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At least 919 records · Page 51
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NASA NTRS1993

Parallel methods for dynamic simulation of multiple manipulator systems

In this paper, efficient dynamic simulation algorithms for a system of m manipulators, cooperating to manipulate a large load, are developed; their performance, using two possible forms of parallelism on a general-purpose parallel computer, is investigated. One form, temporal parallelism, is obtained with the use of parallel numerical integration methods. A speedup of 3.78 on four processors of CRAY Y-MP8 was achieved with a parallel four-point block predictor-corrector method for the simulation of a four manipulator system. These multi-point methods suffer from reduced accuracy, and when comparing these runs with a serial integration method, the speedup can be as low as 1.83 for simulations with the same accuracy. To regain the performance lost due to accuracy problems, a second form of parallelism is employed. Spatial parallelism allows most of the dynamics of each manipulator chain to be computed simultaneously. Used exclusively in the four processor case, this form of parallelism in conjunction with a serial integration method results in a speedup of 3.1 on four processors over the best serial method. In cases where there are either more processors available or fewer chains in the system, the multi-point parallel integration methods are still advantageous despite the reduced accuracy because both forms of parallelism can then combine to generate more parallel tasks and achieve greater effective speedups. This paper also includes results for these cases.

Mcmillan, Scott↗
NASA NTRS1992

Comparison of level-1 and level-2 buckling and postbuckling solutions

The accuracy of the solutions obtained with the Level-1 computational modules of DISDECO (Delft Interactive Shell Design Code) are investigated by comparing them with solutions obtained with ANILISA, a Level-2 computational module. Whereas the Level-1 solutions are based on the use of trigonometric functions to represent the out-of-plane displacement W and involve Galerkin type approximations to reduce the governing partial differential equations to simple algebraic expressions, the Level-2 solutions employ a truncated Fourier expansion in the circumferential direction and solve the resulting ordinary differential equations forming a nonlinear eigenvalue problem by a Stodola like technique. This involves the numerical integration of the set of ordinary differential equations, which in turn makes it possible to satisfy the specified boundary conditions exactly. It is shown that in many applications the Level-1 predictions concerning the critical buckling load of the perfect structure and its imperfection sensitivity are quite accurate and reliable. For those cases where this is not true, it is shown how the pre and postprocessing facilities of DISDECO can be used efficiently to arrive at a reliable prediction. This involves always the use of the Level-2 computational module ANILISA with its rigorous prebuckling solution and its feature which makes it possible to satisfy the specified boundary conditions exactly.

Arbocz, J.↗
NASA NTRS1993

Statistical computation of tolerance limits

Based on a new theory, two computer codes were developed specifically to calculate the exact statistical tolerance limits for normal distributions within unknown means and variances for the one-sided and two-sided cases for the tolerance factor, k. The quantity k is defined equivalently in terms of the noncentral t-distribution by the probability equation. Two of the four mathematical methods employ the theory developed for the numerical simulation. Several algorithms for numerically integrating and iteratively root-solving the working equations are written to augment the program simulation. The program codes generate some tables of k's associated with the varying values of the proportion and sample size for each given probability to show accuracy obtained for small sample sizes.

Wheeler, J. T.↗
NASA NTRS1993

Formation of on-site normal points

We describe our methods of fitting a smoothing function to observational range differences from a predicted orbit, by deducing corrections to the orbit in the radial and along-track directions. The method has been used on observations of a variety of satellites, and using predicted orbits computed both by numerical integration using IRV's as starting values and analytically from orbital elements. The along-track corrections to the predicted orbit have been successfully used in the form of time biases to improve subsequent predictions, and a statistical test has been devised to ensure that the range residuals may be used to form unbiased quick look normal points.

Appleby, G. M.↗
NASA NTRS1993

Dust grain resonant capture: A statistical study

A statistical approach, based on a large number of simultaneous numerical integrations, is adopted to study the capture in external mean motion resonances with the Earth of micron size dust grains perturbed by solar radiation and wind forces. We explore the dependence of the resonant capture phenomenon on the initial eccentricity e(sub 0) and perihelion argument w(sub 0) of the dust particle orbit. The intensity of both the resonant and dissipative (Poynting-Robertson and wind drag) perturbations strongly depends on the eccentricity of the particle while the perihelion argument determines, for low inclination, the mutual geometrical configuration of the particle's orbit with respect to the Earth's orbit. We present results for three j:j+1 commensurabilities (2:3, 4:5 and 6:7) and also for particle sizes s = 15, 30 microns. This study extends our previous work on the long term orbital evolution of single dust particles trapped into resonances with the Earth.

Marzari, F.↗
NASA NTRS1993

Current capabilities for simulating the extreme distortion of thin structures subjected to severe impacts

The explicit transient dynamics technology in use today for simulating the impact and subsequent transient dynamic response of a structure has its origins in the 'hydrocodes' dating back to the late 1940's. The growth in capability in explicit transient dynamics technology parallels the growth in speed and size of digital computers. Computer software for simulating the explicit transient dynamic response of a structure is characterized by algorithms that use a large number of small steps. In explicit transient dynamics software there is a significant emphasis on speed and simplicity. The finite element technology used to generate the spatial discretization of a structure is based on a compromise between completeness of the representation for the physical processes modelled and speed in execution. That is, since it is expected in every calculation that the deformation will be finite and the material will be strained beyond the elastic range, the geometry and the associated gradient operators must be reconstructed, as well as complex stress-strain models evaluated at every time step. As a result, finite elements derived for explicit transient dynamics software use the simplest and barest constructions possible for computational efficiency while retaining an essential representation of the physical behavior. The best example of this technology is the four-node bending quadrilateral derived by Belytschko, Lin and Tsay. Today, the speed, memory capacity and availability of computer hardware allows a number of the previously used algorithms to be 'improved.' That is, it is possible with today's computing hardware to modify many of the standard algorithms to improve their representation of the physical process at the expense of added complexity and computational effort. The purpose is to review a number of these algorithms and identify the improvements possible. In many instances, both the older, faster version of the algorithm and the improved and somewhat slower version of the algorithm are found implemented together in software. Specifically, the following seven algorithmic items are examined: the invariant time derivatives of stress used in material models expressed in rate form; incremental objectivity and strain used in the numerical integration of the material models; the use of one-point element integration versus mean quadrature; shell elements used to represent the behavior of thin structural components; beam elements based on stress-resultant plasticity versus cross-section integration; the fidelity of elastic-plastic material models in their representation of ductile metals; and the use of Courant subcycling to reduce computational effort.

Key, Samuel W.↗
NASA NTRS1993

Three-dimensional solidification and melting using magnetic field control

A new two-fluid mathematical model for fully three dimensional steady solidification under the influence of an arbitrary acceleration vector and with or without an arbitrary externally applied steady magnetic field have been formulated and integrated numerically. The model includes Joule heating and allows for separate temperature dependent physical properties within the melt and the solid. Latent heat of phase change during melting/solidification was incorporated using an enthalpy method. Mushy region was automatically captured by varying viscosity orders of magnitude between liquidus and solidus temperature. Computational results were obtained for silicon melt solidification in a parallelepiped container cooled from above and from a side. The results confirm that the magnetic field has a profound influence on the solidifying melt flow field thus changing convective heat transfer through the boundaries and the amount and shape of the solid accrued. This suggests that development of a quick-response algorithm for active control of three dimensional solidification is feasible since it would require low strength magnetic fields.

Dulikravich, George S.↗
NASA NTRS1994

Computational studies of metal-metal and metal-ligand interactions

Accurate calculations on the bond length, dipole moment, and harmonic frequency of CO are presented, using large basis sets and high levels of electron correlation. The geometric structure, force constants and binding energies of Cr(C0)6 and Cr(CO)5 are computed using large basis sets and high levels of electron correlation. The molecule 04(+) is studied, using large basis sets and high levels of electron correlation, including the CASSCF, CASSI and CASPT2 methods. Binding energies, geometries and frequencies are computed. Symmetry breaking is a particular problem for the antisymmetric stretch, which is addressed using the CASSI method. The symmetry breaking problem in 04(+) has also been studied using the Brueckner coupled cluster method. This gives results in good agreement with CASSI. A multi-region numerical integration scheme is investigated for use in Density Functional Calculations. This scheme is found to give comparable results to a widely used scheme based on the Euler-Maclaurin technique.

Barnes, Leslie A.↗
NASA NTRS1991

Interface behavior of a multi-layer fluid configuration subject to acceleration in a microgravity environment, supplement 1

With the increasing opportunities for research in a microgravity environment, there arises a need for understanding fluid mechanics under such conditions. In particular, a number of material processing configurations involve fluid-fluid interfaces which may experience instabilities in the presence of external forcing. In a microgravity environment, these accelerations may be periodic or impulse-type in nature. This research investigates the behavior of a multi-layer idealized fluid configuration which is infinite in extent. The analysis is linear, and each fluid region is considered inviscid, incompressible, and immiscible. An initial parametric study of confiquration stability in the presence of a constant acceleration field is performed. The zero mean gravity limit case serves as the base state for the subsequent time-dependent forcing cases. A stability analysis of the multi-layer fluid system in the presence of periodic forcing is investigated. Floquet theory is utilized. A parameter study is performed, and regions of stability are identified. For the impulse-type forcing case, asymptotic stability is established for the configuration. Using numerical integration, the time response of the interfaces is determined.

Lyell, M. J.↗
NASA NTRS1995

The initial-value problem for viscous channel flows

Plane viscous channel flows are perturbed and the ensuing initial-value problems are investigated in detail. Unlike traditional methods where traveling wave normal modes are assumed for solution, this works offers a means whereby completely arbitrary initial input can be specified without having to resort to eigenfunction expansions. The full temporal behavior, including both early time transients and the long time asymptotics, can be determined for any initial disturbance. Effects of three-dimensionality can be assessed. The bases for the analysis are: (a) linearization of the governing equations; (b) Fourier decomposition in the spanwise and streamwise directions of the flow; and (c) direct numerical integration of the resulting partial differential equations. All of the stability data that are known for such flows can be reproduced. Also, the optimal initial condition can be determined in a straight forward manner and such optimal conditions clearly reflect transient growth data that is easily determined by a rational choice of a basis for the initial conditions. Although there can be significant transient growth for subcritical values of the Reynolds number using this approach it does not appear possible that arbitrary initial conditions will lead to the exceptionally large transient amplitudes that have been determined by optimization of normal modes. The approach is general and can be applied to other classes of problems where only a finite discrete spectrum exists, such as the boundary layer for example.

Criminale, W. O.↗
NASA NTRS1994

Computational studies of metal-metal and metal-ligand interactions

Accurate calculations on the bond length, dipole moment, and harmonic frequency of CO are presented, using large basis sets and high levels of electron correlation. The geometric structure, force constants and binding energies of Cr(CO)6 and Cr(CO)5 are computed using large basis sets and high levels of electron correlation. The molecule O4(+) is studied, using large basis sets and high levels of electron correlation, including the CASSCF, CASSI,and CASPT2 methods. Binding energies, geometries and frequencies are computed. Symmetry breaking is a particular problem for the antisymmetric stretch, which is addressed using the CASSI method. The symmetry breaking problem in O4(+) has also been studied using the Brueckner coupled-cluster method. This gives results in good agreement with CASSI. A multi-region numerical integration scheme is investigated for use in Density Functional Calculations. This scheme is found to give comparable results to a widely used scheme based on the Euler-Maclaurin technique.

Barnes, Leslie A.↗
NASA NTRS1994

Aeroacoustic computation of gust-blade interaction

To better understand and address the challenges faced in computing the acoustics of flow fields, test problems must be considered. In the present study, the sound radiated by the interaction of a flat plate with an oncoming gust containing a two component, mean velocity is computed. The gust has a uniform mean flow in x with Mach number M(infinity) equal to 0.5. The gust's mean velocity in y is of smaller amplitude and is given by: v = 0.1 sin(pi/8(x/M(sub infinity) - t)). This problem has been posed for an upcoming ICASE/LaRC workshop on benchmark problems in computational aeroacoustics. A plate with a length of 30 units in x is used. The plate is assumed to be infinitesimally thin and is centered at the origin. All variables are made dimensionless using the scales specified. Acoustic quantities are obtained by numerically integrating the linearized Euler equations. Integration is performed on the computational domain -100.0 less than or equal to x less than or equal to 100.0, -100.0 less than or equal to y less than or equal to 100.0, using unit length grid spacing in x and in y. An integration scheme is sought which will provide accurate solution to the small quantities of interest at a minimal computational expense. Results indicate that with the given discretization a scheme of minimal fourth order accuracy might be adequate to approximate the waves within the given flow. Thus, a variation of the MacCormack scheme with fourth order accuracy in space and second order accuracy in time was chosen. A scheme with sixth order accuracy in space has also been implemented and results compared with those of the fourth order accurate scheme. To ensure no mass flux, zero normal velocity is assigned at the plate. This condition will induce a discontinuity in the pressure across the plate location. Values for the perturbation pressure p' along the surface of the plate are obtained using a one-sided, third order Taylor expansion, such that p'(sub y) = O. In accordance with the Kutta condition, perturbation pressure at the trailing edge is assigned to zero. In the far field, radiation boundary conditions have been implemented. The effectiveness of the far field conditions are validated by computing in a larger computational domain and comparing the results. Early in time, sound waves begin to radiate from the plate. A Doppler effect is observed. After the initial transients disappear, the strongest waves leave the trailing edge at an approximate 45 degree angle. The intensity pattern of pressure fluctuations shows five lobes (of increasing magnitude with increasing downstream direction) emerging from the plate. Undesirable short wave contaminants are observed in the computed pressure distribution along the plate surface. For a more accurate solution at small scales, a more refined discretization will be required.

Martin, James E.↗
NASA NTRS1992

Reliability analysis of composite structures

A probabilistic static stress analysis methodology has been developed to estimate the reliability of a composite structure. Closed form stress analysis methods are the primary analytical tools used in this methodology. These structural mechanics methods are used to identify independent variables whose variations significantly affect the performance of the structure. Once these variables are identified, scatter in their values is evaluated and statistically characterized. The scatter in applied loads and the structural parameters are then fitted to appropriate probabilistic distribution functions. Numerical integration techniques are applied to compute the structural reliability. The predicted reliability accounts for scatter due to variability in material strength, applied load, fabrication and assembly processes. The influence of structural geometry and mode of failure are also considerations in the evaluation. Example problems are given to illustrate various levels of analytical complexity.

Kan, Han-Pin↗
NASA NTRS1995

Reliability enhancement of Navier-Stokes codes through convergence acceleration

Methods for enhancing the reliability of Navier-Stokes computer codes through improving convergence characteristics are presented. The improving of these characteristics decreases the likelihood of code unreliability and user interventions in a design environment. The problem referred to as a 'stiffness' in the governing equations for propulsion-related flowfields is investigated, particularly in regard to common sources of equation stiffness that lead to convergence degradation of CFD algorithms. Von Neumann stability theory is employed as a tool to study the convergence difficulties involved. Based on the stability results, improved algorithms are devised to ensure efficient convergence in different situations. A number of test cases are considered to confirm a correlation between stability theory and numerical convergence. The examples of turbulent and reacting flow are presented, and a generalized form of the preconditioning matrix is derived to handle these problems, i.e., the problems involving additional differential equations for describing the transport of turbulent kinetic energy, dissipation rate and chemical species. Algorithms for unsteady computations are considered. The extension of the preconditioning techniques and algorithms derived for Navier-Stokes computations to three-dimensional flow problems is discussed. New methods to accelerate the convergence of iterative schemes for the numerical integration of systems of partial differential equtions are developed, with a special emphasis on the acceleration of convergence on highly clustered grids.

Merkle, Charles L.↗
NASA NTRS1993

Numerical simulation of shock/turbulent boundary layer interaction

Most flows of aerodynamic interest are compressible and turbulent. However, our present knowledge on the structures and mechanisms of turbulence is mostly based on incompressible flows. In the present work, compressibility effects in turbulent, high-speed, boundary layer flows are systematically investigated using the Direct Numerical Simulation (DNS) approach. Three-dimensional, time-dependent, fully nonlinear, compressible Navier-Stokes equations were numerically integrated by high-order finite-difference methods; no modeling for turbulence is used during the solution because the available resolution is sufficient to capture the relevant scales. The boundary layer problem deals with fully-turbulent compressible flows over flat geometries. Apart from its practical relevance to technological flows, turbulent compressible boundary layer flow is the simplest experimentally realizable turbulent compressible flow. Still, measuring difficulties prohibit a detailed experimental description of the flow, especially in the near-wall region. DNS studies provide a viable means to probe the physics of compressible turbulence in this region. The focus of this work is to explore the paths of energy transfer through which compressible turbulence is sustained. The structural similarities and differences between the incompressible and compressible turbulence are also investigated. The energy flow patterns or energy cascades are found to be directly related to the evolution of vortical structures which are generated in the near-wall region. Near-wall structures, and mechanisms which are not readily accessible through physical experiments are analyzed and their critical role on the evolution and the behavior of the flow is documented extensively.

Biringen, Sedat↗
NASA NTRS1994

Numerical simulations of particle orbits around 2060 Chiron

Scattered light from orbiting or coorbiting dust is a primary signature by which Earth-based observers study the activity and atmosphere of the unusual outer solar system object 2060 Chiron. Therefore, it is important to understand the lifetime, dynamics, and loss rates of dust in its coma. We report here dynamical simulations of particles in Chiron's collisionless coma. The orbits of 17,920 dust particles were numerically integrated under the gravitational influence of Chiron, the Sun, and solar radiation pressure. These simulations show that particles ejected from Chiron are more likely to follow suborbital trajectories, or to escape altogether, than to enter quasistable orbits. Significant orbital lifetimes can only be achieved for very specific launch conditions. These results call into question models of a long-term, bound coma generated by discrete outbursts, and instead suggest that Chiron's coma state is closely coupled to the nearly instantaneous level of Chiron's surface activity.

Stern, S. A.↗
NASA NTRS1994

A mapping method for the gravitational few-body problem with dissipation

Recently a new class of numerical integration methods - 'mixed variable symplectic integrators' - has been introduced for studying long-term evolution in the conservative gravitational few-body problem. These integrators are an order of magnitude faster than conventional ordinary differential equations (ODE) integration methods. Here we present a simple modification of this method to include small non-gravitational forces. The new scheme provides a similar advantage of computational speed for a larger class of problems in Solar System dynamics.

Malhotra, Renu↗
NASA NTRS1994

Electron acceleration at nearly perpendicular collisionless shocks. 3: Downstream distributions

Spacecraft observations at the Earth's bow shock and at interplanetary shocks have established that the largest fluxes of accelerated suprathermal electrons occur in so-called shock spike events immediately downstream of the shock ramp. Previous theoretical efforts have mainly focused on explaining upstream energetic electron beams. Here we investigate the general motion and acceleration of energetic electrons in a curved, nearly perpendicular shock by numerically integrating the orbits of solar wind halo electrons in shock fields generated by a hybrid simulation (core electron fluid and kinetic ions). Close to the angle Theta(sub Bn) = 90 degs between the upstream magnetic field and shock normal, the calculations result in a (perpendicular) temperature increase proportional to the magnetic field ratio and give the highest phase space densities in the overshoot. For a steep distribution, the temperature change can correspond to an enhancement of the distribution by several orders of magnitude. These results are in agreement with predictions from adiabatic mapping. With smaller angles Theta(sub Bn), the overshoot and downstream densities fall off quickly, because the adiabatic energy gain is less and fewer electrons transmit. The shock curvature also leads to an accumulation of electrons close to 90 degs. Without pitch angle scattering, energization is only significant within a few (approximately 5 to 10 degs) degrees of the point of tangency. However, shock spike events appear to be observed more easily and farther away from 90 degs. Given that over a region of several degrees around 90 degs the theory gives enhancements of up to approximately 4 orders of magnitude, such electrons could in principle account for the typically observed enhancements of 1 to 2 orders of magnitude, if they were distributed over Theta(sub Bn). To test the idea that scattering could efficiently redistribute the energetic electrons, we have conducted test particle simulations in which artificial pitch angle scattering is included. We find that such a process can indeed be very efficient and can explain observations of shock spike events far away from Theta(sub Bn) is approximately 90 degs. The scattering naturally leads to much higher phase space densities at smaller Theta(sub Bn) than what a local one-dimensional mapping would predict and thus can account for an observed discrepancy with adiabatic theory stated in the literature.

Krauss-Varban, D.↗