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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 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

An implicit algorithm for the conservative transonic full potential equation using an arbitrary mesh

A new, implicit approximate factorization (AF) algorithm designed to solve the conservative full-potential equation for the transonic flow past arbitrary airfoils has been developed. The new algorithm uses an upwind bias of the density coefficient to provide stability in supersonic regions. This allows the simple two- and three-banded matrix form of the AF scheme to be retained over the entire flow field, even in regions of supersonic flow. A numerical transformation is used to establish an arbitrary body-fitted finite-difference mesh. Airfoil pressure distributions have been computed and are in good agreement with independent results.

Holst, T. L.↗
NASA NTRS1978

Theoretical and experimental study of the drag of multielement airfoils

The viscous/potential flow past single-element and multielement airfoils is studied theoretically and experimentally. A computerized analysis, based on iteratively coupled potential-flow and boundary-layer analysis, is used to predict the flow field of the airfoil. The method yields detailed characteristics of conventional laminar and turbulent boundary layers, turbulent wakes, and confluent boundary layers. The viscous flows are analyzed with a method that uses finite-difference solutions of the boundary-layer equations. Reynolds stress in the boundary layers and wakes is simulated with eddy viscosity models for the various flow zones. The viscous calculations are carried into the wake of the airfoil where the drag is found from the defect in the wake momentum.

Olson, L. E.↗
NASA NTRS1978

Operational manual for two-dimensional transonic code TSFOIL

This code solves the two-dimensional, transonic, small-disturbance equations for flow past lifting airfoils in both free air and various wind-tunnel environments by using a variant of the finite-difference method. A description of the theoretical and numerical basis of the code is provided, together with complete operating instructions and sample cases for the general user. In addition, a programmer's manual is also presented to assist the user interested in modifying the code. Included in the programmer's manual are a dictionary of subroutine variables in common and a detailed description of each subroutine.

Stahara, S. S.↗
NASA NTRS1978

Effect of concentration dependence of the diffusion coefficient on homogenization kinetics in multiphase binary alloy systems

Diffusion calculations were performed to establish the conditions under which concentration dependence of the diffusion coefficient was important in single, two, and three phase binary alloy systems. Finite-difference solutions were obtained for each type of system using diffusion coefficient variations typical of those observed in real alloy systems. Solutions were also obtained using average diffusion coefficients determined by taking a logarithmic average of each diffusion coefficient variation considered. The constant diffusion coefficient solutions were used as reference in assessing diffusion coefficient variation effects. Calculations were performed for planar, cylindrical, and spherical geometries in order to compare the effect of diffusion coefficient variations with the effect of interface geometries. In most of the cases considered, the diffusion coefficient of the major-alloy phase was the key parameter that controlled the kinetics of interdiffusion.

Tenney, D. R.↗
NASA NTRS1978

The development of a three-dimensional partially elliptic flow computer program for combustor research

A three dimensional, partially elliptic, computer program was developed. Without requiring three dimensional computer storage locations for all flow variables, the partially elliptic program is capable of predicting three dimensional combustor flow fields with large downstream effects. The program requires only slight increase of computer storage over the parabolic flow program from which it was developed. A finite difference formulation for a three dimensional, fully elliptic, turbulent, reacting, flow field was derived. Because of the negligible diffusion effects in the main flow direction in a supersonic combustor, the set of finite-difference equations can be reduced to a partially elliptic form. Only the pressure field was governed by an elliptic equation and requires three dimensional storage; all other dependent variables are governed by parabolic equations. A numerical procedure which combines a marching integration scheme with an iterative scheme for solving the elliptic pressure was adopted.

Pan, Y. S.↗
NASA NTRS1978

Transonic flow over the NACA 64A006 with an oscillating flap-calculations based on the Euler equations

Exploratory calculations of transonic flows over the airfoil with a quarter-chord oscillating flap were made using a program which obtains approximate solutions to the Euler equations with an explicit, shock-capturing, finite-difference scheme. The calculations, essentially inviscid and for the airfoil at zero angle-of-attack in a free-stream, are at Mach numbers and reduced frequencies which were tested in experiments by Tijdeman. The oscillatory lifts from analogus calculations by various investigators generally agree with one another better than they agree with Tijdeman's data. Inclusion in the calculations of an approximate modelling of boundary conditions expected at slotted wind tunnel walls tends to shift some of the results closer to the experimental values.

Magnus, R. J.↗
NASA NTRS1978

Numerical solution of flow problems using body-fitted coordinate systems

The technique of boundary-fitted coordinate systems is based on a method of automatic numerical generation of a general curvilinear coordinate system having a coordinate line coincident with each boundary of a general multi-connected region containing any number of arbitrarily shaped bodies. Once the curvilinear coordinate system is generated, any partial differential system of interest can be solved on this coordinate system by transforming the equations and solving the resulting system in finite difference approximation on the rectangular transformed plane. This method of automatic body-fitted curvilinear coordinate generation is used to construct finite-difference solutions of the full, time dependent Navier-Stokes equations for the unsteady viscous flow about arbitrary two-dimensional airfoils, or any other two-dimensional bodies. Finally, initial results for three-dimensional applications are also presented.

Thompson, J. F.↗
NASA NTRS1978

Comparative study of the convergence rates of two numerical techniques

The paper examines the applicability of the three-step Stetter (1968) method to the problem of hypersonic viscous flow over a blunt axisymmetric body used for planetary entry probes at zero angle of attack. The flow-field results using the two-step finite-difference MacCormack (1969) method are reported by Kumar and Graves (1977). Only the computational efficiency of Stetter's method is compared with that of MacCormack's in terms of the iterative time steps and computing time required for the steady-state solution. Advantages of Stetter's method over MacCormack's are established.

Kumar, A.↗
NASA NTRS1978

Numerical solution of the Navier-Stokes equations for arbitrary blunt bodies in supersonic flows

A time-dependent, two-dimensional Navier-Stokes code employing the body-fitted coordinate technique has been developed for supersonic flows past blunt bodies of arbitrary shape. The computer program is based on the finite-difference approximation of the compressible Navier-Stokes equations transformed to nonorthogonal curvilinear coordinates with the contravariant components of the velocity vector as dependent variables. The bow shock ahead of the body is obtained as part of the solution, by 'shock capturing'. Numerical solutions of the complete equations are presented in detail for free-stream Mach number 4.6, Reynolds number 10,000, and an isothermal wall temperature of 556 K for a circular cylinder with the free-stream outer boundaries forming a hyperbola in the front and a circular arc in the back.

Warsi, Z. U. A.↗
NASA NTRS1978

Influence of two-dimensional hygrothermal gradients on interlaminar stresses near free edges

Interlaminar stresses are determined for mechanical loading, uniform hygrothermal loading, and gradient moisture loading through implementation of a finite-element computer code. Nonuniform two-dimensional hygroscopic gradients are obtained from a finite-difference solution of the diffusion equation. It is shown that hygroscopic-induced stresses can be larger than those resulting from mechanical and thermal loading, and that the distribution of the interlaminar normal stress may be changed significantly in the presence of a two-dimensional moisture gradient in the boundary layer of a composite laminate.

Farley, G. L.↗
NASA NTRS1978

Thermal control of low-pressure fractionation processes

Thermal models detailing the solidification paths for shallow basaltic magma chambers (both open and closed systems) were calculated using finite-difference techniques. The total solidification time for closed chambers are comparable to previously published calculations; however, the temperature-time paths are not. These paths are dependent on the phase relations and the crystallinity of the system, because both affect the manner in which the latent heat of crystallization is distributed. In open systems, where a chamber would be periodically replenished with additional parental liquid, calculations indicate that the possibility is strong that a steady-state temperature interval is achieved near a major phase boundary. In these cases it is straightforward to analyze fractionation models of the basaltic liquid evolution and their corresponding cumulate sequences. This steady thermal fractionating state can be invoked to explain large amounts of erupted basalts of similar composition over long time periods from the same volcanic center and some rhythmically layered basic cumulate sequences.

Usselman, T. M.↗
NASA NTRS1978

Numerical solution for supersonic flow near the trailing edge of a flat plate

In the present study, problems of laminar and turbulent two-dimensional flow of a viscous compressible fluid near the trailing edge of a thin flat plate are considered. The complete set of Navier-Stokes equations is solved by the finite-difference method of MacCormack (MacCormack and Baldwin, 1975). It is an explicit, predictor-corrector, time-splitting method of second order acuracy. The computational mesh employed has sufficient resolution for all the characteristic lengths suggested by theory. In the laminar case, the present results are compared with the triple deck solution of Daniels (1974). This comparison indicates that the asymptotic triple deck theory for supersonic trailing edge flow is accurate within five percent for Reynolds numbers greater than 1000. In the turbulent case, the Prandtl-Van Driest-Clauser algebraic eddy viscosity model is used. The numerical results show that the region of upstream influence is approximately of the order of the boundary layer thickness. The solutions for skin-friction, pressure and wake center-line velocity are presented.

Degani, D.↗
NASA NTRS1978

An efficient explicit-implicit-characteristic method for solving the compressible Navier-Stokes equations

Explicit, implicit, and characteristic finite-difference methods are applied to solve model equations representative of the compressible Navier-Stokes equations. An approach is then formulated for solving the Navier-Stokes equation at high Reynolds numbers. The approach has drastically reduced the computation time required to obtain viscous flow solutions. Computational results for shock wave separated flows are presented.

Maccormack, R. 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 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 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↗