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At least 523 records · Page 29

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NASA NTRS1986

An implicit flux-difference splitting scheme for three-dimensional, incompressible Navier-Stokes solutions to leading edge vortex flows

A new, implicit finite-difference scheme designed to solve the conservative, flux-difference split Navier-Stokes equations is used to compute incompressible vortex flows around delta wings. The completely vectorizable hybrid algorithm is constructed in delta form for steady state solutions independent of the time-step sizes. The scheme combines approximate factorization in crossflow planes with a symmetric planar Gauss-Seidel relaxation in the remaining spatial direction. The governing equations are solved in curvilinear, body-fitted coordinates for treating complex geometries. The computed flow field results are compared with other theoretical and experimental data.

Hartwich, P.-M.↗

NASA NTRS1986

Navier-Stokes computations of lee-side flows over delta wings

Solutions to the Navier-Stokes equations for the flow over delta wings are computed with emphasis on the separated vortical flows developing on the lee side at high angles of attack. A recently developed implicit algorithm is used which employs upwind differencing for the pressure and convection terms and central differencing for the shear stress and heat transfer terms. Solutions to both the three-dimensional equations and the approximate conical flow equations are compared parametrically with an extensive experimental data base at supersonic speeds. The computations indicate that the conical flow approximation provides results in close agreement with the three-dimensional equations, even to angles of attack as high as 20 degrees. Good agreement with experimentally measured pressures and vapor screen photographs is obtained for the conditions investigated. The method predicts the classical pattern of vortical flow over a delta wing and transition to other flow patterns as the leading edge sweep angle and leading edge normal Mach number are varied.

Thomas, J. L.↗

NASA NTRS1986

An upwind algorithm for the parabolized Navier-Stokes equations

A new upwind algorithm based on Roe's scheme has been developed to solve the two-dimensional parabolized Navier-Stokes (PNS) equations. This method does not require the addition of user specified smoothing terms for the capture of discontinuities such as shock waves. Thus, the method is easy to use and can be applied without modification to a wide variety of supersonic flowfields. The advantages and disadvantages of this adaptation are discussed in relation to those of the conventional Beam-Warming scheme in terms of accuracy, stability, computer time and storage, and programming effort. The new algorithm has been validated by applying it to three laminar test cases including flat plate boundary-layer flow, hypersonic flow past a 15 deg compression corner, and hypersonic flow into a converging inlet. The computed results compare well with experiment and show a dramatic improvement in the resolution of flowfield details when compared with the results obtained using the conventional Beam-Warming algorithm.

Lawrence, S. L.↗

NASA NTRS1986

Study of hypersonic inlet flow fields with a three-dimensional Navier-Stokes code

A three-dimensional Navier-Stokes code is used to study the flow through an inlet with a rectangular capture area, but with circular or essentially circular internal cross-sections. The inlet may have a center body extending partially or fully over the length of the inlet. Calculations are made under a variety of geometrical constraints imposed on the inlet cross-sections to study the flow quality in the inlet. It is observed that for this class of inlets, the boundary layer has a tendency to thicken and separate readily due to the adverse pressure gradient caused by the continuous compression in the inlet. Since no experimental results are yet available, this paper has presented only the numerical results from the present analysis.

Kumar, A.↗

NASA NTRS1985

Algorithms for the Euler and Navier-Stokes equations for supercomputers

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.

Turkel, E.↗

NASA NTRS1985

Marching iterative methods for the Parabolized and Thin Layer Navier-Stokes equations

Downstream marching iterative schemes for the solution of the Parabolized or Thin Layer (PNS or TL) Navier-Stokes equations are described. Modifications of the primitive equation global relaxation sweep procedure result in efficient second-order marching schemes. These schemes take full account of the reduced order of the approximate equations as they behave like the SLOR for a single elliptic equation. The improved smoothing properties permit the introduction of Multi-Grid acceleration. The proposed algorithm is essentially Reynolds number independent and therefore can be applied to the solution of the subsonic Euler equations. The convergence rates are similar to those obtained by the Multi-Grid solution of a single elliptic equation; the storage is also comparable as only the pressure has to be stored on all levels. Extensions to three-dimensional and compressible subsonic flows are discussed. Numerical results are presented.

Israeli, M.↗

NASA NTRS1986

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

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

Vandromme, D.↗

NASA NTRS1986

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

Implicit hybrid algorithms employing symmetric planar Gauss-Seidel (SPGS) relaxation and either block-tridiagonally structured coefficient matrices (AF-SPGS) or block-triangular coefficient matrices (LU-SPGS) are derived to solve the flux-difference-split Navier-Stokes equations for three-dimensional incompressible flow in an upwind scheme. The physical basis of the approach is discussed, and results for problems involving vortex flow around a thin delta wing at Reynolds numbers 900,000 and 10,000 are presented graphically. It is found that AF-SPGS converges faster on vector computers which depend on long vector lengths to achieve optimum performance, whereas LU-SPGS is preferable on sequentially operating machines and vector computers using shorter vector lengths.

Hartwich, P.-M.↗

NASA NTRS1986

Is Navier-Stokes turbulence chaotic?

Whether turbulent solutions of the Navier-Stokes equations are chaotic is considered. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The turbulence is sustained by a nonrandom time-independent external force. The solutions separate exponentially with time, having a positive Liapunov characteristic exponent. Thus the turbulence is characterized as chaotic.

Deissler, R. G.↗

NASA NTRS1986

Analysis of two-dimensional incompressible flow past airfoils using unsteady Navier-Stokes equations

The conservative form of the unsteady Navier-Stokes equations in terms of vorticity and stream function in generalized curvilinear coordinates are used to analyze the flow structure of steady separation and unsteady flow with massive separation. The numerical method solves the discretized equations using an ADI-BGE method. The method is applied to a symmetric 12 percent thick Joukowski airfoil. A conformal clustered grid is generated; several 1-D stretching transformations are used to obtain a grid that attempts to resolve many of the multiple scales of the unsteady flow with massive separation, while maintaining the transformation metrics to be smooth and continuous in the entire flow field. Detailed numerical results are obtained for three flow configurations (1) Re = 1000, alpha = 5 deg., (2) Re =1000, alpha = 15 deg., (3) Re = 10,000, alpha = 5 deg. No artificial dissipation was added; however, lack of a fine grid in the normal direction has presently led to results which are considered qualitative, especially for case (3).

Ghia, K. N.↗

NASA NTRS1986

Numerical Solution of the Incompressible Navier-Stokes Equations in Three-dimensional Generalized Curvilinear Coordinates

Numerically solving the incompressible Navier-Stokes equations is known to be time consuming and expensive. Testing of the INS3D computers code, which solves these equations with the use of the pseudocompressibility method, shows this method to be an efficient way to obtain the steady state solution. The effects of the waves introduced by the pseudocompressibility method are analyzed and criteria are set and tested for the choice of the pseudocompressibility parameter which governs the artificial sound speed. The code is tested using laminar flow over a two dimensional backward-facing step, and laminar flow over a two dimensional circular cylinder. The results of the computations over the backward-facing step are in excellent agreement with experimental results. The transient solution of the flow over the cylinder impulsively started from rest is in good agreement with experimental results. However, the computed frequency of periodic shedding of vortices behind the cylinder is not in agreement with the experimental value. For a three dimensional test case, computations were conducted for a cylinder end wall junction. The saddle point separation and horseshoe vortex system appear in the computed field. The solution also shows secondary vortex filaments which wrap around the cylinder and spiral up in the wake.

Rogers, S. E.↗

NASA NTRS1986

Implicit time-marching solution of the Navier-Stokes equations for thrust reversing and thrust vectoring nozzle flows

An implicit finite volume method is investigated for the solution of the compressible Navier-Stokes equations for flows within thrust reversing and thrust vectoring nozzles. Thrust reversing nozzles typically have sharp corners, and the rapid expansion and large turning angles near these corners are shown to cause unacceptable time step restrictions when conventional approximate factorization methods are used. In this investigation these limitations are overcome by using second-order upwind differencing and line Gauss-Siedel relaxation. This method is implemented with a zonal mesh so that flows through complex nozzle geometries may be efficiently calculated. Results are presented for five nozzle configurations including two with time varying geometries. Three cases are compared with available experimental data and the results are generally acceptable.

Imlay, S. T.↗

NASA NTRS1986

Computation of nozzle flow fields using the PARC2D Navier-Stokes code

Supersonic nozzles which operate at low Reynolds numbers and have large expansion ratios have very thick boundary layers at their exit. This leads to a very strong viscous/inviscid interaction upon the flow within the nozzle and the traditional nozzle design techniques which correct the inviscid core with a boundary layer displacement do not accurately predict the nozzle exit conditions. A full Navier-Stokes code (PARC2D) was used to compute the nozzle flow field. Grids were generated using the interactive grid generator code TBGG. All computations were made on the NASA MSFC CRAY X-MP computer. Comparison was made between the computations and in-house wall pressure measurements for CO2 flow through a conical nozzle having an area ratio of 40. Satisfactory agreement existed between the computations and measurements for a stagnation pressure of 29.4 psia and stagnation temperature of 1060 R. However, agreement did not exist at a stagnation pressure of 7.4 psia. Several reasons for the lack of agreement are possible. The computational code assumed a constant gas gamma whereas gamma for CO2 varied from 1.22 in the plenum chamber to 1.38 at the nozzle exit. Finally, it is possible that condensation occurred during the expansion at the lower stagnation pressure.

Collins, Frank G.↗

NASA NTRS1986

An LU-SSOR scheme for the Euler and Navier-Stokes equations

A new multigrid relaxation scheme, lower-upper symmetric successive overrelaxation (LU-SSOR) is developed for the steady-state solution of the Euler and Navier-Stokes equations. The scheme, which is based on central differences, does not require flux splitting for approximate Newton iteration. Application to transonic flow shows that the new method is efficient and robust. The vectorizable LU-SSOR scheme needs only scalar diagonal inversions.

Yoon, Seokkwan↗

NASA NTRS1987

A Navier-Stokes solver using the LU-SSOR TVD algorithm

A new Navier-Stokes solver is developed by combining the efficiency of the LU-SSOR scheme and the accuracy of the flux-limited dissipation scheme. Application to laminar and turbulent flows and hypersonic flows proves the reliability of the new algorithm.

Yoon, Seokkwan↗

NASA NTRS1987

Artificial dissipation and central difference schemes for the Euler and Navier-Stokes equations

An artificial dissipation model, including boundary treatment, that is employed in many central difference schemes for solving the Euler and Navier-Stokes equations is discussed. Modifications of this model such as the eigenvalue scaling suggested by upwind differencing are examined. Multistage time stepping schemes with and without a multigrid method are used to investigate the effects of changes in the dissipation model on accuracy and convergence. Improved accuracy for inviscid and viscous airfoil flow is obtained with the modified eigenvalue scaling. Slower convergence rates are experienced with the multigrid method using such scaling. The rate of convergence is improved by applying a dissipation scaling function that depends on mesh cell aspect ratio.

Swanson, R. C.↗

NASA NTRS1987

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

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

Abarbanel, Saul↗

NASA NTRS1986

Some aspects of vortex flows determined from the thin-layer Navier-Stokes equations

Vortex flows caused by a swept wing are described in some detail. The thin-shear-layer Navier-Stokes equations with an algebraic eddy-viscosity turbulence model are solved. An implicit, factored numerical scheme is used. On the upper surface of the wing, flow is primarily along the free-stream and spanwise direction, respectively, at small and large angles of attack.

Mehta, Unmeel↗