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At least 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Numerical analysis of the scramjet inlet flow field using two-dimensional Navier-Stokes equations

A computer code has been developed to solve the full two-dimensional Navier-Stokes equations in a scramjet inlet. The analysis uses a numerical coordinate transformation which generates a set of boundary fitted curvilinear coordinates. The explicit finite-difference algorithm of MacCormack is used to solve the governing equations. A two-layer eddy viscosity model is used for the turbulent flow. The code can analyze both inviscid and viscous flows with multiple struts in the flow field. Detailed results are presented for two model problems and two scramjet inlets with one and two struts. The application of the two-dimensional analysis in the preliminary design of the actual scramjet inlet is briefly discussed.

Kumar, A.↗
NASA NTRS1982

A vectorized, finite-volume, adaptive-grid algorithm for Navier-Stokes calculations

An adaptive grid, finite-volume method has been used to solve the Navier-Stokes equations for complete (forebody and afterbody) flowfields around blunt bodies. The code, which is applicable for axisymmetric or two-dimensional flows, allows the mesh to adjust during the computation to provide a closer spacing of mesh points in regions of high gradients, thus minimizing the number of required computational points. The solution technique is explicit, utilizing a maximum time-step advancement at each grid point to accelerate convergence to the steady state. The code has been fully vectorized for efficient solution on the CYBER 203 computer. A very flexible rezoning routine is used to concentrate mesh points anywhere in the field, either by a user-defined weighting function or by allowing high gradient regions to adjust the grid. The grid adjustment routine is implicit in nature and represents a very small portion of the total computational cost. Currently, the code runs in approximately 0.000016 seconds per grid point per iteration.

Gnoffo, P. A.↗
NASA NTRS1984

Navier-Stokes Simulation of Homogeneous Turbulence on the CYBER 205

A computer code which solves the Navier-Stokes equations for three dimensional, time-dependent, homogenous turbulence has been written for the CYBER 205. The code has options for both 64-bit and 32-bit arithmetic. With 32-bit computation, mesh sizes up to 64 (3) are contained within core of a 2 million 64-bit word memory. Computer speed timing runs were made for various vector lengths up to 6144. With this code, speeds a little over 100 Mflops have been achieved on a 2-pipe CYBER 205. Several problems encountered in the coding are discussed.

Wu, C. T.↗
NASA NTRS1984

Finite-analytic numerical method for unsteady two-dimensional Navier-Stokes equations

A finite analytic (FA) numerical solution is developed for unsteady two-dimensional Navier-Stokes equations. The FA method utilizes the analytic solution in a small local element to formulate the algebraic representation of partial differential equations. The combination of linear and exponential functions that satisfy the governing equation is adopted as the boundary function, thereby improving the accuracy of the finite analytic solution. Two flows, one a starting cavity flow and the other a vortex shedding flow behind a rectangular block, are solved by the FA method. The starting square cavity flow is solved for Reynolds number of 400, 1000, and 2000 to show the accuracy and stability of the FA solution. The FA solution for flow over a rectangular block (H x H/4) predicts the Strouhal number for Reynolds numbers of 100 and 500 to be 0.156 and 0.125. Details of the flow patterns are given. In addition to streamlines and vorticity distribution, rest-streamlines are given to illustrate the vortex motion downstream of the block.

Chen, C.-J.↗
NASA NTRS1985

Calculation of steady and unsteady airfoil flow fields via the Navier-Stokes equations

A compressible time-dependent procedure for the two-dimensional ensemble averaged Navier-Stokes equations has been applied to the isolated airfoil problem in steady and unsteady flows. The procedure solves the governing equations via the linearized block implicit technique. Turbulence is modeled either via a mixing length or turbulence energy approach. The equations are solved in general non-orthogonal form with no-slip boundary conditions applied at the airfoil surface. Results are presented for airfoils at constant incidence, an airfoil in ramp motion and an airfoil oscillating through a dynamic stall loop. In general, steady converged solutions are obtained within 70 time steps over the range of Mach numbers considered. Comparisons with measured data show good agreement between computation and measurement.

Shamroth, S. J.↗
NASA NTRS1987

On the accuracy of the pseudocompressibility method in solving the incompressible Navier-Stokes equations

The method of pseudocompressibility is tested for its accuracy in solving the incompressible Navier-Stokes equations. An implicit, finite difference computer code is used to solve the equations in a three-dimensional, curvilinear coordinate system. The code employs artificial compressibiity for solving the pressure field, coupled with an implicit, approximate factorization scheme. This coupling is known as the pseudocompressibility method and introduces pressure waves of finite speed into the fluid medium that would otherwise have an infinite sound speed. The waves die out as the solution converges, and the steady state solution approaches a divergence-free condition. These waves, however, limit the time accuracy of the computations. The effects of these waves are analysed and criteria are set for choosing the pseudocompressibility parameter that governs the pressure wave speed; test cases are presented that verify these criteria. The code is tested by computing laminar flow over a two-dimensional, backward-facing step and over a two-dimensional, impulsively started circular cylinder.

Rogers, S. E.↗
NASA NTRS1986

A Petrov-Galerkin finite element method for the compressible Euler and Navier-Stokes equations

An overview of a new finite element method for the compressible Euler and Navier-Stokes equations is presented. The discretization is based on entropy variables. The method is developed within the framework of a Petrov-Galerkin formulation. Two perturbations are added to the weighting function; one is a generalization of the SUPG operator and the other is designed to enhance shock capturing capability. The treatment of boundary conditions and the consistent calculation of boundary fluxes are addressed. Results of numerical tests are presented which confirm the robustness and wide applicability of the method.

Franca, L. P.↗
NASA NTRS1987

Application of an upwind algorithm to the three-dimensional parabolized Navier-Stokes equations

A new computer code for the solution of the three-dimensional parabolized Navier-Stokes equations has been developed. The code employs a state-of-the-art upwind algorithm to capture strong shock waves. The algorithm is implicit, uses finite volumes, and is second-order accurate in the crossflow directions. The new code is validated through application to laminar hypersonic flows past two simple body shapes: a circular cone of 10 deg half-angle, and a generic all-body hypersonic vehicle. Cone flow solutions were computed at angles of attack of 12, 20, and 24 deg and results are in agreement with experimental data. Results are also presented for the flow past the all-body vehicle at angles of incidence of 0 and 10 deg.

Lawrence, Scott L.↗
NASA NTRS1987

An efficient iteration strategy for upwind/relaxation solutions to the thin-layer Navier-Stokes equations

A previously developed upwind/relaxation algorithm for solving the unsteady, compressible, thin-layer Navier-Stokes equations is presently modified so that the downstream influence of the subsonic part of the boundary layer in an otherwise supersonic flow is suppressed by restricting the streamwise pressure gradient. A 'parabolized' solution is then efficiently obtained by marching downstream and iterating locally in each crossflow plane until achieving convergence. This parabolized solution is an excellent final one for problems without large adverse streamwise pressure gradients.

Newsome, Richard W.↗
NASA NTRS1987

Study of instability and active control of boundary layers using Navier-Stokes equations

Spatial stability of a three-dimensional growing boundary layer is studied using Navier-Stokes equations. The finite difference method used is an explicit, predictor-corrector type which is fourth-order accurate in space and second-order in time. Active control of two-dimensional disturbances is simulated by localized surface heating. The computations show features of the flow relevant to early stages of transition such as lifting of vorticity away from the wall and localized regions of intense shear. Active control with single heating strip is only marginally effective, but may be improved by multiple strips.

Parikh, Paresh↗
NASA NTRS1988

A streamwise upwind algorithm for the Euler and Navier-Stokes equations applied to transonic flows

A new algorithm was developed for the Euler and Navier-Stokes equations that uses upwind differencing based on the streawise direction. This algorithm is time accurate and can be used in codes for calculating unsteady transonic flows over wings. Such codes can be used for the flutter analysis of wings. In this algorithm, the coordinate system is locally rotated to align with the streamwise direction. For differencing the convective terms in the streamwise direction, a new form of flux splitting is employed, in which the biasing depends on the local Mach number. In the plane perpendicular to the stream direction, the new flux splitting uses the condition of no flow in that local plane. By using a locally rotated coordinate system, the convective flux vector biasing depends on the total Mach number. Hence, the switching of the flux vector biasing occurs across shock waves and the proper domain of dependence is used in supersonic regions. For comparison, many other upwind methods switch differencing based on Mach number of shock waves in multidimensional flows. The formulas for the convective flux vector differencing do not contain any user specified parameters. So, the amount of numerical dissipation is automatically determined.

Goorjian, Peter M.↗
NASA NTRS1988

Navier-Stokes calculations using Cartesian grids. I - Laminar flows

A finite-volume formulation for the Navier-Stokes equations using Cartesian grids is used to study flows past airfoils. In addition to the solution of the complete equations, solutions for two simplified versions of the governing equations were obtained and compared with those using body-fitted grids. Results are presented for two airfoil sections, NACA 0012 and RAE 2822, for a range of Mach numbers, angles of attack, and Reynolds numbers. It is shown that the results are highly dependent on the smoothness of the surface grid. Without such smoothness, the skin friction and pressure converge to nonuniform distributions. On the other hand, when surface cells with smoothly varying areas are used, the results compared favorably with calculations employing body-fitted grids.

Frymier, Paul D., Jr.↗
NASA NTRS1989

Unsteady Navier-Stokes computations past oscillating delta wing at high incidence

The unsteady, thin-layer, compressible Navier-Stokes equations, written in the moving frame of reference for the flow relative motion, is solved for the steady and unsteady supersonic flow around a round-edged delta wing. For supersonic flow, local conical flow solution has been obtained from the three-dimensional equations. Pseudotime stepping is used for the steady flow, while time-accurate stepping is used for the unsteady flow. The computational scheme is an implicit approximately-factored finite volume scheme which uses explicit and implicit dissipation terms. The scheme is verified for the steady flow solution. The scheme is then applied to a delta wing undergoing rolling oscillation at a reduced frequency of 1.137 with 15- deg maximum amplitude about a mean angle of attack of 10 deg for a Mach number of 2 and a Reynolds number of 500,000.

Kandil, Osama A.↗
NASA NTRS1989

Comparisons of TVD schemes applied to the Navier-Stokes equations

In this study, the following total variation diminishing (TVD) schemes for solving the Navier-Stokes equations have been tested: the Chakravarthy and Szema (1985) upwind biased TVD scheme, the Harten's upwind TVD scheme described by Yee et al. (1983), and the Yee's (1985) symmetric TVD scheme. The schemes have been compared using three test cases. The first case was the one-dimensional shock tube problem which tested the shock-capturing abilities of the schemes. Chakravarthy's and Harten's schemes gave similar results which were found to be more accurate than the results from Yee's scheme. The second case was a compressible boundary layer which tested the schemes's abilities to solve fiscous flows. In this case, the three schemes yielded almost identical results. Finally, the shock/boundary-layer interaction case studied experimentally by Hakkinen et al. (1959) was computed. Here, Chakravarthy's and Yee's schemes compared most favorably with the published data, with Yee's scheme giving slightly better results.

Buelow, Philip E.↗
NASA NTRS1989

Development of an efficient multigrid code for 3-D Navier-Stokes equations

A multigrid acceleration technique has been developed to solve the three-dimensional Navier-Stokes equations efficiently. An explicit multistage Runge-Kutta type of time-stepping scheme is used as the basic algorithm in conjunction with the multigrid scheme. Solutions for flow over a finite wing have been obtained on extremely fine meshes in order to achieve grid convergence of the solutions. Present solutions indicate that the number of multigrid cycles required to achieve a given level of convergence does not increase with the number of mesh points employed, making it a very attractive scheme for fine meshes.

Vatsa, Veer N.↗
NASA NTRS1988

A streamwise upwind algorithm for the Euler and Navier-Stokes equations applied to transonic flows

A new algorithm was developed for the Euler and Navier-Stokes equations that uses upwind differencing based on the streamwise direction. This algorithm is time accurate and can be used in codes for calculating unsteady transonic flows over wings. Such codes can be used for the flutter analysis of wings. In this algorithm, the coordinate system is locally rotated to align with the streamwise direction. For differencing the convective terms in the streamwise direction, a new form of flux splitting is employed, in which the biasing depends on the local Mach number. In the plane perpendicular to the stream direction, the new flux splitting uses the condition of no flow in that local plane. By using a locally rotated coordinate system, the convective flux vector biasing depends on the total Mach number. Hence, the switching of the flux vector biasing occurs across shock waves and the proper domain of dependence is used in supersonic regions. For comparison, many other upwind methods switch differencing based on Mach number of shock wave in multidimensional flows. The formulas for the convective flux vector differencing do not contain any user specified parameters. So, the amount of numerical dissipation is automatically determined.

Goorjian, P. M.↗
NASA NTRS1990

PARC Navier-Stokes code upgrade and validation for high speed aeroheating predictions

Applications of the PARC full Navier-Stokes code for hypersonic flowfield and aeroheating predictions around blunt bodies such as the Aeroassist Flight Experiment (AFE) and Aeroassisted Orbital Transfer Vehicle (AOTV) are evaluated. Two-dimensional/axisymmetric and three-dimensional perfect gas versions of the code were upgraded and tested against benchmark wind tunnel cases of hemisphere-cylinder, three-dimensional AFE forebody, and axisymmetric AFE and AOTV aerobrake/wake flowfields. PARC calculations are in good agreement with experimental data and results of similar computer codes. Difficulties encountered in flowfield and heat transfer predictions due to effects of grid density, boundary conditions such as singular stagnation line axis and artificial dissipation terms are presented together with subsequent improvements made to the code. The experience gained with the perfect gas code is being currently utilized in applications of an equilibrium air real gas PARC version developed at REMTECH.

Liver, Peter A.↗