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NASA NTRS1982

Solutions of the compressible Navier-Stokes equations using the integral method

The integral representation method was used to obtain numerical solutions of the compressible, unsteady, two-dimensional Navier-Stokes equations for subsonic flows. The equations were written with the vorticity, the dilatation, the density, and the enthalpy as the dependent variables. The method was tested by solving the following problems: the flow over a flat plate, around a circular cylinder, and around a Joukowski airfoil. The last two problems involved massive flow separation. The approach offers the capability of confining the domain of computations to the region where two quantities, the vorticity and the difference in dilatation between the real flow and the potential flow around the body, are non-negligible.

Elrefaee, M. M.↗
NASA NTRS1982

Numerical boundary condition procedures and multigrid methods; Proceedings of the Symposium, NASA Ames Research Center, Moffett Field, CA, October 19-22, 1981

Papers presented in this volume provide an overview of recent work on numerical boundary condition procedures and multigrid methods. The topics discussed include implicit boundary conditions for the solution of the parabolized Navier-Stokes equations for supersonic flows; far field boundary conditions for compressible flows; and influence of boundary approximations and conditions on finite-difference solutions. Papers are also presented on fully implicit shock tracking and on the stability of two-dimensional hyperbolic initial boundary value problems for explicit and implicit schemes.

Source record↗
NASA NTRS1986

Aerodynamics of Engine-Airframe Interaction

The report describes progress in research directed towards the efficient solution of the inviscid Euler and Reynolds-averaged Navier-Stokes equations for transonic flows through engine inlets, and past complete aircraft configurations, with emphasis on the flowfields in the vicinity of engine inlets. The research focusses upon the development of solution-adaptive grid procedures for these problems, and the development of multi-grid algorithms in conjunction with both, implicit and explicit time-stepping schemes for the solution of three-dimensional problems. The work includes further development of mesh systems suitable for inlet and wing-fuselage-inlet geometries using a variational approach. Work during this reporting period concentrated upon two-dimensional problems, and has been in two general areas: (1) the development of solution-adaptive procedures to cluster the grid cells in regions of high (truncation) error;and (2) the development of a multigrid scheme for solution of the two-dimensional Euler equations using a diagonalized alternating direction implicit (ADI) smoothing algorithm.

Caughey, D. A.↗
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 NTRS1987

Performance studies of the multigrid algorithms implemented on hypercube multiprocessor systems

In this paper, we analyze and compare the performance on a hypercube multiprocessor of some of the major multigrid techniques used in practice. The model problem considered here is that of solving the 2-D incompressible Navier-Stokes equations representing the flow between two parallel plates. Results obtained by implementing the different multigrid schemes on an iPSC are presented. Effects on the overall performance of various parameters of the algorithms, of the partitioning strategies employed, and of some of the characteristics of the underlying architecture are discussed.

Naik, Vijay K.↗
NASA NTRS1986

Development of a finite volume time marching method

Progress made in the development of a time-marching finite volume method from September 1984 to December 1984 is reported. The objective of the work is to develop and demonstrate a Navier-Stokes approach for transonic flow which includes viscous terms in the finite volume method. The accuracy of the computational method will be verified using a transonic diffuser as a test case. The computational goal is to calculate the flow in sufficient detail and with sufficient accuracy that the loss generating mechanisms can be studied to assess the sources of inefficiency in the transonic diffuser.

Nicholson, Stephen↗
NASA NTRS1988

On the coupling of hyperbolic and parabolic systems: Analytical and numerical approach

The coupling of hyperbolic and parabolic systems is discussed in a domain Omega divided into two distinct subdomains omega(+) and omega(-). The main concern is to find the proper interface conditions to be fulfilled at the surface separating the two domains. Next, they are used in the numerical approximation of the problem. The justification of the interface conditions is based on a singular perturbation analysis, i.e., the hyperbolic system is rendered parabolic by adding a small artifical viscosity. As this goes to zero, the coupled parabolic-parabolic problem degenerates into the original one, yielding some conditions at the interface. These are taken as interface conditions for the hyperbolic-parabolic problem. Actually, two alternative sets of interface conditions are discussed according to whether the regularization procedure is variational or nonvariational. It is shown how these conditions can be used in the frame of a numerical approximation to the given problem. Furthermore, a method of resolution is discussed which alternates the resolution of the hyperbolic problem within omega(-) and of the parabolic one within omega(+). The spectral collocation method is proposed, as an example of space discretization (different methods could be used as well); both explicit and implicit time-advancing schemes are considered. The present study is a preliminary step toward the analysis of the coupling between Euler and Navier-Stokes equations for compressible flows.

Gastaldi, Fabio↗
NASA NTRS1990

On the numerical simulation of spatial disturbances in blunt-nose flat plate flow

The feasibility of the simulation of the evolution of spatially amplified disturbances in realistic airfoil flows using a standard Navier-Stokes airfoil code is considered for a blunt-nose flat plate flow. A basic stationary flow and its linear-stability-theory characteristics are analyzed. A computational C-grid is generated using an algebraic grid-generation technique. It is concluded that further improvements to the computational grid and to the code are necessary to make the proposed simulations economical.

Laurien, Eckart↗
NASA NTRS1991

Generalized conjugate-gradient methods for the Navier-Stokes equations

A generalized conjugate-gradient method is used to solve the two-dimensional, compressible Navier-Stokes equations of fluid flow. The equations are discretized with an implicit, upwind finite-volume formulation. Preconditioning techniques are incorporated into the new solver to accelerate convergence of the overall iterative method. The superiority of the new solver is demonstrated by comparisons with a conventional line Gauss-Siedel Relaxation solver. Computational test results for transonic flow (trailing edge flow in a transonic turbine cascade) and hypersonic flow (M = 6.0 shock-on-shock phenoena on a cylindrical leading edge) are presented. When applied to the transonic cascade case, the new solver is 4.4 times faster in terms of number of iterations and 3.1 times faster in terms of CPU time than the Relaxation solver. For the hypersonic shock case, the new solver is 3.0 times faster in terms of number of iterations and 2.2 times faster in terms of CPU time than the Relaxation solver.

Ajmani, Kumud↗
NASA NTRS1991

An iterative implicit diagonally-dominant factorization algorithm for solving the Navier-Stokes equations

Presented here is an algorithm for solving the multidimensional unsteady Navier-Stokes equations for compressible flows. It is based on a diagonally-dominant approximate factorization procedure. The factorization error and the timewise linearization error associated with this procedure are reduced by performing Newton-type inner iterations at each time step. The inviscid fluxes are evaluated by the fourth-order central differencing scheme amended with a numerical dissipation directly proportional to the entire dissipative part of the truncation error intrinsic to the third order biased upwind scheme. The important features of the proposed solution are elucidated by the numerical results of the convection of a vortex and the backward-facing step flows.

Chen, Shu-Cheng↗
NASA NTRS1992

Postflight aerothermodynamic analysis of Pegasus(tm) using computational fluid dynamic techniques

The objective was to validate the computational capability of the NASA Ames Navier-Stokes code, F3D, for flows at high Mach numbers using comparison flight test data from the Pegasus (tm) air launched, winged space booster. Comparisons were made with temperature and heat fluxes estimated from measurements on the wing surfaces and wing-fuselage fairings. Tests were conducted for solution convergence, sensitivity to grid density, and effects of distributing grid points to provide high density near temperature and heat flux sensors. The measured temperatures were from sensors embedded in the ablating thermal protection system. Surface heat fluxes were from plugs fabricated of highly insulative, nonablating material, and mounted level with the surface of the surrounding ablative material. As a preflight design tool, the F3D code produces accurate predictions of heat transfer and other aerodynamic properties, and it can provide detailed data for assessment of boundary layer separation, shock waves, and vortex formation. As a postflight analysis tool, the code provides a way to clarify and interpret the measured results.

Kuhn, Gary D.↗
NASA NTRS1992

Adaptive mesh strategies for the spectral element method

An adaptive spectral method was developed for the efficient solution of time dependent partial differential equations. Adaptive mesh strategies that include resolution refinement and coarsening by three different methods are illustrated on solutions to the 1-D viscous Burger equation and the 2-D Navier-Stokes equations for driven flow in a cavity. Sharp gradients, singularities, and regions of poor resolution are resolved optimally as they develop in time using error estimators which indicate the choice of refinement to be used. The adaptive formulation presents significant increases in efficiency, flexibility, and general capabilities for high order spectral methods.

Mavriplis, Catherine↗
NASA NTRS1992

An investigation of shock/turbulent boundary layer bleed interactions

A numerical investigation was conducted to determine the effect of bleed on oblique shock wave/turbulent boundary layer interactions. The numerical solution to the compressible Navier-Stokes equations reveal the flow details throughout the interaction zone and inside the normal bleed slot. Results are presented for an incident oblique shock of sufficient strength to cause boundary layer separation in the absence of bleed. Bleed is applied across the shock impingement location over a range of bleed mass flow rates corresponding to different values of plenum pressures. The results indicate a complex flow structure with large variations in both normal and tangential flow velocities across the bleed slot. The flow entrainment into the slot is accompanied by an expansion-compression wave system with a bow shock originating inside the bleed slot. Increasing the bleed mass flow by decreasing the plenum pressure caused an initial decrease then a later increase in the boundary layer momentum and displacement thickness downstream of the interaction.

Hamed, A.↗
NASA NTRS1993

Hypersonic blunt body wake computations using DSMC and Navier-Stokes solvers

Numerical results obtained with direct simulation Monte Carlo (DSMC) and Navier-Stokes methods are presented for Mach 20 nitrogen flow about a 70-deg blunted cone. The flow conditions simulated are those that can be obtained in existing low-density hypersonic wind tunnels. Three sets of flow conditions are considered with freestream Knudsen numbers ranging from 0.03 to 0.001. The focus is on the wake structure: how does the wake structure change as a function of rarefaction, what are the afterbody levels of heating, and to what limits are continuum models realistic as rarefaction in the wake is progressively increased. Calculations are made with and without an afterbody sting. Results for the afterbody sting are emphasized in anticipation of an experimental study for the current flow conditions and model configuration. The Navier-Stokes calculations were made with and without slip boundary conditions. Comparisons of the results obtained with the two simulation methodologies are made for both flowfield structure and surface quantities.

Moss, James N.↗
NASA NTRS1993

Numerical simulation and physical aspects of supersonic vortex breakdown

Existing numerical simulations and physical aspects of subsonic and supersonic vortex-breakdown modes are reviewed. The solution to the problem of supersonic vortex breakdown is emphasized in this paper and carried out with the full Navier-Stokes equations for compressible flows. Numerical simulations of vortex-breakdown modes are presented in bounded and unbounded domains. The effects of different types of downstream-exit boundary conditions are studied and discussed.

Liu, C. H.↗
NASA NTRS1947

A device for measuring sonic velocity and compressor Mach number

A device has been developed which measures the velocity of sound in fluids at stagnation and is especially adaptable to turbine and compressor testing for which the constituency of the working fluid may be in doubt. By utilizing the shaft frequency of a rotary compressor, the instrument can also be used to provide a direct measurement of the compressor Mach number (ratio of blade-tip velocity to inlet velocity of sound at stagnation). A Helmholtz resonator is employed in the measurement of the sound velocity. Viscous effects in the orifice of the Helmholtz resonator are shown to be important and can be taken into account with the help of a parameter obtained from Stokes solution of the flow near an oscillating wall. This parameter includes the kinematic viscosity of the fluid and the frequency of sound in the resonator. When these effects are recognized, the resonator can be calibrated to measure velocity of sound or compressor Mach number to an accuracy of better than 0.5 percent.

Huber, Paul W↗