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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 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

A modified Dodge algorithm for the parabolized Navier-Stokes equation and compressible duct flows

A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition. Qualitive agreement with analytical predictions and experimental results was obtained for some flows with well-known solutions.

Cooke, C. H.↗
NASA NTRS1980

A vectorized code for calculating laminar and turbulent hypersonic flows about blunt axisymmetric bodies at zero and small angles of attack

A user's guide is provided for a computer code which calculates the laminar and turbulent hypersonic flows about blunt axisymmetric bodies, such as spherically blunted cones, hyperboloids, etc., at zero and small angles of attack. The code is written in STAR FORTRAN language for the CDC-STAR-100 computer. Time-dependent, viscous-shock-layer-type equations are used to describe the flow field. These equations are solved by an explicit, two-step, time asymptotic, finite-difference method. For the turbulent flow, a two-layer, eddy-viscosity model is used. The code provides complete flow-field properties including shock location, surface pressure distribution, surface heating rates, and skin-friction coefficients. This report contains descriptions of the input and output, the listing of the program, and a sample flow-field solution.

Kumar, A.↗
NASA NTRS1980

User's guide for the computer code COLTS for calculating the coupled laminar and turbulent flow over a Jovian entry probe

A user's guide for a computer code 'COLTS' (Coupled Laminar and Turbulent Solutions) is provided which calculates the laminar and turbulent hypersonic flows with radiation and coupled ablation injection past a Jovian entry probe. Time-dependent viscous-shock-layer equations are used to describe the flow field. These equations are solved by an explicit, two-step, time-asymptotic finite-difference method. Eddy viscosity in the turbulent flow is approximated by a two-layer model. In all, 19 chemical species are used to describe the injection of carbon-phenolic ablator in the hydrogen-helium gas mixture. The equilibrium composition of the mixture is determined by a free-energy minimization technique. A detailed frequency dependence of the absorption coefficient for various species is considered to obtain the radiative flux. The code is written for a CDC-CYBER-203 computer and is capable of providing solutions for ablated probe shapes also.

Kumar, A.↗
NASA NTRS1981

Computation of airfoil buffet boundaries

The ILLIAC IV computer has been programmed with an implicit, finite-difference code for solving the thin layer compressible Navier-Stokes equation. Results presented for the case of the buffet boundaries of a conventional and a supercritical airfoil section at high Reynolds numbers are found to be in agreement with experimentally determined buffet boundaries, especially at the higher freestream Mach numbers and lower lift coefficients where the onset of unsteady flows is associated with shock wave-induced boundary layer separation.

Levy, L. L., Jr.↗
NASA NTRS1981

Flow aerodynamics modeling of an MHD swirl combustor - Calculations and experimental verification

The paper describes a computer code for calculating the flow dynamics of a constant-density flow in the second-stage trumpet shaped nozzle section of a two-stage MHD swirl combustor for application to a disk generator. The primitive pressure-velocity variable, finite-difference computer code has been developed for the computation of inert nonreacting turbulent swirling flows in an axisymmetric MHD model swirl combustor. The method and program involve a staggered grid system for axial and radial velocities, and a line relaxation technique for the efficient solution of the equations. The code produces as output the flow field map of the nondimensional stream function, axial and swirl velocity. It was found that the best location for seed injection to obtain a uniform distribution at the combustor exit is in the central location for seed injected at the entrance to the second stage combustor.

Gupta, A. K.↗
NASA NTRS1981

Test problems for inviscid transonic flow

The paper discusses some results obtained in the solving of test problems for inviscid transonic flow with shock waves using the TRANDES program. The method used employs the full inviscid perturbation-potential flow equation in a Cartesian grid system that is stretched to infinity. The equation is represented by a nonconservative system of finite-difference equations that includes at supersonic points a rotated difference scheme and is solved by column relaxation. Except for the NACA 0012 case with the freestream Mach number equal to 0.95, all test problems were solved straightforwardly and appeared to be converged or close to convergence. The only difficulty was some sensitivity to grid placement, which is typical of the Cartesian formulation

Carlson, L. A.↗
NASA NTRS1981

Use of interactive graphics to analyze QUICK-geometry

The QUICK InterActive Graphics Analysis (QUIAGA) program and its advantages for displaying aircraft QUICK-geometry to aid in detection and analysis of errors are described. The QUICK-geometry system generates a completely analytical aircraft geometry description for use by finite-difference flow codes. The QUIAGA program was developed to exercise the QUICK-geometry subroutines to examine the analytic definition of a configuration by plotting cross sections and body lines on a graphics terminal. A number of options are available, including multiple cross-section views, hidden-line removal, and display of control point locations. Use of these options for the detection and analysis of errors in the QUICK-geometry definition can be of great assistance in speedily arriving at a correct analytical geometry description for flow-field computation. The QUIAGA program has been used in developing a QUICK-geometry model of the NASA Space Shuttle Orbiter, and examples from this experience are given to show some of the program's features. Details of program usage and an example session are given in the appendixes.

Townsend, J. C.↗
NASA NTRS1981

Mesh generation by conformal and quasiconformal mappings

It is pointed out that many recent advances in the finite-difference solution of elliptic equations have been limited to regions whose boundary contours coincide with coordinate lines of the Cartesian coordinate system. The reason for this is related to the fact that in the case of an arbitrary curvilinear coordinate system the original equation becomes much more complex. However, there is no added complexity if an orthogonal coordinate system is generated from a conformal mapping. In the present investigation, a finite difference method developed for the construction of conformal mappings has been generalized to construct quasi-conformal mappings. It is expected that the use of more sophisticated numerical algorithms could lead to improvements in both speed and accuracy. Quasi-conformal mappings have applications not only in the solution of elliptic equations but also in other areas such as orthogonal mesh generation on surfaces and the solution of certain fluid flow problems.

Mastin, C. W.↗
NASA NTRS1947

Determination of elastic stresses in gas-turbine disks

A method is presented for the calculation of elastic stresses in symmetrical disks typical of those of a high-temperature gas turbine. The method is essentially a finite-difference solution of the equilibrium and compatibility equations for elastic stresses in a symmetrical disk. Account can be taken of point-to-point variations in disk thickness, in temperature, in elastic modulus, in coefficient of thermal expansion, in material density, and in Poisson's ratio. No numerical integration or trial-and-error procedures are involved and the computations can be performed in rapid and routine fashion by nontechnical computers with little engineering supervision. Checks on problems for which exact mathematical solutions are known indicate that the method yields results of high accuracy. Illustrative examples are presented to show the manner of treating solid disks, disks with central holes, and disks constructed either of a single material or two or more welded materials. The effect of shrink fitting is taken into account by a very simple device.

Manson, S S↗
NASA NTRS1950

Direct method of design and stress analysis of rotating disks with temperature gradient

A method is presented for the determination of the contour of disks, typified by those of aircraft gas turbines, to incorporate arbitrary elastic-stress distributions resulting from either centrifugal or combined centrifugal and thermal effects. The specified stress may be radial, tangential, or any combination of the two. Use is made of the finite-difference approach in solving the stress equations, the amount of computation necessary in the evolution of a design being greatly reduced by the judicious selection of point stations by the aid of a design chart. Use of the charts and of a preselected schedule of point stations is also applied to the direct problem of finding the elastic and plastic stress distribution in disks of a given design, thereby effecting a great reduction in the amount of calculation. Illustrative examples are presented to show computational procedures in the determination of a new design and in analyzing an existing design for elastic stress and for stresses resulting from plastic flow.

Manson, S S↗
NASA NTRS1980

Fast, Conservative Algorithm for Solving the Transonic Full-Potential Equation

A fast, fully implicit approximate factorization algorithm designed to solve the conservative, transonic, full-potential equation in either two or three dimensions is described. The algorithm uses an upwind bias of the density coefficient for stability in supersonic regions. This provides an effective upwind difference of the streamwise terms for any orientation of the velocity vector (i.e., rotated differencing), thereby greatly enhancing the reliability of the present algorithm. A numerical transformation is used to establish an arbitrary body-fitted, finite-difference mesh. Computed results for both airfoils and simplified wings demonstrate substantial improvement in convergence speed for the new algorithm relative to standard successive-line over-relaxation algorithms.

Holst, Terry L.↗
NASA NTRS1981

Two-Dimensional Inlet Simulation Using a Diagonal Implicit Algorithm

A modification of an implicit approximate-factorization finite-difference algorithm applied to the two-dimensional Euler and Navier-Stokes equations in general curvilinear coordinates is presented for supersonic freestream flow about and through inlets. The modification transforms the coupled system of equations Into an uncoupled diagonal form which requires less computation work. For steady-state applications the resulting diagonal algorithm retains the stability and accuracy characteristics of the original algorithm. Solutions are given for inviscid and laminar flow about a two-dimensional wedge inlet configuration. Comparisons are made between computed results and exact theory.

Chaussee, D.S.↗
NASA NTRS1961

Cross-Sectional Deformations of Monocoque Beams and Their Effects on the Natural Vibration Frequencies

The variational principle, differential equations, and boundary conditions governing the cross-sectional distortions due to inertia loading of a two-dimensional model of a thin monocoque wing are shown. A theoretical analysis of this simplified model is made in order to determine the nature of the coupling between the cross-sectional modes and the spanwise deformation modes. General solutions are obtained in finite-difference form for arbitrary cross sections and an exact solution is presented for a parabolic-arc cross section of constant cover thickness. The application of these results in evaluating the coupled frequencies of the actual structure is discussed. Frequencies evaluated for a parabolic-arc monocoque beam show good agreement with experimental values.

Thomson, Robert G.↗
NASA NTRS1981

Calculation of Unsteady Transonic Flow over an Airfoil

An implicit finite-difference solver for either the Euler equations or the "thin-layer" Navier-Stokes equations was used to calculate a transonic flow over the NACA 64A010 airfoil pitching about its one-quarter chord. An unsteady automatic grid-generation procedure that will improve significantly the computational efficiency of various unsteady flow problems is described. The calculated results for both inviscid and viscous flows at Much number 0.8 over the airfoil oscillating with reduced frequency referenced to one-half chord, 0.2, are compared with experimental data measured in the Ames 11 x 11-ft Transonic Wind Tunnel. Nonlinear, unsteady effects of the flow on the surface pressure variations, shock-wave excursions, and overall airloads are examined. Good agreements between the results of computations and experiments were obtained. In the shock-wave region, however, the results of the viscous-flow computations showed closer agreement with the experimental data.

Chyu, W. J.↗
NASA NTRS1981

Nonreflecting Far-Field Boundary Conditions for Unsteady Transonic Flow Computation

The approximate nonreflecting far-field boundary condition, as proposed by Engquisi and Majda, is implemented In the computer code LTRAN2. This code solves the Implicit finite-difference representation of the small-disturbance equations for unsteady transonic flows about airfoils. The nonreflecting boundary condition and the description of the algorithm for Implementing these conditions In LTRAN2 tire discussed. Various cases re computed and compared with results from the older, more conventional procedures. One concludes that the nonreflecting far-field boundary approximation allows the far-field boundary to be located closer to the airfoil; this permits a decrease in the computer lime required to obtain the solution through the use of fewer mesh points.

Kwak, D.↗
NASA NTRS1975

Advances in Application of Fast Semidirect Computational Methods in Transonic Flow

This paper is intended as a review and summary of the advances made in a recently developed approach for rapid numerical solution of the equations of inviscid transonic aerodynamics. The investigation has been limited to two-dimensional, steady, inviscid flow over airfoils in a subsonic free stream, with emphasis on development of a rapid computational technique, rather than on generality of application. The approach uses finite-difference algorithms called "fast direct elliptic solvers" within an iteration scheme. "Direct" means that the entire computation field is solved at once, rather than in successive traverses over the field as in a point- or line-relaxation method. Such an iterative method is referred to as "semidirect." The iterative convergence can be faster than in other relaxation methods because changes are felt simultaneously at all points in each succeeding iteration. Direct elliptic solvers and semidirect methods have restrictions, but these are gradually being removed. Direct solvers were first developed for solving Poisson's equation on a rectangle without interior boundaries. A method to treat first-order systems, a direct Cauchy-Riemann solver has also been developed. Numerical treatment of part of a system of nonlinear equations by a Poisson solver has been reported. Also Poisson solvers in semidirect methods were used for nonseparable elliptic equations. The semidirect method was extended to the solution of a problem of mixed type, where the improved Murman-Cole transonic small-disturbance difference equations were solved. A slightly supercritical flow over a biconvex airfoil was treated successfully, but the iterations did not converge for more strongly supercritical conditions In another work the addition of terms ot both sides of the difference equations stabilized the iteration for supercritical conditions with large supersonic zones. For this, the Cauchy-Riemann solver was revised to incl,ude the needed terms. Most recently, the evaluation of parameters for rapid convergence and comparisons, with Murman's line-relaxation method was described. The method was extended to full second order accuracy in a fully conservative formulation in another work.

Martin, E. Dale↗