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At least 325 records · Page 18

2-D/Axisymmetric Formulation of Multi-dimensional Upwind Scheme

A multi-dimensional upwind discretization of the two-dimensional/axisymmetric Navier-Stokes equations is detailed for unstructured meshes. The algorithm is an extension of the fluctuation splitting scheme of Sidilkover. Boundary conditions are implemented weakly so that all nodes are updated using the base scheme, and eigen-value limiting is incorporated to suppress expansion shocks. Test cases for Mach numbers ranging from 0.1-17 are considered, with results compared against an unstructured upwind finite volume scheme. The fluctuation splitting inviscid distribution requires fewer operations than the finite volume routine, and is seen to produce less artificial dissipation, leading to generally improved solution accuracy.

Wood, William A.↗

A Hybrid Parallel Preconditioning Algorithm For CFD

A new hybrid preconditioning algorithm will be presented which combines the favorable attributes of incomplete lower-upper (ILU) factorization with the favorable attributes of the approximate inverse method recently advocated by numerous researchers. The quality of the preconditioner is adjustable and can be increased at the cost of additional computation while at the same time the storage required is roughly constant and approximately equal to the storage required for the original matrix. In addition, the preconditioning algorithm suggests an efficient and natural parallel implementation with reduced communication. Sample calculations will be presented for the numerical solution of multi-dimensional advection-diffusion equations. The matrix solver has also been embedded into a Newton algorithm for solving the nonlinear Euler and Navier-Stokes equations governing compressible flow. The full paper will show numerous examples in CFD to demonstrate the efficiency and robustness of the method.

Barth,Timothy J.↗

Some Experiences with Nonoverlapping Schur Complement Parallel Preconditioning for CFD Calculations

In this work we consider solving matrices which arise from the discretization of advection-diffusion field equations on arbitrary triangulated domains using stabilized numerical methods. The talk will discuss several candidate matrix preconditioning algorithms based on the 2 x 2 block factorization induced by an apriori partitioning of the triangulated domain. Application of the 2 x 2 block preconditioner requires the formation and inversion of the Schur complement submatrix. We consider several strategies for simplifying this task: incomplete Schur complement factorizations, drop tolerance element filling, Schur complement probing, and localized Schur complement inversion. Numerical results will be shown comparing performance and efficiency of these approximations. The matrix preconditioner has also been embedded into a Newton algorithm for solving the nonlinear Euler and Navier-Stokes equations governing compressible flow. The remainder of the talk will show numerous examples in CFD to demonstrate the efficiency and robustness of the techniques.

Barth, Timothy J.↗

Unstructured Unsteady Flow Solver Applicable to MSU TURBO and Computational Design

This paper presents numerical simulations for a high-speed transonic compressor rotor, NASA Rotor 35, using an unstructured grid flow solver U2NCLE. It solves Reynolds averaged Navier-Stokes equations using an arbitrary Mach number solution algorithm. Experiments were conducted at the NASA Glen Research Center to investigate compressor stability enhancement using steady and discrete tip injections. The mass injection upstream of the tip of a high- speed axial compressor rotor has shown effectiveness in suppressing stall in tip-critical rotors. This work presents numerical simulations of a high-speed compressor rotor with and without tip injections. Methods to model the flow injection are described. Numerical simulations are conducted at 80 and 100 percent of the design speed. Results show that numerical solutions are consistent with the experimental trends.

Newman, James C., III↗

Unsteady Three-Dimensional Simulation of a Shear Coaxial GO2/GH2 Rocket Injector with RANS and Hybrid-RAN-LES/DES Using Flamelet Models

Historically, the analysis and design of liquid rocket engines (LREs) has relied on full‐scale testing and one‐dimensional empirical tools. The testing is extremely expensive and the one‐dimensional tools are not designed to capture the highly complex, and multi‐dimensional features that are inherent to LREs. Recent advances in computational fluid dynamics (CFD) tools have made it possible to predict liquid rocket engine performance, stability, to assess the effect of complex flow features, and to evaluate injector‐driven thermal environments, to mitigate the cost of testing. Extensive efforts to verify and validate these CFD tools have been conducted, to provide confidence for using them during the design cycle. Previous validation efforts have documented comparisons of predicted heat flux thermal environments with test data for a single element gaseous oxygen (GO2) and gaseous hydrogen (GH2) injector. The most notable validation effort was a comprehensive validation effort conducted by Tucker et al. [1], in which a number of different groups modeled a GO2/GH2 single element configuration by Pal et al [2]. The tools used for this validation comparison employed a range of algorithms, from both steady and unsteady Reynolds Averaged Navier‐Stokes (U/RANS) calculations, large‐eddy simulations (LES), detached eddy simulations (DES), and various combinations. A more recent effort by Thakur et al. [3] focused on using a state‐of‐the‐art CFD simulation tool, Loci/STREAM, on a two‐dimensional grid. Loci/STREAM was chosen because it has a unique, very efficient flamelet parameterization of combustion reactions that are too computationally expensive to simulate with conventional finite‐rate chemistry calculations. The current effort focuses on further advancement of validation efforts, again using the Loci/STREAM tool with the flamelet parameterization, but this time with a three‐dimensional grid. Comparisons to the Pal et al. heat flux data will be made for both RANS and Hybrid RANSLES/ Detached Eddy simulations (DES). Computation costs will be reported, along with comparison of accuracy and cost to much less expensive two‐dimensional RANS simulations of the same geometry.

Westra, Doug G.↗

On multigrid methods for the Navier-Stokes Computer

The overall architecture of the multipurpose parallel-processing Navier-Stokes Computer (NSC) being developed by Princeton and NASA Langley (Nosenchuck et al., 1986) is described and illustrated with extensive diagrams, and the NSC implementation of an elementary multigrid algorithm for simulating isotropic turbulence (based on solution of the incompressible time-dependent Navier-Stokes equations with constant viscosity) is characterized in detail. The present NSC design concept calls for 64 nodes, each with the performance of a class VI supercomputer, linked together by a fiber-optic hypercube network and joined to a front-end computer by a global bus. In this configuration, the NSC would have a storage capacity of over 32 Gword and a peak speed of over 40 Gflops. The multigrid Navier-Stokes code discussed would give sustained operation rates of about 25 Gflops.

Nosenchuck, D. M.↗

Two-Dimensional Inlet Simulation Using a Diagonal Implicit Algorithm

A modification of an implicit approximate-factorization finite-difference algorithm applied to the two-dimensional Euler and Navier-Stokes equations in general curvilinear coordinates is presented for supersonic freestream flow about and through inlets. The modification transforms the coupled system of equations Into an uncoupled diagonal form which requires less computation work. For steady-state applications the resulting diagonal algorithm retains the stability and accuracy characteristics of the original algorithm. Solutions are given for inviscid and laminar flow about a two-dimensional wedge inlet configuration. Comparisons are made between computed results and exact theory.

Chaussee, D.S.↗

PNS predictions for supersonic/hypersonic flows over finned missile configurations

Finned missile design entails accurate and computationally fast numerical techniques for predicting viscous flows over complex lifting configurations at small to moderate angles of attack and over Mach 3 to 15; these flows are often characterized by strong embedded shocks, so that numerical algorithms are also required to capture embedded shocks. The recent real-gas Flux Vector Splitting technique is here extended to investigate the Mach 3 flow over a typical finned missile configuration with/without side fin deflections. Elliptic grid-generation techniques for Mach 15 flows are shown to be inadequate for Mach 3 flows over finned configurations and need to be modified. Fin-deflection studies indicate that even small amounts of missile fin deflection can substantially modify vehicle aerodynamics. This 3D parabolized Navier-Stokes scheme is also extended into an efficient embedded algorithm for studying small axially separated flow regions due to strong fin and control surface deflections.

Bhutta, Bilal A.↗

A dual potential formulation of the Navier-Stokes equations

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.

Gegg, S. G.↗

Navier-Stokes solutions for flows related to store separation

The objective is developing CFD capabilities to obtain solutions for viscous flows about generic configurations of internally and externally carried stores. The emphasis is placed on the supersonic flow regime with extensions being made to the transonic regime. The project is broken into four steps: (1) Cavity flows for internal carriage configurations; (2) High angle of attack flows, which may be experienced during the separation of the stores: (3) Flows about a body near a flat plate for external carriage configurations; and (4) Flows about a body inside or in the proximity of a cavity. Three-dimensional unsteady cavity flow solutions are obtained by an explicit, MacCormack algorithm, EMCAV3, for open, close, and transitional cavities. High angle of attack flows past cylinders are solved by an implicit, upwind algorithm. All the results compare favorably with the experimental data. For flows about multiple body configurations, the Chimera embedding scheme is modified for finite-volume and multigrid algorithms, MaGGiE. Then a finite volume, implicit, upwind, multigrid Navier-Stokes solver which uses on overlapped/embedded and zonal grids, VUMXZ3, is developed from the CFL3D code. Supersonic flows past a cylinder near a flat plate are computed using this code. The results are compared with the experimental data. Currently the VUMXZ3 code is being modified to accomplish step 4 of this project. Wind tunnel experiments are also being conducted for validation purposes.

Baysal, Oktay↗

Implicit, vectorizable schemes for the flux-difference split, three-dimensional Navier-Stokes equations

Two hybrid upwind models are defined for solving the Euler equations. The algorithms both employ approximate factorization (AF) in crossplane and symmetric block Gauss-Seidel relaxation in the third direction. One approach adds an additional factorization step to lower the number of required grid point operations for inversion of the block tridiagonal matrices; however, the move permits only one third of the operations to be vectorized. Finite difference solutions are calculated on a C-H-type grid, in this case enveloping a slender, sharp-edged delta wing. Sample data are provided for the calculated vortex flow for Re of 10,000, at a 20.5 deg angle of attack, represented in a crossflow velocity vector plot and in a spanwise pressure coefficient distribution. The AF scheme, without additional factorization, when used with a grid covering 51 x 51 x 72 points provides a convergent solution with no time step lasting longer than 0.00001 sec.

Liu, C. H.↗

A patched-grid algorithm for complex aircraft configurations

A patched-grid algorithm for the analysis of complex configurations with an implicit, upwind-biased Navier-Stokes solver is presented. Through the use of a generalized coordinate transformation at the zonal interface between two or more blocks, the algorithm can be applied to highly stretched viscous grids and to arbitrarily-shaped patch boundaries. Applications are made to the SR71 reconnaissance aircraft in a high-altitude environment at a supersonic speed and to the F/A-18 forebody-strake configuration at subsonic, high-alpha conditions, in support of the NASA High-Alpha Research Program.

Walters, Robert W.↗

Navier-Stokes simulation of flow through a highly contoured subsonic diffuser

The flow through a highly offset subsonic diffuser with cross-sectional profiles that varied from rectangular at the duct entrance to circular at the engine face was numerically simulated. A multizonal approach combined with a two-grid topology was used to represent both the internal and external flowfields, and an implicit, approximately-factored, partially flux-split finite-difference algorithm was used to solve the three-dimensional thin-layer Navier-Stokes equations. The computed static pressures along the inlet wall and total pressures on the engine face were compared with experimental data. In addition, the overall flowfield within the duct was examined in detail. Good agreement is shown between experiment and computations, with the limiting factor being the lack of a reliable turbulence model for internal flow problems.

Chyu, W. J.↗

Numerical simulation of viscous-inviscid interactions on indented nose tips

An implicit numerical algorithm to solve the unsteady thin-layer Navier-Stokes equations in a strong conservative form has been used to compute the viscous flow over indented nose tips placed in a supersonic free stream. Numerical solutions are presented for axisymmetric and three-dimensional indented configurations for laminar flow conditions. Results demonstrate the capability of the present numerical procedure to predict flow fields that contain strong viscous-inviscid interactions, including boundary-layer separation, reattachment, and embedded discontinuities. Comparisons with available experimental data for the shock shape and surface pressure are also given.

Rizk, Y. M.↗

Numerical simulation of the interaction of a vortex with stationary airfoil in transonic flow

A perturbation form of an implicit conservative, noniterative numerical algorithm for the two-dimensional thin layer Navier-Stokes and Euler equations is used to compute the interaction flow-field of a vortex with stationary airfoil. A Lamb-like analytical vortex having a finite core is chosen to interact with a thick (NACA 0012) and a thin (NACA 64A006) airfoil independently in transonic flow. Two different configurations of vortex interaction are studied, viz., (1) when the vortex is fixed at one location in the flowfield, and (2) when the vortex is convecting past the airfoil at freestream velocity. Parallel computations of this interacting flowfield are also done using a version of the Transonic Small Disturbance Code (ATRAN2). A special treatment of the leading edge region for thin airfoils is included in this code. With this, the three methods gave qualitatively similar results for the weaker interactions considered in this study. However, the strongest interactions considered proved to be beyond the capabilities of the small disturbance code. The results also show a far greater influence of the vortex on the airfoil flowfield when the vortex is stationary than when it is convecting with the flow.

Srinivasan, G. R.↗

A multistage time-stepping scheme for the thin-layer Navier-Stokes equations

A finite-volume scheme for numerical integration of the Euler equations was extended to allow solution of the thin-layer Navier-Stokes equations in two and three dimensions. The extended algorithm, which is based on a class of four-stage Runge-Kutta time-stepping schemes, was made numerically efficient through the following convergence acceleration technique: (1) local time stepping, (2) enthalpy damping, and (3) residual smoothing. Also, the high degree of vectorization possible with the algorithm has yielded an efficient program for vector processors. The scheme was evaluated by solving laminar and turbulent flows. Numerical results have compared well with either theoretical or other numerical solutions and/or experimental data.

Swanson, R. C., Jr.↗

A numerical simulation of vortex breakdown

A numerical simulation of vortex breakdown using the time-dependent Navier-Stokes equations is performed. Unlike previous studies, the numerical algorithm, formulated in terms of the velocity and vorticity, is not restricted by axisymmetry conditions. The vortex is parameterized in terms of the Reynolds number and Rossby number. The resulting breakdown structure is analyzed using contour plots of velocity, vorticity and pressure as well as axial, radial, and swirl velocity profiles at various streamwise locations. The relationship of these results to experimentally observed structures and previous numerical results is discussed.

Spall, R. E.↗

Simulation of fundamental atomization mechanisms in fuel sprays

Growth of instabilities on the liquid/gas interface in the initial region of fuel sprays is studied by means of numerical simulations. The simulations are based on solutions of the variable-density incompressible Navier-Stokes equations, which are obtained with a new numerical algorithm. The simulations give good agreement with analytical results for the instabilities on a liquid cylinder induced by surface tension and wind-induced instabilities. The effects of boundary layers on the wind-induced instabilities are investigated. It is found that a boundary layer reduces the growth rate for a single interface, and a comparison with inviscid theory suggests that boundary layer effects may be significantly more important than surface tension effects. The results yield a better estimate than inviscid theory for the drop sizes as reported for diesel sprays. Results for the planar jet show that boundary layer effects hasten the growth of Squire's 'symmetric' mode, which is responsible for jet disintegration. This result helps explain the rapid atomization which occurs in swirl and air-blast atomizers.

Childs, Robert, E.↗