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At least 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Multigrid solution of the Navier-Stokes equations on triangular meshes

A new Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite-element Galerkin approximation, which can be shown to be equivalent to a finite-volume approximation for regular equilateral triangular meshes. Integration to steady-state is performed using a multistage time-stepping scheme, and convergence is accelerated by means of implicit residual smoothing and an unstructured multigrid algorithm. The convergence efficiency of the present method is shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms.

Mavriplis, D. J.↗
NASA NTRS1989

A set of strongly coupled, upwind algorithms for computing flows in chemical nonequilibrium

Two new algorithms have been developed to predict the flow of viscous, hypersonic, chemically reacting gases over three-dimensional bodies. Both take advantage of the benefits of upwind differencing, Total Variation Diminishing (TVD) techniques and of a finite-volume framework, but obtain their solution in two separate manners. The first algorithym is a time-marching scheme, and is generally used to obtain solutions in the subsonic portions of the flow field. The second algorithm is a much less expensive, space-marching scheme and can be used for the computation of the larger, supersonic portion of the flow field. Both codes compute their interface fluxes with a new temporal Riemann solver and the resulting schemes are made fully implicit including the chemical source terms.

Molvik, Gregory A.↗
NASA NTRS1989

A simple time-accurate turbomachinery algorithm with numerical solutions of an uneven blade count configuration

The present computer algorithm for the time-accurate flow analysis of rotating turbomachines is based on the finite-volume method and employs a high-resolution approximate Riemann solver for interface flux definitions and an implicit numerical scheme that possesses apparent unconditional stability. Block-block interfaces, including dynamic ones, are treated in such a way as to mimic interior block communication. The turbomachine configurations treated by way of illustration are 8-8-bladed and 11-9-bladed versions of a contrarotating unducted fan engine.

Janus, J. Mark↗
NASA NTRS1989

Application of direct solvers to unstructured meshes for the Euler and Navier-Stokes equations using upwind schemes

The application of Newton iteration to inviscid and viscous airfoil calculations on unstructured meshes is examined. A cell-centered finite volume scheme is employed on an unstructured mesh consisting of triangles. Roe's flux difference splitting scheme is used to compute the inviscid fluxes. Higher order accuracy is achieved by an interpolation procedure that makes use of auxiliary gradients. The efficient solution of the sparse linear system of equations which arises upon linearization in time is addressed. Results are presented for inviscid and viscous test cases. The complications which arise due to the introduction of nonlinear limiters are addressed.

Venkatakrishnan, V.↗
NASA NTRS1989

A multigrid and upwind viscous flow solver on 3-D embedded and overlapped grids

A numerically efficient method is presented for solving the three-dimensional governing equations of the viscous compressible flow about complex configurations with topologically different components. The physical domain is decomposed into regions for which the grid generation is relatively simple and virtually with no significant restrictions. The Navier-Stokes equations are solved by an implicit, approximately factored, upwind, finite-volume scheme. The block inversions and the diagonalized scalar inversions of the coefficient matrices are modified to allow the holes created in the computational domain by the embedded and overlapped grids. The convergence is accelerated by a multigrid algorithm despite the existence of such holes. The solution for s supersonic flow past a blunt-nose-cylinder at high angle-of-attack is obtained using a C-O grid embedded in a global Cartesian grid.

Baysal, Oktay↗
NASA NTRS1989

Numerical solution of unsteady incompressible viscous flows in generalized moving coordinate systems

A solution method of the time-accurate, incompressible Navier-Stokes equations in generalized curvilinear moving coordinate systems is presented in this paper. Accuracy is achieved by a conservative finite-volume discretization which satisfies the geometric conservation laws in generalized moving coordinate systems. The solution method is second-order accurate in space and first-order accurate in time. A fractional step solution method is used to efficiently solve the discrete equations. The unknowns, namely the pressure and the volume-fluxes, are chosen to facilitate the formulation of a consistent Poisson equation and to obtain a robust Poisson solver with favorable convergence properties. The method is validated by comparisons to other numerical and experimental solutions. The comparisons show good agreement.

Rosenfeld, Moshe↗
NASA NTRS1989

An investigation of cell centered and cell vertex multigrid schemes for the Navier-Stokes equations

Two efficient and robust finite-volume multigrid schemes for solving the Navier-Stokes equations are investigated. These schemes employ either a cell centered or a cell vertex discretization technique. An explicit Runge-Kutta algorithm is used to advance the solution in time. Acceleration techniques are applied to obtain faster steady-state convergence. Accuracy and convergence of the schemes are examined. Computational results for transonic airfoil flows are essentially the same, even for a coarse mesh. Both schemes exhibit good convergence rates for a broad range of artificial dissipation coefficients.

Radespiel, R.↗
NASA NTRS1989

Numerical modeling of turbulent supersonic reacting coaxial jets

The paper considers the mixing and subsequent combustion within turbulent reacting shear layers. A computer program was developed to solve the axisymmetric Reynolds averaged Navier-Stokes equations. The numerical method integrates the Reynolds averaged Navier-Stokes equations using a finite volume approach while advancing the solution forward in time using a Runge-Kutta scheme. Three separate flowfields are investigated and it is found that no single turbulence model considered could accurately predict the degree of mixing for all three cases.

Eklund, Dean R.↗
NASA NTRS1989

Three-dimensional calculation of supersonic reacting flows using an LU scheme

A new three-dimensional numerical program incorporated with comprehensive real gas property models has been developed to simulate supersonic reacting flows. The code employs an implicit finite volume, Lower-Upper (LU) time-marching method to solve the complete Navier-Stokes and species equations in a fully-coupled and very efficient manner. A chemistry model with nine species and eighteen reaction steps are adopted in the program to represent the chemical reaction of H2 and air. To demonstrate the capability of the program, flow fields of underexpanded hydrogen jets transversely injected into supersonic air stream inside the combustors of scramjets are calculated. Results clearly depict the flow characteristics, including the shock structure, separated flow regions around the injector, and the distribution of the combustion products.

Yu, Sheng-Tao↗
NASA NTRS1989

Calculations of rotational flows using stream function

The stream function equation is solved for steady two-dimensional (and axisymmetric) rotational flows. Both finite differences and finite volumes discretization techniques are studied, using generalized body fitted coordinates and unstructured staggered grids, respectively. For inviscid transonic flows, a new artificial viscosity scheme which does not produce any artificial vorticity is introduced, for the stability of the mixed flow calculations and for capturing shocks. The solution of Euler equations, in primitive variables, are also considered. The effects of the artificial viscosity and numerical boundary conditions on the total enthalpy and the vorticity distributions are demonstrated.

Hafez, M.↗
NASA NTRS1989

Unsteady Euler algorithm with unstructured dynamic mesh for complex-aircraft aeroelastic analysis

A finite-volume unstructured-grid FEM scheme with multistage Runge-Kutta time stepping is applied to the three-dimensional time-dependent Euler equations for inviscid flows on complex aircraft configurations undergoing structural deformation. The derivation of the model, the solution procedure, and the computer implementation are described, and results are presented graphically for a NASA Langley supersonic fighter aircraft model in steady and unsteady (harmonic oscillation in complete-vehicle bending mode) flow regimes. Good agreement between FEM predictions and experimental data is demonstrated.

Batina, John T.↗
NASA NTRS1989

Euler flutter analysis of airfoils using unstructured dynamic meshes

Modifications to a two-dimensional unsteady Euler code for the aeroelastic analysis of airfoils are described. The modifications involve including the structural equations of motion and their simultaneous time-integration with the governing flow equations. A novel aspect of the capability is that the solutions are obtained using unstructured grids made up of triangles. Comparisons are made with parallel calculations performed using linear theory and a structured grid Euler code to assess the accuracy of the unstructured grid Euler results. Results are presented for a flat plate airfoil and the NACA 0012 airfoil to demonstrate applications of the Euler code for generalized force computations and aeroelastic analysis. In these comparisons, two different finite-volume discretizations of the Euler equations on unstructured meshes were employed. Sensitivity of the Euler results to changes in numerical parameters were also investigated.

Rausch, Russ D.↗
NASA NTRS1989

A computational study on the interaction between a vortex and a shock wave

A computational study of two-dimensional shock vortex interaction is discussed in this paper. A second order upwind finite volume method is used to solve the Euler equations in conservation form. In this method, the shock wave is captured rather than fitted so that the cases where shock vortex interaction may cause secondary shocks can also be investigated. The effects of vortex strength on the computed flow and acoustic field generated by the interaction are qualitatively evaluated.

Meadows, Kristine R.↗
NASA NTRS1989

Calculation of unsteady flows in turbomachinery using the linearized Euler equations

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

Hall, Kenneth C.↗
NASA NTRS1989

Supersonic flow computations by two-equation turbulence modeling

In the present work a solver for the Reynolds averaged compressible Navier-Stokes equations, to compute high speed turbulent flows characterized by interacting shock waves and viscous layers, is presented. A k-epsilon turbulence model that accounts for compressibility effects is developed. The numerical algorithm is based on a finite volume multistage Runge Kutta technique that is explicit for the solution of the mean flow variables, and implicit for the solution of the k-epsilon equations. The model is validated by extensive comparison with experimental results of flows over compression ramps characterized by interacting shock waves/boundary layers.

Grasso, Francesco↗
NASA NTRS1989

LU-SGS implicit algorithm for three-dimensional incompressible Navier-Stokes equations with source term

A numerical method is developed for solving the incompressible Navier-Stokes equations using the concept of pseudocompressibility. A lower-upper symmetric-Gauss-Seidel implicit scheme is developed for three-dimensional incompressible viscous flow computations. The present algorithm offers additional advantages when solving the flow equations with source terms. Complete vectorizability of the algorithm on oblique planes of sweep in three-dimensions is accomplished in a new flow solver, INS3D-LU code. Spatial differencing is a second-order accurate semi-discrete finite-volume method augmented by a third-order accurate numerical dissipation model which is based on spectral-radii. Comparison of numerical solutions for a curved duct with experimental data shows good agreement. The method is applied to calculate the inducer flow of the Space Shuttle Main Engine turbopump.

Yoon, Seokkwan↗
NASA NTRS1989

A simple algebraic grid adaptation scheme with applications to two- and three-dimensional flow problems

An algebraic adaptive grid scheme based on the concept of arc equidistribution is presented which provides high flowfield resolution when applied to two-dimensional and three-dimensional flow problems. The present scheme locally adjusts the grid density using gradients of selected flow variables from either finite difference or finite volume calculations, and it can specify user-prescribed grid stretching such that control of the grid spacing can be maintained in areas of known flowfield behavior. A robust and efficient grid smoothing technique has been incorporated into the adaptive grid routine.

Hsu, Andrew T.↗
NASA NTRS1989

Vortex-dominated conical-flow computations using unstructured adaptively-refined meshes

A conical Euler/Navier-Stokes algorithm is presented for the computation of vortex-dominated flows. The flow solver involves a multistage Runge-Kutta time stepping scheme which uses a finite-volume spatial discretization on an unstructured grid made up of triangles. The algorithm also employs an adaptive mesh refinement procedure which enriches the mesh locally to more accurately resolve the vortical flow features. Results are presented for several highly-swept delta wing and circular cone cases at high angles of attack and at supersonic freestream flow conditions. Accurate solutions were obtained more efficiently when adaptive mesh refinement was used in contrast with refining the grid globally. The paper presents descriptions of the conical Euler/Navier-Stokes flow solver and adaptive mesh refinement procedures along with results which demonstrate the capability.

Batina, John T.↗