable to all-speed flows, is described. Two-phase flows are formulated based on the Eulerian-Lagrange scheme in which the continuous phase is described by the Navier-Stokes equation (or Reynolds equations for turbulent flows). Dispersed phase is formulated by a Lagrangian tracking scheme. The numerical solution algorithms utilized for fluid flows is a newly developed pressure-implicit algorithm based on the operator-splitting technique in generalized nonorthogonal coordinates. This operator split allows separate operation on each of the variable fields to handle pressure-velocity coupling. The obtained pressure correction equation has the hyperbolic nature and is effective for Mach numbers ranging from the incompressible limit to supersonic flow regimes. The present code adopts a nonstaggered grid arrangement; thus, the velocity components and other dependent variables are collocated at the same grid. A sequence of benchmark-quality problems, including incompressible, subsonic, transonic, supersonic, gas-droplet two-phase flows, as well as spray-combustion problems, were performed to demonstrate the robustness and accuracy of the present code.

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

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

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

2013-01-15

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

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.

Boundary-Layer Stability Analysis of the Mean Flows Obtained Using Unstructured Grids

NASA Technical Reports Server (NTRS)

Liao, Wei; Malik, Mujeeb R.; Lee-Rausch, Elizabeth M.; Li, Fei; Nielsen, Eric J.; Buning, Pieter G.; Chang, Chau-Lyan; Choudhari, Meelan M.

2012-01-01

Boundary-layer stability analyses of mean flows extracted from unstructured-grid Navier- Stokes solutions have been performed. A procedure has been developed to extract mean flow profiles from the FUN3D unstructured-grid solutions. Extensive code-to-code validations have been performed by comparing the extracted mean ows as well as the corresponding stability characteristics to the predictions based on structured-grid solutions. Comparisons are made on a range of problems from a simple at plate to a full aircraft configuration-a modified Gulfstream-III with a natural laminar flow glove. The future aim of the project is to extend the adjoint-based design capability in FUN3D to include natural laminar flow and laminar flow control by integrating it with boundary-layer stability analysis codes, such as LASTRAC.

Acoustic streaming: an arbitrary Lagrangian-Eulerian perspective.

PubMed

Nama, Nitesh; Huang, Tony Jun; Costanzo, Francesco

2017-08-25

We analyse acoustic streaming flows using an arbitrary Lagrangian Eulerian (ALE) perspective. The formulation stems from an explicit separation of time scales resulting in two subproblems: a first-order problem, formulated in terms of the fluid displacement at the fast scale, and a second-order problem, formulated in terms of the Lagrangian flow velocity at the slow time scale. Following a rigorous time-averaging procedure, the second-order problem is shown to be intrinsically steady, and with exact boundary conditions at the oscillating walls. Also, as the second-order problem is solved directly for the Lagrangian velocity, the formulation does not need to employ the notion of Stokes drift, or any associated post-processing, thus facilitating a direct comparison with experiments. Because the first-order problem is formulated in terms of the displacement field, our formulation is directly applicable to more complex fluid-structure interaction problems in microacoustofluidic devices. After the formulation's exposition, we present numerical results that illustrate the advantages of the formulation with respect to current approaches.

Acoustic streaming: an arbitrary Lagrangian–Eulerian perspective

PubMed Central

Nama, Nitesh; Huang, Tony Jun; Costanzo, Francesco

2017-01-01

We analyse acoustic streaming flows using an arbitrary Lagrangian Eulerian (ALE) perspective. The formulation stems from an explicit separation of time scales resulting in two subproblems: a first-order problem, formulated in terms of the fluid displacement at the fast scale, and a second-order problem, formulated in terms of the Lagrangian flow velocity at the slow time scale. Following a rigorous time-averaging procedure, the second-order problem is shown to be intrinsically steady, and with exact boundary conditions at the oscillating walls. Also, as the second-order problem is solved directly for the Lagrangian velocity, the formulation does not need to employ the notion of Stokes drift, or any associated post-processing, thus facilitating a direct comparison with experiments. Because the first-order problem is formulated in terms of the displacement field, our formulation is directly applicable to more complex fluid–structure interaction problems in microacoustofluidic devices. After the formulation’s exposition, we present numerical results that illustrate the advantages of the formulation with respect to current approaches. PMID:29051631

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.

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.

Some recent applications of Navier-Stokes codes to rotorcraft

NASA Technical Reports Server (NTRS)

Mccroskey, W. J.

1992-01-01

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

A family of approximate solutions and explicit error estimates for the nonlinear stationary Navier-Stokes problem

NASA Technical Reports Server (NTRS)

Gabrielsen, R. E.; Karel, S.

1975-01-01

An algorithm for solving the nonlinear stationary Navier-Stokes problem is developed. Explicit error estimates are given. This mathematical technique is potentially adaptable to the separation problem.

Navier-Stokes computations for circulation control airfoils

NASA Technical Reports Server (NTRS)

Pulliam, Thomas H.; Jespersen, Dennis C.; Barth, Timothy J.

1987-01-01

Navier-Stokes computations of subsonic to transonic flow past airfoils with augmented lift due to rearward jet blowing over a curved trailing edge are presented. The approach uses a spiral grid topology. Solutions are obtained using a Navier-Stokes code which employs an implicit finite difference method, an algebraic turbulence model, and developments which improve stability, convergence, and accuracy. Results are compared against experiments for no jet blowing and moderate jet pressures and demonstrate the capability to compute these complicated flows.

Navier-Stokes computations for circulation controlled airfoils

NASA Technical Reports Server (NTRS)

Pulliam, T. H.; Jesperen, D. C.; Barth, T. J.

1986-01-01

Navier-Stokes computations of subsonic to transonic flow past airfoils with augmented lift due to rearward jet blowing over a curved trailing edge are presented. The approach uses a spiral grid topology. Solutions are obtained using a Navier-Stokes code which employs an implicit finite difference method, an algebraic turbulence model, and developments which improve stability, convergence, and accuracy. Results are compared against experiments for no jet blowing and moderate jet pressures and demonstrate the capability to compute these complicated flows.

Verification of the proteus two-dimensional Navier-Stokes code for flat plate and pipe flows

NASA Technical Reports Server (NTRS)

Conley, Julianne M.; Zeman, Patrick L.

1991-01-01

The Proteus Navier-Stokes Code is evaluated for 2-D/axisymmetric, viscous, incompressible, internal, and external flows. The particular cases to be discussed are laminar and turbulent flows over a flat plate, laminar and turbulent developing pipe flows, and turbulent pipe flow with swirl. Results are compared with exact solutions, empirical correlations, and experimental data. A detailed description of the code set-up, including boundary conditions, initial conditions, grid size, and grid packing is given for each case.

A Reconstructed Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations on Arbitrary Grids

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

Hong Luo; Luqing Luo; Robert Nourgaliev

2010-09-01

A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier–Stokes equations on arbitrary grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier–Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need tomore » judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on arbitrary grids. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG method is able to deliver the same accuracy as the well-known Bassi–Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier–Stokes equations, clearly demonstrating its superior performance over the existing DG methods for solving the compressible Navier–Stokes equations.« less

A Reconstructed Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations on Arbitrary Grids

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

Hong Luo; Luqing Luo; Robert Nourgaliev

2010-01-01

A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need tomore » judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on arbitrary grids. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG method is able to deliver the same accuracy as the well-known Bassi-Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier-Stokes equations, clearly demonstrating its superior performance over the existing DG methods for solving the compressible Navier-Stokes equations.« less

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.

On some Approximation Schemes for Steady Compressible Viscous Flow

NASA Astrophysics Data System (ADS)

Bause, M.; Heywood, J. G.; Novotny, A.; Padula, M.

This paper continues our development of approximation schemes for steady compressible viscous flow based on an iteration between a Stokes like problem for the velocity and a transport equation for the density, with the aim of improving their suitability for computations. Such schemes seem attractive for computations because they offer a reduction to standard problems for which there is already highly refined software, and because of the guidance that can be drawn from an existence theory based on them. Our objective here is to modify a recent scheme of Heywood and Padula [12], to improve its convergence properties. This scheme improved upon an earlier scheme of Padula [21], [23] through the use of a special ``effective pressure'' in linking the Stokes and transport problems. However, its convergence is limited for several reasons. Firstly, the steady transport equation itself is only solvable for general velocity fields if they satisfy certain smallness conditions. These conditions are met here by using a rescaled variant of the steady transport equation based on a pseudo time step for the equation of continuity. Another matter limiting the convergence of the scheme in [12] is that the Stokes linearization, which is a linearization about zero, has an inevitably small range of convergence. We replace it here with an Oseen or Newton linearization, either of which has a wider range of convergence, and converges more rapidly. The simplicity of the scheme offered in [12] was conducive to a relatively simple and clearly organized proof of its convergence. The proofs of convergence for the more complicated schemes proposed here are structured along the same lines. They strengthen the theorems of existence and uniqueness in [12] by weakening the smallness conditions that are needed. The expected improvement in the computational performance of the modified schemes has been confirmed by Bause [2], in an ongoing investigation.

A Comparison of Simplified Two-dimensional Flow Models Exemplified by Water Flow in a Cavern

NASA Astrophysics Data System (ADS)

Prybytak, Dzmitry; Zima, Piotr

2017-12-01

The paper shows the results of a comparison of simplified models describing a two-dimensional water flow in the example of a water flow through a straight channel sector with a cavern. The following models were tested: the two-dimensional potential flow model, the Stokes model and the Navier-Stokes model. In order to solve the first two, the boundary element method was employed, whereas to solve the Navier-Stokes equations, the open-source code library OpenFOAM was applied. The results of numerical solutions were compared with the results of measurements carried out on a test stand in a hydraulic laboratory. The measurements were taken with an ADV probe (Acoustic Doppler Velocimeter). Finally, differences between the results obtained from the mathematical models and the results of laboratory measurements were analysed.

A quasi-Lagrangian finite element method for the Navier-Stokes equations in a time-dependent domain

NASA Astrophysics Data System (ADS)

Lozovskiy, Alexander; Olshanskii, Maxim A.; Vassilevski, Yuri V.

2018-05-01

The paper develops a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method builds on a quasi-Lagrangian formulation of the problem. The paper provides stability and convergence analysis of the fully discrete (finite-difference in time and finite-element in space) method. The analysis does not assume any CFL time-step restriction, it rather needs mild conditions of the form $\\Delta t\\le C$, where $C$ depends only on problem data, and $h^{2m_u+2}\\le c\\,\\Delta t$, $m_u$ is polynomial degree of velocity finite element space. Both conditions result from a numerical treatment of practically important non-homogeneous boundary conditions. The theoretically predicted convergence rate is confirmed by a set of numerical experiments. Further we apply the method to simulate a flow in a simplified model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.

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.

Stokes drift

NASA Astrophysics Data System (ADS)

van den Bremer, T. S.; Breivik, Ø.

2017-12-01

During its periodic motion, a particle floating at the free surface of a water wave experiences a net drift velocity in the direction of wave propagation, known as the Stokes drift (Stokes 1847 Trans. Camb. Philos. Soc. 8, 441-455). More generally, the Stokes drift velocity is the difference between the average Lagrangian flow velocity of a fluid parcel and the average Eulerian flow velocity of the fluid. This paper reviews progress in fundamental and applied research on the induced mean flow associated with surface gravity waves since the first description of the Stokes drift, now 170 years ago. After briefly reviewing the fundamental physical processes, most of which have been established for decades, the review addresses progress in laboratory and field observations of the Stokes drift. Despite more than a century of experimental studies, laboratory studies of the mean circulation set up by waves in a laboratory flume remain somewhat contentious. In the field, rapid advances are expected due to increasingly small and cheap sensors and transmitters, making widespread use of small surface-following drifters possible. We also discuss remote sensing of the Stokes drift from high-frequency radar. Finally, the paper discusses the three main areas of application of the Stokes drift: in the coastal zone, in Eulerian models of the upper ocean layer and in the modelling of tracer transport, such as oil and plastic pollution. Future climate models will probably involve full coupling of ocean and atmosphere systems, in which the wave model provides consistent forcing on the ocean surface boundary layer. Together with the advent of new space-borne instruments that can measure surface Stokes drift, such models hold the promise of quantifying the impact of wave effects on the global atmosphere-ocean system and hopefully contribute to improved climate projections. This article is part of the theme issue 'Nonlinear water waves'.

On Stationary Navier-Stokes Flows Around a Rotating Obstacle in Two-Dimensions

NASA Astrophysics Data System (ADS)

Higaki, Mitsuo; Maekawa, Yasunori; Nakahara, Yuu

2018-05-01

We study the two-dimensional stationary Navier-Stokes equations describing the flows around a rotating obstacle. The unique existence of solutions and their asymptotic behavior at spatial infinity are established when the rotation speed of the obstacle and the given exterior force are sufficiently small.

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.

Discontinuous finite volume element discretization for coupled flow-transport problems arising in models of sedimentation

NASA Astrophysics Data System (ADS)

Bürger, Raimund; Kumar, Sarvesh; Ruiz-Baier, Ricardo

2015-10-01

The sedimentation-consolidation and flow processes of a mixture of small particles dispersed in a viscous fluid at low Reynolds numbers can be described by a nonlinear transport equation for the solids concentration coupled with the Stokes problem written in terms of the mixture flow velocity and the pressure field. Here both the viscosity and the forcing term depend on the local solids concentration. A semi-discrete discontinuous finite volume element (DFVE) scheme is proposed for this model. The numerical method is constructed on a baseline finite element family of linear discontinuous elements for the approximation of velocity components and concentration field, whereas the pressure is approximated by piecewise constant elements. The unique solvability of both the nonlinear continuous problem and the semi-discrete DFVE scheme is discussed, and optimal convergence estimates in several spatial norms are derived. Properties of the model and the predicted space accuracy of the proposed formulation are illustrated by detailed numerical examples, including flows under gravity with changing direction, a secondary settling tank in an axisymmetric setting, and batch sedimentation in a tilted cylindrical vessel.

Preconditioned conjugate-gradient methods for low-speed flow calculations

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

Preconditioned Conjugate Gradient methods for low speed flow calculations

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

Computational fluid dynamics in a marine environment

NASA Technical Reports Server (NTRS)

Carlson, Arthur D.

1987-01-01

The introduction of the supercomputer and recent advances in both Reynolds averaged, and large eddy simulation fluid flow approximation techniques to the Navier-Stokes equations, have created a robust environment for the exploration of problems of interest to the Navy in general, and the Naval Underwater Systems Center in particular. The nature of problems that are of interest, and the type of resources needed for their solution are addressed. The goal is to achieve a good engineering solution to the fluid-structure interaction problem. It is appropriate to indicate that a paper by D. Champman played a major role in developing the interest in the approach discussed.

Level-set simulations of soluble surfactant driven flows

NASA Astrophysics Data System (ADS)

Cleret de Langavant, Charles; Guittet, Arthur; Theillard, Maxime; Temprano-Coleto, Fernando; Gibou, Frédéric

2017-11-01

We present an approach to simulate the diffusion, advection and adsorption-desorption of a material quantity defined on an interface in two and three spatial dimensions. We use a level-set approach to capture the interface motion and a Quad/Octree data structure to efficiently solve the equations describing the underlying physics. Coupling with a Navier-Stokes solver enables the study of the effect of soluble surfactants that locally modify the parameters of surface tension on different types of flows. The method is tested on several benchmarks and applied to three typical examples of flows in the presence of surfactant: a bubble in a shear flow, the well-known phenomenon of tears of wine, and the Landau-Levich coating problem.

A frequency domain linearized Navier-Stokes equations approach to acoustic propagation in flow ducts with sharp edges.

PubMed

Kierkegaard, Axel; Boij, Susann; Efraimsson, Gunilla

2010-02-01

Acoustic wave propagation in flow ducts is commonly modeled with time-domain non-linear Navier-Stokes equation methodologies. To reduce computational effort, investigations of a linearized approach in frequency domain are carried out. Calculations of sound wave propagation in a straight duct are presented with an orifice plate and a mean flow present. Results of transmission and reflections at the orifice are presented on a two-port scattering matrix form and are compared to measurements with good agreement. The wave propagation is modeled with a frequency domain linearized Navier-Stokes equation methodology. This methodology is found to be efficient for cases where the acoustic field does not alter the mean flow field, i.e., when whistling does not occur.

Computational simulations of supersonic magnetohydrodynamic flow control, power and propulsion systems

NASA Astrophysics Data System (ADS)

Wan, Tian

This work is motivated by the lack of fully coupled computational tool that solves successfully the turbulent chemically reacting Navier-Stokes equation, the electron energy conservation equation and the electric current Poisson equation. In the present work, the abovementioned equations are solved in a fully coupled manner using fully implicit parallel GMRES methods. The system of Navier-Stokes equations are solved using a GMRES method with combined Schwarz and ILU(0) preconditioners. The electron energy equation and the electric current Poisson equation are solved using a GMRES method with combined SOR and Jacobi preconditioners. The fully coupled method has also been implemented successfully in an unstructured solver, US3D, and convergence test results were presented. This new method is shown two to five times faster than the original DPLR method. The Poisson solver is validated with analytic test problems. Then, four problems are selected; two of them are computed to explore the possibility of onboard MHD control and power generation, and the other two are simulation of experiments. First, the possibility of onboard reentry shock control by a magnetic field is explored. As part of a previous project, MHD power generation onboard a re-entry vehicle is also simulated. Then, the MHD acceleration experiments conducted at NASA Ames research center are simulated. Lastly, the MHD power generation experiments known as the HVEPS project are simulated. For code validation, the scramjet experiments at University of Queensland are simulated first. The generator section of the HVEPS test facility is computed then. The main conclusion is that the computational tool is accurate for different types of problems and flow conditions, and its accuracy and efficiency are necessary when the flow complexity increases.

Simulations of solid-fluid coupling with application to crystal entrainment in vigorous convection

NASA Astrophysics Data System (ADS)

Suckale, J.; Elkins-Tanton, L. T.; Sethian, J.; Yu, J.

2009-12-01

Many problems in computational geophysics require the accurate coupling of a solid body to viscous flow. Examples range from understanding the role of highly crystalline magma for the dynamic of volcanic eruptions to crystal entrainment in magmatic flow and the emplacement of xenoliths. In this paper, we present and validate a numerical method for solid-fluid coupling. The algorithm relies on a two-step projection scheme: In the first step, we solve the multiple-phase Navier-Stokes or Stokes equation in both domains. In the second step, we project the velocity field in the solid domain onto a rigid-body motion by enforcing that the deformation tensor in the respective domain is zero. This procedure is also used to enforce the no-slip boundary condition on the solid-fluid interface. We perform several benchmark computations to validate our computations. More precisely, we investigate the formation of a wake behind both fixed and mobile cylinders and cuboids with and without imposed velocity fields in the fluid. These preliminary tests indicate that our code is able to simulate solid-fluid coupling for Reynolds numbers of up to 1000. Finally, we apply our method to the problem of crystal entrainment in vigorous convection. The interplay between sedimentation and re-entrainment of crystals in convective flow is of fundamental importance for understanding the compositional evolution of magmatic reservoirs of various sizes from small lava ponds to magma oceans at the planetary scale. Previous studies of this problem have focused primarily on laboratory experiments, often with conflicting conclusions. Our work is complementary to these prior studies as we model the competing processes of gravitational sedimentation and entrainment of crystals at the length scale of the size of the crystals.

Numerical boundary condition procedures and multigrid methods; Proceedings of the Symposium, NASA Ames Research Center, Moffett Field, CA, October 19-22, 1981

NASA Technical Reports Server (NTRS)

1982-01-01

Papers presented in this volume provide an overview of recent work on numerical boundary condition procedures and multigrid methods. The topics discussed include implicit boundary conditions for the solution of the parabolized Navier-Stokes equations for supersonic flows; far field boundary conditions for compressible flows; and influence of boundary approximations and conditions on finite-difference solutions. Papers are also presented on fully implicit shock tracking and on the stability of two-dimensional hyperbolic initial boundary value problems for explicit and implicit schemes.

A general algorithm using finite element method for aerodynamic configurations at low speeds

NASA Technical Reports Server (NTRS)

Balasubramanian, R.

1975-01-01

A finite element algorithm for numerical simulation of two-dimensional, incompressible, viscous flows was developed. The Navier-Stokes equations are suitably modelled to facilitate direct solution for the essential flow parameters. A leap-frog time differencing and Galerkin minimization of these model equations yields the finite element algorithm. The finite elements are triangular with bicubic shape functions approximating the solution space. The finite element matrices are unsymmetrically banded to facilitate savings in storage. An unsymmetric L-U decomposition is performed on the finite element matrices to obtain the solution for the boundary value problem.

The Need for a Kinetics for Biological Transport

PubMed Central

Schindler, A. M.; Iberall, A. S.

1973-01-01

The traditional theory of transport across capillary membranes via a laminar Poiseuille flow is shown to be invalid. It is demonstrated that the random, diffusive nature of the molecular flow and interactions with the “pore” walls play an important role in the transport process. Neither the continuum Navier-Stokes theory nor the equivalent theory of irreversible thermodynamics is adequate to treat the problem. Combination of near-continuum hydrodynamic theory, noncontinuum kinetic theory, and the theory of fluctuations provides a first step toward modeling both liquid processes in general and membrane transport processes as a specific application. PMID:4726880

Numerical simulation of swept-wing flows

NASA Technical Reports Server (NTRS)

Reed, Helen L.

1991-01-01

Efforts of the last six months to computationally model the transition process characteristics of flow over swept wings are described. Specifically, the crossflow instability and crossflow/Tollmien-Schlichting wave interactions are analyzed through the numerical solution of the full 3D Navier-Stokes equations including unsteadiness, curvature, and sweep. This approach is chosen because of the complexity of the problem and because it appears that linear stability theory is insufficient to explain the discrepancies between different experiments and between theory and experiment. The leading edge region of a swept wing is considered in a 3D spatial simulation with random disturbances as the initial conditions.

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.

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.

A globally well-posed finite element algorithm for aerodynamics applications

NASA Technical Reports Server (NTRS)

Iannelli, G. S.; Baker, A. J.

1991-01-01

A finite element CFD algorithm is developed for Euler and Navier-Stokes aerodynamic applications. For the linear basis, the resultant approximation is at least second-order-accurate in time and space for synergistic use of three procedures: (1) a Taylor weak statement, which provides for derivation of companion conservation law systems with embedded dispersion-error control mechanisms; (2) a stiffly stable second-order-accurate implicit Rosenbrock-Runge-Kutta temporal algorithm; and (3) a matrix tensor product factorization that permits efficient numerical linear algebra handling of the terminal large-matrix statement. Thorough analyses are presented regarding well-posed boundary conditions for inviscid and viscous flow specifications. Numerical solutions are generated and compared for critical evaluation of quasi-one- and two-dimensional Euler and Navier-Stokes benchmark test problems.

A computational study of the flowfield surrounding the Aeroassist Flight Experiment vehicle

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.; Greene, Francis A.

1987-01-01

A symmetric total variation diminishing (STVD) algorithm has been applied to the solution of the three-dimensional hypersonic flowfield surrounding the Aeroassist Flight Experiment (AFE) vehicle. Both perfect-gas and chemical nonequilibrium models have been used. The perfect-gas flows were computed at two different Reynolds numbers, including a flight trajectory point at maximum dynamic pressure, and on two different grids. Procedures for coupling the solution of the species continuity equations with the Navier-Stokes equations in the presence of chemical nonequilibrium are reviewed and tested on the forebody of the AFE and on the complete flowfield assuming noncatalytic wall and no species diffusion. Problems with the STVD algorithm unique to flows with variable thermodynamic properties (real gas) are identified and algorithm modifications are suggested. A potential heating problem caused by strong flow impingement on the nozzle lip in the near wake at 0-deg angle of attack has been identified.

Low- and high-order accurate boundary conditions: From Stokes to Darcy porous flow modeled with standard and improved Brinkman lattice Boltzmann schemes

NASA Astrophysics Data System (ADS)

Silva, Goncalo; Talon, Laurent; Ginzburg, Irina

2017-04-01

The present contribution focuses on the accuracy of reflection-type boundary conditions in the Stokes-Brinkman-Darcy modeling of porous flows solved with the lattice Boltzmann method (LBM), which we operate with the two-relaxation-time (TRT) collision and the Brinkman-force based scheme (BF), called BF-TRT scheme. In parallel, we compare it with the Stokes-Brinkman-Darcy linear finite element method (FEM) where the Dirichlet boundary conditions are enforced on grid vertices. In bulk, both BF-TRT and FEM share the same defect: in their discretization a correction to the modeled Brinkman equation appears, given by the discrete Laplacian of the velocity-proportional resistance force. This correction modifies the effective Brinkman viscosity, playing a crucial role in the triggering of spurious oscillations in the bulk solution. While the exact form of this defect is available in lattice-aligned, straight or diagonal, flows; in arbitrary flow/lattice orientations its approximation is constructed. At boundaries, we verify that such a Brinkman viscosity correction has an even more harmful impact. Already at the first order, it shifts the location of the no-slip wall condition supported by traditional LBM boundary schemes, such as the bounce-back rule. For that reason, this work develops a new class of boundary schemes to prescribe the Dirichlet velocity condition at an arbitrary wall/boundary-node distance and that supports a higher order accuracy in the accommodation of the TRT-Brinkman solutions. For their modeling, we consider the standard BF scheme and its improved version, called IBF; this latter is generalized in this work to suppress or to reduce the viscosity correction in arbitrarily oriented flows. Our framework extends the one- and two-point families of linear and parabolic link-wise boundary schemes, respectively called B-LI and B-MLI, which avoid the interference of the Brinkman viscosity correction in their closure relations. The performance of LBM and FEM is thoroughly evaluated in three benchmark tests, which are run throughout three distinctive permeability regimes. The first configuration is a horizontal porous channel, studied with a symbolic approach, where we construct the exact solutions of FEM and BF/IBF with different boundary schemes. The second problem refers to an inclined porous channel flow, which brings in as new challenge the formation of spurious boundary layers in LBM; that is, numerical artefacts that arise due to a deficient accommodation of the bulk solution by the low-accurate boundary scheme. The third problem considers a porous flow past a periodic square array of solid cylinders, which intensifies the previous two tests with the simulation of a more complex flow pattern. The ensemble of numerical tests provides guidelines on the effect of grid resolution and the TRT free collision parameter over the accuracy and the quality of the velocity field, spanning from Stokes to Darcy permeability regimes. It is shown that, with the use of the high-order accurate boundary schemes, the simple, uniform-mesh-based TRT-LBM formulation can even surpass the accuracy of FEM employing hardworking body-fitted meshes.

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.

Calculation of periodic flows in a continuously stratified fluid

NASA Astrophysics Data System (ADS)

Vasiliev, A.

2012-04-01

Analytic theory of disturbances generated by an oscillating compact source in a viscous continuously stratified fluid was constructed. Exact solution of the internal waves generation problem was constructed taking into account diffusivity effects. This analysis is based on set of fundamental equations of incompressible flows. The linearized problem of periodic flows in a continuously stratified fluid, generated by an oscillating part of the inclined plane was solved by methods of singular perturbation theory. A rectangular or disc placed on a sloping plane and oscillating linearly in an arbitrary direction was selected as a source of disturbances. The solutions include regularly perturbed on dissipative component functions describing internal waves and a family of singularly perturbed functions. One of the functions from the singular components family has an analogue in a homogeneous fluid that is a periodic or Stokes' flow. Its thickness is defined by a universal micro scale depending on kinematics viscosity coefficient and a buoyancy frequency with a factor depending on the wave slope. Other singular perturbed functions are specific for stratified flows. Their thickness are defined the diffusion coefficient, kinematic viscosity and additional factor depending on geometry of the problem. Fields of fluid density, velocity, vorticity, pressure, energy density and flux as well as forces acting on the source are calculated for different types of the sources. It is shown that most effective source of waves is the bi-piston. Complete 3D problem is transformed in various limiting cases that are into 2D problem for source in stratified or homogeneous fluid and the Stokes problem for an oscillating infinite plane. The case of the "critical" angle that is equality of the emitting surface and the wave cone slope angles needs in separate investigations. In this case, the number of singular component is saved. Patterns of velocity and density fields were constructed and analyzed by methods of computational mathematics. Singular components of the solution affect the flow pattern of the inhomogeneous stratified fluid, not only near the source of the waves, but at a large distance. Analytical calculations of the structure of wave beams are matched with laboratory experiments. Some deviations at large distances from the source are formed due to the contribution of background wave field associated with seiches in the laboratory tank. In number of the experiments vortices with closed contours were observed on some distances from the disk. The work was supported by Ministry of Education and Science RF (Goscontract No. 16.518.11.7059), experiments were performed on set up USU "HPC IPMec RAS".

Simulation of the turbulent Rayleigh-Benard problem using a spectral/finite difference technique

NASA Technical Reports Server (NTRS)

Eidson, T. M.; Hussaini, M. Y.; Zang, T. A.

1986-01-01

The three-dimensional, incompressible Navier-Stokes and energy equations with the Bousinesq assumption have been directly simulated at a Rayleigh number of 3.8 x 10 to the 5th power and a Prandtl number of 0.76. In the vertical direction, wall boundaries were used and in the horizontal, periodic boundary conditions were used. A spectral/finite difference numerical method was used to simulate the flow. The flow at these conditions is turbulent and a sufficiently fine mesh was used to capture all relevant flow scales. The results of the simulation are compared to experimental data to justify the conclusion that the small scale motion is adequately resolved.

The CMC/3DPNS computer program for prediction of three-dimension, subsonic, turbulent aerodynamic juncture region flow. Volume 2: Users' manual

NASA Technical Reports Server (NTRS)

Manhardt, P. D.

1982-01-01

The CMC fluid mechanics program system was developed to transmit the theoretical solution of finite element numerical solution methodology, applied to nonlinear field problems into a versatile computer code for comprehensive flow field analysis. Data procedures for the CMC 3 dimensional Parabolic Navier-Stokes (PNS) algorithm are presented. General data procedures a juncture corner flow standard test case data deck is described. A listing of the data deck and an explanation of grid generation methodology are presented. Tabulations of all commands and variables available to the user are described. These are in alphabetical order with cross reference numbers which refer to storage addresses.

The Influence of Viscous Effects on Ice Accretion Prediction and Airfoil Performance Predictions

NASA Technical Reports Server (NTRS)

Kreeger, Richard E.; Wright, William B.

2005-01-01

A computational study was conducted to evaluate the effectiveness of using a viscous flow solution in an ice accretion code and the resulting accuracy of aerodynamic performance prediction. Ice shapes were obtained for one single-element and one multi-element airfoil using both potential flow and Navier-Stokes flowfields in the LEWICE ice accretion code. Aerodynamics were then calculated using a Navier-Stokes flow solver.

Numerical methods in laminar and turbulent flow; Proceedings of the 7th International Conference, Stanford Univ., CA, July 15-19, 1991. Vol. 7, pts. 1 & 2

NASA Technical Reports Server (NTRS)

Taylor, C. (Editor); Chin, J. H. (Editor); Homsy, G. M. (Editor)

1991-01-01

Consideration is given to the impulse response of a laminar boundary layer and receptivity; numerical transition to turbulence in plane Poiseuille flow; large eddy simulation of turbulent wake flow; a viscous model and loss calculation of a multisplitter cascade; vortex initiation during dynamic stall of an airfoil; a numerical analysis of isothermal flow in a combustion chamber; and compressible flow calculations with a two-equation turbulence model and unstructured grids. Attention is also given to a 2D calculation of a buoyant flow around a burning sphere, a fast multigrid method for 3D turbulent incompressible flows, a streaming flow induced by an oscillating cascade of circular cylinders, an algebraic multigrid scheme for solving the Navier-Stokes equations on unstructured meshes; and nonlinear coupled multigrid solutions to thermal problems employing different nodal grid arrangements and convective transport approximations.

Separated flow over bodies of revolution using an unsteady discrete-vorticity cross wake. Part 1: Theory and application

NASA Technical Reports Server (NTRS)

Marshall, F. J.; Deffenbaugh, F. D.

1974-01-01

A method is developed to determine the flow field of a body of revolution in separated flow. The technique employed is the use of the computer to integrate various solutions and solution properties of the sub-flow fields which made up the entire flow field without resorting to a finite difference solution to the complete Navier-Stokes equations. The technique entails the use of the unsteady cross flow analogy and a new solution to the required two-dimensional unsteady separated flow problem based upon an unsteady, discrete-vorticity wake. Data for the forces and moments on aerodynamic bodies at low speeds and high angle of attack (outside the range of linear inviscid theories) such that the flow is substantially separated are produced which compare well with experimental data. In addition, three dimensional steady separation regions and wake vortex patterns are determined.

Separated flow over bodies of revolution using an unsteady discrete-vorticity cross wake. Part 2: Computer program description

NASA Technical Reports Server (NTRS)

Marshall, F. J.; Deffenbaugh, F. D.

1974-01-01

A method is developed to determine the flow field of a body of revolution in separated flow. The computer was used to integrate various solutions and solution properties of the sub-flow fields which made up the entire flow field without resorting to a finite difference solution to the complete Navier-Stokes equations. The technique entails the use of the unsteady cross flow analogy and a new solution to the two-dimensional unsteady separated flow problem based upon an unsteady, discrete-vorticity wake. Data for the forces and moments on aerodynamic bodies at low speeds and high angle of attack (outside the range of linear inviscid theories) such that the flow is substantially separated are produced which compare well with experimental data. In addition, three dimensional steady separated regions and wake vortex patterns are determined. The computer program developed to perform the numerical calculations is described.

Navier-Stokes, dynamics and aeroelastic computations for vortical flows, buffet and flutter applications

NASA Technical Reports Server (NTRS)

Kandil, Osama A.

1993-01-01

Research on Navier-Stokes, dynamics, and aeroelastic computations for vortical flows, buffet, and flutter applications was performed. Progress during the period from 1 Oct. 1992 to 30 Sep. 1993 is included. Papers on the following topics are included: vertical tail buffet in vortex breakdown flows; simulation of tail buffet using delta wing-vertical tail configuration; shock-vortex interaction over a 65-degree delta wing in transonic flow; supersonic vortex breakdown over a delta wing in transonic flow; and prediction and control of slender wing rock.

Self-similarity in incompressible Navier-Stokes equations.

PubMed

Ercan, Ali; Kavvas, M Levent

2015-12-01

The self-similarity conditions of the 3-dimensional (3D) incompressible Navier-Stokes equations are obtained by utilizing one-parameter Lie group of point scaling transformations. It is found that the scaling exponents of length dimensions in i = 1, 2, 3 coordinates in 3-dimensions are not arbitrary but equal for the self-similarity of 3D incompressible Navier-Stokes equations. It is also shown that the self-similarity in this particular flow process can be achieved in different time and space scales when the viscosity of the fluid is also scaled in addition to other flow variables. In other words, the self-similarity of Navier-Stokes equations is achievable under different fluid environments in the same or different gravity conditions. Self-similarity criteria due to initial and boundary conditions are also presented. Utilizing the proposed self-similarity conditions of the 3D hydrodynamic flow process, the value of a flow variable at a specified time and space can be scaled to a corresponding value in a self-similar domain at the corresponding time and space.

An error analysis of least-squares finite element method of velocity-pressure-vorticity formulation for Stokes problem

NASA Technical Reports Server (NTRS)

Chang, Ching L.; Jiang, Bo-Nan

1990-01-01

A theoretical proof of the optimal rate of convergence for the least-squares method is developed for the Stokes problem based on the velocity-pressure-vorticity formula. The 2D Stokes problem is analyzed to define the product space and its inner product, and the a priori estimates are derived to give the finite-element approximation. The least-squares method is found to converge at the optimal rate for equal-order interpolation.

Fluid-structure interaction in Taylor-Couette flow

NASA Astrophysics Data System (ADS)

Kempf, Martin Horst Willi

1998-10-01

The linear stability of a viscous fluid between two concentric, rotating cylinders is considered. The inner cylinder is a rigid boundary and the outer cylinder has an elastic layer exposed to the fluid. The subject is motivated by flow between two adjoining rollers in a printing press. The governing equations of the fluid layer are the incompressible Navier-Stokes equations, and the governing equations of the elastic layer are Navier's equations. A narrow gap, neutral stability, and axisymmetric disturbances are assumed. The solution involves a novel technique for treating two layer stability problems, where an exact solution in the elastic layer is used to isolate the problem in the fluid layer. The results show that the presence of the elastic layer has only a slight effect on the critical Taylor numbers for the elastic parameters of modern printing presses. However, there are parameter values where the critical Taylor number is dramatically different than the classical Taylor-Couette problem.

A Numerical Study of Mesh Adaptivity in Multiphase Flows with Non-Newtonian Fluids

NASA Astrophysics Data System (ADS)

Percival, James; Pavlidis, Dimitrios; Xie, Zhihua; Alberini, Federico; Simmons, Mark; Pain, Christopher; Matar, Omar

2014-11-01

We present an investigation into the computational efficiency benefits of dynamic mesh adaptivity in the numerical simulation of transient multiphase fluid flow problems involving Non-Newtonian fluids. Such fluids appear in a range of industrial applications, from printing inks to toothpastes and introduce new challenges for mesh adaptivity due to the additional ``memory'' of viscoelastic fluids. Nevertheless, the multiscale nature of these flows implies huge potential benefits for a successful implementation. The study is performed using the open source package Fluidity, which couples an unstructured mesh control volume finite element solver for the multiphase Navier-Stokes equations to a dynamic anisotropic mesh adaptivity algorithm, based on estimated solution interpolation error criteria, and conservative mesh-to-mesh interpolation routine. The code is applied to problems involving rheologies ranging from simple Newtonian to shear-thinning to viscoelastic materials and verified against experimental data for various industrial and microfluidic flows. This work was undertaken as part of the EPSRC MEMPHIS programme grant EP/K003976/1.

On a class of unsteady three-dimensional Navier Stokes solutions relevant to rotating disc flows: Threshold amplitudes and finite time singularities

NASA Technical Reports Server (NTRS)

Hall, Philip; Balakumar, P.

1990-01-01

A class of exact steady and unsteady solutions of the Navier Stokes equations in cylindrical polar coordinates is given. The flows correspond to the motion induced by an infinite disc rotating with constant angular velocity about the z-axis in a fluid occupying a semi-infinite region which, at large distances from the disc, has velocity field proportional to (x,-y,O) with respect to a Cartesian coordinate system. It is shown that when the rate of rotation is large, Karman's exact solution for a disc rotating in an otherwise motionless fluid is recovered. In the limit of zero rotation rate a particular form of Howarth's exact solution for three-dimensional stagnation point flow is obtained. The unsteady form of the partial differential system describing this class of flow may be generalized to time-periodic equilibrium flows. In addition the unsteady equations are shown to describe a strongly nonlinear instability of Karman's rotating disc flow. It is shown that sufficiently large perturbations lead to a finite time breakdown of that flow whilst smaller disturbances decay to zero. If the stagnation point flow at infinity is sufficiently strong, the steady basic states become linearly unstable. In fact there is then a continuous spectrum of unstable eigenvalues of the stability equations but, if the initial value problem is considered, it is found that, at large values of time, the continuous spectrum leads to a velocity field growing exponentially in time with an amplitude decaying algebraically in time.

Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Jiang, Yi-Tsann

1993-01-01

A general solution adaptive scheme-based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required.

Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

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

1993-01-01

A general solution adaptive scheme based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required.

Lagrangian flows within reflecting internal waves at a horizontal free-slip surface

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

Zhou, Qi, E-mail: q.zhou@damtp.cam.ac.uk; Diamessis, Peter J.

In this paper sequel to Zhou and Diamessis [“Reflection of an internal gravity wave beam off a horizontal free-slip surface,” Phys. Fluids 25, 036601 (2013)], we consider Lagrangian flows within nonlinear internal waves (IWs) reflecting off a horizontal free-slip rigid lid, the latter being a model of the ocean surface. The problem is approached both analytically using small-amplitude approximations and numerically by tracking Lagrangian fluid particles in direct numerical simulation (DNS) datasets of the Eulerian flow. Inviscid small-amplitude analyses for both plane IWs and IW beams (IWBs) show that Eulerian mean flow due to wave-wave interaction and wave-induced Stokes driftmore » cancels each other out completely at the second order in wave steepness A, i.e., O(A{sup 2}), implying zero Lagrangian mean flow up to that order. However, high-accuracy particle tracking in finite-Reynolds-number fully nonlinear DNS datasets from the work of Zhou and Diamessis suggests that the Euler-Stokes cancelation on O(A{sup 2}) is not complete. This partial cancelation significantly weakens the mean Lagrangian flows but does not entirely eliminate them. As a result, reflecting nonlinear IWBs produce mean Lagrangian drifts on O(A{sup 2}) and thus particle dispersion on O(A{sup 4}). The above findings can be relevant to predicting IW-driven mass transport in the oceanic surface and subsurface region which bears important observational and environmental implications, under circumstances where the effect of Earth rotation can be ignored.« less

Variational principle for the Navier-Stokes equations.

PubMed

Kerswell, R R

1999-05-01

A variational principle is presented for the Navier-Stokes equations in the case of a contained boundary-driven, homogeneous, incompressible, viscous fluid. Based upon making the fluid's total viscous dissipation over a given time interval stationary subject to the constraint of the Navier-Stokes equations, the variational problem looks overconstrained and intractable. However, introducing a nonunique velocity decomposition, u(x,t)=phi(x,t) + nu(x,t), "opens up" the variational problem so that what is presumed a single allowable point over the velocity domain u corresponding to the unique solution of the Navier-Stokes equations becomes a surface with a saddle point over the extended domain (phi,nu). Complementary or dual variational problems can then be constructed to estimate this saddle point value strictly from above as part of a minimization process or below via a maximization procedure. One of these reduced variational principles is the natural and ultimate generalization of the upper bounding problem developed by Doering and Constantin. The other corresponds to the ultimate Busse problem which now acts to lower bound the true dissipation. Crucially, these reduced variational problems require only the solution of a series of linear problems to produce bounds even though their unique intersection is conjectured to correspond to a solution of the nonlinear Navier-Stokes equations.

Feasibility of a special-purpose computer to solve the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Gritton, E. C.; King, W. S.; Sutherland, I.; Gaines, R. S.; Gazley, C., Jr.; Grosch, C.; Juncosa, M.; Petersen, H.

1978-01-01

Orders-of-magnitude improvements in computer performance can be realized with a parallel array of thousands of fast microprocessors. In this architecture, wiring congestion is minimized by limiting processor communication to nearest neighbors. When certain standard algorithms are applied to a viscous flow problem and existing LSI technology is used, performance estimates of this conceptual design show a dramatic decrease in computational time when compared to the CDC 7600.

Direct numerical simulation of two-dimensional wall-bounded turbulent flows from receptivity stage.

PubMed

Sengupta, T K; Bhaumik, S; Bhumkar, Y G

2012-02-01

Deterministic route to turbulence creation in 2D wall boundary layer is shown here by solving full Navier-Stokes equation by dispersion relation preserving (DRP) numerical methods for flow over a flat plate excited by wall and free stream excitations. Present results show the transition caused by wall excitation is predominantly due to nonlinear growth of the spatiotemporal wave front, even in the presence of Tollmien-Schlichting (TS) waves. The existence and linear mechanism of creating the spatiotemporal wave front was established in Sengupta, Rao and Venkatasubbaiah [Phys. Rev. Lett. 96, 224504 (2006)] via the solution of Orr-Sommerfeld equation. Effects of spatiotemporal front(s) in the nonlinear phase of disturbance evolution have been documented by Sengupta and Bhaumik [Phys. Rev. Lett. 107, 154501 (2011)], where a flow is taken from the receptivity stage to the fully developed 2D turbulent state exhibiting a k(-3) energy spectrum by solving the Navier-Stokes equation without any artifice. The details of this mechanism are presented here for the first time, along with another problem of forced excitation of the boundary layer by convecting free stream vortices. Thus, the excitations considered here are for a zero pressure gradient (ZPG) boundary layer by (i) monochromatic time-harmonic wall excitation and (ii) free stream excitation by convecting train of vortices at a constant height. The latter case demonstrates neither monochromatic TS wave, nor the spatiotemporal wave front, yet both the cases eventually show the presence of k(-3) energy spectrum, which has been shown experimentally for atmospheric dynamics in Nastrom, Gage and Jasperson [Nature 310, 36 (1984)]. Transition by a nonlinear mechanism of the Navier-Stokes equation leading to k(-3) energy spectrum in the inertial subrange is the typical characteristic feature of all 2D turbulent flows. Reproduction of the spectrum noted in atmospheric data (showing dominance of the k(-3) spectrum over the k(-5/3) spectrum in Nastrom et al.) in laboratory scale indicates universality of this spectrum for all 2D turbulent flows. Creation of universal features of 2D turbulence by a deterministic route has been established here for the first time by solving the Navier-Stokes equation without any modeling, as has been reported earlier in the literature by other researchers.

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.

A Unified View of Global Instabilities of Compressible Flow Over Open Cavities

DTIC Science & Technology

2005-06-30

the early work of Rossiter [3], have treated the shear-layer emanating from the upstream comer of the cavity in isolation ( using parallel flow... using a domain-decomposition method. The code has optional equation sets to solve either (i) nonlinear Navier-Stokes, (ii) Navier-Stokes equations...early experments of Maull and East [15]. They used oil flow visualization of surface streamlines on the cavity bottom to show the existence, under certain

A CFD-based aerodynamic design procedure for hypersonic wind-tunnel nozzles

NASA Technical Reports Server (NTRS)

Korte, John J.

1993-01-01

A new procedure which unifies the best of current classical design practices, computational fluid dynamics (CFD), and optimization procedures is demonstrated for designing the aerodynamic lines of hypersonic wind-tunnel nozzles. The new procedure can be used to design hypersonic wind tunnel nozzles with thick boundary layers where the classical design procedure has been shown to break down. An efficient CFD code, which solves the parabolized Navier-Stokes (PNS) equations using an explicit upwind algorithm, is coupled to a least-squares (LS) optimization procedure. A LS problem is formulated to minimize the difference between the computed flow field and the objective function, consisting of the centerline Mach number distribution and the exit Mach number and flow angle profiles. The aerodynamic lines of the nozzle are defined using a cubic spline, the slopes of which are optimized with the design procedure. The advantages of the new procedure are that it allows full use of powerful CFD codes in the design process, solves an optimization problem to determine the new contour, can be used to design new nozzles or improve sections of existing nozzles, and automatically compensates the nozzle contour for viscous effects as part of the unified design procedure. The new procedure is demonstrated by designing two Mach 15, a Mach 12, and a Mach 18 helium nozzles. The flexibility of the procedure is demonstrated by designing the two Mach 15 nozzles using different constraints, the first nozzle for a fixed length and exit diameter and the second nozzle for a fixed length and throat diameter. The computed flow field for the Mach 15 least squares parabolized Navier-Stokes (LS/PNS) designed nozzle is compared with the classically designed nozzle and demonstrates a significant improvement in the flow expansion process and uniform core region.

Generalized INF-SUP condition for Chebyshev approximation of the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bernardi, Christine; Canuto, Claudio; Maday, Yvon

1986-01-01

An abstract mixed problem and its approximation are studied; both are well-posed if and only if several inf-sup conditions are satisfied. These results are applied to a spectral Galerkin method for the Stokes problem in a square, when it is formulated in Chebyshev weighted Sobolev spaces. Finally, a collocation method for the Navier-Stokes equations at Chebyshev nodes is analyzed.

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

From the Highly Compressible Navier-Stokes Equations to Fast Diffusion and Porous Media Equations, Existence of Global Weak Solution for the Quasi-Solutions

NASA Astrophysics Data System (ADS)

Haspot, Boris

2016-06-01

We consider the compressible Navier-Stokes equations for viscous and barotropic fluids with density dependent viscosity. The aim is to investigate mathematical properties of solutions of the Navier-Stokes equations using solutions of the pressureless Navier-Stokes equations, that we call quasi solutions. This regime corresponds to the limit of highly compressible flows. In this paper we are interested in proving the announced result in Haspot (Proceedings of the 14th international conference on hyperbolic problems held in Padova, pp 667-674, 2014) concerning the existence of global weak solution for the quasi-solutions, we also observe that for some choice of initial data (irrotationnal) the quasi solutions verify the porous media, the heat equation or the fast diffusion equations in function of the structure of the viscosity coefficients. In particular it implies that it exists classical quasi-solutions in the sense that they are {C^{∞}} on {(0,T)× {R}N} for any {T > 0}. Finally we show the convergence of the global weak solution of compressible Navier-Stokes equations to the quasi solutions in the case of a vanishing pressure limit process. In particular for highly compressible equations the speed of propagation of the density is quasi finite when the viscosity corresponds to {μ(ρ)=ρ^{α}} with {α > 1}. Furthermore the density is not far from converging asymptotically in time to the Barrenblatt solution of mass the initial density {ρ0}.

Bypass Transitional Flow Calculations Using a Navier-Stokes Solver and Two-Equation Models

NASA Technical Reports Server (NTRS)

Liuo, William W.; Shih, Tsan-Hsing; Povinelli, L. A. (Technical Monitor)

2000-01-01

Bypass transitional flows over a flat plate were simulated using a Navier-Stokes solver and two equation models. A new model for the bypass transition, which occurs in cases with high free stream turbulence intensity (TI), is described. The new transition model is developed by including an intermittency correction function to an existing two-equation turbulence model. The advantages of using Navier-Stokes equations, as opposed to boundary-layer equations, in bypass transition simulations are also illustrated. The results for two test flows over a flat plate with different levels of free stream turbulence intensity are reported. Comparisons with the experimental measurements show that the new model can capture very well both the onset and the length of bypass transition.

Electroosmotic flow in capillary channels filled with nonconstant viscosity electrolytes: exact solution of the Navier-Stokes equation.

PubMed

Otevrel, Marek; Klepárník, Karel

2002-10-01

The partial differential equation describing unsteady velocity profile of electroosmotic flow (EOF) in a cylindrical capillary filled with a nonconstant viscosity electrolyte was derived. Analytical solution, based on the general Navier-Stokes equation, was found for constant viscosity electrolytes using the separation of variables (Fourier method). For the case of a nonconstant viscosity electrolyte, the steady-state velocity profile was calculated assuming that the viscosity decreases exponentially in the direction from the wall to the capillary center. Since the respective equations with nonconstant viscosity term are not solvable in general, the method of continuous binding conditions was used to solve this problem. In this method, an arbitrary viscosity profile can be modeled. The theoretical conclusions show that the relaxation times at which an EOF approaches the steady state are too short to have an impact on a separation process in any real systems. A viscous layer at the wall affects EOF significantly, if it is thicker than the Debye length of the electric double layer. The presented description of the EOF dynamics is applicable to any microfluidic systems.

Flow and Turbulence Modeling and Computation of Shock Buffet Onset for Conventional and Supercritical Airfoils

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

1998-01-01

Flow and turbulence models applied to the problem of shock buffet onset are studied. The accuracy of the interactive boundary layer and the thin-layer Navier-Stokes equations solved with recent upwind techniques using similar transport field equation turbulence models is assessed for standard steady test cases, including conditions having significant shock separation. The two methods are found to compare well in the shock buffet onset region of a supercritical airfoil that involves strong trailing-edge separation. A computational analysis using the interactive-boundary layer has revealed a Reynolds scaling effect in the shock buffet onset of the supercritical airfoil, which compares well with experiment. The methods are next applied to a conventional airfoil. Steady shock-separated computations of the conventional airfoil with the two methods compare well with experiment. Although the interactive boundary layer computations in the shock buffet region compare well with experiment for the conventional airfoil, the thin-layer Navier-Stokes computations do not. These findings are discussed in connection with possible mechanisms important in the onset of shock buffet and the constraints imposed by current numerical modeling techniques.

Composite solvers for linear saddle point problems arising from the incompressible Stokes equations with highly heterogeneous viscosity structure

NASA Astrophysics Data System (ADS)

Sanan, P.; Schnepp, S. M.; May, D.; Schenk, O.

2014-12-01

Geophysical applications require efficient forward models for non-linear Stokes flow on high resolution spatio-temporal domains. The bottleneck in applying the forward model is solving the linearized, discretized Stokes problem which takes the form of a large, indefinite (saddle point) linear system. Due to the heterogeniety of the effective viscosity in the elliptic operator, devising effective preconditioners for saddle point problems has proven challenging and highly problem-dependent. Nevertheless, at least three approaches show promise for preconditioning these difficult systems in an algorithmically scalable way using multigrid and/or domain decomposition techniques. The first is to work with a hierarchy of coarser or smaller saddle point problems. The second is to use the Schur complement method to decouple and sequentially solve for the pressure and velocity. The third is to use the Schur decomposition to devise preconditioners for the full operator. These involve sub-solves resembling inexact versions of the sequential solve. The choice of approach and sub-methods depends crucially on the motivating physics, the discretization, and available computational resources. Here we examine the performance trade-offs for preconditioning strategies applied to idealized models of mantle convection and lithospheric dynamics, characterized by large viscosity gradients. Due to the arbitrary topological structure of the viscosity field in geodynamical simulations, we utilize low order, inf-sup stable mixed finite element spatial discretizations which are suitable when sharp viscosity variations occur in element interiors. Particular attention is paid to possibilities within the decoupled and approximate Schur complement factorization-based monolithic approaches to leverage recently-developed flexible, communication-avoiding, and communication-hiding Krylov subspace methods in combination with `heavy' smoothers, which require solutions of large per-node sub-problems, well-suited to solution on hybrid computational clusters. To manage the combinatorial explosion of solver options (which include hybridizations of all the approaches mentioned above), we leverage the modularity of the PETSc library.

Multiple-grid convergence acceleration of viscous and inviscid flow computations

NASA Technical Reports Server (NTRS)

Johnson, G. M.

1983-01-01

A multiple-grid algorithm for use in efficiently obtaining steady solution to the Euler and Navier-Stokes equations is presented. The convergence of a simple, explicit fine-grid solution procedure is accelerated on a sequence of successively coarser grids by a coarse-grid information propagation method which rapidly eliminates transients from the computational domain. This use of multiple-gridding to increase the convergence rate results in substantially reduced work requirements for the numerical solution of a wide range of flow problems. Computational results are presented for subsonic and transonic inviscid flows and for laminar and turbulent, attached and separated, subsonic viscous flows. Work reduction factors as large as eight, in comparison to the basic fine-grid algorithm, were obtained. Possibilities for further performance improvement are discussed.

A new Eulerian model for viscous and heat conducting compressible flows

NASA Astrophysics Data System (ADS)

Svärd, Magnus

2018-09-01

In this article, a suite of physically inconsistent properties of the Navier-Stokes equations, associated with the lack of mass diffusion and the definition of velocity, is presented. We show that these inconsistencies are consequences of the Lagrangian derivation that models viscous stresses rather than diffusion. A new model for compressible and diffusive (viscous and heat conducting) flows of an ideal gas, is derived in a purely Eulerian framework. We propose that these equations supersede the Navier-Stokes equations. A few numerical experiments demonstrate some differences and similarities between the new system and the Navier-Stokes equations.

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

NASA Technical Reports Server (NTRS)

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

1988-01-01

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

Computational Hemodynamic Simulation of Human Circulatory System under Altered Gravity

NASA Technical Reports Server (NTRS)

Kim. Chang Sung; Kiris, Cetin; Kwak, Dochan

2003-01-01

A computational hemodynamics approach is presented to simulate the blood flow through the human circulatory system under altered gravity conditions. Numerical techniques relevant to hemodynamics issues are introduced to non-Newtonian modeling for flow characteristics governed by red blood cells, distensible wall motion due to the heart pulse, and capillary bed modeling for outflow boundary conditions. Gravitational body force terms are added to the Navier-Stokes equations to study the effects of gravity on internal flows. Six-type gravity benchmark problems are originally presented to provide the fundamental understanding of gravitational effects on the human circulatory system. For code validation, computed results are compared with steady and unsteady experimental data for non-Newtonian flows in a carotid bifurcation model and a curved circular tube, respectively. This computational approach is then applied to the blood circulation in the human brain as a target problem. A three-dimensional, idealized Circle of Willis configuration is developed with minor arteries truncated based on anatomical data. Demonstrated is not only the mechanism of the collateral circulation but also the effects of gravity on the distensible wall motion and resultant flow patterns.

Stokes drift.

PubMed

van den Bremer, T S; Breivik, Ø

2018-01-28

During its periodic motion, a particle floating at the free surface of a water wave experiences a net drift velocity in the direction of wave propagation, known as the Stokes drift (Stokes 1847 Trans. Camb. Philos. Soc. 8 , 441-455). More generally, the Stokes drift velocity is the difference between the average Lagrangian flow velocity of a fluid parcel and the average Eulerian flow velocity of the fluid. This paper reviews progress in fundamental and applied research on the induced mean flow associated with surface gravity waves since the first description of the Stokes drift, now 170 years ago. After briefly reviewing the fundamental physical processes, most of which have been established for decades, the review addresses progress in laboratory and field observations of the Stokes drift. Despite more than a century of experimental studies, laboratory studies of the mean circulation set up by waves in a laboratory flume remain somewhat contentious. In the field, rapid advances are expected due to increasingly small and cheap sensors and transmitters, making widespread use of small surface-following drifters possible. We also discuss remote sensing of the Stokes drift from high-frequency radar. Finally, the paper discusses the three main areas of application of the Stokes drift: in the coastal zone, in Eulerian models of the upper ocean layer and in the modelling of tracer transport, such as oil and plastic pollution. Future climate models will probably involve full coupling of ocean and atmosphere systems, in which the wave model provides consistent forcing on the ocean surface boundary layer. Together with the advent of new space-borne instruments that can measure surface Stokes drift, such models hold the promise of quantifying the impact of wave effects on the global atmosphere-ocean system and hopefully contribute to improved climate projections.This article is part of the theme issue 'Nonlinear water waves'. © 2017 The Author(s).

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

NASA Technical Reports Server (NTRS)

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

2009-01-01

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

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.

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.

A finite element solver for 3-D compressible viscous flows

NASA Technical Reports Server (NTRS)

Reddy, K. C.; Reddy, J. N.; Nayani, S.

1990-01-01

Computation of the flow field inside a space shuttle main engine (SSME) requires the application of state of the art computational fluid dynamic (CFD) technology. Several computer codes are under development to solve 3-D flow through the hot gas manifold. Some algorithms were designed to solve the unsteady compressible Navier-Stokes equations, either by implicit or explicit factorization methods, using several hundred or thousands of time steps to reach a steady state solution. A new iterative algorithm is being developed for the solution of the implicit finite element equations without assembling global matrices. It is an efficient iteration scheme based on a modified nonlinear Gauss-Seidel iteration with symmetric sweeps. The algorithm is analyzed for a model equation and is shown to be unconditionally stable. Results from a series of test problems are presented. The finite element code was tested for couette flow, which is flow under a pressure gradient between two parallel plates in relative motion. Another problem that was solved is viscous laminar flow over a flat plate. The general 3-D finite element code was used to compute the flow in an axisymmetric turnaround duct at low Mach numbers.

Additive schemes for certain operator-differential equations

NASA Astrophysics Data System (ADS)

Vabishchevich, P. N.

2010-12-01

Unconditionally stable finite difference schemes for the time approximation of first-order operator-differential systems with self-adjoint operators are constructed. Such systems arise in many applied problems, for example, in connection with nonstationary problems for the system of Stokes (Navier-Stokes) equations. Stability conditions in the corresponding Hilbert spaces for two-level weighted operator-difference schemes are obtained. Additive (splitting) schemes are proposed that involve the solution of simple problems at each time step. The results are used to construct splitting schemes with respect to spatial variables for nonstationary Navier-Stokes equations for incompressible fluid. The capabilities of additive schemes are illustrated using a two-dimensional model problem as an example.

Incompressible Navier-Stokes Solvers in Primative Variables and their Applications to Steady and Unsteady Flow Simulations

NASA Technical Reports Server (NTRS)

Kiris, Cetin C.; Kwak, Dochan; Rogers, Stuart E.

2002-01-01

This paper reviews recent progress made in incompressible Navier-Stokes simulation procedures and their application to problems of engineering interest. Discussions are focused on the methods designed for complex geometry applications in three dimensions, and thus are limited to primitive variable formulation. A summary of efforts in flow solver development is given followed by numerical studies of a few example problems of current interest. Both steady and unsteady solution algorithms and their salient features are discussed. Solvers discussed here are based on a structured-grid approach using either a finite -difference or a finite-volume frame work. As a grand-challenge application of these solvers, an unsteady turbopump flow simulation procedure has been developed which utilizes high performance computing platforms. In the paper, the progress toward the complete simulation capability of the turbo-pump for a liquid rocket engine is reported. The Space Shuttle Main Engine (SSME) turbo-pump is used as a test case for evaluation of two parallel computing algorithms that have been implemented in the INS3D code. The relative motion of the grid systems for the rotorstator interaction was obtained using overact grid techniques. Unsteady computations for the SSME turbo-pump, which contains 114 zones with 34.5 million grid points, are carried out on SCSI Origin 3000 systems at NASA Ames Research Center. The same procedure has been extended to the development of NASA-DeBakey Ventricular Assist Device (VAD) that is based on an axial blood pump. Computational, and clinical analysis of this device are presented.

COMOC 2: Two-dimensional aerodynamics sequence, computer program user's guide

NASA Technical Reports Server (NTRS)

Manhardt, P. D.; Orzechowski, J. A.; Baker, A. J.

1977-01-01

The COMOC finite element fluid mechanics computer program system is applicable to diverse problem classes. The two dimensional aerodynamics sequence was established for solution of the potential and/or viscous and turbulent flowfields associated with subsonic flight of elementary two dimensional isolated airfoils. The sequence is constituted of three specific flowfield options in COMOC for two dimensional flows. These include the potential flow option, the boundary layer option, and the parabolic Navier-Stokes option. By sequencing through these options, it is possible to computationally construct a weak-interaction model of the aerodynamic flowfield. This report is the user's guide to operation of COMOC for the aerodynamics sequence.

Analysis of a Stabilized CNLF Method with Fast Slow Wave Splittings for Flow Problems

DOE PAGES

Jiang, Nan; Tran, Hoang A.

2015-04-01

In this work, we study Crank-Nicolson leap-frog (CNLF) methods with fast-slow wave splittings for Navier-Stokes equations (NSE) with a rotation/Coriolis force term, which is a simplification of geophysical flows. We propose a new stabilized CNLF method where the added stabilization completely removes the method's CFL time step condition. A comprehensive stability and error analysis is given. We also prove that for Oseen equations with the rotation term, the unstable mode (for which u(n+1) + u(n-1) equivalent to 0) of CNLF is asymptotically stable. Numerical results are provided to verify the stability and the convergence of the methods.

Numerical simulation of gas distribution in goaf under Y ventilation mode

NASA Astrophysics Data System (ADS)

Li, Shengzhou; Liu, Jun

2018-04-01

Taking the Y type ventilation of the working face as the research object, diffusion equation is introduced to simulate the diffusion characteristics of gas, using Navier-Stokes equation and Brinkman equation to simulate the gas flow in working face and goaf, the physical model of gas flow in coal mining face was established. With numerical simulation software COMSOL multiphysics methods, gas distribution in goaf under Y ventilation mode is simulated and gas distribution of the working face, the upper corner and goaf is analysised. The results show that the Y type ventilation system can effectively improve the corner gas accumulation and overrun problem.

Numerical simulation of fluid flow through simplified blade cascade with prescribed harmonic motion using discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Vimmr, Jan; Bublík, Ondřej; Prausová, Helena; Hála, Jindřich; Pešek, Luděk

2018-06-01

This paper deals with a numerical simulation of compressible viscous fluid flow around three flat plates with prescribed harmonic motion. This arrangement presents a simplified blade cascade with forward wave motion. The aim of this simulation is to determine the aerodynamic forces acting on the flat plates. The mathematical model describing this problem is formed by Favre-averaged system of Navier-Stokes equations in arbitrary Lagrangian-Eulerian (ALE) formulation completed by one-equation Spalart-Allmaras turbulence model. The simulation was performed using the developed in-house CFD software based on discontinuous Galerkin method, which offers high order of accuracy.

Selected computations of transonic cavity flows

NASA Technical Reports Server (NTRS)

Atwood, Christopher A.

1993-01-01

An efficient diagonal scheme implemented in an overset mesh framework has permitted the analysis of geometrically complex cavity flows via the Reynolds averaged Navier-Stokes equations. Use of rapid hyperbolic and algebraic grid methods has allowed simple specification of critical turbulent regions with an algebraic turbulence model. Comparisons between numerical and experimental results are made in two dimensions for the following problems: a backward-facing step; a resonating cavity; and two quieted cavity configurations. In three-dimensions the flow about three early concepts of the stratospheric Observatory For Infrared Astronomy (SOFIA) are compared to wind-tunnel data. Shedding frequencies of resolved shear layer structures are compared against experiment for the quieted cavities. The results demonstrate the progress of computational assessment of configuration safety and performance.

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

NASA Technical Reports Server (NTRS)

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

1986-01-01

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

Comparison of Several Dissipation Algorithms for Central Difference Schemes

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Radespiel, R.; Turkel, E.

1997-01-01

Several algorithms for introducing artificial dissipation into a central difference approximation to the Euler and Navier Stokes equations are considered. The focus of the paper is on the convective upwind and split pressure (CUSP) scheme, which is designed to support single interior point discrete shock waves. This scheme is analyzed and compared in detail with scalar and matrix dissipation (MATD) schemes. Resolution capability is determined by solving subsonic, transonic, and hypersonic flow problems. A finite-volume discretization and a multistage time-stepping scheme with multigrid are used to compute solutions to the flow equations. Numerical results are also compared with either theoretical solutions or experimental data. For transonic airfoil flows the best accuracy on coarse meshes for aerodynamic coefficients is obtained with a simple MATD scheme.

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.

CFD methodology and validation for turbomachinery flows

NASA Astrophysics Data System (ADS)

Hirsch, Ch.

1994-05-01

The essential problem today, in the application of 3D Navier-Stokes simulations to the design and analysis of turbomachinery components, is the validation of the numerical approximation and of the physical models, in particular the turbulence modelling. Although most of the complex 3D flow phenomena occurring in turbomachinery bladings can be captured with relatively coarse meshes, many detailed flow features are dependent on mesh size, on the turbulence and transition models. A brief review of the present state of the art of CFD methodology is given with emphasis on quality and accuracy of numerical approximations related to viscous flow computations. Considerations related to the mesh influence on solution accuracy are stressed. The basic problems of turbulence and transition modelling are discussed next, with a short summary of the main turbulence models and their applications to representative turbomachinery flows. Validations of present turbulence models indicate that none of the available turbulence models is able to predict all the detailed flow behavior in complex flow interactions. In order to identify the phenomena that can be captured on coarser meshes a detailed understanding of the complex 3D flow in compressor and turbines is necessary. Examples of global validations for different flow configurations, representative of compressor and turbine aerodynamics are presented, including secondary and tip clearance flows.

Three-dimensional thermocapillary flow regimes with evaporation

NASA Astrophysics Data System (ADS)

Bekezhanova, V. B.; Goncharova, O. N.

2017-10-01

A three-dimensional problem of evaporative convection in a system of the immiscible media with a common thermocapillary interface is studied. New exact solution, which is a generalization of the Ostroumov - Birikh solution of the Navier - Stokes equations in the Oberbeck - Boussinesq approximation, is presented in order to describe the joint flows of the liquid and gas - vapor mixture in an infinite channel with a rectangular cross-section. The motion occurs in the bulk force field under action of a constant longitudinal temperature gradient. The velocity components depend only on the transverse coordinates. The functions of pressure, temperature and concentration of vapor in the gas are characterized by the linear dependence on the longitudinal coordinate. In the framework of the problem statement, which takes into account diffusive mass flux through the interface and zero vapor flux at the upper boundary of the channel, the influence of the gravity and intensity of the thermal action on flow structure is studied. The original three-dimensional problem is reduced to a chain of two-dimensional problems which are solved numerically with help of modification of the method of alternating directions. Arising flows can be characterized as a translational-rotational motion, under that the symmetrical double, quadruple or sextuple vortex structures are formed. Quantity, shape and structure of the vortexes also depend on properties of the working media.

Wall effects in Stokes experiment with a liquid foam

NASA Astrophysics Data System (ADS)

Gao, Haijing; Subramani, Hariprasad; Harris, Michael; Basaran, Osman

2011-11-01

Liquid foams are widely used in numerous applications ranging from the oil and gas industry to beauty, healthcare, and household products industries. A fundamental understanding of the relationships between the properties of liquid foams and their flow responses is, however, still in its infancy compared to that involving the fluid dynamics of simple fluids. In this talk, the flow of a dry liquid foam around a spherical bead, i.e. the Stokes problem for liquid foams, is studied experimentally. In contrast to previous work (cf. Cantat 2006), the focus of the present research is to probe the effect of a solid wall that is located a few bubble radii from the bead. The new experimental results show that the elastic modulus of dry liquid foams is directly proportional to the surface tension of the foaming agents and inversely proportional to the average bubble size in the foams, in agreement with previous theoretical and experimental studies. The experiments further show that the close proximity of the solid wall causes profound structural changes to the gas bubbles as the foam flows past the bead. A good understanding of these structural changes and how they can affect the elastic modulus of foams can be indispensable in formulating improved models for accurately describing the dynamical response of foams within the realm of continuum mechanics.

Least-squares/parabolized Navier-Stokes procedure for optimizing hypersonic wind tunnel nozzles

NASA Technical Reports Server (NTRS)

Korte, John J.; Kumar, Ajay; Singh, D. J.; Grossman, B.

1991-01-01

A new procedure is demonstrated for optimizing hypersonic wind-tunnel-nozzle contours. The procedure couples a CFD computer code to an optimization algorithm, and is applied to both conical and contoured hypersonic nozzles for the purpose of determining an optimal set of parameters to describe the surface geometry. A design-objective function is specified based on the deviation from the desired test-section flow-field conditions. The objective function is minimized by optimizing the parameters used to describe the nozzle contour based on the solution to a nonlinear least-squares problem. The effect of the changes in the nozzle wall parameters are evaluated by computing the nozzle flow using the parabolized Navier-Stokes equations. The advantage of the new procedure is that it directly takes into account the displacement effect of the boundary layer on the wall contour. The new procedure provides a method for optimizing hypersonic nozzles of high Mach numbers which have been designed by classical procedures, but are shown to produce poor flow quality due to the large boundary layers present in the test section. The procedure is demonstrated by finding the optimum design parameters for a Mach 10 conical nozzle and a Mach 6 and a Mach 15 contoured nozzle.

Particle and Blood Cell Dynamics in Oscillatory Flows Final Report

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

Juan M. Restrepo

2008-09-01

Our aim has been to uncover fundamental aspects of the suspension and dislodgement of particles in wall-bounded oscillatory flows, in flows characterized by Reynolds numbers en- compassing the situation found in rivers and near shores (and perhaps in some industrial processes). Our research tools are computational and our coverage of parameter space fairly broad. Computational means circumvent many complications that make the measurement of the dynamics of particles in a laboratory setting an impractical task, especially on the broad range of parameter space we plan to report upon. The impact of this work on the geophysical problem of sedimentation ismore » boosted considerably by the fact that the proposed calculations can be considered ab-initio, in the sense that little to no modeling is done in generating dynamics of the particles and of the moving fluid: we use a three-dimensional Navier Stokes solver along with straightforward boundry conditions. Hence, to the extent that Navier Stokes is a model for an ideal incompressible isotropic Newtonian fluid, the calculations yield benchmark values for such things as the drag, buoyancy, and lift of particles, in a highly controlled environment. Our approach will be to make measurements of the lift, drag, and buoyancy of particles, by considering progressively more complex physical configurations and physics.« less

Modelling uncertainty in incompressible flow simulation using Galerkin based generalized ANOVA

NASA Astrophysics Data System (ADS)

Chakraborty, Souvik; Chowdhury, Rajib

2016-11-01

This paper presents a new algorithm, referred to here as Galerkin based generalized analysis of variance decomposition (GG-ANOVA) for modelling input uncertainties and its propagation in incompressible fluid flow. The proposed approach utilizes ANOVA to represent the unknown stochastic response. Further, the unknown component functions of ANOVA are represented using the generalized polynomial chaos expansion (PCE). The resulting functional form obtained by coupling the ANOVA and PCE is substituted into the stochastic Navier-Stokes equation (NSE) and Galerkin projection is employed to decompose it into a set of coupled deterministic 'Navier-Stokes alike' equations. Temporal discretization of the set of coupled deterministic equations is performed by employing Adams-Bashforth scheme for convective term and Crank-Nicolson scheme for diffusion term. Spatial discretization is performed by employing finite difference scheme. Implementation of the proposed approach has been illustrated by two examples. In the first example, a stochastic ordinary differential equation has been considered. This example illustrates the performance of proposed approach with change in nature of random variable. Furthermore, convergence characteristics of GG-ANOVA has also been demonstrated. The second example investigates flow through a micro channel. Two case studies, namely the stochastic Kelvin-Helmholtz instability and stochastic vortex dipole, have been investigated. For all the problems results obtained using GG-ANOVA are in excellent agreement with benchmark solutions.

Pore-scale modeling of moving contact line problems in immiscible two-phase flow

NASA Astrophysics Data System (ADS)

Kucala, Alec; Noble, David; Martinez, Mario

2016-11-01

Accurate modeling of moving contact line (MCL) problems is imperative in predicting capillary pressure vs. saturation curves, permeability, and preferential flow paths for a variety of applications, including geological carbon storage (GCS) and enhanced oil recovery (EOR). Here, we present a model for the moving contact line using pore-scale computational fluid dynamics (CFD) which solves the full, time-dependent Navier-Stokes equations using the Galerkin finite-element method. The MCL is modeled as a surface traction force proportional to the surface tension, dependent on the static properties of the immiscible fluid/solid system. We present a variety of verification test cases for simple two- and three-dimensional geometries to validate the current model, including threshold pressure predictions in flows through pore-throats for a variety of wetting angles. Simulations involving more complex geometries are also presented to be used in future simulations for GCS and EOR problems. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Skin friction enhancement in a model problem of undulatory swimming

NASA Astrophysics Data System (ADS)

Ehrenstein, Uwe; Eloy, Christophe

2013-10-01

To calculate the energy costs of swimming, it is crucial to evaluate the drag force originating from skin friction. In this paper we examine the assumption, known as the 'Bone-Lighthill boundary-layer thinning hypothesis', that undulatory swimming motions induce a drag increase because of the compression of the boundary layer. Studying analytically an incoming flow along a flat plate moving at a normal velocity as a limit case of a yawed cylinder in uniform flow under the laminar boundary layer assumption, we demonstrate that the longitudinal drag scales as the square root of the normal velocity component. This analytical prediction is interpreted in the light of a three-dimensional numerical simulation result for a plate of finite length and width. An analogous two-dimensional Navier-Stokes problem by artificially accelerating the flow in a channel of finite height is proposed and solved numerically, showing the robustness of the analytical results. Solving the problem for an undulatory plate motion similar to fish swimming, we find a drag enhancement which can be estimated to be of the order of 20 %.

A rigorous solution of the Navier-Stokes equations for unsteady viscous flow at high Reynolds numbers around oscillating airfoils

NASA Technical Reports Server (NTRS)

Bratanow, T.; Aksu, H.; Spehert, T.

1975-01-01

A method based on the Navier-Stokes equations was developed for analyzing the unsteady incompressible viscous flow around oscillating airfoils at high Reynolds numbers. The Navier-Stokes equations have been integrated in their classical Helmholtz vorticity transport equation form, and the instantaneous velocity field at each time step was determined by the solution of Poisson's equation. A refined finite element was utilized to allow for a conformable solution of the stream function and its first space derivatives at the element interfaces. A corresponding set of accurate boundary conditions was applied; thus obtaining a rigorous solution for the velocity field. The details of the computational procedure and examples of computed results describing the unsteady flow characteristics around the airfoil are presented.

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.

Clustering and relative velocity of heavy particles under gravitational settling in isotropic turbulent flows

NASA Astrophysics Data System (ADS)

Jin, Guodong; He, Guo-Wei

2015-11-01

Clustering and intermittency in radial relative velocity (RRV) of heavy particles of same size settling in turbulent flows can be remarkably changed due to gravity. Clustering is monotonically reduced at Stokes number less than 1 under gravity due to the disability of the centrifugal mechanism, however it is non-monotonically enhanced at Stokes number greater than 1 due to the multiplicative amplification in the case that the proposed effective Kubo number is less than 1. Although gravity causes monotonical reduction in the rms of RRV of particles at a given Stokes number with decreasing Froude number, the variation tendency in the tails of standardized PDF of RRV versus Froude number is obviously different: the tails become narrower at a small Stokes number, while they become broader at a large Stokes number. The mechanism of this variation stems from the compromise between the following two competing factors. The mitigation of correlation of particle positions and the regions of high strain rate which are more intermittent reduces the intermittency in RRV at small Stokes numbers, while the significant reduction in the backward-in-time relative separations will make particle pairs see small-scale structures, leading to a higher intermittency in RRV at large Stokes numbers. NSAF of China (grant number U1230126); NSFC (grant numbers 11072247 and 11232011).

Computation of Discrete Slanted Hole Film Cooling Flow Using the Navier-Stokes Equations.

DTIC Science & Technology

1982-07-01

7 -121 796 COMPUTATION OF DISCRETE SLANTED HOLE FILM COOLING FLOW i/ i USING THE NAVIER- ..(U) CIENTIFIC RESEARCH ASSOCIATES INC GLASTONBURY CT H...V U U6-IMSA P/ & .OS,-TR. 82-1004 Report R82-910002-4 / COMPUTATION OF DISCRETE SLAMED HOLE FILM COOLING FLOW ( USING THE XAVIER-STOKES EQUATIONS H...CL SIT %GE (f.en Dae Entere)04 REPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM REPORT NUMBER 2. GOVT ACCESSION NO] S. RECIPIENT’S CATALOG NUMBERAO

Boundary Asymptotic Analysis for an Incompressible Viscous Flow: Navier Wall Laws

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

El Jarroudi, M.; Brillard, A.

2008-06-15

We consider a new way of establishing Navier wall laws. Considering a bounded domain {omega} of R{sup N}, N=2,3, surrounded by a thin layer {sigma}{sub {epsilon}}, along a part {gamma}{sub 2} of its boundary {partial_derivative}{omega}, we consider a Navier-Stokes flow in {omega} union {partial_derivative}{omega} union {sigma}{sub {epsilon}} with Reynolds' number of order 1/{epsilon} in {sigma}{sub {epsilon}}. Using {gamma}-convergence arguments, we describe the asymptotic behaviour of the solution of this problem and get a general Navier law involving a matrix of Borel measures having the same support contained in the interface {gamma}{sub 2}. We then consider two special cases where wemore » characterize this matrix of measures. As a further application, we consider an optimal control problem within this context.« less

Rotorcraft Downwash Flow Field Study to Understand the Aerodynamics of Helicopter Brownout

NASA Technical Reports Server (NTRS)

Wadcock, Alan J.; Ewing, Lindsay A.; Solis, Eduardo; Potsdam, Mark; Rajagopalan, Ganesh

2008-01-01

Rotorcraft brownout is caused by the entrainment of dust and sand particles in helicopter downwash, resulting in reduced pilot visibility during low, slow flight and landing. Recently, brownout has become a high-priority problem for military operations because of the risk to both pilot and equipment. Mitigation of this problem has focused on flight controls and landing maneuvers, but current knowledge and experimental data describing the aerodynamic contribution to brownout are limited. This paper focuses on downwash characteristics of a UH-60 Blackhawk as they pertain to particle entrainment and brownout. Results of a full-scale tuft test are presented and used to validate a high-fidelity Navier-Stokes computational fluid dynamics (CFD) calculation. CFD analysis for an EH-101 Merlin helicopter is also presented, and its flow field characteristics are compared with those of the UH-60.

A Numerical Study of Non-hydrostatic Shallow Flows in Open Channels

NASA Astrophysics Data System (ADS)

Zerihun, Yebegaeshet T.

2017-06-01

The flow field of many practical open channel flow problems, e.g. flow over natural bed forms or hydraulic structures, is characterised by curved streamlines that result in a non-hydrostatic pressure distribution. The essential vertical details of such a flow field need to be accounted for, so as to be able to treat the complex transition between hydrostatic and non-hydrostatic flow regimes. Apparently, the shallow-water equations, which assume a mild longitudinal slope and negligible vertical acceleration, are inappropriate to analyse these types of problems. Besides, most of the current Boussinesq-type models do not consider the effects of turbulence. A novel approach, stemming from the vertical integration of the Reynolds-averaged Navier-Stokes equations, is applied herein to develop a non-hydrostatic model which includes terms accounting for the effective stresses arising from the turbulent characteristics of the flow. The feasibility of the proposed model is examined by simulating flow situations that involve non-hydrostatic pressure and/or nonuniform velocity distributions. The computational results for free-surface and bed pressure profiles exhibit good correlations with experimental data, demonstrating that the present model is capable of simulating the salient features of free-surface flows over sharply-curved overflow structures and rigid-bed dunes.

Shape Optimization for Navier-Stokes Equations with Algebraic Turbulence Model: Existence Analysis

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

Bulicek, Miroslav; Haslinger, Jaroslav; Malek, Josef

2009-10-15

We study a shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to an optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by a generalized stationary Navier-Stokes system with nontrivial mixed boundary conditions. In this paper we prove the existence of solutions both to the generalized Navier-Stokes system and tomore » the shape optimization problem.« less

Hypersonic flow analysis

NASA Technical Reports Server (NTRS)

Chow, Chuen-Yen; Ryan, James S.

1987-01-01

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

Lagrangian turbulence near walls: Structures and mixing in admissible model flows

NASA Astrophysics Data System (ADS)

Ottino, J. M.

1989-05-01

The general objective of work during this period was to bridge the gap between modern ideas from dynamical systems and chaos and more traditional approaches to turbulence. In order to reach this objective we conducted theoretical and computational work on two systems: a perturbed Kelvin cat eyes flow, and prototype solutions of the Navier-Stokes equations near solid walls. The main results obtained are two-fold: production flows capable of producing complex distributions of vorticity, and constructed flow fields, based on solutions of the Navier Stokes equations, which are capable of displaying both Eulerian and Lagrangian turbulence.

Control and instanton trajectories for random transitions in turbulent flows

NASA Astrophysics Data System (ADS)

Bouchet, Freddy; Laurie, Jason; Zaboronski, Oleg

2011-12-01

Many turbulent systems exhibit random switches between qualitatively different attractors. The transition between these bistable states is often an extremely rare event, that can not be computed through DNS, due to complexity limitations. We present results for the calculation of instanton trajectories (a control problem) between non-equilibrium stationary states (attractors) in the 2D stochastic Navier-Stokes equations. By representing the transition probability between two states using a path integral formulation, we can compute the most probable trajectory (instanton) joining two non-equilibrium stationary states. Technically, this is equivalent to the minimization of an action, which can be related to a fluid mechanics control problem.

Computations of Drop Collision and Coalescence

NASA Technical Reports Server (NTRS)

Tryggvason, Gretar; Juric, Damir; Nas, Selman; Mortazavi, Saeed

1996-01-01

Computations of drops collisions, coalescence, and other problems involving drops are presented. The computations are made possible by a finite difference/front tracking technique that allows direct solutions of the Navier-Stokes equations for a multi-fluid system with complex, unsteady internal boundaries. This method has been used to examine the various collision modes for binary collisions of drops of equal size, mixing of two drops of unequal size, behavior of a suspension of drops in linear and parabolic shear flows, and the thermal migration of several drops. The key results from these simulations are reviewed. Extensions of the method to phase change problems and preliminary results for boiling are also shown.

Numerics made easy: solving the Navier-Stokes equation for arbitrary channel cross-sections using Microsoft Excel.

PubMed

Richter, Christiane; Kotz, Frederik; Giselbrecht, Stefan; Helmer, Dorothea; Rapp, Bastian E

2016-06-01

The fluid mechanics of microfluidics is distinctively simpler than the fluid mechanics of macroscopic systems. In macroscopic systems effects such as non-laminar flow, convection, gravity etc. need to be accounted for all of which can usually be neglected in microfluidic systems. Still, there exists only a very limited selection of channel cross-sections for which the Navier-Stokes equation for pressure-driven Poiseuille flow can be solved analytically. From these equations, velocity profiles as well as flow rates can be calculated. However, whenever a cross-section is not highly symmetric (rectangular, elliptical or circular) the Navier-Stokes equation can usually not be solved analytically. In all of these cases, numerical methods are required. However, in many instances it is not necessary to turn to complex numerical solver packages for deriving, e.g., the velocity profile of a more complex microfluidic channel cross-section. In this paper, a simple spreadsheet analysis tool (here: Microsoft Excel) will be used to implement a simple numerical scheme which allows solving the Navier-Stokes equation for arbitrary channel cross-sections.

Finite volume solution for two-phase flow in a straight capillary

NASA Astrophysics Data System (ADS)

Yelkhovsky, Alexander; Pinczewski, W. Val

2018-04-01

The problem of two-phase flow in straight capillaries of polygonal cross section displays many of the dynamic characteristics of rapid interfacial motions associated with pore-scale displacements in porous media. Fluid inertia is known to be important in these displacements but is usually ignored in network models commonly used to predict macroscopic flow properties. This study presents a numerical model for two-phase flow which describes the spatial and temporal evolution of the interface between the fluids. The model is based on an averaged Navier-Stokes equation and is shown to be successful in predicting the complex dynamics of both capillary rise in round capillaries and imbibition along the corners of polygonal capillaries. The model can form the basis for more realistic network models which capture the effect of capillary, viscous, and inertial forces on pore-scale interfacial dynamics and consequent macroscopic flow properties.

Physics and (patho)physiology in confined flows: from colloidal patterns to cytoplasmic rheology and sickle cell anemia

NASA Astrophysics Data System (ADS)

Mahadevan, L.

2015-03-01

I will discuss a few problems that involve the interaction of fluids and solids in confined spaces. (i) Jamming in pressure-driven suspension flows that show a transition from Stokes flows to Darcy flows as the solids start to lock, as in evaporative patterning in colloids (e.g. coffee stain formation) .(ii) Jamming and clogging of red blood cells, as in sickle-cell pathophysiology, with implications for other diseases that involve jamming. (iii) The mechanical response of crowded networks of filaments bathed in a fluid, as in the cytoskeleton, that can be described by poroelasticity theory. In each case, I will show how simple theories of multiphase flow and deformation can be used to explain a range of experimental observations, while failing to account for others, along with some thoughts on how to improve them.

A numerical solution of the supersonic flow over a rearward facing step with transverse non-reacting hydrogen injection

NASA Technical Reports Server (NTRS)

Berman, H. A.; Anderson, J. D., Jr.; Drummond, J. P.

1982-01-01

The present investigation represents an application of computational fluid dynamics to a problem associated with the flow in the combustor region of a supersonic combustion ramjet engine (scramjet). The governing equations are considered, taking into account the Navier-Stokes equations, a molecular viscosity calculation, the molecular thermal conductivity, molecular diffusion, and a turbulence model. The employed numerical solution is patterned after the explicit, time-dependent, unsplit, predictor-corrector, finite-difference method given by MacCormack (1969). The calculation is concerned with the supersonic flow over a rearward-facing step with transverse H2 injection at conditions germane to the combustor region of a scramjet engine. The H2 jet acts as an effective body which essentially shields the primary flow from the rearward-facing step, thus substantially changing the wave pattern in the primary flow.

Simulation of dilute polymeric fluids in a three-dimensional contraction using a multiscale FENE model

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

Griebel, M., E-mail: griebel@ins.uni-bonn.de, E-mail: ruettgers@ins.uni-bonn.de; Rüttgers, A., E-mail: griebel@ins.uni-bonn.de, E-mail: ruettgers@ins.uni-bonn.de

The multiscale FENE model is applied to a 3D square-square contraction flow problem. For this purpose, the stochastic Brownian configuration field method (BCF) has been coupled with our fully parallelized three-dimensional Navier-Stokes solver NaSt3DGPF. The robustness of the BCF method enables the numerical simulation of high Deborah number flows for which most macroscopic methods suffer from stability issues. The results of our simulations are compared with that of experimental measurements from literature and show a very good agreement. In particular, flow phenomena such as a strong vortex enhancement, streamline divergence and a flow inversion for highly elastic flows are reproduced.more » Due to their computational complexity, our simulations require massively parallel computations. Using a domain decomposition approach with MPI, the implementation achieves excellent scale-up results for up to 128 processors.« less

Numerical simulation of transient hypervelocity flow in an expansion tube

NASA Technical Reports Server (NTRS)

Jacobs, P. A.

1992-01-01

Several numerical simulations of the transient flow of helium in an expansion tube are presented. The aim of the exercise is to provide further information on the operational problems of the NASA Langley expansion tube. The calculations were performed with an axisymmetric Navier-Stokes code based on a finite-volume formulation and upwinding techniques. Although laminar flow and ideal bursting of the diaphragms was assumed, the simulations showed some of the important features seen in the experiments. In particular, the discontinuity in the tube diameter at the primary diaphragm station introduced a transverse perturbation to the expanding driver gas, and this perturbation was seen to propagate into the test gas under some flow conditions. The disturbances seen in the test flow can be characterized as either 'small-amplitude' noise possibly introduced during shock compression or 'large-amplitude' noise associated with the passage of the reflected head of the unsteady expansion.

Computational fluid dynamics: An engineering tool?

NASA Astrophysics Data System (ADS)

Anderson, J. D., Jr.

1982-06-01

Computational fluid dynamics in general, and time dependent finite difference techniques in particular, are examined from the point of view of direct engineering applications. Examples are given of the supersonic blunt body problem and gasdynamic laser calculations, where such techniques are clearly engineering tools. In addition, Navier-Stokes calculations of chemical laser flows are discussed as an example of a near engineering tool. Finally, calculations of the flowfield in a reciprocating internal combustion engine are offered as a promising future engineering application of computational fluid dynamics.

Research in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Murman, Earll M.

1987-01-01

The numerical integration of quasi-one-dimensional unsteady flow problems which involve finite rate chemistry are discussed, and are expressed in terms of conservative form Euler and species conservation equations. Hypersonic viscous calculations for delta wing geometries is also examined. The conical Navier-Stokes equations model was selected in order to investigate the effects of viscous-inviscid interations. The more complete three-dimensional model is beyond the available computing resources. The flux vector splitting method with van Leer's MUSCL differencing is being used. Preliminary results were computed for several conditions.

A multidomain spectral collocation method for the Stokes problem

NASA Technical Reports Server (NTRS)

Landriani, G. Sacchi; Vandeven, H.

1989-01-01

A multidomain spectral collocation scheme is proposed for the approximation of the two-dimensional Stokes problem. It is shown that the discrete velocity vector field is exactly divergence-free and we prove error estimates both for the velocity and the pressure.

An investigation into inflection-point instability in the entrance region of a pulsating pipe flow

PubMed Central

Wang, R. H.; Jian, T. W.; Hsu, Y. T.

2017-01-01

This paper investigates the inflection-point instability that governs the flow disturbance initiated in the entrance region of a pulsating pipe flow. Under such a flow condition, the flow instability grows within a certain phase region in a pulsating cycle, during which the inflection point in the unsteady mean flow lifts away from the viscous effect-dominated region known as the Stokes layer. The characteristic frequency of the instability is found to be in agreement with that predicted by the mixing-layer model. In comparison with those cases not falling in this category, it is further verified that the flow phenomenon will take place only if the inflection point lifts away sufficiently from the Stokes layer. PMID:28265188

A cell-vertex multigrid method for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Radespiel, R.

1989-01-01

A cell-vertex scheme for the Navier-Stokes equations, which is based on central difference approximations and Runge-Kutta time stepping, is described. Using local time stepping, implicit residual smoothing, a multigrid method, and carefully controlled artificial dissipative terms, very good convergence rates are obtained for a wide range of two- and three-dimensional flows over airfoils and wings. The accuracy of the code is examined by grid refinement studies and comparison with experimental data. For an accurate prediction of turbulent flows with strong separations, a modified version of the nonequilibrium turbulence model of Johnson and King is introduced, which is well suited for an implementation into three-dimensional Navier-Stokes codes. It is shown that the solutions for three-dimensional flows with strong separations can be dramatically improved, when a nonequilibrium model of turbulence is used.

Transitioning from a single-phase fluid to a porous medium: a boundary layer approach

NASA Astrophysics Data System (ADS)

Dalwadi, Mohit P.; Chapman, S. Jon; Oliver, James M.; Waters, Sarah L.

2014-11-01

Pressure-driven laminar channel flow is a classic problem in fluid mechanics, and the resultant Poiseuille flow is one of the few exact solutions to the Navier-Stokes equations. If the channel interior is a porous medium (governed by Darcy's law) rather than a single-phase fluid, the resultant behaviour is plug flow. But what happens when these two flow regions are coupled, as is the case for industrial membrane filtration systems or biological tissue engineering problems? How does one flow transition to the other? We use asymptotic methods to investigate pressure-driven flow through a long channel completely blocked by a finite-length porous obstacle. We analytically solve for the flow at both small and large Reynolds number (whilst remaining within the laminar regime). The boundary layer structure is surprisingly intricate for large Reynolds number. In that limit, the structure is markedly different depending on whether there is inflow or outflow through the porous medium, there being six asymptotic regions for inflow and three for outflow. We have extended this result to a wide class of 3D porous obstacles within a Hele-Shaw cell. We obtain general boundary conditions to couple the outer flows, and find that these conditions are far from obvious at higher order.

ARC-2012-ACD12-0020-005

NASA Image and Video Library

2012-02-10

Then and Now: These images illustrate the dramatic improvement in NASA computing power over the last 23 years, and its effect on the number of grid points used for flow simulations. At left, an image from the first full-body Navier-Stokes simulation (1988) of an F-16 fighter jet showing pressure on the aircraft body, and fore-body streamlines at Mach 0.90. This steady-state solution took 25 hours using a single Cray X-MP processor to solve the 500,000 grid-point problem. Investigator: Neal Chaderjian, NASA Ames Research Center At right, a 2011 snapshot from a Navier-Stokes simulation of a V-22 Osprey rotorcraft in hover. The blade vortices interact with the smaller turbulent structures. This very detailed simulation used 660 million grid points, and ran on 1536 processors on the Pleiades supercomputer for 180 hours. Investigator: Neal Chaderjian, NASA Ames Research Center; Image: Tim Sandstrom, NASA Ames Research Center

A mixed volume grid approach for the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Coirier, William J.; Jorgenson, Philip C. E.

1996-01-01

An approach for solving the compressible Euler and Navier-Stokes equations upon meshes composed of nearly arbitrary polyhedra is described. Each polyhedron is constructed from an arbitrary number of triangular and quadrilateral face elements, allowing the unified treatment of tetrahedral, prismatic, pyramidal, and hexahedral cells, as well the general cut cells produced by Cartesian mesh approaches. The basics behind the numerical approach and the resulting data structures are described. The accuracy of the mixed volume grid approach is assessed by performing a grid refinement study upon a series of hexahedral, tetrahedral, prismatic, and Cartesian meshes for an analytic inviscid problem. A series of laminar validation cases are made, comparing the results upon differing grid topologies to each other, to theory, and experimental data. A computation upon a prismatic/tetrahedral mesh is made simulating the laminar flow over a wall/cylinder combination.

Stokes paradox in electronic Fermi liquids

NASA Astrophysics Data System (ADS)

Lucas, Andrew

2017-03-01

The Stokes paradox is the statement that in a viscous two-dimensional fluid, the "linear response" problem of fluid flow around an obstacle is ill posed. We present a simple consequence of this paradox in the hydrodynamic regime of a Fermi liquid of electrons in two-dimensional metals. Using hydrodynamics and kinetic theory, we estimate the contribution of a single cylindrical obstacle to the global electrical resistance of a material, within linear response. Momentum relaxation, present in any realistic electron liquid, resolves the classical paradox. Nonetheless, this paradox imprints itself in the resistance, which can be parametrically larger than predicted by Ohmic transport theory. We find a remarkably rich set of behaviors, depending on whether or not the quasiparticle dynamics in the Fermi liquid should be treated as diffusive, hydrodynamic, or ballistic on the length scale of the obstacle. We argue that all three types of behavior are observable in present day experiments.

A least-squares finite element method for 3D incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Lin, T. L.; Hou, Lin-Jun; Povinelli, Louis A.

1993-01-01

The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations, and results in symmetric, positive definite algebraic system. An additional compatibility equation, i.e., the divergence of vorticity vector should be zero, is included to make the first-order system elliptic. The Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. The flow in a half of 3D cubic cavity is calculated at Re = 100, 400, and 1,000 with 50 x 52 x 25 trilinear elements. The Taylor-Gortler-like vortices are observed at Re = 1,000.

Prospects for computing airfoil aerodynamics with Reynolds averaged Navier-Stokes codes

NASA Technical Reports Server (NTRS)

Deiwert, G. S.; Bailey, H. E.

1979-01-01

The Reynolds averaged Navier-Stokes equations are solved numerically for a variety of transonic airfoil configurations where viscous phenomena are important. Illustrative examples include flows past sensitive geometries, Reynolds number effects, and buffet phenomena.

Two-boundary grid generation for the solution of the three dimensional compressible Navier-Stokes equations. Ph.D. Thesis - Old Dominion Univ.

NASA Technical Reports Server (NTRS)

Smith, R. E.

1981-01-01

A grid generation technique called the two boundary technique is developed and applied for the solution of the three dimensional Navier-Stokes equations. The Navier-Stokes equations are transformed from a cartesian coordinate system to a computational coordinate system, and the grid generation technique provides the Jacobian matrix describing the transformation. The two boundary technique is based on algebraically defining two distinct boundaries of a flow domain and the distribution of the grid is achieved by applying functions to the uniform computational grid which redistribute the computational independent variables and consequently concentrate or disperse the grid points in the physical domain. The Navier-Stokes equations are solved using a MacCormack time-split technique. Grids and supersonic laminar flow solutions are obtained for a family of three dimensional corners and two spike-nosed bodies.

Rarefaction and Non-equilibrium Effects in Hypersonic Flows about Leading Edges of Small Bluntness

NASA Astrophysics Data System (ADS)

Ivanov, Mikhail; Khotyanovsky, Dmitry; Kudryavtsev, Alexey; Shershnev, Anton; Bondar, Yevgeniy; Yonemura, Shigeru

2011-05-01

A hypersonic flow about a cylindrically blunted thick plate at a zero angle of attack is numerically studied with the kinetic (DSMC) and continuum (Navier-Stokes equations) approaches. The Navier-Stokes equations with velocity slip and temperature jump boundary conditions correctly predict the flow fields and surface parameters for values of the Knudsen number (based on the radius of leading edge curvature) smaller than 0.1. The results of computations demonstrate significant effects of the entropy layer on the boundary layer characteristics.

Navier-Stokes calculations for DFVLR F5-wing in wind tunnel using Runge-Kutta time-stepping scheme

NASA Technical Reports Server (NTRS)

Vatsa, V. N.; Wedan, B. W.

1988-01-01

A three-dimensional Navier-Stokes code using an explicit multistage Runge-Kutta type of time-stepping scheme is used for solving the transonic flow past a finite wing mounted inside a wind tunnel. Flow past the same wing in free air was also computed to assess the effect of wind-tunnel walls on such flows. Numerical efficiency is enhanced through vectorization of the computer code. A Cyber 205 computer with 32 million words of internal memory was used for these computations.

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.

Compressible Navier-Stokes equations: A study of leading edge effects

NASA Technical Reports Server (NTRS)

Hariharan, S. I.; Karbhari, P. R.

1987-01-01

A computational method is developed that allows numerical calculations of the time dependent compressible Navier-Stokes equations.The current results concern a study of flow past a semi-infinite flat plate.Flow develops from given inflow conditions upstream and passes over the flat plate to leave the computational domain without reflecting at the downstream boundary. Leading edge effects are included in this paper. In addition, specification of a heated region which gets convected with the flow is considered. The time history of this convection is obtained, and it exhibits a wave phenomena.

On the scalability of the Albany/FELIX first-order Stokes approximation ice sheet solver for large-scale simulations of the Greenland and Antarctic ice sheets

DOE PAGES

Tezaur, Irina K.; Tuminaro, Raymond S.; Perego, Mauro; ...

2015-01-01

We examine the scalability of the recently developed Albany/FELIX finite-element based code for the first-order Stokes momentum balance equations for ice flow. We focus our analysis on the performance of two possible preconditioners for the iterative solution of the sparse linear systems that arise from the discretization of the governing equations: (1) a preconditioner based on the incomplete LU (ILU) factorization, and (2) a recently-developed algebraic multigrid (AMG) preconditioner, constructed using the idea of semi-coarsening. A strong scalability study on a realistic, high resolution Greenland ice sheet problem reveals that, for a given number of processor cores, the AMG preconditionermore » results in faster linear solve times but the ILU preconditioner exhibits better scalability. In addition, a weak scalability study is performed on a realistic, moderate resolution Antarctic ice sheet problem, a substantial fraction of which contains floating ice shelves, making it fundamentally different from the Greenland ice sheet problem. We show that as the problem size increases, the performance of the ILU preconditioner deteriorates whereas the AMG preconditioner maintains scalability. This is because the linear systems are extremely ill-conditioned in the presence of floating ice shelves, and the ill-conditioning has a greater negative effect on the ILU preconditioner than on the AMG preconditioner.« less

Turbine Vane External Heat Transfer. Volume 2. Numerical Solutions of the Navier-stokes Equations for Two- and Three-dimensional Turbine Cascades with Heat Transfer

NASA Technical Reports Server (NTRS)

Yang, R. J.; Weinberg, B. C.; Shamroth, S. J.; Mcdonald, H.

1985-01-01

The application of the time-dependent ensemble-averaged Navier-Stokes equations to transonic turbine cascade flow fields was examined. In particular, efforts focused on an assessment of the procedure in conjunction with a suitable turbulence model to calculate steady turbine flow fields using an O-type coordinate system. Three cascade configurations were considered. Comparisons were made between the predicted and measured surface pressures and heat transfer distributions wherever available. In general, the pressure predictions were in good agreement with the data. Heat transfer calculations also showed good agreement when an empirical transition model was used. However, further work in the development of laminar-turbulent transitional models is indicated. The calculations showed most of the known features associated with turbine cascade flow fields. These results indicate the ability of the Navier-Stokes analysis to predict, in reasonable amounts of computation time, the surface pressure distribution, heat transfer rates, and viscous flow development for turbine cascades operating at realistic conditions.

Implementation and Validation of the Chien k-epsilon Turbulence Model in the Wind Navier-Stokes Code

NASA Technical Reports Server (NTRS)

Yoder, Dennis A.; Georgiadis, Nicholas J.

1999-01-01

The two equation k-epsilon turbulence model of Chien has been implemented in the WIND Navier-Stokes flow solver. Details of the numerical solution algorithm, initialization procedure, and stability enhancements are described. Results obtained with this version of the model are compared with those from the Chien k-epsilon model in the NPARC Navier-Stokes code and from the WIND SST model for three validation cases: the incompressible flow over a smooth flat plate, the incompressible flow over a backward facing step, and the shock-induced flow separation inside a transonic diffuser. The k-epsilon model results indicate that the WIND model functions very similarly to that in NPARC, though the WIND code appears to he slightly more accurate in the treatment of the near-wall region. Comparisons of the k-epsilon model results with those from the SST model were less definitive, as each model exhibited strengths and weaknesses for each particular case.

A numerical study of the interaction between unsteady free-stream disturbances and localized variations in surface geometry

NASA Technical Reports Server (NTRS)

Bodonyi, R. J.; Tadjfar, M.; Welch, W. J. C.; Duck, P. W.

1989-01-01

A numerical study of the generation of Tollmien-Schlichting (T-S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite-difference and spectral methods. The nonlinear steady flow is of the viscous-inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier-Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T-S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T-S waves.

Modeling electrokinetics in ionic liquids: General

DOE PAGES

Wang, Chao; Bao, Jie; Pan, Wenxiao; ...

2017-04-01

Using direct numerical simulations, we provide a thorough study regarding the electrokinetics of ionic liquids. In particular, modified Poisson–Nernst–Planck equations are solved to capture the crowding and overscreening effects characteristic of an ionic liquid. For modeling electrokinetic flows in an ionic liquid, the modified Poisson-Nernst-Planck equations are coupled with Navier–Stokes equations to study the coupling of ion transport, hydrodynamics, and electrostatic forces. Specifically, we consider the ion transport between two parallel charged surfaces, charging dynamics in a nanopore, capacitance of electric double-layer capacitors, electroosmotic flow in a nanochannel, electroconvective instability on a plane ion-selective surface, and electroconvective flow on amore » curved ionselective surface. Lastly, we also discuss how crowding and overscreening and their interplay affect the electrokinetic behaviors of ionic liquids in these application problems.« less

LES, DNS and RANS for the analysis of high-speed turbulent reacting flows

NASA Technical Reports Server (NTRS)

Givi, Peyman; Taulbee, Dale B.; Adumitroaie, Virgil; Sabini, George J.; Shieh, Geoffrey S.

1994-01-01

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 Sep. 1993 - 1 Sep. 1994, we have focused our efforts on two research problems: (1) developments of 'algebraic' moment closures for statistical descriptions of nonpremixed reacting systems, and (2) assessments of the Dirichlet frequency in presumed scalar probability density function (PDF) methods in stochastic description of turbulent reacting flows. This report provides a complete description of our efforts during this past year as supported by the NASA Langley Research Center under Grant NAG1-1122.

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.

Water-Rock Differentiation of Icy Bodies by Darcy law, Stokes law, and Two-Phase Flow

NASA Astrophysics Data System (ADS)

Neumann, Wladimir; Breuer, Doris; Spohn, Tilman

2016-10-01

The early Solar system produced a variety of bodies with different properties. Among the small bodies, objects that contain notable amounts of water ice are of particular interest. Water-rock separation on such worlds is probable and has been confirmed in some cases. We couple accretion and water-rock separation in a numerical model. The model is applicable to Ceres, icy satellites, and Kuiper belt objects, and is suited to assess the thermal metamorphism of the interior and the present-day internal structures. The relative amount of ice determines the differentiation regime according to porous flow or Stokes flow. Porous flow considers differentiation in a rock matrix with a small degree of ice melting and is typically modelled either with the Darcy law or two-phase flow. We find that for small icy bodies two-phase flow differs from the Darcy law. Velocities derived from two-phase flow are at least one order of magnitude smaller than Darcy velocities. The latter do not account for the matrix resistance against the deformation and overestimate the separation velocity. In the Stokes regime that should be used for large ice fractions, differentiation is at least four orders of magnitude faster than porous flow with the parameters used here.

Thrust chamber performance using Navier-Stokes solution. [space shuttle main engine viscous nozzle calculation

NASA Technical Reports Server (NTRS)

Chan, J. S.; Freeman, J. A.

1984-01-01

The viscous, axisymmetric flow in the thrust chamber of the space shuttle main engine (SSME) was computed on the CRAY 205 computer using the general interpolants method (GIM) code. Results show that the Navier-Stokes codes can be used for these flows to study trends and viscous effects as well as determine flow patterns; but further research and development is needed before they can be used as production tools for nozzle performance calculations. The GIM formulation, numerical scheme, and computer code are described. The actual SSME nozzle computation showing grid points, flow contours, and flow parameter plots is discussed. The computer system and run times/costs are detailed.

Three dimensional viscous analysis of a hypersonic inlet

NASA Technical Reports Server (NTRS)

Reddy, D. R.; Smith, G. E.; Liou, M.-F.; Benson, Thomas J.

1989-01-01

The flow fields in supersonic/hypersonic inlets are currently being studied at NASA Lewis Research Center using 2- and 3-D full Navier-Stokes and Parabolized Navier-Stokes solvers. These tools have been used to analyze the flow through the McDonnell Douglas Option 2 inlet which has been tested at Calspan in support of the National Aerospace Plane Program. Comparisons between the computational and experimental results are presented. These comparisons lead to better overall understanding of the complex flows present in this class of inlets. The aspects of the flow field emphasized in this work are the 3-D effects, the transition from laminar to turbulent flow, and the strong nonuniformities generated within the inlet.

Three-D Flow Analysis of the Alternate SSME HPOT TAD

NASA Technical Reports Server (NTRS)

Kubinski, Cheryl A.

1993-01-01

This paper describes the results of numerical flow analyses performed in support of design development of the Space Shuttle Main Engine Alternate High Pressure Oxidizer Turbine Turn-around duct (TAD). The flow domain has been modeled using a 3D, Navier-Stokes, general purpose flow solver. The goal of this effort is to achieve an alternate TAD exit flow distribution which closely matches that of the baseline configuration. 3D Navier Stokes CFD analyses were employed to evaluate numerous candidate geometry modifications to the TAD flowpath in order to achieve this goal. The design iterations are summarized, as well as a description of the computational model, numerical results and the conclusions based on these calculations.

CNSFV code development, virtual zone Navier-Stokes computations of oscillating control surfaces and computational support of the laminar flow supersonic wind tunnel

NASA Technical Reports Server (NTRS)

Klopfer, Goetz H.

1993-01-01

The work performed during the past year on this cooperative agreement covered two major areas and two lesser ones. The two major items included further development and validation of the Compressible Navier-Stokes Finite Volume (CNSFV) code and providing computational support for the Laminar Flow Supersonic Wind Tunnel (LFSWT). The two lesser items involve a Navier-Stokes simulation of an oscillating control surface at transonic speeds and improving the basic algorithm used in the CNSFV code for faster convergence rates and more robustness. The work done in all four areas is in support of the High Speed Research Program at NASA Ames Research Center.

Symmetric flows for compressible heat-conducting fluids with temperature dependent viscosity coefficients

NASA Astrophysics Data System (ADS)

Wan, Ling; Wang, Tao

2017-06-01

We consider the Navier-Stokes equations for compressible heat-conducting ideal polytropic gases in a bounded annular domain when the viscosity and thermal conductivity coefficients are general smooth functions of temperature. A global-in-time, spherically or cylindrically symmetric, classical solution to the initial boundary value problem is shown to exist uniquely and converge exponentially to the constant state as the time tends to infinity under certain assumptions on the initial data and the adiabatic exponent γ. The initial data can be large if γ is sufficiently close to 1. These results are of Nishida-Smoller type and extend the work (Liu et al. (2014) [16]) restricted to the one-dimensional flows.

Data Parallel Line Relaxation (DPLR) Code User Manual: Acadia - Version 4.01.1

NASA Technical Reports Server (NTRS)

Wright, Michael J.; White, Todd; Mangini, Nancy

2009-01-01

Data-Parallel Line Relaxation (DPLR) code is a computational fluid dynamic (CFD) solver that was developed at NASA Ames Research Center to help mission support teams generate high-value predictive solutions for hypersonic flow field problems. The DPLR Code Package is an MPI-based, parallel, full three-dimensional Navier-Stokes CFD solver with generalized models for finite-rate reaction kinetics, thermal and chemical non-equilibrium, accurate high-temperature transport coefficients, and ionized flow physics incorporated into the code. DPLR also includes a large selection of generalized realistic surface boundary conditions and links to enable loose coupling with external thermal protection system (TPS) material response and shock layer radiation codes.

A Turbulence model taking into account the longitudinal flow inhomogeneity in mixing layers and jets

NASA Astrophysics Data System (ADS)

Troshin, A. I.

2017-06-01

The problem of potential core length overestimation of subsonic free jets by Reynolds-averaged Navier-Stokes (RANS) based turbulence models is addressed. It is shown that the issue is due to the incorrect velocity profile modeling of the jet mixing layers. An additional source term in ω equation is proposed which takes into account the effect of longitudinal flow inhomogeneity on turbulence in mixing layers. Computations confirm that the modified Speziale-Sarkar-Gatski/Launder- Reece-Rodi-omega (SSG/LRR-ω) turbulence model correctly predicts the mean velocity profiles in both initial and far-field regions of subsonic free plane jet as well as the centerline velocity decay rate.

Analysis of wall shear stress around a competitive swimmer using 3D Navier-Stokes equations in CFD.

PubMed

Popa, C V; Zaidi, H; Arfaoui, A; Polidori, G; Taiar, R; Fohanno, S

2011-01-01

This paper deals with the flow dynamics around a competitive swimmer during underwater glide phases occurring at the start and at every turn. The influence of the head position, namely lifted up, aligned and lowered, on the wall shear stress and the static pressure distributions is analyzed. The problem is considered as 3D and in steady hydrodynamic state. Three velocities (1.4 m/s, 2.2 m/s and 3.1 m/s) that correspond to inter-regional, national and international swimming levels are studied. The flow around the swimmer is assumed turbulent. The Reynolds-averaged Navier-Stokes (RANS) equations are solved with the standard k-ω turbulent model by using the CFD (computational fluid dynamics) numerical method based on a volume control approach. Numerical simulations are carried out with the ANSYS FLUENT® CFD code. The results show that the wall shear stress increases with the velocity and consequently the drag force opposing the movement of the swimmer increases as well. Also, high wall shear stresses are observed in the areas where the body shape, globally rigid in form, presents complex surface geometries such as the head, shoulders, buttocks, heel and chest.

A propagator matrix method for the Rayleigh-Taylor instability of multiple layers: a case study on crustal delamination in the early Earth

NASA Astrophysics Data System (ADS)

Mondal, Puskar; Korenaga, Jun

2018-03-01

The dispersion relation of the Rayleigh-Taylor instability, a gravitational instability associated with unstable density stratification, is of profound importance in various geophysical contexts. When more than two layers are involved, a semi-analytical technique based on the biharmonic formulation of Stokes flow has been extensively used to obtain such dispersion relation. However, this technique may become cumbersome when applied to lithospheric dynamics, where a number of layers are necessary to represent the continuous variation of viscosity over many orders of magnitude. Here, we present an alternative and more efficient method based on the propagator matrix formulation of Stokes flow. With this approach, the original instability problem is reduced to a compact eigenvalue equation whose size is solely determined by the number of primary density contrasts. We apply this new technique to the stability of the early crust, and combined with the Monte Carlo sensitivity analysis, we derive an empirical formula to compute the growth rate of the Rayleigh-Taylor instability for this particular geophysical setting. Our analysis indicates that the likelihood of crustal delamination hinges critically on the effective viscosity of eclogite.

Monolithic multigrid method for the coupled Stokes flow and deformable porous medium system

NASA Astrophysics Data System (ADS)

Luo, P.; Rodrigo, C.; Gaspar, F. J.; Oosterlee, C. W.

2018-01-01

The interaction between fluid flow and a deformable porous medium is a complicated multi-physics problem, which can be described by a coupled model based on the Stokes and poroelastic equations. A monolithic multigrid method together with either a coupled Vanka smoother or a decoupled Uzawa smoother is employed as an efficient numerical technique for the linear discrete system obtained by finite volumes on staggered grids. A specialty in our modeling approach is that at the interface of the fluid and poroelastic medium, two unknowns from the different subsystems are defined at the same grid point. We propose a special discretization at and near the points on the interface, which combines the approximation of the governing equations and the considered interface conditions. In the decoupled Uzawa smoother, Local Fourier Analysis (LFA) helps us to select optimal values of the relaxation parameter appearing. To implement the monolithic multigrid method, grid partitioning is used to deal with the interface updates when communication is required between two subdomains. Numerical experiments show that the proposed numerical method has an excellent convergence rate. The efficiency and robustness of the method are confirmed in numerical experiments with typically small realistic values of the physical coefficients.

Scalable smoothing strategies for a geometric multigrid method for the immersed boundary equations

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

Bhalla, Amneet Pal Singh; Knepley, Matthew G.; Adams, Mark F.

2016-12-20

The immersed boundary (IB) method is a widely used approach to simulating fluid-structure interaction (FSI). Although explicit versions of the IB method can suffer from severe time step size restrictions, these methods remain popular because of their simplicity and generality. In prior work (Guy et al., Adv Comput Math, 2015), some of us developed a geometric multigrid preconditioner for a stable semi-implicit IB method under Stokes flow conditions; however, this solver methodology used a Vanka-type smoother that presented limited opportunities for parallelization. This work extends this Stokes-IB solver methodology by developing smoothing techniques that are suitable for parallel implementation. Specifically,more » we demonstrate that an additive version of the Vanka smoother can yield an effective multigrid preconditioner for the Stokes-IB equations, and we introduce an efficient Schur complement-based smoother that is also shown to be effective for the Stokes-IB equations. We investigate the performance of these solvers for a broad range of material stiffnesses, both for Stokes flows and flows at nonzero Reynolds numbers, and for thick and thin structural models. We show here that linear solver performance degrades with increasing Reynolds number and material stiffness, especially for thin interface cases. Nonetheless, the proposed approaches promise to yield effective solution algorithms, especially at lower Reynolds numbers and at modest-to-high elastic stiffnesses.« less

Asymptotic theory of two-dimensional trailing-edge flows

NASA Technical Reports Server (NTRS)

Melnik, R. E.; Chow, R.

1975-01-01

Problems of laminar and turbulent viscous interaction near trailing edges of streamlined bodies are considered. Asymptotic expansions of the Navier-Stokes equations in the limit of large Reynolds numbers are used to describe the local solution near the trailing edge of cusped or nearly cusped airfoils at small angles of attack in compressible flow. A complicated inverse iterative procedure, involving finite-difference solutions of the triple-deck equations coupled with asymptotic solutions of the boundary values, is used to accurately solve the viscous interaction problem. Results are given for the correction to the boundary-layer solution for drag of a finite flat plate at zero angle of attack and for the viscous correction to the lift of an airfoil at incidence. A rational asymptotic theory is developed for treating turbulent interactions near trailing edges and is shown to lead to a multilayer structure of turbulent boundary layers. The flow over most of the boundary layer is described by a Lighthill model of inviscid rotational flow. The main features of the model are discussed and a sample solution for the skin friction is obtained and compared with the data of Schubauer and Klebanoff for a turbulent flow in a moderately large adverse pressure gradient.

Physical aspects of computing the flow of a viscous fluid

NASA Technical Reports Server (NTRS)

Mehta, U. B.

1984-01-01

One of the main themes in fluid dynamics at present and in the future is going to be computational fluid dynamics with the primary focus on the determination of drag, flow separation, vortex flows, and unsteady flows. A computation of the flow of a viscous fluid requires an understanding and consideration of the physical aspects of the flow. This is done by identifying the flow regimes and the scales of fluid motion, and the sources of vorticity. Discussions of flow regimes deal with conditions of incompressibility, transitional and turbulent flows, Navier-Stokes and non-Navier-Stokes regimes, shock waves, and strain fields. Discussions of the scales of fluid motion consider transitional and turbulent flows, thin- and slender-shear layers, triple- and four-deck regions, viscous-inviscid interactions, shock waves, strain rates, and temporal scales. In addition, the significance and generation of vorticity are discussed. These physical aspects mainly guide computations of the flow of a viscous fluid.

Investigation of supersonic chemically reacting and radiating channel flow

NASA Technical Reports Server (NTRS)

Mani, Mortaza; Tiwari, Surendra N.

1988-01-01

The 2-D time-dependent Navier-Stokes equations are used to investigate supersonic flows undergoing finite rate chemical reaction and radiation interaction for a hydrogen-air system. The explicit multistage finite volume technique of Jameson is used to advance the governing equations in time until convergence is achieved. The chemistry source term in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The multidimensional radiative transfer equations for a nongray model are provided for a general configuration and then reduced for a planar geometry. Both pseudo-gray and nongray models are used to represent the absorption-emission characteristics of the participating species. The supersonic inviscid and viscous, nonreacting flows are solved by employing the finite volume technique of Jameson and the unsplit finite difference scheme of MacCormack. The specified problem considered is of the flow in a channel with a 10 deg compression-expansion ramp. The calculated results are compared with those of an upwind scheme. The problem of chemically reacting and radiating flows are solved for the flow of premixed hydrogen-air through a channel with parallel boundaries, and a channel with a compression corner. Results obtained for specific conditions indicate that the radiative interaction can have a significant influence on the entire flow field.

Navier-Stokes analysis of radial turbine rotor performance

NASA Technical Reports Server (NTRS)

Larosiliere, L. M.

1993-01-01

An analysis of flow through a radial turbine rotor using the three-dimensional, thin-layer Navier-Stokes code RVC3D is described. The rotor is a solid version of an air-cooled metallic radial turbine having thick trailing edges, shroud clearance, and scalloped-backface clearance. Results are presented at the nominal operating condition using both a zero-clearance model and a model simulating the effects of the shroud and scalloped-backface clearance flows. A comparison with the available test data is made and details of the internal flow physics are discussed, allowing a better understanding of the complex flow distribution within the rotor.

Reynolds-Averaged Navier-Stokes Analysis of Zero Efflux Flow Control over a Hump Model

NASA Technical Reports Server (NTRS)

Rumsey, Christopher L.

2006-01-01

The unsteady flow over a hump model with zero efflux oscillatory flow control is modeled computationally using the unsteady Reynolds-averaged Navier-Stokes equations. Three different turbulence models produce similar results, and do a reasonably good job predicting the general character of the unsteady surface pressure coefficients during the forced cycle. However, the turbulent shear stresses are underpredicted in magnitude inside the separation bubble, and the computed results predict too large a (mean) separation bubble compared with experiment. These missed predictions are consistent with earlier steady-state results using no-flow-control and steady suction, from a 2004 CFD validation workshop for synthetic jets.

Reynolds-Averaged Navier-Stokes Analysis of Zero Efflux Flow Control Over a Hump Model

NASA Technical Reports Server (NTRS)

Rumsey, Christopher L.

2006-01-01

The unsteady flow over a hump model with zero efflux oscillatory flow control is modeled computationally using the unsteady Reynolds-averaged Navier-Stokes equations. Three different turbulence models produce similar results, and do a reasonably good job predicting the general character of the unsteady surface pressure coefficients during the forced cycle. However, the turbulent shear stresses are underpredicted in magnitude inside the separation bubble, and the computed results predict too large a (mean) separation bubble compared with experiment. These missed predictions are consistent with earlier steady-state results using no-flow-control and steady suction, from a 2004 CFD validation workshop for synthetic jets.

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.

Counterflow diffusion flames: effects of thermal expansion and non-unity Lewis numbers

NASA Astrophysics Data System (ADS)

Koundinyan, Sushilkumar P.; Matalon, Moshe; Stewart, D. Scott

2018-05-01

In this work we re-examine the counterflow diffusion flame problem focusing in particular on the flame-flow interactions due to thermal expansion and its influence on various flame properties such as flame location, flame temperature, reactant leakage and extinction conditions. The analysis follows two different procedures: an asymptotic approximation for large activation energy chemical reactions, and a direct numerical approach. The asymptotic treatment follows the general theory of Cheatham and Matalon, which consists of a free-boundary problem with jump conditions across the surface representing the reaction sheet, and is well suited for variable-density flows and for mixtures with non-unity and distinct Lewis numbers for the fuel and oxidiser. Due to density variations, the species and energy transport equations are coupled to the Navier-Stokes equations and the problem does not possess an analytical solution. We thus propose and implement a methodology for solving the free-boundary problem numerically. Results based on the asymptotic approximation are then verified against those obtained from the 'exact' numerical integration of the governing equations, comparing predictions of the various flame properties.

Preconditioned Mixed Spectral Element Methods for Elasticity and Stokes Problems

NASA Technical Reports Server (NTRS)

Pavarino, Luca F.

1996-01-01

Preconditioned iterative methods for the indefinite systems obtained by discretizing the linear elasticity and Stokes problems with mixed spectral elements in three dimensions are introduced and analyzed. The resulting stiffness matrices have the structure of saddle point problems with a penalty term, which is associated with the Poisson ratio for elasticity problems or with stabilization techniques for Stokes problems. The main results of this paper show that the convergence rate of the resulting algorithms is independent of the penalty parameter, the number of spectral elements Nu and mildly dependent on the spectral degree eta via the inf-sup constant. The preconditioners proposed for the whole indefinite system are block-diagonal and block-triangular. Numerical experiments presented in the final section show that these algorithms are a practical and efficient strategy for the iterative solution of the indefinite problems arising from mixed spectral element discretizations of elliptic systems.

Navier-Stokes-like equations for traffic flow.

PubMed

Velasco, R M; Marques, W

2005-10-01

The macroscopic traffic flow equations derived from the reduced Paveri-Fontana equation are closed starting with the maximization of the informational entropy. The homogeneous steady state taken as a reference is obtained for a specific model of the desired velocity and a kind of Chapman-Enskog method is developed to calculate the traffic pressure at the Navier-Stokes level. Numerical solution of the macroscopic traffic equations is obtained and its characteristics are analyzed.

Finite element methods and Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Cuvelier, C.; Segal, A.; van Steenhoven, A. A.

This book is devoted to two and three-dimensional FEM analysis of the Navier-Stokes (NS) equations describing one flow of a viscous incompressible fluid. Three different approaches to the NS equations are described: a direct method, a penalty method, and a method that constructs discrete solenoidal vector fields. Subjects of current research which are important from the industrial/technological viewpoint are considered, including capillary-free boundaries, nonisothermal flows, turbulence, and non-Newtonian fluids.

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.

Unsteady Aerodynamic Modeling of A Maneuvering Aircraft Using Indicial Functions

DTIC Science & Technology

2016-03-30

indicial functions are directly calculated using the results of unsteady Reynolds-averaged Navier - Stokes simulation and a grid-movement tool. Results are...but meanwhile, the full-order model based on Unsteady Reynolds-averaged Navier - Stokes (URANS) equation is too computationally expensive to be used...The flow solver used in this study solves the unsteady, three-dimensional and compressible Navier - Stokes equations. The equations in terms of

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 Models of Human Circulatory System under Altered Gravity: Brain Circulation

NASA Technical Reports Server (NTRS)

Kim, Chang Sung; Kiris, Cetin; Kwak, Dochan; David, Tim

2003-01-01

A computational fluid dynamics (CFD) approach is presented to model the blood flow through the human circulatory system under altered gravity conditions. Models required for CFD simulation relevant to major hemodynamic issues are introduced such as non-Newtonian flow models governed by red blood cells, a model for arterial wall motion due to fluid-wall interactions, a vascular bed model for outflow boundary conditions, and a model for auto-regulation mechanism. The three-dimensional unsteady incompressible Navier-Stokes equations coupled with these models are solved iteratively using the pseudocompressibility method and dual time stepping. Moving wall boundary conditions from the first-order fluid-wall interaction model are used to study the influence of arterial wall distensibility on flow patterns and wall shear stresses during the heart pulse. A vascular bed modeling utilizing the analogy with electric circuits is coupled with an auto-regulation algorithm for multiple outflow boundaries. For the treatment of complex geometry, a chimera overset grid technique is adopted to obtain connectivity between arterial branches. For code validation, computed results are compared with experimental data for steady and unsteady non-Newtonian flows. Good agreement is obtained for both cases. In sin-type Gravity Benchmark Problems, gravity source terms are added to the Navier-Stokes equations to study the effect of gravitational variation on the human circulatory system. This computational approach is then applied to localized blood flows through a realistic carotid bifurcation and two Circle of Willis models, one using an idealized geometry and the other model using an anatomical data set. A three- dimensional anatomical Circle of Willis configuration is reconstructed from human-specific magnetic resonance images using an image segmentation method. The blood flow through these Circle of Willis models is simulated to provide means for studying gravitational effects on the brain circulation under auto-regulation.

Phase-field-based lattice Boltzmann modeling of large-density-ratio two-phase flows

NASA Astrophysics Data System (ADS)

Liang, Hong; Xu, Jiangrong; Chen, Jiangxing; Wang, Huili; Chai, Zhenhua; Shi, Baochang

2018-03-01

In this paper, we present a simple and accurate lattice Boltzmann (LB) model for immiscible two-phase flows, which is able to deal with large density contrasts. This model utilizes two LB equations, one of which is used to solve the conservative Allen-Cahn equation, and the other is adopted to solve the incompressible Navier-Stokes equations. A forcing distribution function is elaborately designed in the LB equation for the Navier-Stokes equations, which make it much simpler than the existing LB models. In addition, the proposed model can achieve superior numerical accuracy compared with previous Allen-Cahn type of LB models. Several benchmark two-phase problems, including static droplet, layered Poiseuille flow, and spinodal decomposition are simulated to validate the present LB model. It is found that the present model can achieve relatively small spurious velocity in the LB community, and the obtained numerical results also show good agreement with the analytical solutions or some available results. Lastly, we use the present model to investigate the droplet impact on a thin liquid film with a large density ratio of 1000 and the Reynolds number ranging from 20 to 500. The fascinating phenomena of droplet splashing is successfully reproduced by the present model and the numerically predicted spreading radius exhibits to obey the power law reported in the literature.

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.

Helmholtz decomposition revisited: Vorticity generation and trailing edge condition. I - Incompressible flows

NASA Technical Reports Server (NTRS)

Morino, L.

1986-01-01

Using the decomposition for the infinite-space, the issue of the nonuniqueness of the Helmholtz decomposition for the problem of the three-dimensional unsteady incompressible flow around a body is considered. A representation for the velocity that is valid for both the fluid region and the region inside the boundary surface is employed, and the motion of the boundary is described as the limiting case of a sequence of impulsive accelerations. At each instant of velocity discontinuity, vorticity is shown to be generated by the boundary condition on the normal component of the velocity, for both inviscid and viscous flows. In viscous flows, the vorticity is shown to diffuse into the surroundings, and the no-slip conditions are automatically satisfied. A trailing edge condition must be satisfied for the solution to the Euler equations to be the limit of the solution of the Navier-Stokes equations.

Small-scale collisions with big-scale effects: Direct numerical simulations of crystal interactions in dense suspensions and ramifications for magmatic differentiation

NASA Astrophysics Data System (ADS)

Sethian, J.; Suckale, J.; Yu, J.; Elkins-Tanton, L. T.

2011-12-01

Numerous problems in the Earth sciences involve the dynamic interaction between solid bodies and viscous flow. The goal of this contribution is to develop and validate a computational methodology for modeling complex solid-fluid interactions with minimal simplifying assumptions. The approach we develop is general enough to be applicable in a wide range of geophysical systems ranging from crystal-bearing lava flows to sediment-rich rivers and aerosol transport. Our algorithm relies on a two-step projection scheme: In the first step, we solve the multiple-phase Navier-Stokes or Stokes equation, respectively, in both domains. In the second step, we project the velocity field in the solid domain onto a rigid-body motion by enforcing that the deformation tensor in the respective domain is zero. An important component of the numerical scheme is the accurate treatment of collisions between an arbitrary number of suspended solid bodies based on the impact Stokes number and the elasticity parameters of the solid phase. We perform several benchmark computations to validate our computations including wake formation behind fixed and mobile cylinders and cuboids, the settling speed of particles, and laboratory experiments of collision modes. Finally, we apply our method to investigate the competing effect of entrainment and fractionation in crystalline suspensions - an important question in the context of magma differentiation processes in magma chambers and magma oceans. We find that the properties and volume fraction of the crystalline phase play an important role for evaluating differentiation efficiency.

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.

The 3D Navier-Stokes analysis of a Mach 2.68 bifurcated rectangular mixed-compression inlet

NASA Technical Reports Server (NTRS)

Mizukami, M.; Saunders, J. D.

1995-01-01

The supersonic diffuser of a Mach 2.68 bifurcated, rectangular, mixed-compression inlet was analyzed using a three-dimensional (3D) Navier-Stokes flow solver. A two-equation turbulence model, and a porous bleed model based on unchoked bleed hole discharge coefficients were used. Comparisons were made with experimental data, inviscid theory, and two-dimensional Navier-Stokes analyses. The main objective was to gain insight into the inlet fluid dynamics. Examination of the computational results along with the experimental data suggest that the cowl shock-sidewall boundary layer interaction near the leading edge caused a substantial separation in the wind tunnel inlet model. As a result, the inlet performance may have been compromised by increased spillage and higher bleed mass flow requirements. The internal flow contained substantial waves that were not in the original inviscid design. 3D effects were fairly minor for this inlet at on-design conditions. Navier-Stokes analysis appears to be an useful tool for gaining insight into the inlet fluid dynamics. It provides a higher fidelity simulation of the flowfield than the original inviscid design, by taking into account boundary layers, porous bleed, and their interactions with shock waves.

Deterministic particle transport in a ratchet flow.

PubMed

Beltrame, Philippe; Makhoul, Mounia; Joelson, Maminirina

2016-01-01

This study is motivated by the issue of the pumping of particle through a periodic modulated channel. We focus on a simplified deterministic model of small inertia particles within the Stokes flow framework that we call "ratchet flow." A path-following method is employed in the parameter space in order to retrace the scenario which from bounded periodic solutions leads to particle transport. Depending on whether the magnitude of the particle drag is moderate or large, two main transport mechanisms are identified in which the role of the parity symmetry of the flow differs. For large drag, transport is induced by flow asymmetry, while for moderate drag, since the full transport solution bifurcation structure already exists for symmetric settings, flow asymmetry only makes the transport effective. We analyzed the scenarios of current reversals for each mechanism as well as the role of synchronization. In particular we show that, for large drag, the particle drift is similar to phase slip in a synchronization problem.

Computation of incompressible viscous flows through artificial heart devices with moving boundaries

NASA Technical Reports Server (NTRS)

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

1991-01-01

The extension of computational fluid dynamics techniques to artificial heart flow simulations is illustrated. Unsteady incompressible Navier-Stokes equations written in 3-D generalized curvilinear coordinates are solved iteratively at each physical time step until the incompressibility condition is satisfied. The solution method is based on the pseudo compressibility approach and uses an implicit upwind differencing scheme together with the Gauss-Seidel line relaxation method. The efficiency and robustness of the time accurate formulation of the algorithm are tested by computing the flow through model geometries. A channel flow with a moving indentation is computed and validated with experimental measurements and other numerical solutions. In order to handle the geometric complexity and the moving boundary problems, a zonal method and an overlapping grid embedding scheme are used, respectively. Steady state solutions for the flow through a tilting disk heart valve was compared against experimental measurements. Good agreement was obtained. The flow computation during the valve opening and closing is carried out to illustrate the moving boundary capability.

Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations

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

Dascaliuc, Radu; Thomann, Enrique; Waymire, Edward C., E-mail: waymire@math.oregonstate.edu

2015-07-15

The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to the respective equations coincide. While the uniqueness problem itself remains unresolved, these connections provide interesting problems and possible methods for investigating symmetry breaking and the uniqueness problem for Navier-Stokes equations. In particular, new branching Markov chains, including a dilogarithmic branching random walk on the multiplicative group (0, ∞), naturallymore » arise as a result of this investigation.« less

Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations.

PubMed

Dascaliuc, Radu; Michalowski, Nicholas; Thomann, Enrique; Waymire, Edward C

2015-07-01

The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to the respective equations coincide. While the uniqueness problem itself remains unresolved, these connections provide interesting problems and possible methods for investigating symmetry breaking and the uniqueness problem for Navier-Stokes equations. In particular, new branching Markov chains, including a dilogarithmic branching random walk on the multiplicative group (0, ∞), naturally arise as a result of this investigation.

Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications

NASA Technical Reports Server (NTRS)

Taylor, Arthur C., III; Hou, Gene W.

1993-01-01

In this study involving advanced fluid flow codes, an incremental iterative formulation (also known as the delta or correction form) together with the well-known spatially-split approximate factorization algorithm, is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis. For smaller 2D problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. Iterative methods are needed for larger 2D and future 3D applications, however, because direct methods require much more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioning of the coefficient matrix; this problem can be overcome when these equations are cast in the incremental form. These and other benefits are discussed. The methodology is successfully implemented and tested in 2D using an upwind, cell-centered, finite volume formulation applied to the thin-layer Navier-Stokes equations. Results are presented for two sample airfoil problems: (1) subsonic low Reynolds number laminar flow; and (2) transonic high Reynolds number turbulent flow.

SPLASH program for three dimensional fluid dynamics with free surface boundaries

NASA Astrophysics Data System (ADS)

Yamaguchi, A.

1996-05-01

This paper describes a three dimensional computer program SPLASH that solves Navier-Stokes equations based on the Arbitrary Lagrangian Eulerian (ALE) finite element method. SPLASH has been developed for application to the fluid dynamics problems including the moving boundary of a liquid metal cooled Fast Breeder Reactor (FBR). To apply SPLASH code to the free surface behavior analysis, a capillary model using a cubic Spline function has been developed. Several sample problems, e.g., free surface oscillation, vortex shedding development, and capillary tube phenomena, are solved to verify the computer program. In the analyses, the numerical results are in good agreement with the theoretical value or experimental observance. Also SPLASH code has been applied to an analysis of a free surface sloshing experiment coupled with forced circulation flow in a rectangular tank. This is a simplified situation of the flow field in a reactor vessel of the FBR. The computational simulation well predicts the general behavior of the fluid flow inside and the free surface behavior. Analytical capability of the SPLASH code has been verified in this study and the application to more practical problems such as FBR design and safety analysis is under way.

Single-grid spectral collocation for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bernardi, Christine; Canuto, Claudio; Maday, Yvon; Metivet, Brigitte

1988-01-01

The aim of the paper is to study a collocation spectral method to approximate the Navier-Stokes equations: only one grid is used, which is built from the nodes of a Gauss-Lobatto quadrature formula, either of Legendre or of Chebyshev type. The convergence is proven for the Stokes problem provided with inhomogeneous Dirichlet conditions, then thoroughly analyzed for the Navier-Stokes equations. The practical implementation algorithm is presented, together with numerical results.

Three-Dimensional Navier-Stokes Simulation of Space Shuttle Main Propulsion 17-inch Disconnect Valves

NASA Technical Reports Server (NTRS)

Kandula, M.; Pearce, D. G.

1991-01-01

A steady incompressible three-dimensional viscous flow analysis has been conducted for the Space Shuttle external tank/orbiter propellant feed line disconnect flapper valves with upstream elbows. The Navier-Stokes code, INS3D, is modified to handle interior obstacles and a simple turbulence model. The flow solver is tested for stability and convergence in the presence of interior flappers. An under-relaxation scheme has been incorporated to improve the solution stability. Important flow characteristics such as secondary flows, recirculation, vortex and wake regions, and separated flows are observed. Computed values for forces, moments, and pressure drop are in satisfactory agreement with water flow test data covering a maximum tube Reynolds number of 3.5 million. The predicted hydrodynamical stability of the flappers correlates well with the measurements.

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

NASA Technical Reports Server (NTRS)

Schlueter, J. U.

2003-01-01

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

Application of Navier-Stokes code PAB3D with kappa-epsilon turbulence model to attached and separated flows

NASA Technical Reports Server (NTRS)

Abdol-Hamid, Khaled S.; Lakshmanan, B.; Carlson, John R.

1995-01-01

A three-dimensional Navier-Stokes solver was used to determine how accurately computations can predict local and average skin friction coefficients for attached and separated flows for simple experimental geometries. Algebraic and transport equation closures were used to model turbulence. To simulate anisotropic turbulence, the standard two-equation turbulence model was modified by adding nonlinear terms. The effects of both grid density and the turbulence model on the computed flow fields were also investigated and compared with available experimental data for subsonic and supersonic free-stream conditions.

Three-dimensional multigrid Navier-Stokes computations for turbomachinery applications

NASA Astrophysics Data System (ADS)

Subramanian, S. V.

1989-07-01

The fully three-dimensional, time-dependent compressible Navier-Stokes equations in cylindrical coordinates are presently used, in conjunction with the multistage Runge-Kutta numerical integration scheme for solution of the governing flow equations, to simulate complex flowfields within turbomechanical components whose pertinent effects encompass those of viscosity, compressibility, blade rotation, and tip clearance. Computed results are presented for selected cascades, emphasizing the code's capabilities in the accurate prediction of such features as airfoil loadings, exit flow angles, shocks, and secondary flows. Computations for several test cases have been performed on a Cray-YMP, using nearly 90,000 grid points.

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.

The motion of a cloud of solid spherical particles falling in a cellular flow field at low Stokes number

NASA Astrophysics Data System (ADS)

Marchetti, Benjamin; Bergougnoux, Laurence; Guazzelli, Elisabeth

2017-11-01

We present a jointed experimental and numerical study examining the influence of vortical structures on the settling of a cloud of solid spherical particles under the action of gravity at low Stokes numbers. The two-dimensional model experiment uses electro-convection to generate a two-dimensional array of controlled vortices which mimics a simplified vortical flow. Particle image-velocimetry and tracking are used to examine the motion of the cloud within this vortical flow. The cloud motion is compared to the predictions of a two-way-coupling numerical simulation.

Nonlinear initial-boundary value solutions by the finite element method. [for Navier-Stokes equations of two dimensional flow

NASA Technical Reports Server (NTRS)

Baker, A. J.

1974-01-01

The finite-element method is used to establish a numerical solution algorithm for the Navier-Stokes equations for two-dimensional flows of a viscous compressible fluid. Numerical experiments confirm the advection property for the finite-element equivalent of the nonlinear convection term for both unidirectional and recirculating flowfields. For linear functionals, the algorithm demonstrates good accuracy using coarse discretizations and h squared convergence with discretization refinement.

Algorithms for the Euler and Navier-Stokes equations for supercomputers

NASA Technical Reports Server (NTRS)

Turkel, E.

1985-01-01

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

Parametric Studies of the Ejector Process within a Turbine-Based Combined-Cycle Propulsion System

NASA Technical Reports Server (NTRS)

Georgiadis, Nicholas J.; Walker, James F.; Trefny, Charles J.

1999-01-01

Performance characteristics of the ejector process within a turbine-based combined-cycle (TBCC) propulsion system are investigated using the NPARC Navier-Stokes code. The TBCC concept integrates a turbine engine with a ramjet into a single propulsion system that may efficiently operate from takeoff to high Mach number cruise. At the operating point considered, corresponding to a flight Mach number of 2.0, an ejector serves to mix flow from the ramjet duct with flow from the turbine engine. The combined flow then passes through a diffuser where it is mixed with hydrogen fuel and burned. Three sets of fully turbulent Navier-Stokes calculations are compared with predictions from a cycle code developed specifically for the TBCC propulsion system. A baseline ejector system is investigated first. The Navier-Stokes calculations indicate that the flow leaving the ejector is not completely mixed, which may adversely affect the overall system performance. Two additional sets of calculations are presented; one set that investigated a longer ejector region (to enhance mixing) and a second set which also utilized the longer ejector but replaced the no-slip surfaces of the ejector with slip (inviscid) walls in order to resolve discrepancies with the cycle code. The three sets of Navier-Stokes calculations and the TBCC cycle code predictions are compared to determine the validity of each of the modeling approaches.

Hypersonic Shock/Boundary-Layer Interaction Database

NASA Technical Reports Server (NTRS)

Settles, G. S.; Dodson, L. J.

1991-01-01

Turbulence modeling is generally recognized as the major problem obstructing further advances in computational fluid dynamics (CFD). A closed solution of the governing Navier-Stokes equations for turbulent flows of practical consequence is still far beyond grasp. At the same time, the simplified models of turbulence which are used to achieve closure of the Navier-Stokes equations are known to be rigorously incorrect. While these models serve a definite purpose, they are inadequate for the general prediction of hypersonic viscous/inviscid interactions, mixing problems, chemical nonequilibria, and a range of other phenomena which must be predicted in order to design a hypersonic vehicle computationally. Due to the complexity of turbulence, useful new turbulence models are synthesized only when great expertise is brought to bear and considerable intellectual energy is expended. Although this process is fundamentally theoretical, crucial guidance may be gained from carefully-executed basic experiments. Following the birth of a new model, its testing and validation once again demand comparisons with data of unimpeachable quality. This report concerns these issues which arise from the experimental aspects of hypersonic modeling and represents the results of the first phase of an effort to develop compressible turbulence models.

Development of a Windbreak Dust Predictive Model and Mitigation Planning Tool

DTIC Science & Technology

2013-12-01

laminar and turbulent flow (Uo = 5 m/s and Ls = 1 cm). Figure 28 Deposition fraction, DF, as a function of Stk * showing the collapse of the artificial...Figure 30 Deposition fraction, DF, as a function of the modified Stokes number ( Stk *). Figure 31 The measured decrease in horizontal PM10 flux, F...concentration. Sb Particle travel distance vi SERDP Strategic Environmental Research and Development Program Stk Stokes number Stk * Modified Stokes

Multi-zonal Navier-Stokes code with the LU-SGS scheme

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Yoon, S.

1993-01-01

The LU-SGS (lower upper symmetric Gauss Seidel) algorithm has been implemented into the Compressible Navier-Stokes, Finite Volume (CNSFV) code and validated with a multizonal Navier-Stokes simulation of a transonic turbulent flow around an Onera M6 transport wing. The convergence rate and robustness of the code have been improved and the computational cost has been reduced by at least a factor of 2 over the diagonal Beam-Warming scheme.

Low-dimensional representations of exact coherent states of the Navier-Stokes equations from the resolvent model of wall turbulence.

PubMed

Sharma, Ati S; Moarref, Rashad; McKeon, Beverley J; Park, Jae Sung; Graham, Michael D; Willis, Ashley P

2016-02-01

We report that many exact invariant solutions of the Navier-Stokes equations for both pipe and channel flows are well represented by just a few modes of the model of McKeon and Sharma [J. Fluid Mech. 658, 336 (2010)]. This model provides modes that act as a basis to decompose the velocity field, ordered by their amplitude of response to forcing arising from the interaction between scales. The model was originally derived from the Navier-Stokes equations to represent turbulent flows and has been used to explain coherent structure and to predict turbulent statistics. This establishes a surprising new link between the two distinct approaches to understanding turbulence.

Low-dimensional representations of exact coherent states of the Navier-Stokes equations from the resolvent model of wall turbulence

NASA Astrophysics Data System (ADS)

Sharma, Ati S.; Moarref, Rashad; McKeon, Beverley J.; Park, Jae Sung; Graham, Michael D.; Willis, Ashley P.

2016-02-01

We report that many exact invariant solutions of the Navier-Stokes equations for both pipe and channel flows are well represented by just a few modes of the model of McKeon and Sharma [J. Fluid Mech. 658, 336 (2010), 10.1017/S002211201000176X]. This model provides modes that act as a basis to decompose the velocity field, ordered by their amplitude of response to forcing arising from the interaction between scales. The model was originally derived from the Navier-Stokes equations to represent turbulent flows and has been used to explain coherent structure and to predict turbulent statistics. This establishes a surprising new link between the two distinct approaches to understanding turbulence.

Theoretical study on the constricted flow phenomena in arteries

NASA Astrophysics Data System (ADS)

Sen, S.; Chakravarty, S.

2012-12-01

The present study is dealt with the constricted flow characteristics of blood in arteries by making use of an appropriate mathematical model. The constricted artery experiences the generated wall shear stress due to flow disturbances in the presence of constriction. The disturbed flow in the stenosed arterial segment causes malfunction of the cardiovascular system leading to serious health problems in the form of heart attack and stroke. The flowing blood contained in the stenosed artery is considered to be non-Newtonian while the flow is treated to be two-dimensional. The present pursuit also accounts for the motion of the arterial wall and its effect on local fluid mechanics. The flow analysis applies the time-dependent, two-dimensional incompressible nonlinear Navier-Stokes equations for non-Newtonian fluid representing blood. An extensive quantitative analysis presented at the end of the paper based on large scale numerical computations of the quantities of major physiological significance enables one to estimate the constricted flow characteristics in the arterial system under consideration which deviates significantly from that of normal physiological flow conditions.

Modified Finite Particle Methods for Stokes problems

NASA Astrophysics Data System (ADS)

Montanino, A.; Asprone, D.; Reali, A.; Auricchio, F.

2018-04-01

The Modified Finite Particle Method (MFPM) is a numerical method belonging to the class of meshless methods, nowadays widely investigated due to their characteristic of being capable to easily model large deformation and fluid-dynamic problems. Here we use the MFPM to approximate the Stokes problem. Since the classical formulation of the Stokes problem may lead to pressure spurious oscillations, we investigate alternative formulations and focus on how MFPM discretization behaves in those situations. Some of the investigated formulations, in fact, do not enforce strongly the incompressibility constraint, and therefore an important issue of the present work is to verify if the MFPM is able to correctly reproduce the incompressibility in those cases. The numerical results show that for the formulations in which the incompressibility constraint is properly satisfied from a numerical point of view, the expected second-order is achieved, both in static and in dynamic problems.

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.

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.

Lagrangian turbulence: Structures and mixing in admissible model flows

NASA Astrophysics Data System (ADS)

Ottino, Julio M.

1991-12-01

The goal of our research was to bridge the gap between modern ideas from dynamical systems and chaos and more traditional approaches to turbulence. In order to reach this objective we conducted theoretical and computational work on two systems: (1) a perturbed-Kelvin cat eyes flow, and (2) prototype solutions of the Navier-Stokes equations near solid walls. The main results obtained are two-fold: we have been able to produce flows capable of producing complex distributions of vorticity, and we have been able to construct flowfields, based on solutions of the Navier-Stokes equations, which are capable of displaying both Eulerian and Lagrangian turbulence. These results exemplify typical mechanisms of mixing enhancement in transitional flows.

Two-dimensional lift-up problem for a rigid porous bed

NASA Astrophysics Data System (ADS)

Chang, Y.; Huang, L. H.; Yang, F. P. Y.

2015-05-01

The present study analytically reinvestigates the two-dimensional lift-up problem for a rigid porous bed that was studied by Mei, Yeung, and Liu ["Lifting of a large object from a porous seabed," J. Fluid Mech. 152, 203 (1985)]. Mei, Yeung, and Liu proposed a model that treats the bed as a rigid porous medium and performed relevant experiments. In their model, they assumed the gap flow comes from the periphery of the gap, and there is a shear layer in the porous medium; the flow in the gap is described by adhesion approximation [D. J. Acheson, Elementary Fluid Dynamics (Clarendon, Oxford, 1990), pp. 243-245.] and the pore flow by Darcy's law, and the slip-flow condition proposed by Beavers and Joseph ["Boundary conditions at a naturally permeable wall," J. Fluid Mech. 30, 197 (1967)] is applied to the bed interface. In this problem, however, the gap flow initially mainly comes from the porous bed, and the shear layer may not exist. Although later the shear effect becomes important, the empirical slip-flow condition might not physically respond to the shear effect, and the existence of the vertical velocity affects the situation so greatly that the slip-flow condition might not be appropriate. In contrast, the present study proposes a more general model for the problem, applying Stokes flow to the gap, the Brinkman equation to the porous medium, and Song and Huang's ["Laminar poroelastic media flow," J. Eng. Mech. 126, 358 (2000)] complete interfacial conditions to the bed interface. The exact solution to the problem is found and fits Mei's experiments well. The breakout phenomenon is examined for different soil beds, mechanics that cannot be illustrated by Mei's model are revealed, and the theoretical breakout times obtained using Mei's model and our model are compared. The results show that the proposed model is more compatible with physics and provides results that are more precise.

Program of research in severe storms

NASA Technical Reports Server (NTRS)

1979-01-01

Two modeling areas, the development of a mesoscale chemistry-meteorology interaction model, and the development of a combined urban chemical kinetics-transport model are examined. The problems associated with developing a three dimensional combined meteorological-chemical kinetics computer program package are defined. A similar three dimensional hydrostatic real time model which solves the fundamental Navier-Stokes equations for nonviscous flow is described. An urban air quality simulation model, developed to predict the temporal and spatial distribution of reactive and nonreactive gases in and around an urban area and to support a remote sensor evaluation program is reported.

High-order ENO schemes applied to two- and three-dimensional compressible flow

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang; Erlebacher, Gordon; Zang, Thomas A.; Whitaker, David; Osher, Stanley

1991-01-01

High order essentially non-oscillatory (ENO) finite difference schemes are applied to the 2-D and 3-D compressible Euler and Navier-Stokes equations. Practical issues, such as vectorization, efficiency of coding, cost comparison with other numerical methods, and accuracy degeneracy effects, are discussed. Numerical examples are provided which are representative of computational problems of current interest in transition and turbulence physics. These require both nonoscillatory shock capturing and high resolution for detailed structures in the smooth regions and demonstrate the advantage of ENO schemes.

The Craik-Leibovich Vortex Force as a Skin Effect

NASA Astrophysics Data System (ADS)

Malecha, Ziemowit; Chini, Gregory; Julien, Keith

2013-11-01

The Craik-Leibovich (CL) equations are a surface-wave filtered version of the instantaneous Navier-Stokes equations in which the rectified effects of the surface waves are captured through a so-called ``vortex force'' term: the cross-product of the Stokes, or Lagrangian, mass drift associated with the filtered surface waves and the filtered vorticity vector. For locally generated wind waves, the Stokes drift is very strongly surface confined. In this scenario, the induced body force may be represented as a surface, or skin, effect. Using matched asymptotic analysis in this limit, we derive effective boundary conditions (BCs) for the flow beneath the Stokes drift layer (i.e. in the bulk of the mixed layer). We establish the regime of validity of the resulting formulation by performing linear stability analyses and numerical simulations of both the asymptotic model and the full CL equations for a variety of vertical Stokes drift profiles. The effective BC formulation offers both theoretical and computational advantages, and should be particularly useful for LES of Langmuir turbulence for which the need to resolve very small scale near-surface flow structures imposes severe computational constraints. GPC would like to acknowledge funding from the NSF award 0934827, administered by the Physical Oceanography Program.

Boundary-layer receptivity due to a wall suction and control of Tollmien-Schlichting waves

NASA Technical Reports Server (NTRS)

Bodonyi, R. J.; Duck, P. W.

1992-01-01

A numerical study of the generation of Tollmien-Schlichting (T-S) waves due to the interaction between a small free-stream disturbance and a small localized suction slot on an otherwise flat surface was carried out using finite difference methods. The nonlinear steady flow is of the viscous-inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier-Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of T-S waves generated by the interaction between the free-stream disturbance and the suction slot, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T-S waves and the demonstration of the possible active control of the growth of T-S waves.

Boundary-layer receptivity due to a wall suction and control of Tollmien-Schlichting waves

NASA Technical Reports Server (NTRS)

Bodonyi, R. J.; Duck, P. W.

1990-01-01

A numerical study of the generation of Tollmien-Schlichting (T-S) waves due to the interaction between a small free-stream disturbance and a small localized suction slot on an otherwise flat surface was carried out using finite difference methods. The nonlinear steady flow is of the viscous-inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier-Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of T-S waves generated by the interaction between the free-stream disturbance and the suction slot, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T-S waves and the demonstration of the possible active control of the growth of T-S waves.

Direct observation of vibrational energy flow in cytochrome c.

PubMed

Fujii, Naoki; Mizuno, Misao; Mizutani, Yasuhisa

2011-11-10

Vibrational energy flow in ferric cytochrome c has been examined by picosecond time-resolved anti-Stokes ultraviolet resonance Raman (UVRR) measurements. By taking advantage of the extremely short nonradiative excited state lifetime of heme in the protein (< ps), excess vibrational energy of 20000-25000 cm(-1) was optically deposited selectively at the heme site. Subsequent energy relaxation in the protein moiety was investigated by monitoring the anti-Stokes UVRR intensities of the Trp59 residue, which is a single tryptophan residue involved in the protein that is located close to the heme group. It was found from temporal changes of the anti-Stokes UVRR intensities that the energy flow from the heme to Trp59 and the energy release from Trp59 took place with the time constants of 1-3 and ~8 ps, respectively. These data are consistent with the time constants for the vibrational relaxation of the heme and heating of water reported for hemeproteins. The kinetics of the energy flow were not affected by the amount of excess energy deposited at the heme group. These results demonstrate that the present technique is a powerful tool for studying the vibrational energy flow in proteins.

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.

Establishing Approaches to Modeling the Ares I-X and Ares I Roll Control System with Free-stream Interaction

NASA Technical Reports Server (NTRS)

Pao, S. Paul; Deere, Karen A.; Abdol-Hamid, Khales S.

2011-01-01

Approaches were established for modeling the roll control system and analyzing the jet interactions of the activated roll control system on Ares-type configurations using the USM3D Navier-Stokes solver. Components of the modeling approach for the roll control system include a choice of turbulence models, basis for computing a dynamic equivalence of the real gas rocket exhaust flow in terms of an ideal gas, and techniques to evaluate roll control system performance for wind tunnel and flight conditions. A simplified Ares I-X configuration was used during the development phase of the roll control system modeling approach. A limited set of Navier-Stokes solutions was obtained for the purposes of this investigation and highlights of the results are included in this paper. The USM3D solutions were compared to equivalent solutions at select flow conditions from a real gas Navier- Stokes solver (Loci-CHEM) and a structured overset grid Navier-Stokes solver (OVERFLOW).

Modeling Vortex Generators in a Navier-Stokes Code

NASA Technical Reports Server (NTRS)

Dudek, Julianne C.

2011-01-01

A source-term model that simulates the effects of vortex generators was implemented into the Wind-US Navier-Stokes code. The source term added to the Navier-Stokes equations simulates the lift force that would result from a vane-type vortex generator in the flowfield. The implementation is user-friendly, requiring the user to specify only three quantities for each desired vortex generator: the range of grid points over which the force is to be applied and the planform area and angle of incidence of the physical vane. The model behavior was evaluated for subsonic flow in a rectangular duct with a single vane vortex generator, subsonic flow in an S-duct with 22 corotating vortex generators, and supersonic flow in a rectangular duct with a counter-rotating vortex-generator pair. The model was also used to successfully simulate microramps in supersonic flow by treating each microramp as a pair of vanes with opposite angles of incidence. The validation results indicate that the source-term vortex-generator model provides a useful tool for screening vortex-generator configurations and gives comparable results to solutions computed using gridded vanes.

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.

Comparisons of a Three-Dimensional, Full Navier Stokes Computer Model with High Mach Number Combuster Test Data

NASA Technical Reports Server (NTRS)

Watkins, William B.

1990-01-01

Comparisons between scramjet combustor data and a three-dimensional full Navier-Stokes calculation have been made to verify and substantiate computational fluid dynamics (CFD) codes and application procedures. High Mach number scramjet combustor development will rely heavily on CFD applications to provide wind tunnel-equivalent data of quality sufficient to design, build and fly hypersonic aircraft. Therefore. detailed comparisons between CFD results and test data are imperative. An experimental case is presented, for which combustor wall static pressures were measured and flow-fieid interferograms were obtained. A computer model was done of the experiment, and counterpart parameters are compared with experiment. The experiment involved a subscale combustor designed and fabricated for the National Aero-Space Plane Program, and tested in the Calspan Corporation 96" hypersonic shock tunnel. The combustor inlet ramp was inclined at a 20 angle to the shock tunnel nozzle axis, and resulting combustor entrance flow conditions simulated freestream M=10. The combustor body and cowl walls were instrumented with static pressure transducers, and the combustor lateral walls contained windows through which flowfield holographic interferograms were obtained. The CFD calculation involved a three-dimensional time-averaged full Navier-Stokes code applied to the axial flow segment containing fuel injection and combustion. The full Navier-Stokes approach allowed for mixed supersonic and subsonic flow, downstream-upstream communication in subsonic flow regions, and effects of adverse pressure gradients. The code included hydrogen-air chemistry in the combustor segment which begins near fuel injection and continues through combustor exhaust. Combustor ramp and inlet segments on the combustor lateral centerline were modelled as two dimensional. Comparisons to be shown include calculated versus measured wall static pressures as functions of axial flow coordinate, and calculated path-averaged density contours versus an holographic Interferogram.

Techniques and Software for Monolithic Preconditioning of Moderately-sized Geodynamic Stokes Flow Problems

NASA Astrophysics Data System (ADS)

Sanan, Patrick; May, Dave A.; Schenk, Olaf; Bollhöffer, Matthias

2017-04-01

Geodynamics simulations typically involve the repeated solution of saddle-point systems arising from the Stokes equations. These computations often dominate the time to solution. Direct solvers are known for their robustness and ``black box'' properties, yet exhibit superlinear memory requirements and time to solution. More complex multilevel-preconditioned iterative solvers have been very successful for large problems, yet their use can require more effort from the practitioner in terms of setting up a solver and choosing its parameters. We champion an intermediate approach, based on leveraging the power of modern incomplete factorization techniques for indefinite symmetric matrices. These provide an interesting alternative in situations in between the regimes where direct solvers are an obvious choice and those where complex, scalable, iterative solvers are an obvious choice. That is, much like their relatives for definite systems, ILU/ICC-preconditioned Krylov methods and ILU/ICC-smoothed multigrid methods, the approaches demonstrated here provide a useful addition to the solver toolkit. We present results with a simple, PETSc-based, open-source Q2-Q1 (Taylor-Hood) finite element discretization, in 2 and 3 dimensions, with the Stokes and Lamé (linear elasticity) saddle point systems. Attention is paid to cases in which full-operator incomplete factorization gives an improvement in time to solution over direct solution methods (which may not even be feasible due to memory limitations), without the complication of more complex (or at least, less-automatic) preconditioners or smoothers. As an important factor in the relevance of these tools is their availability in portable software, we also describe open-source PETSc interfaces to the factorization routines.

NASCRIN - NUMERICAL ANALYSIS OF SCRAMJET INLET

NASA Technical Reports Server (NTRS)

Kumar, A.

1994-01-01

The NASCRIN program was developed for analyzing two-dimensional flow fields in supersonic combustion ramjet (scramjet) inlets. NASCRIN solves the two-dimensional Euler or Navier-Stokes equations in conservative form by an unsplit, explicit, two-step finite-difference method. A more recent explicit-implicit, two-step scheme has also been incorporated in the code for viscous flow analysis. An algebraic, two-layer eddy-viscosity model is used for the turbulent flow calculations. NASCRIN can analyze both inviscid and viscous flows with no struts, one strut, or multiple struts embedded in the flow field. NASCRIN can be used in a quasi-three-dimensional sense for some scramjet inlets under certain simplifying assumptions. Although developed for supersonic internal flow, NASCRIN may be adapted to a variety of other flow problems. In particular, it should be readily adaptable to subsonic inflow with supersonic outflow, supersonic inflow with subsonic outflow, or fully subsonic flow. The NASCRIN program is available for batch execution on the CDC CYBER 203. The vectorized FORTRAN version was developed in 1983. NASCRIN has a central memory requirement of approximately 300K words for a grid size of about 3,000 points.

Calculation of concentration fields of high-inertia aerosol particles in the flow past a cylindrical fibre

NASA Astrophysics Data System (ADS)

Zaripov, T. S.; Gilfanov, A. K.; Zaripov, S. K.; Rybdylova, O. D.; Sazhin, S. S.

2018-01-01

The behaviour of high-inertia aerosol particles’ concentration fields in stationary gas suspension flows around a cylinder is investigated using a numerical solution to the Navier-Stokes equations and the fully Lagrangian approach for four Stokes numbers (Stk = 0.1, 1, 4, 10) and three Reynolds numbers (Re = 1, 10, 100). It has been shown that the points of maximum particle concentration along each trajectory shift downstream both when Stk and/or Re increase.

Global existence and large time asymptotic behavior of strong solutions to the Cauchy problem of 2D density-dependent Navier–Stokes equations with vacuum

NASA Astrophysics Data System (ADS)

Lü, Boqiang; Shi, Xiaoding; Zhong, Xin

2018-06-01

We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Navier–Stokes equations with vacuum as far-field density. It is proved that if the initial density decays not too slow at infinity, the 2D Cauchy problem of the density-dependent Navier–Stokes equations on the whole space admits a unique global strong solution. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states and even have compact support. Furthermore, we also obtain the large time decay rates of the spatial gradients of the velocity and the pressure, which are the same as those of the homogeneous case.

A Liouville Problem for the Stationary Fractional Navier-Stokes-Poisson System

NASA Astrophysics Data System (ADS)

Wang, Y.; Xiao, J.

2017-06-01

This paper deals with a Liouville problem for the stationary fractional Navier-Stokes-Poisson system whose special case k=0 covers the compressible and incompressible time-independent fractional Navier-Stokes systems in R^{N≥2} . An essential difficulty raises from the fractional Laplacian, which is a non-local operator and thus makes the local analysis unsuitable. To overcome the difficulty, we utilize a recently-introduced extension-method in Wang and Xiao (Commun Contemp Math 18(6):1650019, 2016) which develops Caffarelli-Silvestre's technique in Caffarelli and Silvestre (Commun Partial Diff Equ 32:1245-1260, 2007).

A Liouville Problem for the Stationary Fractional Navier-Stokes-Poisson System

NASA Astrophysics Data System (ADS)

Wang, Y.; Xiao, J.

2018-06-01

This paper deals with a Liouville problem for the stationary fractional Navier-Stokes-Poisson system whose special case k=0 covers the compressible and incompressible time-independent fractional Navier-Stokes systems in R^{N≥2}. An essential difficulty raises from the fractional Laplacian, which is a non-local operator and thus makes the local analysis unsuitable. To overcome the difficulty, we utilize a recently-introduced extension-method in Wang and Xiao (Commun Contemp Math 18(6):1650019, 2016) which develops Caffarelli-Silvestre's technique in Caffarelli and Silvestre (Commun Partial Diff Equ 32:1245-1260, 2007).

A diffuse-interface method for two-phase flows with soluble surfactants

PubMed Central

Teigen, Knut Erik; Song, Peng; Lowengrub, John; Voigt, Axel

2010-01-01

A method is presented to solve two-phase problems involving soluble surfactants. The incompressible Navier–Stokes equations are solved along with equations for the bulk and interfacial surfactant concentrations. A non-linear equation of state is used to relate the surface tension to the interfacial surfactant concentration. The method is based on the use of a diffuse interface, which allows a simple implementation using standard finite difference or finite element techniques. Here, finite difference methods on a block-structured adaptive grid are used, and the resulting equations are solved using a non-linear multigrid method. Results are presented for a drop in shear flow in both 2D and 3D, and the effect of solubility is discussed. PMID:21218125

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

Ghosh, Debojyoti; Constantinescu, Emil M.

The numerical simulation of meso-, convective-, and microscale atmospheric flows requires the solution of the Euler or the Navier-Stokes equations. Nonhydrostatic weather prediction algorithms often solve the equations in terms of derived quantities such as Exner pressure and potential temperature (and are thus not conservative) and/or as perturbations to the hydrostatically balanced equilibrium state. This paper presents a well-balanced, conservative finite difference formulation for the Euler equations with a gravitational source term, where the governing equations are solved as conservation laws for mass, momentum, and energy. Preservation of the hydrostatic balance to machine precision by the discretized equations is essentialmore » because atmospheric phenomena are often small perturbations to this balance. The proposed algorithm uses the weighted essentially nonoscillatory and compact-reconstruction weighted essentially nonoscillatory schemes for spatial discretization that yields high-order accurate solutions for smooth flows and is essentially nonoscillatory across strong gradients; however, the well-balanced formulation may be used with other conservative finite difference methods. The performance of the algorithm is demonstrated on test problems as well as benchmark atmospheric flow problems, and the results are verified with those in the literature.« less

Capabilities and performance of Elmer/Ice, a new generation ice-sheet model

NASA Astrophysics Data System (ADS)

Gagliardini, O.; Zwinger, T.; Gillet-Chaulet, F.; Durand, G.; Favier, L.; de Fleurian, B.; Greve, R.; Malinen, M.; Martín, C.; Råback, P.; Ruokolainen, J.; Sacchettini, M.; Schäfer, M.; Seddik, H.; Thies, J.

2013-03-01

The Fourth IPCC Assessment Report concluded that ice-sheet flow models are unable to forecast the current increase of polar ice sheet discharge and the associated contribution to sea-level rise. Since then, the glaciological community has undertaken a huge effort to develop and improve a new generation of ice-flow models, and as a result, a significant number of new ice-sheet models have emerged. Among them is the parallel finite-element model Elmer/Ice, based on the open-source multi-physics code Elmer. It was one of the first full-Stokes models used to make projections for the evolution of the whole Greenland ice sheet for the coming two centuries. Originally developed to solve local ice flow problems of high mechanical and physical complexity, Elmer/Ice has today reached the maturity to solve larger scale problems, earning the status of an ice-sheet model. Here, we summarise almost 10 yr of development performed by different groups. We present the components already included in Elmer/Ice, its numerical performance, selected applications, as well as developments planned for the future.

Molecular description of steady supersonic free jets

NASA Astrophysics Data System (ADS)

Montero, S.

2017-09-01

A detailed analysis of the non-local thermal equilibrium (n-LTE) problem in the paraxial zone of silence of supersonic free jets is reported. The study is based on a hybrid approach that combines Navier-Stokes equations with a kinetic equation derived from the generalized Boltzmann (Waldmann-Snider) equation. The resulting system is solved for those flow quantities not easily amenable to experimental measure (translational temperature, flow velocity, and entropy) in terms of the quantities that can be measured accurately (distance, number density, population of rotational states, and their gradients). The reported solutions are essentially exact and are formulated in terms of macroscopic quantities, as well as in terms of elementary collision processes. Emphasis is made on the influence of dissipative effects onto the flow (viscous and diabatic) and of the breakdown of thermal equilibrium onto the evolution of entropy and translational temperature. The influence of inelastic collisions onto these effects is analysed in depth. The reported equations are aimed at optimizing the experimental knowledge of the n-LTE problem and its quantitative interpretation in terms of state-to-state rates for inelastic collisions.

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for high Reynolds number laminar flows

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook

1988-01-01

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables were interpolated using complete quadratic shape functions and the pressure was interpolated using linear shape functions. For the two dimensional case, the pressure is defined on a triangular element which is contained inside the complete biquadratic element for velocity variables; and for the three dimensional case, the pressure is defined on a tetrahedral element which is again contained inside the complete tri-quadratic element. Thus the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow for Reynolds number of 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorable with those of the finite difference methods as well as experimental data available. A finite elememt computer program for incompressible, laminar flows is presented.

Evolution of shock-induced pressure on a flat-face/flat-base body and afterbody flow separation

NASA Technical Reports Server (NTRS)

Yoshikawa, K. K.; Wray, A. A.

1982-01-01

The time-dependent, compressible Reynolds-averaged, Navier-Stokes equations are applied to solve an axisymmetric supersonic flow around a flat-face/flat-base body with and without a sting support. Important transient phenomena, not yet well understood, are investigated, and the significance of the present solution to the phenomena is discussed. The phenomena, described in detail, are as follows: the transient formation of the bow and recompression shock waves; the evolution of a pressure buildup due to diffraction of the incident shock wave in the forebody and afterbody regions, including the luminosity accompanying the pressure buildup; the separation of the flow as influenced by pressure buildup; the location of the separation and the reattachment points; and the transient period of the shock-induced base flow. The important influence of the nonsteady (transient) and steady flow on the aerodynamic characteristics, radiative heat transfer, and, thus, on the survivability or safeguard problems for an aircraft fuselage, missile, or planetary entry probe at very high flight speeds is described.

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.

CFD analyses for advanced pump design

NASA Technical Reports Server (NTRS)

Dejong, F. J.; Choi, S.-K.; Govindan, T. R.

1994-01-01

As one of the activities of the NASA/MSFC Pump Stage Technology Team, the present effort was focused on using CFD in the design and analysis of high performance rocket engine pumps. Under this effort, a three-dimensional Navier-Stokes code was used for various inducer and impeller flow field calculations. An existing algebraic grid generation procedure was-extended to allow for nonzero blade thickness, splitter blades, and hub/shroud cavities upstream or downstream of the (main) blades. This resulted in a fast, robust inducer/impeller geometry/grid generation package. Problems associated with running a compressible flow code to simulate an incompressible flow were resolved; related aspects of the numerical algorithm (viz., the matrix preconditioning, the artificial dissipation, and the treatment of low Mach number flows) were addressed. As shown by the calculations performed under the present effort, the resulting code, in conjunction with the grid generation package, is an effective tool for the rapid solution of three-dimensional viscous inducer and impeller flows.

Adaptive multigrid domain decomposition solutions for viscous interacting flows

NASA Technical Reports Server (NTRS)

Rubin, Stanley G.; Srinivasan, Kumar

1992-01-01

Several viscous incompressible flows with strong pressure interaction and/or axial flow reversal are considered with an adaptive multigrid domain decomposition procedure. Specific examples include the triple deck structure surrounding the trailing edge of a flat plate, the flow recirculation in a trough geometry, and the flow in a rearward facing step channel. For the latter case, there are multiple recirculation zones, of different character, for laminar and turbulent flow conditions. A pressure-based form of flux-vector splitting is applied to the Navier-Stokes equations, which are represented by an implicit lowest-order reduced Navier-Stokes (RNS) system and a purely diffusive, higher-order, deferred-corrector. A trapezoidal or box-like form of discretization insures that all mass conservation properties are satisfied at interfacial and outflow boundaries, even for this primitive-variable, non-staggered grid computation.

Instationary Generalized Stokes Equations in Partially Periodic Domains

NASA Astrophysics Data System (ADS)

Sauer, Jonas

2018-06-01

We consider an instationary generalized Stokes system with nonhomogeneous divergence data under a periodic condition in only some directions. The problem is set in the whole space, the half space or in (after an identification of the periodic directions with a torus) bounded domains with sufficiently regular boundary. We show unique solvability for all times in Muckenhoupt weighted Lebesgue spaces. The divergence condition is dealt with by analyzing the associated reduced Stokes system and in particular by showing maximal regularity of the partially periodic reduced Stokes operator.

A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains with Complex Immersed Boundaries.

PubMed

Ge, Liang; Sotiropoulos, Fotis

2007-08-01

A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [1]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus.

A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains with Complex Immersed Boundaries

PubMed Central

Ge, Liang; Sotiropoulos, Fotis

2008-01-01

A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [1]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus. PMID:19194533

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.

Preconditioned conjugate gradient methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

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

1994-01-01

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

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.

Finite dimensional approximation of a class of constrained nonlinear optimal control problems

NASA Technical Reports Server (NTRS)

Gunzburger, Max D.; Hou, L. S.

1994-01-01

An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.

Transonic Navier-Stokes solutions of three-dimensional afterbody flows

NASA Technical Reports Server (NTRS)

Compton, William B., III; Thomas, James L.; Abeyounis, William K.; Mason, Mary L.

1989-01-01

The performance of a three-dimensional Navier-Stokes solution technique in predicting the transonic flow past a nonaxisymmetric nozzle was investigated. The investigation was conducted at free-stream Mach numbers ranging from 0.60 to 0.94 and an angle of attack of 0 degrees. The numerical solution procedure employs the three-dimensional, unsteady, Reynolds-averaged Navier-Stokes equations written in strong conservation form, a thin layer assumption, and the Baldwin-Lomax turbulence model. The equations are solved by using the finite-volume principle in conjunction with an approximately factored upwind-biased numerical algorithm. In the numerical procedure, the jet exhaust is represented by a solid sting. Wind-tunnel data with the jet exhaust simulated by high pressure air were also obtained to compare with the numerical calculations.

Parabolized Navier-Stokes solutions of separation and trailing-edge flows

NASA Technical Reports Server (NTRS)

Brown, J. L.

1983-01-01

A robust, iterative solution procedure is presented for the parabolized Navier-Stokes or higher order boundary layer equations as applied to subsonic viscous-inviscid interaction flows. The robustness of the present procedure is due, in part, to an improved algorithmic formulation. The present formulation is based on a reinterpretation of stability requirements for this class of algorithms and requires only second order accurate backward or central differences for all streamwise derivatives. Upstream influence is provided for through the algorithmic formulation and iterative sweeps in x. The primary contribution to robustness, however, is the boundary condition treatment, which imposes global constraints to control the convergence path. Discussed are successful calculations of subsonic, strong viscous-inviscid interactions, including separation. These results are consistent with Navier-Stokes solutions and triple deck theory.

Solution of the Burnett equations for hypersonic flows near the continuum limit

NASA Technical Reports Server (NTRS)

Imlay, Scott T.

1992-01-01

The INCA code, a three-dimensional Navier-Stokes code for analysis of hypersonic flowfields, was modified to analyze the lower reaches of the continuum transition regime, where the Navier-Stokes equations become inaccurate and Monte Carlo methods become too computationally expensive. The two-dimensional Burnett equations and the three-dimensional rotational energy transport equation were added to the code and one- and two-dimensional calculations were performed. For the structure of normal shock waves, the Burnett equations give consistently better results than Navier-Stokes equations and compare reasonably well with Monte Carlo methods. For two-dimensional flow of Nitrogen past a circular cylinder the Burnett equations predict the total drag reasonably well. Care must be taken, however, not to exceed the range of validity of the Burnett equations.

Numerical modeling of the interaction of liquid drops and jets with shock waves and gas jets

NASA Astrophysics Data System (ADS)

Surov, V. S.

1993-02-01

The motion of a liquid drop (jet) and of the ambient gas is described, in the general case, by Navier-Stokes equations. An approximate solution to the interaction of a plane shock wave with a single liquid drop is presented. Based on the analysis, the general system of Navier-Stokes equations is reduced to two groups of equations, Euler equations for gas and Navier-Stokes equations for liquid; solutions to these equations are presented. The discussion also covers the modeling of the interaction of a shock wave with a drop screen, interaction of a liquid jet with a counterpropagating supersonic gas flow, and modeling of processes in a shock layer during the impact of a drop against an obstacle in gas flow.

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.

Numerical Treatment of Stokes Solvent Flow and Solute-Solvent Interfacial Dynamics for Nonpolar Molecules.

PubMed

Sun, Hui; Zhou, Shenggao; Moore, David K; Cheng, Li-Tien; Li, Bo

2016-05-01

We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems.

Numerical Treatment of Stokes Solvent Flow and Solute-Solvent Interfacial Dynamics for Nonpolar Molecules

PubMed Central

Sun, Hui; Zhou, Shenggao; Moore, David K.; Cheng, Li-Tien; Li, Bo

2015-01-01

We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems. PMID:27365866

Finite-difference method Stokes solver (FDMSS) for 3D pore geometries: Software development, validation and case studies

NASA Astrophysics Data System (ADS)

Gerke, Kirill M.; Vasilyev, Roman V.; Khirevich, Siarhei; Collins, Daniel; Karsanina, Marina V.; Sizonenko, Timofey O.; Korost, Dmitry V.; Lamontagne, Sébastien; Mallants, Dirk

2018-05-01

Permeability is one of the fundamental properties of porous media and is required for large-scale Darcian fluid flow and mass transport models. Whilst permeability can be measured directly at a range of scales, there are increasing opportunities to evaluate permeability from pore-scale fluid flow simulations. We introduce the free software Finite-Difference Method Stokes Solver (FDMSS) that solves Stokes equation using a finite-difference method (FDM) directly on voxelized 3D pore geometries (i.e. without meshing). Based on explicit convergence studies, validation on sphere packings with analytically known permeabilities, and comparison against lattice-Boltzmann and other published FDM studies, we conclude that FDMSS provides a computationally efficient and accurate basis for single-phase pore-scale flow simulations. By implementing an efficient parallelization and code optimization scheme, permeability inferences can now be made from 3D images of up to 109 voxels using modern desktop computers. Case studies demonstrate the broad applicability of the FDMSS software for both natural and artificial porous media.