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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 109 records · Page 6
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NASA NTRS1982

Finite area method for nonlinear conical flows

A fully conservative finite area method for the computation of steady inviscid flow about general conical bodies at incidence is described. The procedure utilizes the potential approximation and implements a body conforming mesh generator. The conical potential is assumed to have its best linear variation inside each mesh cell and a secondary interlocking cell system is used to establish the flux balance required to conserve mass. In the supersonic regions the scheme is desymmetrized by adding appropriate artificial viscosity in conservation form. The algorithm is nearly an order of a magnitude faster than present Euler methods and predicts known results accurately and qualitative features such as nodal point lift off correctly. Results are compared with those of other investigations.

Sritharan, S. S.↗
NASA NTRS1983

Finite area method for nonlinear supersonic conical flows

A fully conservative numerical method for the computation of steady inviscid supersonic flow about general conical bodies at incidence is described. The procedure utilizes the potential approximation and implements a body conforming mesh generator. The conical potential is assumed to have its best linear variation inside each mesh cell; a secondary interlocking cell system is used to establish the flux balance required to conserve mass. In the supersonic regions the scheme is symmetrized by adding artificial viscosity in conservation form. The algorithm is nearly an order of a magnitude faster than present Euler methods and predicts known results accurately and qualitative features such as nodal point lift off correctly. Results are compared with those of other investigators.

Sritharan, S. S.↗
NASA NTRS1983

New discretization and solution techniques for incompressible viscous flow problems

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.

Gunzburger, M. D.↗
NASA NTRS1983

A multi-grid method for the computation of viscid/inviscid interactions on airfoils

An improved version of the 'GRUMFOIL' code has been developed for the computation of airfoil flows. The method employs a conservative difference scheme for the potential equation, integral methods for the boundary layer, and viscous coupling conditions that fully account for the wake and strong interaction effects at trailing edges. The improved version uses Jameson's 'MAD' scheme to accelerate convergence of the inviscid solution, an improved 2nd order artificial viscosity and far field 'TARE' correction to reduce spatial truncation errors and Carter's semi-inverse method for the viscous solution. Results are presented which demonstrate a factor of ten reduction in computing cost.

Melnik, R. E.↗
NASA NTRS1982

ADI on staggered mesh - A method for the calculation of compressible convection

An alternating direction implicit (ADI) method has been applied to a staggered grid for the computation of convection in a highly stratified fluid. Since artificial viscosity is not needed, subtle effects like the onset of convection can be studied. These computations compare well with the 2-D results by Graham (1975) and also agree with standard Boussinesq results when taken to that limit. Good efficiency has been achieved with a time step hundreds of times larger than the stability limit imposed by the explicit treatment of diffusion and the Courant number is not restricted to be below 1. The Navier-Stokes equation contains cross spatial derivatives which are treated explicitly in most ADI schemes. The destabilizing effect of such a practice on a 2-D model system with second-order spatial derivative terms only was analyzed and found to be not excessive.

Chan, K. L.↗
NASA NTRS1982

Computational fluid dynamics of airfoils and wings

It is pointed out that transonic flow is one of the fields where computational fluid dynamics turns out to be most effective. Codes for the design and analysis of supercritical airfoils and wings have become standard tools of the aircraft industry. The present investigation is concerned with mathematical models and theorems which account for some of the progress that has been made. The most successful aerodynamics codes are those for the analysis of flow at off-design conditions where weak shock waves appear. A major breakthrough was achieved by Murman and Cole (1971), who conceived of a retarded difference scheme which incorporates artificial viscosity to capture shocks in the supersonic zone. This concept has been used to develop codes for the analysis of transonic flow past a swept wing. Attention is given to the trailing edge and the boundary layer, entropy inequalities and wave drag, shockless airfoils, and the inverse swept wing code.

Garabedian, P.↗
NASA NTRS1983

Entropy and vorticity corrections for transonic flows

Different models for inviscid transonic flows are examined. The common assumptions that the flow is isentropic and irrotational are critically evaluated. Entropy and vorticity correction procedures for potential and stream function formlations are presented together with the details of the treatment of shocks and wakes, and drag and lift calculations. The nonuniqueness problem is studied using different artificial viscosity forms. Numerical results are compared to Euler solutions.

Hafez, M.↗
NASA NTRS1983

New discretization and solution techniques for incompressible viscous flow problems

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.

Gunzburger, M. D.↗
NASA NTRS1984

High speed inviscid compressible flow by the finite element method

The finite element method and an explicit time stepping algorithm which is based on Taylor-Galerkin schemes with an appropriate artificial viscosity is combined with an automatic mesh refinement process which is designed to produce accurate steady state solutions to problems of inviscid compressible flow in two dimensions. The results of two test problems are included which demonstrate the excellent performance characteristics of the proposed procedures.

Zienkiewicz, O. C.↗
NASA NTRS1984

Spectral methods for compressible flow problems

Recent results concerning numerical simulation of shock waves using spectral methods are reviewed. Shock fitting techniques were discussed as well as shock capturing techniques with finite difference artificial viscosity. Also the notion of the information contained in the numerical results obtained by spectral methods and show how this information is recovered was discussed.

Gottlieb, D.↗
NASA NTRS1984

Implicit treatment of the unsteady full potential equation in conservation form

An implicit, conservative treatment for the unsteady full potential equation in two-dimensions is presented. The method employs a local time linearization for density, and introduces flux biasing concepts based on sonic conditions for the generation of artificial viscosity to capture shocks without any overshoots. The boundary condition is treated implicitly using a splitting procedure consistent with the approximate factorization scheme. This allows for extremely large Courant numbers, even for nonorthogonal grid at the body. The method has application not only to unsteady problems, but also to generate the starting blunt body solution for a supersonic full potential marching code. Results are presented for flows over cylinders, spheres and airfoils. Comparisons are made with available Euler and full potential results, and are in excellent agreement.

Shankar, V.↗
NASA NTRS1982

A minimal residual method for transonic potential flows

For transonic flow calculations, a combination of the successive line over-relaxation (SLOR) and the preconditioned conjugate gradient (CG) method has been suggested by Wong and Hafez (1981). This paper studies the method of minimal residual (MR) which avoids a combined iteration. This method is closely related to the CG method, may be regarded as a first-order gradient method, and is applicable to symmetric and nonsymmetric matrices. The problem is formulated as a nonlinear mixed elliptic-hyperbolic partial differential equation which includes an artificial viscosity and a switching function which is zero in subsonic regions and nonzero in supersonic regions. Alternatives to the SLOR method which provide faster convergence rates are introduced. The preconditioned MR algorithm is developed, and transonic potential flows around NACA 0012 airfoil are calculated for different Mach numbers and angles of attack. Preliminary results are presented, demonstrating that the MR algorithm requires no parameter estimation and rapidly converges for subsonic flows.

Wong, Y. S.↗
NASA NTRS1984

Relaxation and approximate factorization methods for the unsteady full potential equation

The unsteady form of the full potential equation is solved in conservation form, using implicit methods based on approximate factorization and relaxation schemes. A local time linearization for density is introduced to enable solution to the equation in terms of phi, the velocity potential. A novel flux-biasing technique is applied to generate proper forms of the artificial viscosity, to treat hyperbolic regions with shocks and sonic lines present. The wake is properly modeled by accounting not only for jumps in phi, but also for jumps in higher derivatives of phi obtained from requirements of density continuity. The far field is modeled using the Riemann invariants to simulate nonreflecting boundary conditions. Results are presented for flows over airfoils, cylinders, and spheres. Comparisons are made with available Euler and full potential results.

Shankar, V.↗
NASA NTRS1985

Solution method for a hovering helicopter rotor using the Euler equations

A method for the calculation of the flow field of a helicopter rotor blade in hover is presented. The approach uses a finite volume solution of the three dimensional Euler equations for the blade near field. In the Euler solver the velocity field is decomposed into two parts. One is the induced velocity of the vortex wake extending below the blade, found from a free wake calculation procedure. The other part is the unknown additional velocity field of the rotor blade. This approach eliminates numerical diffusion of the rolled up wake vorticity due to truncation error and artificial viscosity. Also, the effects of the far wake are included in the limited computational domain. Solutions are presented for an isolated wing and a model helicopter rotor and compared to experiment.

Roberts, T. W.↗
NASA NTRS1985

Application of Runge Kutta time marching scheme for the computation of transonic flows in turbomachines

Numerical solutions of the unsteady Euler equations are obtained using the classical fourth order Runge Kutta time marching scheme. This method is fully explicit and is applied to the governing equations in the finite volume, conservation law form. In order to determine the efficiency of this scheme for solving turbomachinery flows, steady blade-to-blade solutions are obtained for compressor and turbine cascades under subsonic and transonic flow conditions. Computed results are compared with other numerical methods and wind tunnel measurements. The present study also focuses on other important numerical aspects influencing the performance of the algorithm and the solution accuracy such as grid types, boundary conditions, and artificial viscosity. For this purpose, H, O, and C type computational grids as well as characteristic and extrapolation type boundary conditions are included in the solution procedure.

Subramanian, S. V.↗
NASA NTRS1985

A fast, time-accurate unsteady full potential scheme

The unsteady form of the full potential equation is solved in conservation form by an implicit method based on approximate factorization. At each time level, internal Newton iterations are performed to achieve time accuracy and computational efficiency. A local time linearization procedure is introduced to provide a good initial guess for the Newton iteration. A novel flux-biasing technique is applied to generate proper forms of the artificial viscosity to treat hyperbolic regions with shocks and sonic lines present. The wake is properly modeled by accounting not only for jumps in phi, but also for jumps in higher derivatives of phi, obtained by imposing the density to be continuous across the wake. The far field is modeled using the Riemann invariants to simulate nonreflecting boundary conditions. The resulting unsteady method performs well which, even at low reduced frequency levels of 0.1 or less, requires fewer than 100 time steps per cycle at transonic Mach numbers. The code is fully vectorized for the CRAY-XMP and the VPS-32 computers.

Shankar, V.↗
NASA NTRS1986

Viscous compressible flow direct and inverse computation and illustrations

An algorithm for laminar and turbulent viscous compressible two dimensional flows is presented. For the application of precise boundary conditions over an arbitrary body surface, a body-fitted coordinate system is used in the physical plane. A thin-layer approximation of tne Navier-Stokes equations is introduced to keep the viscous terms relatively simple. The flow field computation is performed in the transformed plane. A factorized, implicit scheme is used to facilitate the computation. Sample calculations, for Couette flow, developing pipe flow, an isolated airflow, two dimensional compressor cascade flow, and segmental compressor blade design are presented. To a certain extent, the effective use of the direct solver depends on the user's skill in setting up the gridwork, the time step size and the choice of the artificial viscosity. The design feature of the algorithm, an iterative scheme to correct geometry for a specified surface pressure distribution, works well for subsonic flows. A more elaborate correction scheme is required in treating transonic flows where local shock waves may be involved.

Yang, T. T.↗
NASA NTRS1986

An entropy correction method for unsteady full potential flows with strong shocks

An entropy correction method for the unsteady full potential equation is presented. The unsteady potential equation is modified to account for entropy jumps across shock waves. The conservative form of the modified equation is solved in generalized coordinates using an implicit, approximate factorization method. A flux-biasing differencing method, which generates the proper amounts of artificial viscosity in supersonic regions, is used to discretize the flow equations in space. Comparisons between the present method and solutions of the Euler equations and between the present method and experimental data are presented. The comparisons show that the present method more accurately models solutions of the Euler equations and experiment than does the isentropic potential formulation.

Whitlow, W., Jr.↗