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NASA NTRS1985

Application of a viscous-inviscid interaction method to predict transonic separated flows

A viscous-inviscid interaction numerical procedure is used to predict turbulent transonic separated flows over axisymmetric bodies. The viscous flow solutions are obtained by solving the boundary-layer equations inversely in a coupled manner by a finite-difference scheme; the inviscid flow is determined by a finite-difference solution to the full-potential equation in conservative form. Parameters affecting the convergence rate of the interaction procedure are discussed. The predictions of a new turbulence model proposed by Johnson and King are compared with experimental data and numerical solutions to the Navier-Stokes equations for flows with large regions of separation.

Lee, D. S.↗

NASA NTRS1985

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 NTRS1985

Theoretical and experimental flow fields for a supersonic cruise fighter forebody

The capability of two numerical methods to predict the flow field about a representative supersonic cruise aircraft was examined. The two codes were a small-disturbance transonic program of Boppe and a conservative form full-potential transonic program of Shankar and Szema. For the former code, comparisons were made with wind-tunnel data at Mach numbers of 0.6, 0.9, and 1.2 and angles of attack of 0 deg, 5 deg, and 10 deg (7.5 deg instead of 10 deg at a Mach number of 1.2). Predictions from the two codes were compared at a Mach number of 1.2 and an angle of attack of 7.5 deg. The comparison criteria were contours of local angle of attack, local angle of sideslip, and local Mach number. The comparisons indicated that both codes may be considered useful for design applications, depending on the degree of accuracy required by the user's solution. Both solutions show an inaccuracy in their predictions, particularly as Mach number and/or angle of attack increases, because of their lack of viscous effects and any mechanisms to predict vortex development.

Yaros, S. F.↗

NASA NTRS1984

User's guide for NASCRIN: A vectorized code for calculating two-dimensional supersonic internal flow fields

A computer program NASCRIN has been developed for analyzing two-dimensional flow fields in high-speed inlets. It solves the two-dimensional Euler or Navier-Stokes equations in conservation form by an explicit, two-step finite-difference method. An explicit-implicit method can also be used at the user's discretion for viscous flow calculations. For turbulent flow, an algebraic, two-layer eddy-viscosity model is used. The code is operational on the CDC CYBER 203 computer system and is highly vectorized to take full advantage of the vector-processing capability of the system. It is highly user oriented and is structured in such a way that for most supersonic flow problems, the user has to make only a few changes. Although the code is primarily written for supersonic internal flow, it can be used with suitable changes in the boundary conditions for a variety of other problems.

Kumar, A.↗

NASA NTRS1986

Preconditioned methods for solving the incompressible and low speed compressible equations

Acceleration methods are presented for solving the steady state incompressible equations. These systems are preconditioned by introducing artificial time derivatives which allow for a faster convergence to the steady state. The compressible equations in conservation form with slow flow are also considered. Two arbitrary functions, alpha and beta, are introduced in the general preconditioning. An analysis of this system is presented and an optimal value for beta is determined given a constant, alpha. It is further shown that the resultant incompressible equations form a symmetric hyperbolic system and so are well posed. Several generalizations to the compressible equations are presented which generalize previous results.

Turkel, E.↗

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.↗

NASA NTRS1986

Transonic viscous and inviscid solutions using a composite velocity procedure

Solutions for transonic viscous and inviscid flows using a composite velocity procedure are presented. The velocity components of the compressible Navier-Stokes equations are written in terms of a multiplicative composite consisting of a viscous or rotational velocity and an inviscid, irrotational, potential like function. For viscous flows, the governing equations are solved using a coupled strongly implicit procedure and the outer inviscid flow corresponds to an irrotational, potential flow. Further investigation of the inviscid flow solution is made so that the correct rotational flow solution may be obtained for the transonic case. The Euler equations are solved for the inviscid flow calculations. Solutions to the full potential equation are recovered unless the axial momentum equation is written in full conservation form.

Gordnier, R. E.↗

NASA NTRS1985

Computations of unsteady transonic flows

During the last eight years, the subject of computational unsteady transonic aerodynamics has undergone a period of rapid growth. A brief survey of some of the fundamental advances during this period is provided, and some of the research done at NASA Ames Research Center is described in detail. The small-distance potential equation is considered, taking into account features of the unsteady transonic flow, the governing equation, the pressure coefficient, the wake condition, the airfoil tangency condition, the downstream boundary condition, the alternating direction implicit (ADI) algorithm, a grid system, boundary conditions, an airfoil with oscillating trailing edge flap, three types of shock-wave motion, and an example of a simple aeroelastic problem. A description is given of an implicit algorithm for the unsteady full potential equation in conservation form.

Goorjian, P. M.↗

NASA NTRS1985

Shock modelling in transonic and supersonic flow

Numerical simulation studies of problems in transonic flow are conducted in connection with the design of aircraft flying near the speed of sound, while recently there has also been a great deal of interest in supersonic and hypersonic flow calculations. Three important models for inviscid compressible gasdynamics are utilized in the study of these flow problems, taking into account the transonic small disturbance equation (TSD), the transonic full potential equation (FP), and the full Euler equations for compressible gasdynamics (EU). The present paper has the objective to provide a description of shock capturing methods recently developed for each model. The design principles behind the algorithms are also examined, giving attention to consistency, conservative form, monotone and sharp discrete shocks, and a bound on the variation, which prevents spurious oscillations.

Osher, S.↗

NASA NTRS1986

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

Whitlow, W., Jr.↗

NASA NTRS1987

Analysis of Scramjet Inlets

NASCRIN program analyzes two-dimensional flow fields in supersoniccombustion ramjet (scramjet) inlets. Solves two-dimensional Euler or Navier-Stokes equations in conservative form by unsplit, explicit, two-step finite-difference method. More recent explicit/implicit, two-step scheme incorporated by analysis of viscous flow. Algebraic, two-layer eddy-viscosity model used for turbulent-flow calculations. Vectorized version, written for CDC CYBER 205, whereas scalar version, can be run on CRAY or other scalar computers.

Kumar, A.↗

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

Application of viscous-inviscid interaction methods to transonic turbulent flows

Two different viscous-inviscid interaction schemes were developed for the analysis of steady, turbulent, transonic, separated flows over axisymmetric bodies. The viscous and inviscid solutions are coupled through the displacement concept using a transpiration velocity approach. In the semi-inverse interaction scheme, the viscous and inviscid equations are solved in an explicitly separate manner and the displacement thickness distribution is iteratively updated by a simple coupling algorithm. In the simultaneous interaction method, local solutions of viscous and inviscid equations are treated simultaneously, and the displacement thickness is treated as an unknown and is obtained as a part of the solution through a global iteration procedure. The inviscid flow region is described by a direct finite-difference solution of a velocity potential equation in conservative form. The potential equation is solved on a numerically generated mesh by an approximate factorization (AF2) scheme in the semi-inverse interaction method and by a successive line overrelaxation (SLOR) scheme in the simultaneous interaction method. The boundary-layer equations are used for the viscous flow region. The continuity and momentum equations are solved inversely in a coupled manner using a fully implicit finite-difference scheme.

Lee, D.↗

NASA NTRS1986

Calculation of external-internal flow fields for mixed-compression inlets

Supersonic inlet flows with mixed external-internal compressions were computed using a combined implicit-explicit (Beam-Warming-Steger/MacCormack) method for solving the three-dimensional unsteady, compressible Navier-Stokes equations in conservation form. Numerical calculations were made of various flows related to such inlet operations as the shock-wave intersections, subsonic spillage around the cowl lip, and inlet started versus unstarted conditions. Some of the computed results were compared with wind tunnel data.

Chyu, W. J.↗

NASA NTRS1986

Transonic flow solutions using a composite velocity procedure for potential, Euler and RNS equations

Solutions for transonic viscous and inviscid flows using a composite velocity procedure are presented. The velocity components of the compressible flow equations are written in terms of a multiplicative composite consisting of a viscous or rotational velocity and an inviscid, irrotational, potential-like function. This provides for an efficient solution procedure that is locally representative of both asymptotic inviscid and boundary layer theories. A modified conservative form of the axial momentum equation that is required to obtain rotational solutions in the inviscid region is presented and a combined conservation/nonconservation form is applied for evaluation of the reduced Navier-Stokes (RNS), Euler and potential equations. A variety of results is presented and the effects of the approximations on entropy production, shock capturing, and viscous interaction are discussed.

Gordnier, R. E.↗

NASA NTRS1986

Euler calculations for rotor configurations in unsteady forward flight

A solution procedure is presented for the lifting transonic flow past modern rotor configurations in forward flight. In this procedure, the three-dimensional, unsteady Euler equations are solved in strong conservation form on a body-fitted moving coordinate system. A hybrid procedure of second order spatial accuracy and first order temporal accuracy is used to integrate the governing equations. In lifting flows, the effect of the elements of wake not captured by the computational procedure, and other aeroelastic effects are accounted for as local angle of attack corrections. Detailed comparisons with experimental data are presented for a 1/7 scale model of the Cobra OLS rotor, and for a three-bladed rotor tested in France. Some preliminary results are also presented for a three-dimensional blade vortex interaction problem.

Sankar, L. N.↗

NASA NTRS1987

Numerical simulation of three-dimensional supersonic inlet flow fields

Supersonic inlet flows with mixed external-internal compressions of an axisymmetric inlet model were computed using a combined implicit-explicit (Beam-Warming-Steger/MacCormack) method for solving the three-dimensional unsteady, compressible Navier-Stokes equations in conservation form. Numerical calculations were made of various flows typically found in supersonic inlets such as shock-wave intersections, flow spillage around the cowl lip, shock-wave/boundary-layer interactions, control of shock-induced flow separation by means of boundary layer bleed, internal normal (terminal) shocks, and the effects of flow incidence. Computed results were compared with available wind tunnel data.

Kawamura, T.↗

NASA NTRS1987

Numerical analysis of flow through scramjet engine inlets

A set of computer programs has been developed to analyze flow through supersonic combustion ramjet (scramjet) inlets. These programs solve either the two- or three-dimensional Euler/Navier-Stokes equations in full conservation form by MacCormack's explicit or explicit-implicit method. An algebraic two-layer eddy viscosity model is used for turbulent flow calculations. The programs are operational on Control Data CYBER-200 series vector-processing computer system and have been optimized to take maximum advantage of the vector processing capability of the system. Since their development, the programs have been extensively verified and used to analyze a number of very complex inlet configurations. In this paper, results are presented from two-dimensional, quasi-three-dimensional, and three-dimensional analyses of the inlet flow field to illustrate the use of the programs.

Kumar, Ajay↗