Results for “solve time” — Page 56

NASA NTRS1991

A two-dimensional, time-dependent, near-earth magnetotail

A kinetic approach is presented for obtaining slowly time-dependent, self-consistent plasma, and magnetic field configurations for this region, using anisotropic particle distributions. At present, a 2D configuration is used. The time variation of the plasma/field configuration is assumed to be driven by a slowly varying, externally imposed electric field (representing, for example, a change in solar wind conditions). The numerical approach involves solving a 2D nonlinear Poisson equation for the magnetic vector potential at each time step. The local current density is calculated from particle velocity distributions under the assumption of adiabatic particle motion. The obtained equations of state are compared with those of double-adiabatic theory. Numerical examples of self-consistent responses of the near-earth plasma and field to an externally imposed electric field pulse are presented.

Whipple, Elden↗

NASA NTRS1975

Three-dimensional time dependent computation of turbulent flow

The three-dimensional, primitive equations of motion are solved numerically for the case of isotropic box turbulence and the distortion of homogeneous turbulence by irrotational plane strain at large Reynolds numbers. A Gaussian filter is applied to governing equations to define the large scale field. This gives rise to additional second order computed scale stresses (Leonard stresses). The residual stresses are simulated through an eddy viscosity. Uniform grids are used, with a fourth order differencing scheme in space and a second order Adams-Bashforth predictor for explicit time stepping. The results are compared to the experiments and statistical information extracted from the computer generated data.

Kwak, D.↗

NASA NTRS1988

Redundant manipulators for momentum compensation in a micro-gravity environment

This paper is concerned with the implementation and assessment of joint motion management strategies for kinematically redundant robotic manipulators operating in the micro-gravity environment of Space Station. These robots must be capable of conducting experiments and manufacturing processes without disturbing the micro-gravity environment through base reactions/motions. The redundant degrees of freedom of the manipulator permit the inverse kinematic problem to be solved simultaneously with the minimization of a cost function. The cost function in this case is the weighted sum of the squares of the base forces and moments and is minimized over discrete time segments. The Generalized Inverse Method and Rayleigh Ritz technique are used to solve the combined optimization/inverse kinematics problem. Numerical examples include various robotic configurations and degrees of manipulator redundancy.

Quinn, R. D.↗

NASA NTRS1977

Timing formulas for dissection algorithms on vector computers

The use of the finite element and finite difference methods often leads to the problem of solving large, sparse, positive definite systems of linear equations. MACSYMA plays a major role in the generation of formulas representing the time required for execution of the dissection algorithms. The use of MACSYMA in the generation of those formulas is described.

Poole, W. G., Jr.↗

NASA NTRS1983

Analysis of cold flow reestablishment time in a circuit breaker nozzle

The deblocking process in a circuit breaker nozzle is similar to the flow starting process in a shock tunnel, and the computer uses this analogy to solve for the deblocking process by utilizing a diaphragm at the throat of a nozzle. At time equal to zero the diaphragm is broken and the throat area increases with time. It is a rarity to have the area as a function of both time and distance. Experimental data obtained from the RPI calibration shock tunnel are utilized to verify some of the calculated results with the area being a function of distance and the agreement is found to be good. The circuit breaker designer can utilize the computer simulation to estimate the deblocking time, an important parameter in the design of circuit breakers.

Leone, S. A.↗

NASA NTRS1994

Multigrid solution of compressible turbulent flow on unstructured meshes using a two-equation model

The steady state solution of the system of equations consisting of the full Navier-Stokes equations and two turbulence equations has been obtained using a multigrid strategy of unstructured meshes. The flow equations and turbulence equations are solved in a loosely coupled manner. The flow equations are advanced in time using a multistage Runge-Kutta time-stepping scheme with a stability-bound local time step, while turbulence equations are advanced in a point-implicit scheme with a time step which guarantees stability and positivity. Low-Reynolds-number modifications to the original two-equation model are incorporated in a manner which results in well-behaved equations for arbitrarily small wall distances. A variety of aerodynamic flows are solved, initializing all quantities with uniform freestream values. Rapid and uniform convergence rates for the flow and turbulence equations are observed.

MULTIGRID SOLUTION↗

NASA NTRS1993

Evaluation of inertial devices for the control of large, flexible, space-based telerobotic arms

Inertial devices, including sensors and actuators, offer the potential of improving the tracking of telerobotic commands for space-based robots by smoothing payload motions and suppressing vibrations. In this paper, inertial actuators (specifically, torque-wheels and reaction-masses) are studied for that potential application. Batch simulation studies are presented which show that torque-wheels can reduce the overshoot in abrupt stop commands by 82 percent for a two-link arm. For man-in-the-loop evaluation, a real-time simulator has been developed which samples a hand-controller, solves the nonlinear equations of motion, and graphically displays the resulting motion on a computer workstation. Currently, two manipulator models, a two-link, rigid arm and a single-link, flexible arm, have been studied. Results are presented which show that, for a single-link arm, a reaction-mass/torque-wheel combination at the payload end can yield a settling time of 3 s for disturbances in the first flexible mode as opposed to 10 s using only a hub motor. A hardware apparatus, which consists of a single-link, highly flexible arm with a hub motor and a torque-wheel, has been assembled to evaluate the concept and is described herein.

Montgomery, Raymond C.↗

NASA NTRS1997

A Study of Convergence of the PMARC Matrices Applicable to WICS Calculations

This report discusses some analytical procedures to enhance the real time solutions of PMARC matrices applicable to the Wall Interference Correction Scheme (WICS) currently being implemented at the 12 foot Pressure Tunell. WICS calculations involve solving large linear systems in a reasonably speedy manner necessitating exploring further improvement in solution time. This paper therefore presents some of the associated theory of the solution of linear systems. Then it discusses a geometrical interpretation of the residual correction schemes. Finally, some results of the current investigation are presented.

Ghosh, Amitabha↗

NASA NTRS1997

A Study of Convergence of the PMARC Matrices Applicable to WICS Calculations

This report discusses some analytical procedures to enhance the real time solutions of PMARC matrices applicable to the Wall Interference Correction Scheme (WICS) currently being implemented at the 12 foot Pressure Tunnel. WICS calculations involve solving large linear systems in a reasonably speedy manner necessitating exploring further improvement in solution time. This paper therefore presents some of the associated theory of the solution of linear systems. Then it discusses a geometrical interpretation of the residual correction schemes. Finally some results of the current investigation are presented.

Ghosh, Amitabha↗

NASA NTRS1993

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 1: Analysis description

A computer code called Proteus 3D has been developed to solve the three dimensional, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort has been to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation have been emphasized. The governing equations are solved in generalized non-orthogonal body-fitted coordinates by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. It describes in detail the governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models.

Towne, Charles E.↗

NASA NTRS1991

Elimination of secular terms from the differential equations for the elements of perturbed two-body motion

In 1961, Sperling linearized and regularized the differential equations of motion of the two-body problem by changing the independent variable from time to fictitious time by Sundman's transformation (r = dt/ds) and by embedding the two-body energy integral and the Laplace vector. In 1968, Burdet developed a perturbation theory which was uniformly valid for all types of orbits using a variation of parameters approach on the elements which appeared in Sperling's equations for the two-body solution. In 1973, Bond and Hanssen improved Burdet's set of differential equations by embedding the total energy (which is a constant when the potential function is explicitly dependent upon time.) The Jacobian constant was used as an element to replace the total energy in a reformulation of the differential equations of motion. In the process, another element which is proportional to a component of the angular momentum was introduced. Recently trajectories computed during numerical studies of atmospheric entry from circular orbits and low thrust beginning in near-circular orbits exhibited numerical instability when solved by the method of Bond and Gottlieb (1989) for long time intervals. It was found that this instability was due to secular terms which appear on the righthand sides of the differential equations of some of the elements. In this paper, this instability is removed by the introduction of another vector integral called the delta integral (which replaces the Laplace Vector) and another scalar integral which removes the secular terms. The introduction of these integrals requires a new derivation of the differential equations for most of the elements. For this rederivation, the Lagrange method of variation of parameters is used, making the development more concise. Numerical examples of this improvement are presented.

Bond, Victor R.↗

NASA NTRS1981

Time-temperature effect in adhesively bonded joints

The viscoelastic analysis of an adhesively bonded lap joint was reconsidered. The adherends are approximated by essentially Reissner plates and the adhesive is linearly viscoelastic. The hereditary integrals are used to model the adhesive. A linear integral differential equations system for the shear and the tensile stress in the adhesive is applied. The equations have constant coefficients and are solved by using Laplace transforms. It is shown that if the temperature variation in time can be approximated by a piecewise constant function, then the method of Laplace transforms can be used to solve the problem. A numerical example is given for a single lap joint under various loading conditions.

Delale, F.↗

NASA NTRS1992

Computerized reduction of elementary reaction sets for CFD combustion modeling

Modeling of chemistry in Computational Fluid Dynamics can be the most time-consuming aspect of many applications. If the entire set of elementary reactions is to be solved, a set of stiff ordinary differential equations must be integrated. Some of the reactions take place at very high rates, requiring short time steps, while others take place more slowly and make little progress in the short time step integration.

Wikstrom, Carl V.↗

NASA NTRS2015

Results of Microgravity Fluid Dynamics Captured With the Spheres-Slosh Experiment

This paper provides an overview of the SPHERES-Slosh Experiment (SSE) aboard the International Space Station (ISS) and presents on-orbit results with data analysis. In order to predict the location of the liquid propellant during all times of a spacecraft mission, engineers and mission analysts utilize Computational Fluid Dynamics (CFD). These state-of-the-art computer programs numerically solve the fluid flow equations to predict the location of the fluid at any point in time during different spacecraft maneuvers. The models and equations used by these programs have been extensively validated on the ground, but long duration data has never been acquired in a microgravity environment. The SSE aboard the ISS is designed to acquire this type of data, used by engineers on earth to validate and improve the CFD prediction models, improving the design of the next generation of space vehicles as well as the safety of current missions. The experiment makes use of two Synchronized Position Hold, Engage, Reorient Experimental Satellites (SPHERES) connected by a frame. In the center of the frame there is a plastic, pill shaped tank that is partially filled with green-colored water. A pair of high resolution cameras records the movement of the liquid inside the tank as the experiment maneuvers within the Japanese Experimental Module test volume. Inertial measurement units record the accelerations and rotations of the tank, making the combination of stereo imaging and inertial data the inputs for CFD model validation.

slosh↗

NASA NTRS2015

Results of Microgravity Fluid Dynamics Captured with the Spheres-Slosh Experiment

This paper provides an overview of the SPHERES-Slosh Experiment (SSE) aboard the International Space Station (ISS) and presents on-orbit results with data analysis. In order to predict the location of the liquid propellant during all times of a spacecraft mission, engineers and mission analysts utilize Computational Fluid Dynamics (CFD). These state-of-the-art computer programs numerically solve the fluid flow equations to predict the location of the fluid at any point in time during different spacecraft maneuvers. The models and equations used by these programs have been extensively validated on the ground, but long duration data has never been acquired in a microgravity environment. The SSE aboard the ISS is designed to acquire this type of data, used by engineers on earth to validate and improve the CFD prediction models, improving the design of the next generation of space vehicles as well as the safety of current missions. The experiment makes use of two Synchronized Position Hold, Engage, Reorient Experimental Satellites (SPHERES) connected by a frame. In the center of the frame there is a plastic, pill shaped tank that is partially filled with green-colored water. A pair of high resolution cameras records the movement of the liquid inside the tank as the experiment maneuvers within the Japanese Experimental Module test volume. Inertial measurement units record the accelerations and rotations of the tank, making the combination of stereo imaging and inertial data the inputs for CFD model validation.

slosh↗

NASA NTRS2015

Result of Microgravity Fluid Dynamics Captured with the SPHERES-Slosh Experiment

This paper provides an overview of the SPHERES-Slosh Experiment (SSE) aboard the International Space Station (ISS) and presents on-orbit results with data analysis. In order to predict the location of the liquid propellant during all times of a spacecraft mission, engineers and mission analysts utilize Computational Fluid Dynamics (CFD). These state-of-the-art computer programs numerically solve the fluid flow equations to predict the location of the fluid at any point in time during different spacecraft maneuvers. The models and equations used by these programs have been extensively validated on the ground, but long duration data has never been acquired in a microgravity environment. The SSE aboard the ISS is designed to acquire this type of data, used by engineers on earth to validate and improve the CFD prediction models, improving the design of the next generation of space vehicles as well as the safety of current missions. The experiment makes use of two Synchronized Position Hold, Engage, Reorient Experimental Satellites (SPHERES) connected by a frame. In the center of the frame there is a plastic, pill shaped tank that is partially filled with green-colored water. A pair of high resolution cameras records the movement of the liquid inside the tank as the experiment maneuvers within the Japanese Experimental Module test volume. Inertial measurement units record the accelerations and rotations of the tank, making the combination of stereo imaging and inertial data the inputs for CFD model validation.

slosh↗

NASA NTRSDate not supplied

Realistic Thermographic Simulation of Impact Damage with Quadrupole Method

Flash thermography has been shown to be an effective method for detection of delaminations in carbon fiber reinforced polymer (CFRP) composite structures. Improved understanding of thelimitations of the technique can be obtained by simulating the inspection process. Time domainfinite difference and finite element methods are well suited for such simulations but can be computationally intensive. An alternate method is to solve the Laplace transform of the heat equation, then invert the Laplace transform to produce a time domain response. Often this is referred to as the thermal quadrupole method and is well suited for simulating flash thermography. The quadrupole method has been used extensively for simulating one-dimensional heat flow in multilayer systems with contact resistances at the interfaces. It is also applicable for three dimensional configurations, in particular for simulation of changes in thermographic response due to delaminations in composites. This presentation discusses three-dimensional simulations with realistic shapes and contact resistances at the interfaces between layers. The results of these simulations are compared to thermography measurements on composites specimens with impact induced delaminations.

Thermography↗

NASA NTRS2003

Gust Acoustic Response of a Single Airfoil Using the Space-Time CE/SE Method

A 2D parallel Euler code based on the space-time conservation element and solution element (CE/SE) method is validated by solving the benchmark problem I in Category 3 of the Third CAA Workshop. This problem concerns the acoustic field generated by the interaction of a convected harmonic vortical gust with a single airfoil. Three gust frequencies, two gust configurations, and three airfoil geometries are considered. Numerical results at both near and far fields are presented and compared with the analytical solutions, a frequency-domain solver GUST3D solutions, and a time-domain high-order Discontinuous Spectral Element Method (DSEM) solutions. It is shown that the CE/SE solutions agree well with the GUST3D solution for the lowest frequency, while there are discrepancies between CE/SE and GUST3D solutions for higher frequencies. However, the CE/SE solution is in good agreement with the DSEM solution for these higher frequencies. It demonstrates that the CE/SE method can produce accurate results of CAA problems involving complex geometries by using unstructured meshes.

Scott, James↗