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At least 1,153 records · Page 64

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NASA NTRS1988

Calculation of symmetric and asymmetric vortex seperation on cones and tangent ogives based on discrete vortex models

An inviscid discrete vortex model, with newly derived expressions for the tangential velocity imposed at the separation points, is used to investigate the symmetric and asymmetric vortex separation on cones and tangent ogives. The circumferential locations of separation are taken from experimental data. Based on a slender body theory, the resulting simultaneous nonlinear algebraic equations in a cross-flow plane are solved with Broyden's modified Newton-Raphson method. Total force coefficients are obtained through momentum principle with new expressions for nonconical flow. It is shown through the method of function deflation that multiple solutions exist at large enough angles of attack, even with symmetric separation points. These additional solutions are asymmetric in vortex separation and produce side force coefficients which agree well with data for cones and tangent ogives.

Chin, S.↗

NASA NTRS1988

A rapid method for the computation of equilibrium chemical composition of air to 15000 K

A rapid computational method has been developed to determine the chemical composition of equilibrium air to 15000 K. Eleven chemically reacting species, i.e., O2, N2, O, NO, N, NO+, e-, N+, O+, Ar, and Ar+ are included. The method involves combining algebraically seven nonlinear equilibrium equations and four linear elemental mass balance and charge neutrality equations. Computational speeds for determining the equilibrium chemical composition are significantly faster than the often used free energy minimization procedure. Data are also included from which the thermodynamic properties of air can be computed. A listing of the computer program together with a set of sample results are included.

Prabhu, Ramadas K.↗

NASA NTRS1988

On the generation of mean flows by the interaction of Goertler vortices and Tollmien-Schlichting waves in curved channel flows

There are many fluid flows where the onset of transition can be caused by different instability mechanisms which compete in the nonlinear regime. The interaction of a centrifugal instability mechanism with the viscous mechanism which causes Tollmein-Schlichting waves is discussed. The interaction between these modes can be strong enough to drive the mean state; the interaction is investigated in the context of curved channel flows so as to avoid difficulties associated with boundary layer growth. Essentially it was found that the mean state adjusts itself so that any modes present are neutrally stable even at finite amplitude. In the first instance, the mean state driven by a vortex of short wavelength in the absence of Tollmein-Schlichting waves is considered. It is shown that for a given channel curvature and vortex wavelength, there is an upper limit to the mass flow rate which the channel can support as the pressure gradient is increased. When the Tollmein-Schlichting waves are present, then the nonlinear differential equation to determine the mean state is modified.

Bassom, Andrew P.↗

NASA NTRS1987

Anisotropic interface kinetics and tilted cells in unidirectional solidification

A nonlinear evolution equation is derived which governs the cellular structure of a binary alloy with a small segregation coefficient, including the effects of anisotropic interface kinetics. This equation, applicable to long-wave instabilities of a planar interface, describes the spatial pattern of the growing disturbances. The presence of anisotropy causes the cells to grow at an angle to the normal of the planar front. This transition to a cellular morphology is shown to be a subcritical instability.

Young, G. W.↗

NASA NTRS1987

Numerical simulation of polar lows and comma clouds using simple dry models

Linear and nonlinear numerical channel models are used to simulate polar low/comma cloud evolution. The basic state of the model is idealized and can be specified analytically. It has strong horizontal as well as vertical wind shear and implicitly includes the effect of sensible heat fluxes from the lower boundary. This is done by having a layer of reduced stability present in the lower troposphere. The results of the linear model study are presented and used to provide input for the nonlinear model integration. It is shown that, given sufficient horizontal resolution, many features of polar low/comma clouds can be simulated by the nonlinear primitive equations model and the idealized basic state, in particular a rapidly growing disturbance with a wavelength on the order of 1000 km.

Mudrick, Stephen E.↗

NASA NTRS1988

A mixed finite difference/Galerkin method for three-dimensional Rayleigh-Benard convection

A fast and accurate numerical method, for nonlinear conservation equation systems whose solutions are periodic in two of the three spatial dimensions, is presently implemented for the case of Rayleigh-Benard convection between two rigid parallel plates in the parameter region where steady, three-dimensional convection is known to be stable. High-order streamfunctions secure the reduction of the system of five partial differential equations to a system of only three. Numerical experiments are presented which verify both the expected convergence rates and the absolute accuracy of the method.

Buell, Jeffrey C.↗

NASA NTRS1988

Isothermal magnetostatic atmospheres. II - Similarity solutions with current proportional to the magnetic potential cubed

The paper presents a family of isothermal magnetostatic atmospheres with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry. The distributed current in the model J is directed along the x-axis, where x is the horizontal ignorable coordinate. The current J is taken to be proportional to the cube of the magnetostatic potential A and falls off exponentially with distance vertical to the base with an e-folding distance equal to the gravitational scale height. A range of similarity solution examples are displayed depending on the values of the similarity parameters. Each similarity parameter corresponds to a symmetry of the underlying nonlinear elliptic equation for A. The similarity parameters also determine the source currents for the potential field solution of the family. The solutions show the interplay between the gravitational force, the J & B force (B, magnetic field induction) and the gas pressure gradient.

Webb, G. M.↗

NASA NTRS1988

A direct interaction approximation treatment of turbulence in a compressible fluid. I - Formalism

The direct interaction approximation is used to treat turbulence in a compressible medium with constant mean gradients. The set of coupled nonlinear integrodifferential equations is derived that is satisfied by the transverse and longitudinal energy spectral functions, Q(T) and Q(L) and by the transverse and longitudinal response functions, G(T) and G(L). Finally, expressions for the average of the product of pairs of physically relevant fluctuating quantities (velocity, temperature, density) are derived in terms of Q(T) and Q(L).

Hartke, Gregory J.↗

NASA NTRS1988

Optimizing advanced propeller designs by simultaneously updating flow variables and design parameters

A scheme is developed for solving constrained optimization problems in which the objective function and the constraint function are dependent on the solution of the nonlinear flow equations. The scheme updates the design parameter iterative solutions and the flow variable iterative solutions simultaneously. It is applied to an advanced propeller design problem with the Euler equations used as the flow governing equations. The scheme's accuracy, efficiency and sensitivity to the computational parameters are tested.

Rizk, Magdi H.↗

NASA NTRS1987

Symbolic modeling of flexible manipulators

An algorithm is presented to symbolically derive the full nonlinear dynamic equations of motion of multilink flexible manipulators. Lagrange's assumed modes method is the basis of new algorithm and adapted in a way suitable for symbolic manipulation by digital computers. It is applied to model a two-link flexible arm by means of a commercially available symbolic manipulation program. The advantages of the algorithm and simulation results are discussed.

Cetinkunt, Sabri↗

NASA NTRS1987

Parallel computations and their impact on mechanics; Proceedings of the Symposium, ASME Winter Annual Meeting, Boston, MA, Dec. 13-18, 1987

The conference presents papers on parallel architectures and the programming environment, parallel numerical algorithms, structural mechanics applications, and fluid dynamics applications. Topics include concurrent computer architecture, the state-of-the-art in highly parallel computer systems, supercomputer programming environments, uniquely parallel algorithms, the parallel solution of nonlinear elliptic equations, highly parallel banded systems solvers, and optimal mapping of irregular finite element domains to parallel processors. Consideration is also given to parallel processing in finite element structural analysis, heirarchical parallelism in a finite element CFD algorithm, and a parallelized elliptic solver for reacting flows.

Noor, Ahmed K.↗

NASA NTRS1987

Automating the parallel processing of fluid and structural dynamics calculations

The NASA Lewis Research Center is actively involved in the development of expert system technology to assist users in applying parallel processing to computational fluid and structural dynamic analysis. The goal of this effort is to eliminate the necessity for the physical scientist to become a computer scientist in order to effectively use the computer as a research tool. Programming and operating software utilities have previously been developed to solve systems of ordinary nonlinear differential equations on parallel scalar processors. Current efforts are aimed at extending these capabilties to systems of partial differential equations, that describe the complex behavior of fluids and structures within aerospace propulsion systems. This paper presents some important considerations in the redesign, in particular, the need for algorithms and software utilities that can automatically identify data flow patterns in the application program and partition and allocate calculations to the parallel processors. A library-oriented multiprocessing concept for integrating the hardware and software functions is described.

Arpasi, Dale J.↗

NASA NTRS1988

Bounds on the Fourier coefficients for the periodic solutions of non-linear oscillator equations

The differential equations describing nonlinear oscillations (as seen in mechanical vibrations, electronic oscillators, chemical and biochemical reactions, acoustic systems, stellar pulsations, etc.) are investigated analytically. The boundedness of the Fourier coefficients for periodic solutions is demonstrated for two special cases, and the extrapolation of the results to higher-dimensionsal systems is briefly considered.

Mickens, R. E.↗

NASA NTRS1988

An adaptive pseudospectral method for discontinuous problems

The accuracy of adaptively chosen, mapped polynomial approximations is studied for functions with steep gradients or discontinuities. It is shown that, for steep gradient functions, one can obtain spectral accuracy in the original coordinate system by using polynomial approximations in a transformed coordinate system with substantially fewer collocation points than are necessary using polynomial expansion directly in the original, physical, coordinate system. It is also shown that one can avoid the usual Gibbs oscillation associated with steep gradient solutions of hyperbolic pde's by approximation in suitably chosen coordinate systems. Continuous, high gradient solutions are computed with spectral accuracy (as measured in the physical coordinate system). Discontinuous solutions associated with nonlinear hyperbolic equations can be accurately computed by using an artificial viscosity chosen to smooth out the solution in the mapped, computational domain. Thus, shocks can be effectively resolved on a scale that is subgrid to the resolution available with collocation only in the physical domain. Examples with Fourier and Chebyshev collocation are given.

Augenbaum, Jeffrey M.↗

NASA NTRS1988

Aerodynamic optimization by simultaneously updating flow variables and design parameters with application to advanced propeller designs

Rizk, Magdi H.↗

NASA NTRS1988

User's manual for an aerodynamic optimization scheeme that updates flow variables and design parameters simultaneously

This user's manual is presented for an aerodynamic optimization program that updates flow variables and design parameters simultaneously. The program was developed for solving constrained optimization problems in which the objective function and the constraint function are dependent on the solution of the nonlinear flow equations. The program was tested by applying it to the problem of optimizing propeller designs. Some reference to this particular application is therefore made in the manual. However, the optimization scheme is suitable for application to general aerodynamic design problems. A description of the approach used in the optimization scheme is first presented, followed by a description of the use of the program.

Rizk, Magdi H.↗

NASA NTRS1989

Mixed formulation for frictionless contact problems

Simple mixed finite element models and a computational precedure are presented for the solution of frictionless contact problems. The analytical formulation is based on a form of Reissner's large rotation theory of the structure with the effects of transverse shear deformation included. The contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the internal forces (stress resultants), the generalized displacements, and the Lagrange multipliers associated with the contact conditions. The element characteristic array are obtained by using a modified form of the two-field Hellinger-Reissner mixed variational principle. The internal forces and the Lagrange multipliers are allowed to be discontinuous at interelement boundaries. The Newton-Raphson iterative scheme is used for the solution of the nonlinear algebraic equations, and the determination of the contact area and the contact pressures.

Noor, Ahmed K.↗

NASA NTRS1988

Rotordynamic analysis of a bearing tester

The properties of the solutions of a system of four coupled nonlinear differential equations that model the behavior of the rotating shaft of a bearing tester are studied. In particular, it is shown how the bounds for the rotations of these equations can be obtained from bounds for the solutions of the linearized equations. By studying the behavior of the Fourier transforms of the solution, the approach to the stability boundary can also be predicted. These conclusions are verified by means of numerical solutions of the equations, and of power spectrum density (PSD) plots.

Zalik, Richard A.↗