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NASA NTRS1982

Comparison of viscous-shock-layer solutions by time-asymptotic and steady-state methods

Two flow-field codes employing the time- and space-marching numerical techniques were evaluated. Both methods were used to analyze the flow field around a massively blown Jupiter entry probe under perfect-gas conditions. In order to obtain a direct point-by-point comparison, the computations were made by using identical grids and turbulence models. For the same degree of accuracy, the space-marching scheme takes much less time as compared to the time-marching method and would appear to provide accurate results for the problems with nonequilibrium chemistry, free from the effect of local differences in time on the final solution which is inherent in time-marching methods. With the time-marching method, however, the solutions are obtainable for the realistic entry probe shapes with massive or uniform surface blowing rates; whereas, with the space-marching technique, it is difficult to obtain converged solutions for such flow conditions. The choice of the numerical method is, therefore, problem dependent. Both methods give equally good results for the cases where results are compared with experimental data.

Gupta, R. N.↗

NASA NTRS1982

Solution of second-order linear system by matched asymptotic expansions

Matched asymptotic expansions (MAE) are used to obtain a first order approximation to the solution of a singularly perturbed second order system. A special case is considered in which the uniform asymptotic solution obtained by MAE is shown to converge to the exact solution. Ways in which the method can be used to sole higher-order linear systems, including those which are not singularly perturbed, are also discussed.

Ardema, M. D.↗

NASA NTRS1982

Numerical solution of Space Shuttle Orbiter flow field

The supersonic, viscous laminar flow around the Space Shuttle Orbiter forebody has been computed with a parabolized Navier-Stokes code using a generalized coordinate transformation. The initial solution for the nose part of the Orbiter geometry was obtained with a three-dimensional time-dependent Navier-Stokes solver. It was necessary to employ a wind axis oriented coordinate system to obtain the initial solution with the time-dependent code. The generalized PNS technique used in this study allows the solution to be marched from the given initial data surface to any desired surface downstream. A grid point clustering scheme was employed to accurately describe the body shape by clustering points at the wing tip and at the wing body juncture. The computed heat transfer coefficients, pressure coefficients, and shock shapes are compared with the available experimental data for 0 degrees and 30 degrees angle of attack.

Venkatapathy, E.↗

NASA NTRS1984

Obtaining Runge-Kutta Solutions Between Time Steps

New interpolation method used with existing Runge-Kutta algorithms. Algorithm evaluates solution at intermediate point within integration step. Only few additional computations required to produce intermediate solution data. Runge-Kutta method provides accurate solution with larger time steps than allowable in other methods.

Horn, M. K.↗

NASA NTRS1982

Solution of axisymmetric fluid structure interaction problems with NASTRAN

The solution of axisymmetric acoustic fluid structure interaction problems, employing the NASTRAN computer program is presented. A previously developed 3-D Cartesian Coordinates pressure element formulation is adapted especially for axisymmetric elements. Analogous to the 3-D Cartesian Coordinate predecessor, the fluid portion of the problem is modeled with finite elements wherein one of the displacement components serves as a dummy variable for the pressure unknowns. Two alternatives for implementation of the analogy are presented: (1) an approximate method by which dummy values of G, and nu are used to approximately invoke the analogy wherein the accuracy of the approximation is made as close as desired to the proper analogy within an arbitrary small parameter epsiton; (2) an exact method whereby the NASTRAN FORTRAN coding is slightly changed to invoke the analogy exactly. Comparison of the finite element solution to the exact solution to the same problem is given.

Kalinowski, A. J.↗

NASA NTRS1982

Solution growth of crystals in zero gravity

A series of experiments will be performed in which triglycine sulfate (TGS) crystals will be grown by a low-temperature solution growth technique in the microgravity environment of the orbital Spacelab. Triglycine sulfate (TGS) crystals will be grown in the Fluid Experiment System (FES) facility on Spacelab 3 by slowly extracting heat at a controlled rate through a seed crystal of TGS suspended on an insulated sting in a saturated solution of TGS. The FES rack assembly designed for SL-3 is shown in Figure I-1, and a detailed view of the test cell layout is presented in Figure I-2. Variations in the liquid density, solution concentration and temperature around the growing crystal will be studied using a variety of techniques, such as schlieren, shadowgraph, and interferometric measurements. Growth in Earth gravity will also be studied by the same optical techniques, and in both cases the resulting crystalline features will be compared and correlated with the growth conditions.

Lai, R. B.↗

NASA NTRS1983

A tire contact solution technique

An efficient method for calculating the contact boundary and interfacial pressure distribution was developed. This solution technique utilizes the discrete Fourier transform to establish an influence coefficient matrix for the portion of the pressurized tire surface that may be in the contact region. This matrix is used in a linear algebra algorithm to determine the contact boundary and the array of forces within the boundary that are necessary to hold the tire in equilibrium against a specified contact surface. The algorithm also determines the normal and tangential displacements of those points on the tire surface that are included in the influence coefficient matrix. Displacements within and outside the contact region are calculated. The solution technique is implemented with a finite-element tire model that is based on orthotropic, nonlinear shell of revolution elements which can respond to nonaxisymmetric loads. A sample contact solution is presented.

Tielking, J. T.↗

NASA NTRS1983

A finite difference solution for the propagation of sound in near sonic flows

An explicit time/space finite difference procedure is used to model the propagation of sound in a quasi one-dimensional duct containing high Mach number subsonic flow. Nonlinear acoustic equations are derived by perturbing the time-dependent Euler equations about a steady, compressible mean flow. The governing difference relations are based on a fourth-order, two-step (predictor-corrector) MacCormack scheme. The solution algorithm functions by switching on a time harmonic source and allowing the difference equations to iterate to a steady state. The principal effect of the non-linearities was to shift acoustical energy to higher harmonics. With increased source strengths, wave steepening was observed. This phenomenon suggests that the acoustical response may approach a shock behavior at at higher sound pressure level as the throat Mach number aproaches unity. On a peak level basis, good agreement between the nonlinear finite difference and linear finite element solutions was observed, even through a peak sound pressure level of about 150 dB occurred in the throat region. Nonlinear steady state waveform solutions are shown to be in excellent agreement with a nonlinear asymptotic theory.

Hariharan, S. I.↗

NASA NTRS1983

Constrained Self-adaptive Solutions Procedures for Structure Subject to High Temperature Elastic-plastic Creep Effects

This paper will develop a new solution strategy which can handle elastic-plastic-creep problems in an inherently stable manner. This is achieved by introducing a new constrained time stepping algorithm which will enable the solution of creep initiated pre/postbuckling behavior where indefinite tangent stiffnesses are encountered. Due to the generality of the scheme, both monotone and cyclic loading histories can be handled. The presentation will give a thorough overview of current solution schemes and their short comings, the development of constrained time stepping algorithms as well as illustrate the results of several numerical experiments which benchmark the new procedure.

Padovan, J.↗

NASA NTRS1983

Large-amplitude hydromagnetic waves in collisionless relativistic plasma - Exact solution for the fast-mode magnetoacoustic wave

An exact nonlinear solution is found to the relativistic kinetic and electrodynamic equations (in their hydromagnetic limit) that describes the large-amplitude fast-mode magnetoacoustic wave propagating normal to the magnetic field in a collisionless, previously uniform plasma. It is pointed out that a wave of this kind will be generated by transverse compression of any collisionless plasma. The solution is in essence independent of the detailed form of the particle momentum distribution functions. The solution is obtained, in part, through the method of characteristics; the wave exhibits the familiar properties of steepening and shock formation. A detailed analysis is given of the ultrarelativistic limit of this wave.

Barnes, A.↗

NASA NTRS1983

Focal depths and fault plane solutions of earthquakes under the Tibetan plateau

Seismic data are used to place constraints on the focal depths and fault plane solutions of 16 crustal earthquakes beneath the highest parts of the Tibetan plateau. Synthetic seismograms were computed for large events from 1962 to 1976, and compared with the observed waveforms. All of the events studied are found to have occurred at depths less than 15 km and probably between 5 and 10 km, suggesting that the crust below 10-15 km is essentially aseismic, as in most of the Western United States. Fault-plane solutions show combinations of normal and strike slip faulting with T axes consistently oriented approximately east-west, supporting the inference that the upper crust of Tibet is actively extending in an east-west direction. In addition, solutions for two intermediate-depth events at depths of 90 and 85 km show primarily normal faulting with east-west T axes. Results show that brittle deformation occurs at shallow depths in the crust and in the uppermost mantle, but the lower crust seems to be aseismic.

Molnar, P.↗

NASA NTRS1982

Post-instability in continuous systems. I - Failure of differentiability of solutions in continuum mechanics

It is pointed out that mathematical models of continua are based on certain assumptions regarding functions which must be at least piece-wise differentiable. The assumption about smoothness of the functions makes it possible to use the mathematical technique of differentiable equations. However, this artificial mathematical limitation follows neither from the principles of mechanics nor from the definition of a continuum. The price paid for such a mathematical convenience is instability (in the class of smooth functions) of the solutions to the corresponding governing equations in some regions of the parameters. A new mathematical technique should, therefore, be developed to describe the solutions which are not necessarily differentiable. The present investigation is concerned with the criteria of applicability of the classical models of continua from the view point of stability of the corresponding solutions, postinstability models derived by reformulation of the original models, and postinstability models in enlarged classes of functions.

Zak, M.↗

NASA NTRS1983

Surface characterization of Ti and Ti (6 percent, Al-4 percent, V) metal powders and interaction with primer solutions

The interaction of Ti and Ti 6-4 powders with water and primer solutions was investigated experimentally by measuring the heats of immersion. Similar comparative studies were made on anatase and rutile TiO2 powders. The surface oxide layers of Ti and Ti 6-4 cracked on heating in vacuum between 300 and 400 C as evidenced by high heats of immersion in both water and primer solutions. Polyimide and polyphenylquinoxaline interacted preferentially, compared with the solvents with both metal powders after outgassing at room temperature. The heats of immersion of Ti 6-4 in water, solvents, and primer solutions increased significantly after pretreatment of the powder by an alkaline etch and a phosphate-fluoride process. The TiO2 powders were not satisfactory models for the surface oxide layer on either Ti or Ti 6-4 powder.

Siriwardane, R. V.↗

NASA NTRS1982

Finite analytic numerical solution of heat transfer and flow past a square channel cavity

A numerical solution of flow and heat transfer characteristics is obtained by the finite analytic method for a two dimensional laminar channel flow over a two-dimensional square cavity. The finite analytic method utilizes the local analytic solution in a small element of the problem region to form the algebraic equation relating an interior nodal value with its surrounding nodal values. Stable and rapidly converged solutions were obtained for Reynolds numbers ranging to 1000 and Prandtl number to 10. Streamfunction, vorticity and temperature profiles are solved. Local and mean Nusselt number are given. It is found that the separation streamlines between the cavity and channel flow are concave into the cavity at low Reynolds number and convex at high Reynolds number (Re greater than 100) and for square cavity the mean Nusselt number may be approximately correlated with Peclet number as Nu(m) = 0.365 Pe exp 0.2.

Chen, C.-J.↗

NASA NTRS1982

Growth of triglycine sulfate (TGS) crystals by solution technique

The growth of crystals from solution is greatly influenced by buoyancy driven convection. In a low-g environment, convection is greatly suppressed and diffusion becomes the predominant mechanism for thermal and mass transport. An experiment to grow TGS crystals by solution technique during the orbital Spacelab III mission has been designed. Crystals are grown by a new and unique technique of extracting heat from the crystal through a sting. The cooling at the sting tip is responsible for the desired supersaturation near the growing crystal. Calculations indicate that the cooled sting technique for solution crystal growth is necessary in low-g to maintain a maximum growth rate of 1 mm/day. Results of groundbased work in support of the flight experiment are discussed.

Lal, R. B.↗

NASA NTRS1982

Finite element analysis of the effect of a non-planar solid-liquid interface on the lateral solute segregation during unidirectional solidification

The effect of solid-liquid interface shape on lateral solute segregation during steady-state unidirectional solidification of a binary mixture is calculated under the assumption of no convection in the liquid. A finite element technique is employed to compute the concentration field in the liquid and the lateral segregation in the solid with a curved boundary between the liquid and solid phases. The computational model is constructed assuming knowledge of the solid-liquid interface shape; no attempt is made to relate this shape to the thermal field. The influence of interface curvature on the lateral compositional variation is investigated over a range of system parameters including diffusivity, growth speed, distribution coefficient, and geometric factors of the system. In the limiting case of a slightly nonplanar interface, numerical results from the finite element technique are in good agreement with the analytical solutions of Coriell and Sekerka obtained by using linear theory. For the general case of highly non-planar interface shapes, the linear theory fails and the concentration field in the liquid as well as the lateral solute segregation in the solid can be calculated by using the finite element method.

Carlson, F. M.↗

NASA NTRS1984

Canonical solutions for unsteady flow fields

The initial value problem of one-dimensional gas-dynamics involving discontinuous, nonuniform initial data is discussed. Canonical solutions which are valid in a small x, t region aroung a discontinuity, and which include the first order effects of nonuniformities in the data, are derived explicitly. The theory is derived by considering a group of elementary piston problems. Solutions with a shock or with a centered expansion wave are worked out individually in order to relate initial flow properties and their gradients to the speed and acceleration of the discontinuity waves. They are then combined to represent the solution of a general initial value problem by regarding the piston path as a contact line. In addition, problems with chemical reaction are discussed in terms of elementary piston problems which involve strong detonation waves, Chapman-Jouguet detonation waves, and deflagration waves.

Liu, G. C.↗

NASA NTRS1984

Numerical solution for the interaction of shock wave with laminar boundary layer in two-dimensional flow on a flat plate

The finite difference computation method was investigated for solving problems of interaction between a shock wave and a laminar boundary layer, through solution of the complete Navier-Stokes equations. This method provided excellent solutions, was simple to perform and needed a relatively short solution time. A large number of runs for various flow conditions could be carried out from which the interaction characteristics and principal factors that influence interaction could be studied.

Landau, U.↗