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NASA NTRS1982

Surface fitting with biharmonic and harmonic models

The physical and geometric interpretation of a surface fitting technique, multiquadric equations (MQ), is discussed. The relation of this method and its reciprocal form to biharmonic and harmonic techniques respectively, is pointed out. In both forms the solutions may be viewed as being numerical approximations of an integral equation in which an unknown density function is the physical source for disturbing potential (reciprocal-MQ) or elastic displacement (MQ).

Hardy, R. L.↗

NASA NTRS1982

Mixture densities, maximum likelihood, and the EM algorithm

The problem of estimating the parameters which determine a mixture density is reviewed as well as maximum likelihood estimation for it. A particular iterative procedure for numerically approximating maximum likelihood estimates for mixture density problems is considered. This EM algorithm, is a specialization to the mixture density context of a general algorithm of the same name used to approximate maximum likelihood estimates for incomplete data problems. The formulation and theoretical and practical properties of the EM algorithm for mixture densities are discussed focussing in particular on mixtures of densities from exponential families.

Redner, R. A.↗

NASA NTRS1983

Tradeoff studies in multiobjective insensitive design of airplane control systems

A computer aided design method for multiobjective parameter-insensitive design of airplane control systems is described. Methods are presented for trading off nominal values of design objectives against sensitivities of the design objectives to parameter uncertainties, together with guidelines for designer utilization of the methods. The methods are illustrated by application to the design of a lateral stability augmentation system for two supersonic flight conditions of the Shuttle Orbiter. Objective functions are conventional handling quality measures and peak magnitudes of control deflections and rates. The uncertain parameters are assumed Gaussian, and numerical approximations of the stochastic behavior of the objectives are described. Results of applying the tradeoff methods to this example show that stochastic-insensitive designs are distinctly different from deterministic multiobjective designs. The main penalty for achieving significant decrease in sensitivity is decreased speed of response for the nominal system.

Schy, A. A.↗

NASA NTRS1984

Bolometers - Ultimate sensitivity, optimization, and amplifier coupling

Theoretical expressions for Johnson noise and thermal noise in bolometers are considered, and optimization with respect to thermal conductivity and bias power is performed. Numerical approximations are given for the ultimate NEP of bolometers as a function of material parameters and compared with photon noise including photon correlations. A resonating capacitor is shown to improve the coupling to an amplifier, so that the amplifier need not limit performance even for very low temperature bolometers.

Mather, J. C.↗

NASA NTRS1985

A 3-dimensional mass conserving element for compressible flows

A variety of finite element schemes has been used in the numerical approximation of compressible flows particularly in underwater acoustics. In many instances instabilities have been generated due to the lack of mass conservation. Two- and three-dimensional elements are developed which avoid these problems.

Fix, G.↗

NASA NTRS1985

Formulation and implementation of nonstationary adaptive estimation algorithm with applications to air-data reconstruction

The dynamics model and data sources used to perform air-data reconstruction are discussed, as well as the Kalman filter. The need for adaptive determination of the noise statistics of the process is indicated. The filter innovations are presented as a means of developing the adaptive criterion, which is based on the true mean and covariance of the filter innovations. A method for the numerical approximation of the mean and covariance of the filter innovations is presented. The algorithm as developed is applied to air-data reconstruction for the space shuttle, and data obtained from the third landing are presented. To verify the performance of the adaptive algorithm, the reconstruction is also performed using a constant covariance Kalman filter. The results of the reconstructions are compared, and the adaptive algorithm exhibits better performance.

Whitmore, S. A.↗

NASA NTRS1984

Hydrogen on Venus - Exospheric distribution and escape

The spatial distribution of suprathermal H in the Venus atmosphere is calculated using an approximate numerical solution of the time-independent Boltzmann equation. Sources of suprathermal H are specified on the basis of Pioneer Venus measurements. Reactions involving H2 are neglected. The computed densities of suprathermal H are in satisfactory agreement with profiles derived from analysis of Lyman-alpha airglow by Mariners 5 and 10 and Veneras 11 and 12. The dayside emission at radial distances larger than 18,000 km is attributed to scattering of solar photons by fast H atoms produced primarily on the nightside near midnight. The nightside ionosphere, and consequently the source of suprathermal H, are both expected to vary in response to changes in the solar wind.

Rodriguez, J. M.↗

NASA NTRS1985

Chemical control of rate and onset temperature of nadimide polymerization

The chemistry of norbornenyl capped imide compounds (nadimides) is briefly reviewed with emphasis on the contribution of Diels-Alder reversion in controlling the rate and onset of the thermal polymerization reaction. Control of onset temperature of the cure exotherm by adjusting the concentration of maleimide is demonstrated using selected model compounds. The effects of nitrophenyl compounds as free radical retarders on nadimide reactivity are discussed. A simple copolymerization model is proposed for the overall nadimide cure reaction. An approximate numerical analysis is carried out to demonstrate the ability of the model to simulate the trends observed for both maleimide and nitrophenyl additions.

Lauver, R. W.↗

NASA NTRS1986

Turbulent flow field predictions in sharply curved turn around ducts

In this investigation, two-dimensional turbulent flow of incompressible Newtonian fluids in sharply curved 180 deg turn around ducts is studied. Results of an approximate numerical flow field analysis utilizing an orthogonal, body-fitted, curvilinear coordinate system are compared to results based on a traditional cylindrical reference frame. Qualitative indication of general streamfield characteristics as well as quantitative benchmarks for the planning of future experimentation are provided. In addition, preliminary results of an augmented kappa-epsilon turbulence model analysis, which explicitly accounts for the effects of streamline curvature and pressure strain in internal turbulent flows, are presented. Specific model difficulties are discussed and comparisons with standard kappa-esilon model predictions are included.

Santi, L. M.↗

NASA NTRS1986

Turbulent flow field predictions in sharply curved turn-around ducts

Two-dimensional turbulent flow of incompressible Newtonian fluids in sharply curved 180 deg turn around ducts is studied. Results of an approximate numerical flow field analysis utilizing an orthogonal, body-fitted, curvilinear coordinate system are compared to results based on a traditional cylindrical reference frame. Qualitative induction of general streamfield characteristics as well as quantitative benchmarks for the planning of future experimentation are provided. In addition, preliminary results of an augmented kappa - epsilon turbulence model analysis, which explicitly accounts for the effects of streamline curvature and pressure strain in internal turbulent flows, are presented. Specific model difficulties are discussed and comparisons with standard kappa - epsilon model predictions are included.

Santi, L. M.↗

NASA NTRS1986

Application of a low order panel method to complex three-dimensional internal flow problems

An evaluation of the ability of a low order panel method to predict complex three-dimensional internal flow fields was made. The computer code VSAERO was used as a basis for the evaluation. Guidelines for modeling internal flow geometries were determined and the effects of varying the boundary conditions and the use of numerical approximations on the solutions accuracy were studied. Several test cases were run and the results were compared with theoretical or experimental results. Modeling an internal flow geometry as a closed box with normal velocities specified on an inlet and exit face provided accurate results and gave the user control over the boundary conditions. The values of the boundary conditions greatly influenced the amount of leakage an internal flow geometry suffered and could be adjusted to eliminate leakage. The use of the far-field approximation to reduce computation time influenced the accuracy of a solution and was coupled with the values of the boundary conditions needed to eliminate leakage. The error induced in the influence coefficients by using the far-field approximation was found to be dependent on the type of influence coefficient, the far-field radius, and the aspect ratio of the panels.

Ashby, D. L.↗

NASA NTRS1985

Formulation and implementation of nonstationary adaptive estimation algorithm with applications to air-data reconstruction

The dynamics model and data sources used to perform air-data reconstruction are discussed, as well as the Kalman filter. The need for adaptive determination of the noise statistics of the process is indicated. The filter innovations are presented as a means of developing the adaptive criterion, which is based on the true mean and covariance of the filter innovations. A method for the numerical approximation of the mean and covariance of the filter innovations is presented. The algorithm as developed is applied to air-data reconstruction for the Space Shuttle, and data obtained from the third landing are presented. To verify the performance of the adaptive algorithm, the reconstruction is also performed using a constant covariance Kalman filter. The results of the reconstructions are compared, and the adaptive algorithm exhibits better performance.

Whitmore, S. A.↗

NASA NTRS1987

Decoupled direct method for sensitivity analysis in combustion kinetics

An efficient, decoupled direct method for calculating the first order sensitivity coefficients of homogeneous, batch combustion kinetic rate equations is presented. In this method the ordinary differential equations for the sensitivity coefficients are solved separately from , but sequentially with, those describing the combustion chemistry. The ordinary differential equations for the thermochemical variables are solved using an efficient, implicit method (LSODE) that automatically selects the steplength and order for each solution step. The solution procedure for the sensitivity coefficients maintains accuracy and stability by using exactly the same steplengths and numerical approximations. The method computes sensitivity coefficients with respect to any combination of the initial values of the thermochemical variables and the three rate constant parameters for the chemical reactions. The method is illustrated by application to several simple problems and, where possible, comparisons are made with exact solutions and those obtained by other techniques.

Radhakrishnan, Krishnan↗

NASA NTRS1986

Formulation and implementation of a practical algorithm for non-stationary adaptive state estimation

Background information on the Kalman filter is given first. A discussion of the filter parameters and their a priori determination follows. The discussion points out the need for adaptive determination of the process noise statistics. The filter innovations are presented as a means for developing the adaptive criteria. The criteria center around the estimation of the true mean and covariance of the filter innovations. A method for the numerical approximation of the mean and covariance of a locally stationary random process is presented. The definition of a local stationarity is presented. Local stationarity allows for the separation of the process statistics into a stationary component and a time-varying component. The separation method is discussed. A method for estimating the stationary and time-varying components is presented. As an example of its application to real problems, the algorithm is applied to the problem to the problem of reentry trajectory estimation for the Space Shuttle. Both the adaptive algorithm and the steady-state Kalman filter are applied to the problem. The results of the reconstructions are presented. The adaptive algorithm exhibits superior performance.

Whitemore, S. A.↗

NASA NTRS1987

Numerical advection algorithms and their role in atmospheric transport and chemistry models

During the last 35 years, well over 100 algorithms for modeling advection processes have been described and tested. This review summarizes the development and improvements that have taken place. The nature of the errors caused by numerical approximation to the advection equation are highlighted. Then the particular devices that have been proposed to remedy these errors are discussed. The extensive literature comparing transport algorithms is reviewed. Although there is no clear cut 'best' algorithm, several conclusions can be made. Spectral and pseudospectral techniques consistently provide the highest degree of accuracy, but expense and difficulties assuring positive mixing ratios are serious drawbacks. Schemes which consider fluid slabs bounded by grid points (volume schemes), rather than the simple specification of constituent values at the grid points, provide accurate positive definite results.

Rood, Richard B.↗

NASA NTRS1987

PIC numerical scheme for a two-dimensional Eulerian code

The present work uses the PIC method with operator splitting to hydroelastoplastic multimaterial flow problems in 2D Eulerian coordinates. The operator splitting procedures are carried out in both Lagrangian and remap phases with alternating direction for each time advancement to maintain the accuracy of one-dimensional scheme. A detail description of the numerical approximations is given with a sample calculation of a tungsten rod penetrating an aluminum target.

Kwak, Dochan↗

NASA NTRS1987

A Taylor weak-statement algorithm for hyperbolic conservation laws

Finite element analysis, applied to computational fluid dynamics (CFD) problem classes, presents a formal procedure for establishing the ingredients of a discrete approximation numerical solution algorithm. A classical Galerkin weak-statement formulation, formed on a Taylor series extension of the conservation law system, is developed herein that embeds a set of parameters eligible for constraint according to specification of suitable norms. The derived family of Taylor weak statements is shown to contain, as special cases, over one dozen independently derived CFD algorithms published over the past several decades for the high speed flow problem class. A theoretical analysis is completed that facilitates direct qualitative comparisons. Numerical results for definitive linear and nonlinear test problems permit direct quantitative performance comparisons.

Baker, A. J.↗

NASA NTRS1988

An automated procedure for material parameter evaluation for viscoplastic constitutive models

An automated procedure is presented for evaluating the material parameters in Walker's exponential viscoplastic constitutive model for metals at elevated temperature. Both physical and numerical approximations are utilized to compute the constants for Inconel 718 at 1100 F. When intermediate results are carefully scrutinized and engineering judgement applied, parameters may be computed which yield stress output histories that are in agreement with experimental results. A qualitative assessment of the theta-plot method for predicting the limiting value of stress is also presented. The procedure may also be used as a basis to develop evaluation schemes for other viscoplastic constitutive theories of this type.

Imbrie, P. K.↗