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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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NASA NTRS1981

Characteristic boundary conditions for the Euler equations

The boundary conditions are demonstrated for the quasi-one-dimensional Euler equations with the extension to two and three dimensions being straightforward. In this application an implicit finite-difference scheme is employed with the boundary conditions being applied implicitly. The boundary application uses both characteristic extrapolations and evaluations which distinguishes it from other theories. Flow fields with shocks are calculated with inflow-outflow conditions of supersonic-subsonic and subsonic-subsonic flow.

T H Pulliam↗
NASA NTRS1981

A numerical simulation of hypersonic viscous flow over arbitrary geometries at angle of attack

An implicit conservative, noniterative, finite-difference algorithm that predicts the supersonic, laminar or turbulent viscous flow about arbitrary geometries at large angles of attack is presented. The three-dimensional parabolized form of the thin-layer Navier-Stokes equations are written in generalized coordinates. These equations are solved using the delta form of the Beam-Warming implicit algorithm. Flow field simulations have been obtained for a blunt biconic with windward and leeward cuts and an X-24C lifting body for both laminar and turbulent flow at various Mach numbers and angles of attack. When compared with experiment or with previous theories, these computational predictions show good agreement.

Chaussee, D. S.↗
NASA NTRS1981

An alternating-direction implicit algorithm for unsteady potential flow

An implicit finite-difference scheme is presented for the efficient computation of unsteady potential flow about airfoils. The formulation uses density and the velocity potential as dependent variables and is cast in conservation form to assure the theoretically correct determination of shockwave location and speed. To enable boundary conditions to be imposed directly on the airfoil surface, a time-varying sheared-rectilinear coordinate transformation is employed. Calculated time-history solutions on a pulsating airfoil are compared with the results of other unsteady transonic codes, including a previous method of the authors. The present method is demonstrated to be unconditionally stable and to give accurate solutions with sharply resolved shocks.

Chipman, R.↗
NASA NTRS1981

Dynamic crack propagation and arrest in orthotropic DCB fiber composite specimens

An orthotropic double cantilever beam (DCB) model is used to study dynamic crack propagation and arrest in 90 deg unidirectional Hercules AS/3501-6 graphite fiber epoxy composites. The dynamic fracture toughness of the composite is determined from tests performed on the long-strip specimen and DCB crack arrest experiments are conducted. By using the dynamic fracture toughness in a finite-difference solution of the DCB governing partial differential equations, a numerical solution of the crack propagation and arrest events is computed. Excellent agreement between the experimental and numerical crack arrest results are obtained.

Williams, J. H., Jr.↗
NASA NTRS1981

Linear/nonlinear behavior in unsteady transonic aerodynamics

The accurate calculation of the aerodynamic forces in unsteady transonic flow requires the solution of the nonlinear flow equations. The aeroelastician, on the other hand, seeks to treat his problems (flutter, for example) by means of linear equations whenever possible. He may do this, even when the underlying flow is nonlinear, if the perturbation forces are linear over some (perhaps small) range of unsteady amplitude of motion. This paper assesses the range of parameters over which linear behavior occurs. In particular calculations are made for an NACA 64A006 airfoil oscillating in pitch over a range of amplitudes, frequencies, and Mach numbers. The primary aerodynamic method used is the well known LTRAN2 code of Ballhaus and Goorjian that provides a finite-difference solution to the low frequency, small disturbance, two-dimensional potential flow equation. Comparisons are made with linear subsonic theory, local linearization, and, for steady flow, with the full potential equation code of Bauer, Garabedian, and Korn.

Dowell, E. H.↗
NASA NTRS1981

Efficient computation of the stability of three-dimensional compressible boundary layers

Methods for the computer analysis of the stability of three-dimensional compressible boundary layers are discussed and the user-oriented Compressible Stability Analysis (COSAL) computer code is described. The COSAL code uses a matrix finite-difference method for local eigenvalue solution when a good guess for the eigenvalue is available and is significantly more computationally efficient than the commonly used initial-value approach. The local eigenvalue search procedure also results in eigenfunctions and, at little extra work, group velocities. A globally convergent eigenvalue procedure is also developed which may be used when no guess for the eigenvalue is available. The global problem is formulated in such a way that no unstable spurious modes appear so that the method is suitable for use in a black-box stability code. Sample stability calculations are presented for the boundary layer profiles of an LFC swept wing.

Malik, M. R.↗
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

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

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↗