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Davis, R. T.

Publications and source records attributed to Davis, R. T..

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Improved method for solving the viscous shock layer equations

An improved method for solving the viscous shock layer equations for supersonic/hypersonic flows past blunt-nosed bodies is presented. The method is capable of handling slender to thick bodies. The solution is obtained by solving a coupled set of five equations, built of the four basic viscous shock layer equations and an additional equation for the standoff distance. The coupling of the equations prevents the local iterations divergence problems encountered by previous methods of solution far downstream on slender bodies. It also eliminates the need for local iterations, which were required by previous methods of solution, for a first-order scheme in the streamwise direction. A new global iteration procedure is employed to impose the shock boundary conditions. The procedure prevents the global iteration instability encountered by the basic method of solution and improves the convergence rate of the global iteration procedure of later methods devised to overcome this difficulty. The new technique reduces the computation time by 65-95 percent as compared to previous methods of solution. The method can efficiently be implemented in vector/parallel computers.

Gordon, Rachel↗
NASA NTRS1986

The calculation of supersonic viscous flows using the parabolized Navier-Stokes equations

Solution of the parabolic Navier-Stokes (PNS) equations for supersonic flows is discussed, and compatibility of the PNS method with the triple-deck theory of Stewartson (1974) is demonstrated. Characteristic and stability analyses show that use of an appropriate filter on the pressure term in the x-momentum equation can suppress the departure solutions, giving the usual desired weak interaction solution. An Alternating Direction Explicit procedure, with minimal computer storage requirements compared to the full Navier-Stokes solvers, is proposed to calculate strongly interacting flows using a global iteration procedure for the PNS equations. The PNS equations are used to solve the hypersonic viscous interaction problem, and good agreement is found with experimental results.

Davis, R. T.↗
NASA NTRS1985

A procedure for the calculation of supersonic flows with strong viscous-inviscid interaction

The present paper is concerned with the calculation of strong viscous-inviscid interactions in two-dimensional laminar supersonic flows with and without separation. The equations solved are the so-called parabolized Navier-Stokes equations. The streamwise pressure gradient term is written as a combination of a forward and a backward difference to provide a path for upstream propagation of information. Global iteration is utilized to repeatedly update the pressure field from an initial guess until convergence is achieved. The numerical scheme employed is a new alternating direction explicit (ADE) procedure which is used as an alternative to the more difficult to program multigrid strategy to accelerate convergence. Results are presented for flows past two flat plate related bodies.

Barnett, M.↗
NASA NTRS1985

Massive separation and dynamic stall on a cusped trailing-edge airfoil

The cross-over from a predominantly attached two-dimensional flow to the bluff body form of separation is modeled via the interacting boundary layer approximation. The initial breakdown of the predominantly attached flow on a cusped trailing edge airfoil is examined using the Hilbert integral form of the unsteady interacting boundary layer equations. In addition, an interacting boundary layer technique is developed for calculating bluff body separation. This new model eliminates the severe scaling problems associated with bluff body separation through the use of a realistic inviscid eddy model, based on the infinite eddy Kirchhoff free-streamline description of separation. Brief consideration is given to the cross-over from bluff body separation to a predominantly attached flow, the extension to finite eddies and cascade flows, and the possible coupling with full, or parabolized, Navier-Stokes calculations.

Rothmayer, A. P.↗
NASA NTRS1983

An interacting boundary layer model for cascades

A laminar, incompressible interacting boundary layer model is developed for two-dimensional cascades. In the limit of large cascade spacing these equations reduce to the interacting boundary layer equations for a single body immersed in an infinite stream. A fully implicit numerical method is used to solve the governing equations, and is found to be at least as efficient as the same technique applied to the single body problem. Solutions are then presented for a cascade of finite flat plates and a cascade of finite sine-waves, with cusped leading and trailing edges.

Davis, R. T.↗
NASA NTRS1982

Simulation of large turbulent structures with the parabolic Navier-Stokes equations

The theoretical basis for well posed marching of a Parabolic Navier-Stokes (PNS) computational technique for supersonic flow is discussed and examples given to verify the analysis. It is demonstrated that stable computations can be made even with very small steps in the marching direction. The method is applied to cones at large angle of attack in high Reynolds number, supersonic flow. Streamline trajectories generated from the numerical solutions demonstrate the development of vortex structures on the lee side of the cone.

Rakich, J. V.↗
NASA NTRS1982

Solution of viscous internal flows on curvilinear grids generated by the Schwarz-Christoffel transformation

The combination of an orthogonal, curvilinear coordinate generation procedure with a stable forward marching viscous flow solution technique is presently employed in the solution of flow fields for arbitrary, axisymmetric ducts. Coordinate generation is accomplished by means of both potential lines and plane potential flow streamlines. Since the coordinate streamlines approximate actual ones, the equations of motion for viscous compressible flow can be parabolized in order to solve for both the boundary layer and the core flow in a single streamwise pass. The method's versatility is demonstrated by two examples of viscous compressible swirling flow through complex radial gas turbine passages.

Anderson, O. L.↗
NASA NTRS1982

Simulation of large turbulent vortex structures with the parabolic Navier-Stokes equations

The theoretical basis for well posed marching of a Parabolic Navier-Stokes (PNS) computational technique for supersonic flow is discussed and examples given to verify the analysis. It is demonstrated that stable computations can be made even with very small steps in the marching direction. The method is applied to cones at large angle of attack in high Reynolds number, supersonic flow. Streamline trajectories generated from the numerical solutions demonstrate the development of vortex structures of the lee side of the cone. Previously announced in STAR as N83-22551

Rakich, J. V.↗
NASA NTRS1981

Implicit boundary conditions for the solution of the parabolized Navier-Stokes equations for supersonic flows

A fully implicit set of boundary conditions is developed for the solution of the parabolized Navier-Stokes equations for supersonic flow in two dimensions. Shock fitting is employed at the shock and the body has no-slip and specified temperature conditions. A specified heat transfer condition at the wall can be handled in a similar manner. In addition, the shock location is advanced in space in a fully implicit manner by utilizing the Rankine-Hugoniot conditions along with global conservation of mass.

Barnett, M.↗
NASA NTRS1981

Progress on interacting boundary-layer computations at high Reynolds number

The purpose of this paper is to review progress made in the solution of the interacting boundary-layer equations for subsonic flow. The interrelationship of triple deck theory and the interacting boundary-layer approach is discussed with emphasis placed on the development of efficient and reliable algorithms for the solution of the interacting boundary-layer equations. Example studies are presented for laminar and turbulent finite flat plate flow, laminar flow past a flat plate with a separation causing depression, and laminar and turbulent flow past a blunt based trailing edge.

Davis, R. T.↗
NASA NTRS1976

Numerical and approximate solution of the high Reynolds number small separation problem

Several possible methods of solving the small separation problem at high Reynolds number are investigated. In addition to using analytical methods, there are several numerical approaches which are used. High Reynolds number laminar two dimensional problems are used for simplicity. A brief discussion is given of the finite difference methods since these methods are discussed in detail. Most of the emphasis is placed on developing an approximate integral method. As a model problem the supersonic compression ramp problem is chosen since several numerical solutions along with experimental data are available. The techniques discussed are modified and applied to other similar type wall geometries.

Davis, R. T.↗
NASA NTRS1973

Three-dimensional compressible laminar boundary layers on sharp and blunt circular cones at angle of attack

A method for solving the three-dimensional compressible laminar boundary layer equations for the case of a circular cone and a sphere-cone body at an angle of attack is presented. The governing equations are modified by a similarity type transformation and then transformed into a Crocco-type form. The resulting set of equations is solved simultaneously by an iterative method using an implicit finite difference scheme by means of an efficient algorithm for equations of tridiagonal form. The effects of streamline swallowing on a sharp cone are included by introducing the true inviscid edge conditions at the distance from the wall equal to the boundary layer thickness. The validity of the approach was established by comparison of the computational results with similar results by other methods and with experimental data. It was concluded that at sufficiently high Mach number and moderate to large angles of attack, the streamline swallowing effects on a sharp cone result in higher values of skin friction and heat transfer as compared with the classical results for constant entropy.

Popinski, Z.↗
NASA NTRS1973

The use of Levy-Lees variables in three-dimensional boundary-layer flows

A method for solving a general class of three-dimensional boundary layer flows is developed. In the development, Levy-Lees variables are extended to three dimensions and equations are placed in these similarity variables. An implicit finite difference scheme which is stable for negative transverse velocities is used to solve these equations. The method developed is applied to obtain solutions for sharp and spherically blunted circular cones at angle of attack. Longitudinal and transverse distributions are presented for these cases. Good agreement is found with the results obtained by other numerical schemes and the experimental data of Tracy, for sharp circular cones at angle of attack. For spherically blunted cones at angle of attack, the results are in good agreement with axisymmetric sphere results up to the region where spherical symmetry holds.

Vatsa, V. N.↗