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At least 1,117 records · Page 62

Orbit improvement from satellite imaging data obtainable from outer planet missions.

Equations of motion are established for a dynamical system in which a spacecraft flies close to and interacts with an outer planet and one or more of its satellites. For the computation of the state and mass partials needed in a simultaneous orbit correction of n interacting bodies, a notably compact set of variational equations is derived. The above system of differential equations is integrated numerically on a computer. Spacecraft-satellite direction measurements accurate to plus or minus 10 sec were simulated along three representative trajectories (Mariner/Jupiter/Saturn 1977 missions) approaching Io, Titan, and Iapetus to within 41000, 13000, and 7000 km, respectively. The paper concludes with a brief discussion of the need for future work on the orbits of the satellites of the outer planets.

Aksnes, K.↗

Symbolic generation of constitutive equations

The use of the symbolic manipulation program MACSYMA for the automatic generation of constitutive equations describing the thermomechanical behavior of complex materials such as metal-matrix composites is demonstrated. Problem-specific algorithms are developed; e.g., for partial differentiation by the chain rule, automatic generation of tree structures, special tensor analysis, and the simplification of expressions. The resulting subprogram package, SDICE, is shown to be fully applicable to both isotropic and anisotropic materials; its potential usefulness as a basis for FEM analyses is indicated.

Tan, H. Q.↗

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition: Inclusion of Exchange - 2

The development of a practical method of accurately calculating the full scattering amplitude, without making a partial wave decomposition is continued. The method is developed in the context of electron-hydrogen scattering, and here exchange is dealt with by considering e-H scattering in the static exchange approximation. The Schroedinger equation in this approximation can be simplified to a set of coupled integro-differential equations. The equations are solved numerically for the full scattering wave function. The scattering amplitude can most accurately be calculated from an integral expression for the amplitude; that integral can be formally simplified, and then evaluated using the numerically determined wave function. The results are essentially identical to converged partial wave results.

Shertzer, Janine↗

Aeroelastic loads prediction for an arrow wing. Task 3: Evaluation of the Boeing three-dimensional leading-edge vortex code

Two separated flow computer programs and a semiempirical method for incorporating the experimentally measured separated flow effects into a linear aeroelastic analysis were evaluated. The three dimensional leading edge vortex (LEV) code is evaluated. This code is an improved panel method for three dimensional inviscid flow over a wing with leading edge vortex separation. The governing equations are the linear flow differential equation with nonlinear boundary conditions. The solution is iterative; the position as well as the strength of the vortex is determined. Cases for both full and partial span vortices were executed. The predicted pressures are good and adequately reflect changes in configuration.

Manro, M. E.↗

Kodiak: An Implementation Framework for Branch and Bound Algorithms

Recursive branch and bound algorithms are often used to refine and isolate solutions to several classes of global optimization problems. A rigorous computation framework for the solution of systems of equations and inequalities involving nonlinear real arithmetic over hyper-rectangular variable and parameter domains is presented. It is derived from a generic branch and bound algorithm that has been formally verified, and utilizes self-validating enclosure methods, namely interval arithmetic and, for polynomials and rational functions, Bernstein expansion. Since bounds computed by these enclosure methods are sound, this approach may be used reliably in software verification tools. Advantage is taken of the partial derivatives of the constraint functions involved in the system, firstly to reduce the branching factor by the use of bisection heuristics and secondly to permit the computation of bifurcation sets for systems of ordinary differential equations. The associated software development, Kodiak, is presented, along with examples of three different branch and bound problem types it implements.

Smith, Andrew P.↗

Surface roughness effect on finite oil journal bearings

A theoretical study of the performance of finite oil journal bearings is made, considering the surface roughness effect. The total load supporting ability under such a condition derives from the hydrodynamic as well as asperity contact pressure. These two components of load are calculated separately. The average Reynolds equation for partially lubricated surfaces is used to evaluate hydrodynamic pressure. An analytical expression for average film thickness is obtained and introduced to modify the average Reynolds equation. The resulting differential equation is then solved numerically by finite difference methods for mean hydrodynamic pressure, which in turn gives the hydrodynamic load. Assuming the surface height distribution as Gaussian, the asperity contact pressure is found. The effect of surface roughness parameter, surface pattern, eccentricity ratio, and length to diameter ratio on hydrodynamic load and on side leakage is investigated. It is shown that hydrodynamic load increases with increasing surface roughness when both journal and bearing surfaces have identical roughness structures or when the journal only has a rough surface. The trend of hydrodynamic load is reversed if the journal surface is smooth and the bearing surface is rough.

Majumdar, B. C.↗

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.↗

Orbit improvement from satellite imaging data obtainable from the Mariner/Jupiter/Saturn 1977 missions

Equations of motion are established for a dynamic system in which a spacecraft flies close to and interacts with an outer planet and one or more of its satellites. For the computation of the state and mass partials needed in the orbit corrections, a set of variational equations is derived. These assume a notably compact form through the introduction of a matrix operator D. The above system of differential equations is integrated numerically on a computer.

Aksnes, K.↗

Analytic partial derivatives for estimating low-thrust parameters.

Analytic partial derivatives for estimating orbital low-thrust parameters via differential correction are developed and compared with two different numerical methods. The formulation is independent of the particular thrust model used and is applicable to all physically possible elliptic orbits. The starting point for the development is the set of variational equations of the elliptic orbital elements in the form due to Lagrange. The first time derivatives of the elements are transformed to derivatives with respect to the space variable, true anomaly, and integrated to first order in closed form in a straightforward general perturbations approach, with one exception: particular attention is given to the mean anomaly as influenced by thrust perturbations in the semimajor axis so that the complete first-order effect is included. The partials of the elements are then taken with respect to any given thrust parameter. Two comparisons are made with numerical methods for computing these thrust partials: numerical quotients and numerical integration of the variational equations for thrust.

Cunningham, G. W.↗

Analysis and design of an ultrahigh temperature hydrogen-fueled MHD generator

A coupled gas dynamics/radiative heat transfer analysis of partially ionized hydrogen, in local thermodynamic equilibrium, flowing through an ultrahigh temperature (10,000-20,000 K) magnetohydrodynamic (MHD) generator is performed. Gas dynamics are modeled by a set of quasi-one-dimensional, nonlinear differential equations which account for friction, convective and radiative heat transfer, and the interaction between the ionized gas and applied magnetic field. Radiative heat transfer is modeled using nongray, absorbing-emitting 2D and 3D P-1 approximations which permit an arbitrary variation of the spectral absorption coefficient with frequency. Gas dynamics and radiative heat transfer are coupled through the energy equation and through the temperature- and density-dependent absorption coefficient. The resulting nonlinear elliptic problem is solved by iterative methods. Design of such MHD generators as onboard, open-cycle, electric power supplies for a particular advanced airbreathing propulsion concept produced an efficient and compact 128-MWe generator characterized by an extraction ratio of 35.5 percent, a power density of 10,500 MWe/cu m, and a specific (extracted) energy of 324 MJe/kg of hydrogen. The maximum wall heat flux and total wall heat load were 453 MW/sq m and 62 MW, respectively.

Moder, Jeffrey P.↗

A simple, analytic 3-dimensional downburst model based on boundary layer stagnation flow

A simple downburst model is developed for use in batch and real-time piloted simulation studies of guidance strategies for terminal area transport aircraft operations in wind shear conditions. The model represents an axisymmetric stagnation point flow, based on velocity profiles from the Terminal Area Simulation System (TASS) model developed by Proctor and satisfies the mass continuity equation in cylindrical coordinates. Altitude dependence, including boundary layer effects near the ground, closely matches real-world measurements, as do the increase, peak, and decay of outflow and downflow with increasing distance from the downburst center. Equations for horizontal and vertical winds were derived, and found to be infinitely differentiable, with no singular points existent in the flow field. In addition, a simple relationship exists among the ratio of maximum horizontal to vertical velocities, the downdraft radius, depth of outflow, and altitude of maximum outflow. In use, a microburst can be modeled by specifying four characteristic parameters, velocity components in the x, y and z directions, and the corresponding nine partial derivatives are obtained easily from the velocity equations.

Oseguera, Rosa M.↗

Carbon Monoxide Accumulation in the Extravehicular Mobility Unit

Introduction: Life support technology in large closed systems like submarines and space stations catalyzes carbon monoxide (CO) to carbon dioxide, which is easily removed. However, in a small system like the Extravehicular Mobility Unit (EMU), spacesuit, CO from exogenous (contaminated oxygen (O (sub 2) supply) and endogenous (human metabolism) sources will accumulate in the free suit volume. The free volume becomes a sink for CO that is rebreathed by the astronaut. The accumulation through time depends on many variables: the amount absorbed by the astronaut, the amount produced by the astronaut (between 0.28 and 0.34 moles per hour per kilogram)[1], the amount that enters the suit from contaminated O (sub 2), the amount removed through suit leak, the free volume of the suit, and the O (sub 2) partial pressure[2], just to list a few. Contamination of the EMU O (sub 2) supply with no greater than 1 part per million CO was the motivation for empirical measurements from CO pulse oximetry (SpCO) as well as mathematical modeling of the EMU as a rebreather for CO. Methods: We developed a first-order differential mixing equation as well as an iterative method to compute CO accumulation in the EMU. Pre-post measurements of SpCO (Rad-57, Masimo Corporation) from EMU ground training and on-orbit extravehicular activities (EVAs) were collected. Results: Initial modeling without consideration of the astronaut as a sink but only the source of CO showed that after 8 hours breathing 100 percent O (sub 2) with a 10 milliliter per minute (760 millimeters Hg at 21 degrees Centigrade standard) suit leak, an endogenous production rate of 0.23 moles per hour per kilogram for a 70 kilogram person with 42 liters (1.5 cubic feet) free suit volume resulted in a peak CO partial pressure (pCO) of 0.047 millimeters Hg at 4.3 pounds per square inch absolute (222 millimeters Hg). Preliminary results based on a 2008 model[3] with consideration of the astronaut as a sink and source of CO suggests that most of the rebreathed CO stays bound to hemoglobin and myoglobin and; therefore, pCO only increased to 0.002 millimeters Hg in the EMU. Hemoglobin saturation after 8 hours was an insignificant 0.4 percent compared to about 4 percent for cigarette smokers in the general population. This preliminary modeling result supplements 11 pre-post index finger SpCO measurements from EMU ground training (mean 0.5 percent versus 1 percent, probability equal to 0.41 from paired t-test) and 10 on-orbit pre-post EVAs (mean 1.5 percent versus 1.1 percent, probability equal to 0.17 from paired t-test) that showed no consistent increase, at least no increase outside the accuracy of the oximeter (1 percent display resolution with plus or minus 3 percent Standard Deviation). Discussion: Simulations continue, but a preliminary conclusion is that rebreathing endogenous CO accumulating in the EMU is not a serious medical issue during EVA. The absence of CO poisoning signs or symptoms following hundreds of EVAs is also good empirical evidence that corroborates the limited SpCO measurements and preliminary modeling results.

Conkin, J.↗

Radiation Transport Around Axisymmetric Blunt Body Vehicles Using a Modified Differential Approximation

A moment method for computing 3-D radiative transport is applied to axisymmetric flows in thermochemical nonequilibrium. Such flows are representative of proposed aerobrake missions. The method uses the P-1 approximation to reduce the governing system of integro-di erential equations to a coupled set of partial di erential equations. A numerical solution method for these equations given actual variations of the radiation properties in thermochemical nonequilibrium blunt body flows is developed. Initial results from the method are shown and compared to tangent slab calculations. The agreement between the transport methods is found to be about 10 percent in the stagnation region, with the difference increasing along the flank of the vehicle.

Hartung, Lin C.↗

Power series representation of partial derivatives required in orbit determination.

A program to integrate the equations of motion by series in powers of the time step can be easily modified to furnish the elements of the matrizant in power series of the time step. In particular, if the series representing the motion are obtained recursively, differentiation of the recurrence relations will provide immediately a recursive scheme for computing the coefficient in the power series for the elements of the matrizant.

Schanzle, A. F.↗

Implementation and Use of a Convergence Test for Iterative Wind Tunnel Balance Load Predictions

A modified and extended version of a convergence test for wind tunnel strain-gage balance load iterations was implemented. The test uses an upper bound of the Lipschitz constant to assess convergence characteristics of balance load predictions if the Iterative Method is applied. Convergence is expected within the use envelope of the balance whenever this upper bound is less than the threshold of one. It is explained in great detail how the convergence test can be applied to the two load iteration equation types that are currently being used in the aerospace testing community. In addition, the application of the test to balances with bi-directional output characteristics is discussed. It is also shown how numerical differentiation can be used in order to obtain partial derivatives that are needed for the calculation of the Lipschitz constant. Finally, machine calibration data of NASA's MC60E six-component force balance is selected to demonstrate both implementation and use of the convergence test.

calibration analysis↗

Implicit Formulation of Muscle Dynamics in OpenSim

Astronauts lose bone and muscle mass during spaceflight. Exercise countermeasure is the primary method for counteracting bone and muscle mass loss in space. New spacecraft exercise device concepts are currently being developed for the NASAs new crew exploration vehicle. The NASA Digital Astronaut Project (DAP) uses computational modeling to help determine if the new exercise devices will be effective as countermeasures. The NASA Digital Astronaut Project is developing the ability to utilize predictive simulation to provide insight into the change in kinematics and kinetics with a change in device and gravitational environment (1-g versus 0-g). For example, in space exercise the subject's body weight is applied in addition to the loads prescribed for musculoskeletal maintenance. How and where these loads are applied obviously directly impacts bone and tissue loads. Additionally, due to space vehicle structural requirements, exercise devices are often placed on vibration isolation systems. This changes the apparent impedance or stiffness of the device as seen by the user. Data collection under these conditions is often impractical and limited. Predictive modeling provides a means to have a virtual subject to test hypotheses. Predictive simulation provides a virtual subject for which we are able to perform studies such as sensitivity to device loading and vibration isolation without the need for laboratory kinematic or kinetic test data.Direct Collocation optimization provides an efficient means to perform task based optimization and predictive modeling. It is relatively straight forward to structure a physical exercise task in a Direct Collocation mathematical formulation: perform a motion such that you start at an initial pose, achieve a given amount of deflection i.e a squat, return to the initial pose, and minimize muscle activation cost. Direct Collocation is advantageous in that it does not require numerical integration to evaluate the objective function. Instead, the system dynamics are transformed to discrete time and the optimizer is constrained such that the solution is not considered to be a valid unless the dynamic equations are satisfied at all time points. The simulation and optimization are effectively done simultaneously. Due to the implicit integration, time steps can be more coarse than in a differential equation solver. In a gait scenario this means that that the model constraints and cost function are evaluated at 100 nodes in the gait cycle versus 10,000 integration steps in a variable-step forward dynamic simulation. Furthermore, no time is wasted on accurate simulations of movements that are far from the optimum. Constrained optimization algorithms require a Jacobian matrix that contains the partial derivatives of each of the dynamic constraints with respect to of each of the state and control variables at all time points. This is a large but sparse matrix. An implicit dynamics formulation requires computation of the dynamic residuals f as a function of the states x and their derivatives, and controls u:f(x, dxdt, u) 0If the dynamics of musculoskeletal system are formulated implicitly, the Jacobian elements are often available analytically, eliminating the need for numerical differentiation; this is obviously computationally advantageous. Additionally, implicit formulation of musculoskeletal dynamics do not suffer from singularities from low mass bodies, zero muscle activation, or other stiff system or

physical exercise↗