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At least 1,297 records · Page 72

Asymptotic (h tending to infinity) absolute stability for BDFs applied to stiff differential equations

Methods based on backward differentiation formulas (BDFs) for solving stiff differential equations require iterating to approximate the solution of the corrector equation on each step. One hope for reducing the cost of this is to make do with iteration matrices that are known to have errors and to do no more iterations than are necessary to maintain the stability of the method. This paper, following work by Klopfenstein, examines the effect of errors in the iteration matrix on the stability of the method. Application of the results to an algorithm is discussed briefly.

Krogh, F. T.↗

Navigation and meteorological error equations for some aerodynamic parameters

Mathematical equations for the analysis of the errors that are expected in a set of postflight aerodynamic parameters are presented. The errors are due to inaccuracies in the Shuttle best estimate trajectory and in the meteorological data obtained in support of the flights. The error analysis shows that the parameter vector, Z, and its associated error covariance matrix, C sub Z, is calculated from a given state vector, X, and its associated covariance matrix, C sub X.

Krikorian, M. J.↗

Global dynamic modeling of a transmission system

The work performed on global dynamic simulation and noise correlation of gear transmission systems at the University of Akron is outlined. The objective is to develop a comprehensive procedure to simulate the dynamics of the gear transmission system coupled with the effects of gear box vibrations. The developed numerical model is benchmarked with results from experimental tests at NASA Lewis Research Center. The modal synthesis approach is used to develop the global transient vibration analysis procedure used in the model. Modal dynamic characteristics of the rotor-gear-bearing system are calculated by the matrix transfer method while those of the gear box are evaluated by the finite element method (NASTRAN). A three-dimensional, axial-lateral coupled bearing model is used to couple the rotor vibrations with the gear box motion. The vibrations between the individual rotor systems are coupled through the nonlinear gear mesh interactions. The global equations of motion are solved in modal coordinates and the transient vibration of the system is evaluated by a variable time-stepping integration scheme. The relationship between housing vibration and resulting noise of the gear transmission system is generated by linear transfer functions using experimental data. A nonlinear relationship of the noise components to the fundamental mesh frequency is developed using the hypercoherence function. The numerically simulated vibrations and predicted noise of the gear transmission system are compared with the experimental results from the gear noise test rig at NASA Lewis Research Center. Results of the comparison indicate that the global dynamic model developed can accurately simulate the dynamics of a gear transmission system.

Choy, F. K.↗

Multilevel Algorithm for Atmospheric Data Assimilation

A multiscale algorithm for the problem of optimal statistical interpolation of observed data has been developed. This problem includes the calculation of the vector of the 'analyzed' (best estimated) atmosphere flow field w(sup a) by the formula: w(sup a) = w(sup f) + P(sup f) H(sup T) y, where the quantity y is defined by the equation (H P(sup f) H(sup T) + R)y = w(sup o) - H w(sup f), using the given model forecast first guess w(sup f) and the vector of observations w(sup o); H is an interpolation operator from the regular grid to the observation network, P(sup f) is the forecast error covariance matrix, and R is the observation error covariance matrix. At this initial stage the case of univariate analysis of single level radiosonde height data is considered. The matrix R is assumed to be diagonal, and the matrix P(sup f) is assumed to be given by the formula P(sub ij)(sup f) = sigma(sub i)(sup f) mu(sub ij) sigma(sub j)(sub f), where mu(sub ij) is a smooth, decreasing function of the distance between the i-th and the j-th points. In this paper we describe a multiscale iterative process based on a multiresolution, simultaneous displacement technique and a localized variational calculation of iteration parameters.

Brandt, Achi↗

An Optical Oxygen Sensor for Long-Term Continuous Monitoring of Dissolved Oxygen in Perfused Bioreactors

For long-term growth of man1ITlalian cells in perfused bioreactors, it is essential to monitor the concentration of dissolved oxygen (DO) present in the culture medium to quantitate and control level of DO. Continuous measurement of the amount of DO in the cell culture medium in-line under sterile conditions in NASA's perfused bioreactor requires that the oxygen sensor provide increased sensitivity and be sterilizable and nontoxic. Additionally, long-term cell culture experiments require that the calibration be maintained several weeks or months. Although there are a number of sensors for dissolved oxygen on the market and under development elsewhere, very few meet these stringent conditions. An optical oxygen sensor (BOXY) based on dynamic fluorescent quenching and a pulsed blue LED light source was developed in our laboratory to address these requirements. Tris( 4,7 -diphenyl-l, 1 O-phenanthroline )ruthenium(II) chloride is employed as the fluorescent dye indicator. The sensing element consists of a glass capillary (OD 4.0 mm; ID 2.0 mm) coated internally with a thin layer of the fluorescent dye in silicone matrix and overlayed with a black shielding layer. Irradiation of the sensing element with blue light (blue LED with emission maximum at 475 nm) generates a red fluorescence centered at 626 nm. The fluorescence intensity is correlated to the concentration of DO present in the culture medium, following the modified non-linear Stern-Volmer equation. By using a pulsed irradiating light source, the problem of dye-bleaching, which is often encountered in long-term continuous measurements of tIns type, 'is minimized. To date we achieved sensor resolution of 0.3 mmHg at 50 mmHg p02, and 0.6 mmHg at 100 mmHg p02, with a response time of about one minute. Calibration was accomplished in sterile phosphate-buffered saline with a blood-gas analyzer (BGA) measurement as reference. Stand-alone software was also developed to control the sensor and bioreactor as well as to acquire data. Two HOXY sensors with a single calibration were employed to continuously monitor the DO in GTSF-2 medium during a Baby Hamster Kidney (BHK-21) cell culture in a Rotating Wall Perfused Vessel (RWPV) bioreactor for 90 days. HOXY sensors were located at the inlet to and outlet from the bioreactor. One of the sensors was placed between an oxygenator and the inlet to the bioreactor. The dissolved oxygen concentrations determined by both sensors were compared with those measured regularly with the BGA reference. The cell culture was maintained for 110 days. Sensor output was found to correlate well with the BGA data throughout the experiment, where the DO of the medium ranged between 25 and 50 mmHg at the bioreactor outlet and 90-130 mmHg at the bioreactor inlet. Measuring DO with the HOXY sensors versus the BGA reference indicated bias values of -2 mmHg and -15 mmHg, and precision values of +/-3mmHg and +/-16 mmHg at the bioreactor inlet and outlet, respectively.

Gao, F. G.↗

Optical potential approach to the electron-atom impact ionization threshold problem

The problem of the threshold law for electron-atom impact ionization is reconsidered as an extrapolation of inelastic cross sections through the ionization threshold. The cross sections are evaluated from a distorted wave matrix element, the final state of which describes the scattering from the Nth excited state of the target atom. The actual calculation is carried for the e-H system, and a model is introduced which is shown to preserve the essential properties of the problem while at the same time reducing the dimensionability of the Schrodinger equation. Nevertheless, the scattering equation is still very complex. It is dominated by the optical potential which is expanded in terms of eigen-spectrum of QHQ. It is shown by actual calculation that the lower eigenvalues of this spectrum descend below the relevant inelastic thresholds; it follows rigorously that the optical potential contains repulsive terms. Analytical solutions of the final state wave function are obtained with several approximations of the optical potential.

Temkin, A.↗

Manipulation based on sensor-directed control: An integrated end effector and touch sensing system

A hand/touch sensing system is described that, when mounted on a position-controlled manipulator, greatly expands the kinds of automated manipulation tasks that can be undertaken. Because of the variety of coordinate conversions, control equations, and completion criteria, control is necessarily dependent upon a small digital computer. The sensing system is designed both to be rugged and to sense the necessary touch and force information required to execute a wide range of manipulation tasks. The system consists of a six-axis wrist sensor, external touch sensors, and a pair of matrix jaw sensors. Details of the construction of the particular sensors, the integration of the end effector into the sensor system, and the control algorithms for using the sensor outputs to perform manipulation tasks automatically are discussed.

Hill, J. W.↗

Approximate polynomial preconditioning applied to biharmonic equations on vector supercomputers

Applying a finite difference approximation to a biharmonic equation results in a very ill-conditioned system of equations. This paper examines the conjugate gradient method used in conjunction with the generalized and approximate polynomial preconditionings for solving such linear systems. An approximate polynomial preconditioning is introduced, and is shown to be more efficient than the generalized polynomial preconditionings. This new technique provides a simple but effective preconditioning polynomial, which is based on another coefficient matrix rather than the original matrix operator as commonly used.

Wong, Yau Shu↗

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for Aircraft Acoustic Nacelle Design

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Baumeister, Kenneth J.↗

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for the Convective Wave Equation

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in ducts. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Baumeister, K. J.↗

On the use of the consistent mass matrix in flexible multibody systems

Two different methods are used in finite element structural analysis to define element mass distribution: consistent and lumped mass approximations. The lumped mass method is currently favored in multibody dynamics software packages because of its computational efficiency. This paper, however, presents a multibody dynamics formulation based on the consistent mass approach which should prove to be as computationally efficient as the lumped mass approach. It is shown that when component flexibility is modelled using modal coordinates, the equations of motion, as formulated by these two methods, are very similar in appearance, thereby facilitating their comparison. It is also shown, through simulation of a simple multibody system, that a system formulated with the lumped mass approximation will often require more finite elements and smaller integration step sizes than the corresponding consistent mass system.

Anthony, Tobin C.↗

Modeling of outgassing and matrix decomposition in carbon-phenolic composites

Work done in the period Jan. - June 1994 is summarized. Two threads of research have been followed. First, the thermodynamics approach was used to model the chemical and mechanical responses of composites exposed to high temperatures. The thermodynamics approach lends itself easily to the usage of variational principles. This thermodynamic-variational approach has been applied to the transpiration cooling problem. The second thread is the development of a better algorithm to solve the governing equations resulting from the modeling. Explicit finite difference method is explored for solving the governing nonlinear, partial differential equations. The method allows detailed material models to be included and solution on massively parallel supercomputers. To demonstrate the feasibility of the explicit scheme in solving nonlinear partial differential equations, a transpiration cooling problem was solved. Some interesting transient behaviors were captured such as stress waves and small spatial oscillations of transient pressure distribution.

Mcmanus, Hugh L.↗

Interior radiances in optically deep absorbing media. 3: Scattering from Haze L

The interior radiances are calculated within an optically deep absorbing medium scattering according to the Haze L phase function. The dependence on the solar zenith angle, the single scattering albedo, and the optical depth within the medium is calculated by the matrix operator method. The development of the asymptotic angular distribution of the radiance in the diffusion region is illustrated through a number of examples; it depends only on the single scattering albedo and on the phase function for single scattering. The exact values of the radiance in the diffusion region are compared with values calculated from the approximate equations proposed by Van de Hulst. The variation of the radiance near the lower boundary of an optically thick medium is illustrated with examples. The attenuation length is calculated for various single scattering albedos and compared with the corresponding values for Rayleigh scattering. The ratio of the upward to the downward flux is found to be remarkably constant within the medium. The heating rate is calculated and found to have a maximum value at an optical depth of two within a Haze L layer when the sun is at the zenith.

Kattawar, G. W.↗

Interior radiances in optically deep absorbing media. III Scattering from Haze L

The interior radiances are calculated within an optically deep absorbing medium scattering according to the Haze L phase function. The dependence on the solar zenith angle, the single scattering albedo, and the optical depth within the medium is calculated by the matrix operator method. The development of the asymptotic angular distribution of the radiance in the diffusion region is illustrated through a number of examples; it depends only on the single scattering albedo and on the phase function for single scattering. The exact values of the radiance in the diffusion region are compared with values calculated from the approximate equations proposed by Van de Hulst. The variation of the radiance near the lower boundary of an optically thick medium is illustrated with examples. The attenuation length is calculated for various single scattering albedos and compared with the corresponding values for Rayleigh scattering. The ratio of the upward to the downward flux is found to be remarkably constant within the medium.

Kattawar, G. W.↗

Polarimetric signatures of a coniferous forest canopy based on vector radiative transfer theory

Complete polarization signatures of a coniferous forest canopy are studied by the iterative solution of the vector radiative transfer equations up to the second order. The forest canopy constituents (leaves, branches, stems, and trunk) are embedded in a multi-layered medium over a rough interface. The branches, stems and trunk scatterers are modeled as finite randomly oriented cylinders. The leaves are modeled as randomly oriented needles. For a plane wave exciting the canopy, the average Mueller matrix is formulated in terms of the iterative solution of the radiative transfer solution and used to determine the linearly polarized backscattering coefficients, the co-polarized and cross-polarized power returns, and the phase difference statistics. Numerical results are presented to investigate the effect of transmitting and receiving antenna configurations on the polarimetric signature of a pine forest. Comparison is made with measurements.

Karam, M. A.↗

Extrapolation techniques applied to matrix methods in neutron diffusion problems

A general matrix method is developed for the solution of characteristic-value problems of the type arising in many physical applications. The scheme employed is essentially that of Gauss and Seidel with appropriate modifications needed to make it applicable to characteristic-value problems. An iterative procedure produces a sequence of estimates to the answer; and extrapolation techniques, based upon previous behavior of iterants, are utilized in speeding convergence. Theoretically sound limits are placed on the magnitude of the extrapolation that may be tolerated. This matrix method is applied to the problem of finding criticality and neutron fluxes in a nuclear reactor with control rods. The two-dimensional finite-difference approximation to the two-group neutron fluxes in a nuclear reactor with control rods. The two-dimensional finite-difference approximation to the two-group neutron-diffusion equations is treated. Results for this example are indicated.

Mccready, Robert R↗

Numerical Model of Flame Spread Over Solids in Microgravity: A Supplementary Tool for Designing a Space Experiment

The recently developed numerical model of concurrent-flow flame spread over thin solids has been used as a simulation tool to help the designs of a space experiment. The two-dimensional and three-dimensional, steady form of the compressible Navier-Stokes equations with chemical reactions are solved. With the coupled multi-dimensional solver of the radiative heat transfer, the model is capable of answering a number of questions regarding the experiment concept and the hardware designs. In this paper, the capabilities of the numerical model are demonstrated by providing the guidance for several experimental designing issues. The test matrix and operating conditions of the experiment are estimated through the modeling results. The three-dimensional calculations are made to simulate the flame-spreading experiment with realistic hardware configuration. The computed detailed flame structures provide the insight to the data collection. In addition, the heating load and the requirements of the product exhaust cleanup for the flow tunnel are estimated with the model. We anticipate that using this simulation tool will enable a more efficient and successful space experiment to be conducted.

Shih, Hsin-Yi↗

Algorithms and software for solving finite element equations on serial and parallel architectures

The primary objective was to compare the performance of state-of-the-art techniques for solving sparse systems with those that are currently available in the Computational Structural Mechanics (MSC) testbed. One of the first tasks was to become familiar with the structure of the testbed, and to install some or all of the SPARSPAK package in the testbed. A brief overview of the CSM Testbed software and its usage is presented. An overview of the sparse matrix research for the Testbed currently employed in the CSM Testbed is given. An interface which was designed and implemented as a research tool for installing and appraising new matrix processors in the CSM Testbed is described. The results of numerical experiments performed in solving a set of testbed demonstration problems using the processor SPK and other experimental processors are contained.

Chu, Eleanor↗