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At least 937 records · Page 52
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NASA NTRS1994

Boundary element analysis on vector and parallel computers

Boundary element analysis (BEA) can be characterized as a numerical technique that generally shifts the computational burden in the analysis toward numerical integration and the solution of nonsymmetric and either dense or blocked sparse systems of algebraic equations. Researchers have explored the concept that the fundamental characteristics of BEA can be exploited to generate effective implementations on vector and parallel computers. In this paper, the results of some of these investigations are discussed. The performance of overall algorithms for BEA on vector supercomputers, massively data parallel single instruction multiple data (SIMD), and relatively fine grained distributed memory multiple instruction multiple data (MIMD) computer systems is described. Some general trends and conclusions are discussed, along with indications of future developments that may prove fruitful in this regard.

Kane, J. H.↗
NASA NTRS1993

The interaction of plume heads with compositional discontinuities in the Earth's mantle

The effects of compositional discontinuities of density and viscosity in the Earth's mantle on the ascent of mantle plume heads is studied using a boundary integral numerical technique. Three specific problems are considered: (1) a plume head rising away from a deformable interface, (2) a plume head passing through an interface, and (3) a plume head approaching the surface of the Earth. For the case of a plume attached to a free-surface, the calculated time-dependent plume shapesare compared with experimental results. Two principle modes of plume head deformation are observed: plume head elingation or the formation of a cavity inside the plume head. The inferred structure of mantle plumes, namely, a large plume head with a long tail, is characteristic of plumes attached to their source region, and also of buoyant material moving away from an interface and of buoyant material moving through an interface from a high- to low-viscosity region. As a rising plume head approaches the upper mantle, most of the lower mantle will quickly drain from the gap between the plume head and the upper mantle if the plume head enters the upper mantle. If the plume head moves from a high- to low-viscosity region, the plume head becomes significantly elongated and, for the viscosity contrasts thought to exist in the Earth, could extend from the 670 km discontinuity to the surface. Plume heads that are extended owing to a viscosity decrease in the upper mantle have a cylindrical geometry. The dynamic surface topography induced by plume heads is bell-shaped when the top of the plume head is at depths greater than about 0.1 plume head radii. As the plume head approaches the surface and spreads, the dynamic topography becomes plateau-shaped. The largest stresses are produced in the early stages of plume spreading when the plume head is still nearly spherical, and the surface expression of these stresses is likely to be dominated by radial extension. As the plume spreads, compressional stresses on the surface are produced beyond the edges of the plume; consequently, extensional features will be produced above the plume head and may be surrounded by a ring of compressional features.

Manga, Michael↗
NASA NTRS1994

Viscoplastic response of structures for intense local heating

A thermoviscoplastic finite element method employing the Bodner-Partom constitutve model is used to investigate the response of simplified thermal-structural models to intense local heating. The computational method formulates the problem in rate and advances the solution in time by numerical integration. The thermoviscoplastic response of simplified structures with prescribed temperatures is investigated. With rapid rises of temperature, the nickel alloy structures display initially higher yield stresses due to strain rate effects. As temperatures approach elevated values, yield stress and stiffness degrade rapidly and pronounced plastic deformation occurs.

Thornton, Earl A.↗
NASA NTRS1994

Chaotic dynamics of corotating magnetospheric convection

The corotating plasma convection system of the Jovian magnetosphere is analyzed. The macroscopic (mhd) model introduced by Summers and Mu, (1992) that incorporates the effects of microdiffusion is extended by including previously neglected density effects. We reduce the governing partial differential equations to a third-order ordinary differential system by the Galerkin technique of mode truncation. We carry out such a severe truncation partly in the interests of tractability, and leave open the question of the efficacy of adding additional modes. Exhaustive numerical integrations are carried out to calculate the long-term solutions, and we discover that a rich array of plasma motions is possible, dependent on the value of the height-integrated ionospheric Pederson conductivity Sigma. If Sigma is less than a certain critical value Sigma(sub c), then plasma motion can be expected to be chaotic (or periodic), while if Sigma is greater than Sigma(sub c), then steady state convection is expected. In the former case, whether the plasma motion is chaotic or periodic (and, if periodic, the magnitude of the period) can be very sensitive to the value of Sigma. The value of Sigma(sub c), which is a function of a parameter q that occurs in the assumed form of the stationary radial profile (varies as L(exp -q) of the plasma mass per unit magnetic flux, lies well within the accepted range of values of Sigma for Jupiter, i.e. Sigma greater than or equal to 0.1 mho and less than or equal to 10 mho.

Summers, Danny↗
NASA NTRS1993

New dynamic variables for rotating spacecraft

This paper introduces two new seven-parameter representations for spacecraft attitude dynamics modeling. The seven parameters are the three components of the total system angular momentum in the spacecraft body frame; the three components of the angular momentum in the inertial reference frame; and an angle variable. These obey a single constraint as do parameterizations that include a quaternion; in this case the constraint is the equality of the sum of the squares of the angular momentum components in the two frames. The two representations are nonsingular if the system angular momentum is non-zero and obeys certain orientation constraints. The new parameterizations of the attitude matrix, the equations of motion, and the relation of the solution of these equations to Euler angles for torque-free motion are developed and analyzed. The superiority of the new parameterizations for numerical integration is shown in a specific example.

Markley, F. Landis↗
NASA NTRS1994

Charged dust in planetary magnetospheres: Hamiltonian dynamics and numerical simulations for highly charged grains

We use a combination of analytical and numerical methods to investigate the dynamics of charged dust grains in planetary magnetospheres. Our emphasis is on obtaining results valid for particles that are not necessarily dominated either by gravitational or electromagnetic forces. A Hamiltonian formulation of the problem yields exact results, for all values of charge-to-mass ratio, when we introduce two constraints: particles remain in the equatorial plane and the magnetic field is taken as axially symmetric. In particular, we obtain locations of equilibrium points, the frequencies of stable periodic orbits, the topology of separatrices in phase space, and the rate of longitudinal drift. These results are significant for specific applications: motion in the nearly aligned dipolar field of Saturn, and the trajectories of arbitrarily charged particles in complex magnetic fields for limited periods of time after ejection from parent bodies. Since the model is restrictive, we also use numerical integrations of the full three-dimensional equations of motion and illustrate under what conditions the constrained problem yields reasonable results. We show that a large fraction of the intermediately charged and highly charged (gyrating) particles will always be lost to a planet's atmosphere within a few hundred hours, for motion through tilted-dipole magnetic fields. We find that grains must have a very high charge-to-mass ratio in order to be mirrored back to the ring plane. Thus, except perhaps at Saturn where the dipole tilt is very small, the likely inhabitants of the dusty ring systems are those particles that are either nearly Keplerian (weakly charged) grains or grains whose charges place them in the lower end of the intermediate charge zone. Fianlly, we demonstrate the effect of plasma drag on the orbits of gyrating particles to be a rapid decrease in gyroradius followed by a slow radial evolution of the guiding center.

Schaffer, L.↗
NASA NTRS1995

Optically thick winds: How is the mass flux determined?

Expanding envelopes of compact objects that possess a buring region at the base of the envelope are commonly observed and modeled. In many cases, such as the late stages of classical nova, the expanding envelope develops into a stationary, optically thick wind of matter escaping from the star. In the usual theoretical formalism there is one more unknown than equations, with closure being obtained by the requirement that the solution pass through the singularity at the sonic point. It is shown analytically that the mass flux, which is one of the unknowns, is almost completely determined by the physical conditions near the base of the envelope just above the burning zone. The sonic point closure relation determines whether the expanding solution can develop into a wind solution. For a given core mass the range of possible wind solutions is an outcome of the great sensitivity of the mass flux to the inner luminosity. Solutions determined through numerical integrations are shown to lie entirely within the narrow analytic boundaries.

Glasner, S. Ami↗
NASA NTRS1995

Nonlinear structure formation in flat cosmological models

This paper describes the formation of nonlinear structure in flat (zero curvature) Friedmann cosmological models. We consider models with two components: the usual nonrelativistic component that evolves under gravity and eventually forms the large-scale structure of the universe, and a uniform dark matter component that does not clump under gravity, and whose energy density varies with the scale factor a(t) like a(t)(sup -n), where n is a free parameter. Each model is characterized by two parameters: the exponent n and the present density parameter Omega(sub 0) of the nonrelativistic component. The linear perturbation equations are derived and solved for these models, for the three different cases n = 3, n is greater than 3, and n is less than 3. The case n = 3 is relevant to model with massive neutrinos. The presence of the uniform component strongly reduces the growth of the perturbation compared with the Einstein-de Sitter model. We show that the Meszaros effect (suppression of growth at high redshift) holds not only for n = 4, radiation-dominated models, but for all models with n is greater than 3. This essentially rules out any such model. For the case n is less than 3, we numerically integrate the perturbation equations from the big bang to the present, for 620 different models with various values of Omega(sub 0) and n. Using these solutions, we show that the function f(Omega(sub 0), n) = (a/delta(sub +))d(delta)(sub +)/da, which enters in the relationship between the present density contrast delta(sub 0) and peculiar velocity field u(sub 0) is essentially independent of n. We derive approximate solutions for the second-order perturbation equations. These second-order solutions are tested against the exact solutions and the Zel'dovich approximation for spherically symmetric perturbations in the marginally nonlinear regime (the absolute value of delta is less than or approximately 1). The second-order and Zel'dovich solutions have comparable accuracy, significantly higher than the accuracy of the linear solutions. We then investigate the dependence of the delta(sub 0) - u(sub 0) relationship upon the value of n in the nonlinear regime using the second-order solutions for marginally nonlinear, general perturbations, and the exact solutions for strongly nonlinear, spherically symmetric perturbations. In both cases, we find that the delta(sub 0) - u(sub 0) relationship remains independent of n. We speculate that this result extends to strongly nonlinear, general perturbations as well. This eliminates any hope to determine the presence of the uniform component or the value of n using dynamical methods. Finally, we compute the nonlinear evolution of the skewness of the distribution of values of delta, assuming Gaussian initial conditions. We find that the skewness is not only independent of n, but also of Omega(sub 0). Thus the skewness cannot be used to discriminate among various models with Gaussian initial conditions. However, it can be used for testing the Gaussianity of the initial conditions themselves. We conclude that the uniform component leaves no observable signature in the present large-scale structure of the universe. To determine its presence and nature, we must investigate the relationship between the past and present universe, using redshift-dependent tests.

Martel, Hugo↗
NASA NTRS1995

Upwind-Differencing Computations Of Incompressible Flows

Report discusses application of upwind-differencing numerical-integration scheme in conjunction with method of pseudocompressibility to computations of flows of incompressible fluids, with emphasis on steady-state flows. Three test cases presented: driven flow in square cavity, flow over backward-facing step, and flow around circular cylinder.

Rogers, Stuart↗
NASA NTRS1996

Heat and Momentum Transfer Studies in High Reynolds Number Wavy Films at Normal and Reduced Gravity Conditions

We examined the effect of the gas flow on the liquid film when the gas flows in the countercurrent direction in a vertical pipe at normal gravity conditions. The most dramatic effect of the simultaneous flow of gas and liquid in pipes is the greatly increased transport rates of heat, mass, and momentum. In practical situations this enhancement can be a benefit or it can result in serious operational problems. For example, gas-liquid flow always results in substantially higher pressure drop and this is usually undesirable. However, much higher heat transfer coefficients can be expected and this can obviously be of benefit for purposes of design. Unfortunately, designers know so little of the behavior of such two phase systems and as a result these advantages are not utilized. Due to the complexity of the second order boundary model as well as the fact that the pressure variation across the film is small compared to the imposed gas phase pressure, the countercurrent gas flow affect was studied for the standard boundary layer model. A different stream function that can compensate the shear stress affect was developed and this stream function also can predict periodic solutions. The discretized model equations were transformed to a traveling wave coordinate system. A stability analysis of these sets of equations showed the presence of a Hopf bifurcation for certain values of the traveling wave velocity and the shear stress. The Hopf celerity was increased due to the countercurrent shear. For low flow rate the increases of celerity are more than for the high flow rate, which was also observed in experiments. Numerical integration of a traveling wave simplification of the model also predicts the existence of chaotic large amplitude, nonperiodic waves as observed in the experiments. The film thickness was increased by the shear.

Balakotaiah, V.↗
NASA NTRS1996

Refinement Of Hexahedral Cells In Euler Flow Computations

Topologically Independent Grid, Euler Refinement (TIGER) computer program solves Euler equations of three-dimensional, unsteady flow of inviscid, compressible fluid by numerical integration on unstructured hexahedral coordinate grid refined where necessary to resolve shocks and other details. Hexahedral cells subdivided, each into eight smaller cells, as needed to refine computational grid in regions of high flow gradients. Grid Interactive Refinement and Flow-Field Examination (GIRAFFE) computer program written in conjunction with TIGER program to display computed flow-field data and to assist researcher in verifying specified boundary conditions and refining grid.

Melton, John E.↗
NASA NTRS1996

A numerical investigation of premixed combustion in wave rotors

Wave rotor cycles which utilize premixed combustion processes within the passages are examined numerically using a one-dimensional CFD-based simulation. Internal-combustion wave rotors are envisioned for use as pressure-gain combustors in gas turbine engines. The simulation methodology is described, including a presentation of the assumed governing equations for the flow and reaction in the channels, the numerical integration method used, and the modeling of external components such as recirculation ducts. A number of cycle simulations are then presented which illustrate both turbulent-deflagration and detonation modes of combustion. Estimates of performance and rotor wall temperatures for the various cycles are made, and the advantages and disadvantages of each are discussed.

Nalim, M. Razi↗
NASA NTRS1996

ASTROP2 Users Manual: A Program for Aeroelastic Stability Analysis of Propfans

This manual describes the input data required for using the second version of the ASTROP2 (Aeroelastic STability and Response Of Propulsion systems - 2 dimensional analysis) computer code. In ASTROP2, version 2.0, the program is divided into two modules: 2DSTRIP, which calculates the structural dynamic information; and 2DASTROP, which calculates the unsteady aerodynamic force coefficients from which the aeroelastic stability can be determined. In the original version of ASTROP2, these two aspects were performed in a single program. The improvements to version 2.0 include an option to account for counter rotation, improved numerical integration, accommodation for non-uniform inflow distribution, and an iterative scheme to flutter frequency convergence. ASTROP2 can be used for flutter analysis of multi-bladed structures such as those found in compressors, turbines, counter rotating propellers or propfans. The analysis combines a two-dimensional, unsteady cascade aerodynamics model and a three dimensional, normal mode structural model using strip theory. The flutter analysis is formulated in the frequency domain resulting in an eigenvalue determinant. The flutter frequency and damping can be inferred from the eigenvalues.

Reddy, T. S. R.↗
NASA NTRS1996

Technique for Extension of Small Antenna Array Mutual-Coupling Data to Larger Antenna Arrays

A technique is presented whereby the mutual interaction between a small number of elements in a planar array can be interpolated and extrapolated to accurately predict the combined interactions in a much larger array of many elements. An approximate series expression is developed, based upon knowledge of the analytical characteristic behavior of the mutual admittance between small aperture antenna elements in a conducting ground plane. This expression is utilized to analytically extend known values for a few spacings and orientations to other element configurations, thus eliminating the need to numerically integrate a large number of highly oscillating and slowly converging functions. This paper shows that the technique can predict very accurately the mutual coupling between elements in a very large planar array with a knowledge of the self-admittance of an isolated element and the coupling between only two-elements arranged in eight different pair combinations. These eight pair combinations do not necessarily have to correspond to pairs in the large array, although all of the individual elements must be identical.

Bailey, M. C.↗
NASA NTRS1996

Designing ROW Methods

There are many aspects to consider when designing a Rosenbrock-Wanner-Wolfbrandt (ROW) method for the numerical integration of ordinary differential equations (ODE's) solving initial value problems (IVP's). The process can be simplified by constructing ROW methods around good Runge-Kutta (RK) methods. The formulation of a new, simple, embedded, third-order, ROW method demonstrates this design approach.

Freed, Alan D.↗
NASA NTRS1996

The Development of Computational Techniques for the Nonlinear Analysis of Composite Structures at High Temperature

The objective of this research project was to develop robust and efficient computational tools for deformation and life analysis techniques. This included: development of viscoplastic continuum models, associated numerical integration techniques, suitable micromechanics models/methods, and coupled deformation and damage algorithms. The work was involved with models/methods applicable to composite structures on both microscale and macroscale levels. The microscale analysis utilized Aboudi's generalized method of cells (GMS) micromechanical model as well as finite element models of similar composite architectures, i.e., square and hexagonal fiber pack models.

Keith, Theo G., Jr.↗
NASA NTRS1997

Wave Number Selection for Incompressible Parallel Jet Flows Periodic in Space

The temporal instability of a spatially periodic parallel flow of an incompressible inviscid fluid for various jet velocity profiles is studied numerically using Floquet Analysis. The transition matrix at the end of a period is evaluated by direct numerical integration. For verification, a method based on approximating a continuous function by a series of step functions was used. Unstable solutions were found only over a limited range of wave numbers and have a band type structure. The results obtained are analogous to the behavior observed in systems exhibiting complexity at the edge of order and chaos.

Miles, Jeffrey Hilton↗
NASA NTRS1997

The Uncertain Nature of Cometary Motions

The number of active short- and long-periodic comets crossing the Earth's orbit each year is less than 10 percent of the corresponding number of asteroids crossing the Earth's orbit. However, the higher relative velocities of comets with respect to the Earth and the uncertainties associated with accurately computing their future trajectories can cause considerable problems when assessing the risks of Earth-crossing objects. Unlike asteroids, the motions of active comets are often affected by so-called nongravitational (outgassing) forces that are imperfectly modeled. In addition, the astrometric optical observations that are used to refine a comet's orbit are often imprecise because a comet's center of mass can be hidden by atmospheric gas and dust. For long-period comets, there is the additional problem of having to base orbital solutions on relatively short observational data intervals. Long-term numerical integrations extending two centuries into the future have been carried out to investigate upcoming Earth-close approaches by known periodic comets. Error analyses and impact probabilities have been computed for those comets that will pass closest to the Earth. Although there are no known comets that will make dangerously close Earth approaches in the next two centuries, there are a few objects that warrant future monitoring.

Yeomans, Donald K.↗