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At least 1,171 records · Page 65

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NASA NTRS1983

Shock-capturing parabolized Navier-Stokes model /SCIPVIS/ for the analysis of turbulent underexpanded jets

A new computational model, SCIPVIS, has been developed to predict the multiple-cell wave/shock structure in under or over-expanded turbulent jets. SCIPVIS solves the parabolized Navier-Stokes jet mixing equations utilizing a shock-capturing approach in supersonic regions of the jet and a pressure-split approach in subsonic regions. Turbulence processes are represented by the solution of compressibility corrected two-equation turbulence models. The formation of Mach discs in the jet and the interactive turbulent mixing process occurring behind the disc are handled in a detailed fashion. SCIPVIS presently analyzes jets exhausting into a quiescent or supersonic external stream for which a single-pass spatial marching solution can be obtained. The iterative coupling of SCIPVIS with a potential flow solver for the analysis of subsonic/transonic external streams is under development.

Dash, S. M.↗

NASA NTRS1983

Postbuckling of long orthotropic plates in combined shear and compression

The nonlinear large-deflection partial differential equations of von karman for orthotropic plates loaded in combined shear and compression are converted into a set of first-order nonlinear ordinary differential equations by assuming trigonometric functions in one direction. These equations are solved numerically using a two point boundary problem solver which makes use of Newton's method. Results are obtained which determine the postbuckling behavior of rectangular plates with loading up to about three times the buckling load. Both isotropic and orthotropic composite plates are considered. Results show that orthotropic plates may behave quite differently than isotropic plates and that in-plane boundary conditions are important for plates loaded in shear.

Stein, M.↗

NASA NTRS1983

Improving the convergence rate of parabolic ADI methods

The rate of convergence to steady state of parabolic Alternating Direction Implicit (ADI) solvers is analyzed in terms of the L(2)-norms of the residuals. The analysis allows one to predict the number of iterations necessary for convergence as function of the Courant number, Lambda. A simple modification of existing ADI codes is devised. It improves the convergence rate substantially and is insensitive to the Courant number in a large range of Lambda.

Abarbanel, S. S.↗

NASA NTRS1983

A new stream function formulation for the Euler equations

A new stream function formulation is developed for the solution of Euler's equations in the transonic flow region. The stream function and the density are the dependent variables in this method, while the governing equations for adiabatic flow are the momentum equations which are solved in the strong conservation law form. The application of this method does not require a knowledge of the vorticity. The algorithm is combined with the automatic grid solver (GRAPE) of Steger and Sorenson (1979) in order to study arbitrary geometries. Results of the application of this method are presented for the NACA 0012 airfoil at various Mach numbers and angles of attack, and cylinders. In addition, detailed comparisons are made with other solutions of the Euler equations.

Atkins, H. L.↗

NASA NTRS1983

A nonstationary relaxation method for the Cauchy-Riemann and 1-D Euler equations

The Cauchy-Riemann equations and the 1-D Euler equations are expressed in generalized coordinates and then cast in finite difference form by using central differencing throughout. The resulting matrix representation has an eigensystem that permits the development of an annihilation process using complex arithmetic in a block tridiagonal solver. Initial numerical experiments show that the process has potential for use as a relaxation procedure for the Euler equations.

Liu, Y.↗

NASA NTRS1983

A new algorithm for constrained nonlinear least-squares problems, part 1

A Gauss-Newton algorithm is presented for solving nonlinear least squares problems. The problem statement may include simple bounds or more general constraints on the unknowns. The algorithm uses a trust region that allows the objective function to increase with logic for retreating to best values. The computations for the linear problem are done using a least squares system solver that allows for simple bounds and linear constraints. The trust region limits are defined by a box around the current point. In its current form the algorithm is effective only for problems with small residuals, linear constraints and dense Jacobian matrices. Results on a set of test problems are encouraging.

Hanson, R. J.↗

NASA NTRS1983

Computational methods for ideal compressible flow

Conservative dissipative difference schemes for computing one dimensional flow are introduced, and the recognition and representation of flow discontinuities are discussed. Multidimensional methods are outlined. Second order finite volume schemes are introduced. Conversion of difference schemes for a single linear convection equation into schemes for the hyperbolic system of the nonlinear conservation laws of ideal compressible flow is explained. Approximate Riemann solvers are presented. Monotone initial value interpolation; and limiters, switches, and artificial dissipation are considered.

Vanleer, B.↗

NASA NTRS1984

Fast algorithms for combustion kinetics calculations: A comparison

To identify the fastest algorithm currently available for the numerical integration of chemical kinetic rate equations, several algorithms were examined. Findings to date are summarized. The algorithms examined include two general-purpose codes EPISODE and LSODE and three special-purpose (for chemical kinetic calculations) codes CHEMEQ, CRK1D, and GCKP84. In addition, an explicit Runge-Kutta-Merson differential equation solver (IMSL Routine DASCRU) is used to illustrate the problems associated with integrating chemical kinetic rate equations by a classical method. Algorithms were applied to two test problems drawn from combustion kinetics. These problems included all three combustion regimes: induction, heat release and equilibration. Variations of the temperature and species mole fraction are given with time for test problems 1 and 2, respectively. Both test problems were integrated over a time interval of 1 ms in order to obtain near-equilibration of all species and temperature. Of the codes examined in this study, only CREK1D and GCDP84 were written explicitly for integrating exothermic, non-isothermal combustion rate equations. These therefore have built-in procedures for calculating the temperature.

Radhakrishnan, K.↗

NASA NTRS1984

The computation of all plane/surface intersections for CAD/CAM applications

The problem of the computation and display of all intersections of a given plane with a rational bicubic surface patch for use on an interactive CAD/CAM system is examined. The general problem of calculating all intersections of a plane and a surface consisting of rational bicubic patches is reduced to the case of a single generic patch by applying a rejection algorithm which excludes all patches that do not intersect the plane. For each pertinent patch the algorithm presented computed the intersection curves by locating an initial point on each curve, and computes successive points on the curve using a tolerance step equation. A single cubic equation solver is used to compute the initial curve points lying on the boundary of a surface patch, and the method of resultants as applied to curve theory is used to determine critical points which, in turn, are used to locate initial points that lie on intersection curves which are in the interior of the patch. Examples are given to illustrate the ability of this algorithm to produce all intersection curves.

Hoitsma, D. H., Jr.↗

NASA NTRS1984

Numerical simulation of the tip vortex off a low-aspect-ratio wing at transonic speed

The viscous transonic flow around a low aspect ratio wing was computed by an implicit, three dimensional, thin-layer Navier-Stokes solver. The grid around the geometry of interest is obtained numerically as a solution to a Dirichlet problem for the cube. A low aspect ratio wing with large sweep, twist, taper, and camber is the chosen geometry. The topology chosen to wrap the mesh around the wing with good tip resolution is a C-O type mesh. The flow around the wing was computed for a free stream Mach number of 0.82 at an angle of attack of 5 deg. At this Mach number, an oblique shock forms on the upper surface of the wing, and a tip vortex and three dimensional flow separation off the wind surface are observed. Particle path lines indicate that the three dimensional flow separation on the wing surface is part of the roots of the tip vortex formation. The lifting of the tip vortex before the wing trailing edge is observed by following the trajectory of particles release around the wing tip.

Mansour, N. N.↗

NASA NTRS1984

Analytical results for postbuckling behavior of plates in compression and shear

The postbuckling behavior of long rectangular isotropic and orthotropic plates is determined. By assuming trigonometric functions in one direction, the nonlinear partial differential equations of von Karman large deflection plate theory are converted into nonlinear ordinary differential equations. The ordinary differential equations are solved numerically using an available boundary value problem solver which makes use of Newton's method. Results for longitudinal compression show different postbuckling behavior between isotropic and orthotropic plates. Results for shear show that change in inplane edge constraints can cause large change in postbuckling stiffness.

Stein, M.↗

NASA NTRS1983

The efficient solution of transonic wing flow fields

An evaluation of the transonic-wing-analysis computer code TWING is presented. TWING utilizes a fully implicit, approximate-factorization iteration scheme to solve the full-potential equation in conservative form. A numerical elliptic-solver grid-generation scheme is used to generate the required finite-difference mesh. Several wing configurations have been analyzed, and comparisons of computed results have been made with available experimental data. Results indicate that the code is robust, accurate (when significant viscous effects are not present), and efficient. TWING generally produces solutions an order of magnitude faster than other conservative, full-potential codes using successive-line overrelaxation. The present method is applicable to a wide range of isolated wing configurations, including high-aspect-ratio transport wings and low-aspect-ratio, high-sweep, fighter configurations.

Holst, T. L.↗

NASA NTRS1984

Numerical simulation of the tip vortex off a low-aspect-ratio wing at transonic speed

The viscous transonic flow around a low-aspect-ratio wing has been computed using an implicit, three-dimensional, 'thin-layer' Navier-Stokes solver. The grid around the geometry of interest is obtained numerically as a solution to a Dirichlet problem for the cube. The geometry chosen for this study is a low-aspect-ratio wing with large sweep, twist, taper, and camber. The topology chosen to wrap the mesh around the wing with good tip resolution is a C-O type mesh. Using this grid, the flow around the wing was computed for a free-stream Mach number of 0.82 at an angle of attack of 5 deg. At this Mach number, an oblique shock forms on the upper surface of the wing, and a tip vortex and three-dimensional flow separation off the wing surface are observed. Particle path lines indicate that the three-dimensional flow separation on the wing surface is part of the roots of the tip-vortex formation. The lifting of the tip vortex before the wing trailing edge is clearly observed by following the trajectory of particles released around the wing tip.

Mansour, N. N.↗

NASA NTRS1984

Two recent extensions of the vortex method

The vortex method, coupled to an integral boundary-layer solver, is applied to the numerical simulation of high-Reynolds-number, separated flows in two new cases: a bluff body in a wind tunnel and flow in a cascade. In the bluff body case, the blockage effect of the tunnel walls is included approximately, assuming an inviscid boundary condition at the walls. The resulting increase in drag is computed, and compares well with a small-disturbance theory and with experiments. The results for flow in a cascade are compared with results from two finite-difference codes for a single-blade case, and good agreement is found. When a staggered cascade is treated with five independent blades, the simulation predicts rotating stall, depending on the angle of attack, and the essential features of the flow are correct. The sensitivity of this phenomenon to various parameters is studied and the stall boundary is found.

Spalart, P. R.↗

NASA NTRS1983

Models of human problem solving - Detection, diagnosis, and compensation for system failures

The role of the human operator as a problem solver in man-machine systems such as vehicles, process plants, transportation networks, etc. is considered. Problem solving is discussed in terms of detection, diagnosis, and compensation. A wide variety of models of these phases of problem solving are reviewed and specifications for an overall model outlined.

Rouse, W. B.↗

NASA NTRS1984

Development of a dynamically adaptive grid method for multidimensional problems

An approach to solution adaptive grid generation for use with finite difference techniques, previously demonstrated on model problems in one space dimension, has been extended to multidimensional problems. The method is based on the popular elliptic steady grid generators, but is 'dynamically' adaptive in the sense that a grid is maintained at all times satisfying the steady grid law driven by a solution-dependent source term. Testing has been carried out on Burgers' equation in one and two space dimensions. Results appear encouraging both for inviscid wave propagation cases and viscous boundary layer cases, suggesting that application to practical flow problems is now possible. In the course of the work, obstacles relating to grid correction, smoothing of the solution, and elliptic equation solvers have been largely overcome. Concern remains, however, about grid skewness, boundary layer resolution and the need for implicit integration methods. Also, the method in 3-D is expected to be very demanding of computer resources.

Holcomb, J. E.↗

NASA NTRS1984

Plasma response to the injection of an electron beam

The results of Vlasov-Poisson-solver numerical simulations of the detailed temporal response of a Maxwellian plasma to the sudden injection of an electron beam are presented in graphs and maps and discussed. Phenomena characterized include ion bursts, electron shocks and holes, plasma heating and expulsion, density gradients; cavitons, deep-density-front and solitary-pulse propagation down the density gradient, and Bunemann-mode excitation leading to formation of a virtual cathode and double layers which are at first monotonic or have low-potential-side dips or high-potential-side bumps and become strong as the electron-current density decreases. The strength of the double layer is found to be roughly proportional to the beam energy.

Singh, N.↗

NASA NTRS1984

A combined direct/inverse three-dimensional transonic wing design method for vector computers

A three-dimensional transonic-wing design algorithm for vector computers is developed, and the results of sample computations are presented graphically. The method incorporates the direct/inverse scheme of Carlson (1975), a Cartesian grid system with boundary conditions applied at a mean plane, and a potential-flow solver based on the conservative form of the full potential equation and using the ZEBRA II vectorizable solution algorithm of South et al. (1980). The accuracy and consistency of the method with regard to direct and inverse analysis and trailing-edge closure are verified in the test computations.

Weed, R. A.↗