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DOE OSTI2022

A New 1-step Arrhenius Decomposition Model for PBX 9501: Calibration with Isochoric-Adiabatic High-Activation-Energy Asymptotics and Uncertainty Quantification

Here we present a new 1-step Arrhenius thermal decomposition model of PBX 9501. As opposed to previous studies, we use high-energy asymptotic theory, and previously published equations of state to parameterize the model to experimental critical-time data. The model parameters were fit to experimental data using a bootstrapping procedure to capture the effects of experimental uncertainty. Subsequent implementation of the model in a chemicalkinetics ODE solver shows good agreement of times to ignition vs initial temperature in isochoric thermal explosion calculations with the results of the high-energy asymptotic theory. We also compare the resultant ZND structures to those of one of our previously calibrated burn models.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

NASA NTRS1971

Noncoplanar minimum delta V two-impulse and three-impulse orbital transfer from a regressing oblate earth assembly parking ellipse onto a flyby trans-Mars asymptotic velocity vector.

Comparison of two-impulse and three-impulse orbital transfer, using data from a 63-case numerical study. For each case investigated for which coplanarity of the regressing assembly parking ellipse was attained with the target asymptotic velocity vector, a two-impulse maneuver (or a one-impulse equivalent) was found for which the velocity expenditure was within 1% of a reference absolute minimum lower bound. Therefore, for the coplanar cases, use of a minimum delta-V three-impulse maneuver afforded scant improvement in velocity penalty. However, as the noncoplanarity of the parking ellipse and the target asymptotic velocity vector increased, there was a significant increase in the superiority of minimum delta-V three-impulse maneuvers for slowing the growth of velocity expenditure. It is concluded that a multiple-impulse maneuver should be contemplated if nonnominal launch conditions could occur.

Bean, W. C.↗

NASA NTRS1971

Optimum transfer between hyperbolic asymptotes with turn angle less than the maximum natural turn angle.

The impulsive transfer of minimum characteristic velocity between two given hyperbolic asymptotes associated with a real planet is considered. The constraint of remaining above the surface of the planet introduces a maximum natural turn angle. This divides the problem naively into two categories. The first is the case when the turn angle required by the given asymptotes is less than or equal to the maximum natural turn angle. This is the more reasonable situation for a swingby maneuver, and is the case considered in this paper. The resulting optimal transfers are of five basic types. In boundary conditions space, by far the largest area of transfers are either single impulse transfers or transfers through the parabolic level requiring two finite impulses. In no case has an optimal transfer been found which uses more than two finite impulses and three infinitesimal impulses. Complete results are presented for the case in which the given turn angle is less than or equal to the maximum natural turn angle.

Walton, J. M.↗

NASA NTRS1972

Progress in nonlinear finite element analysis using asymptotic solution techniques.

The existence of standard forms of finite element equations for nonlinear analysis is observed. These are noted to provide a sufficiently special circumstance to admit the construction of asymptotic solution techniques. Although efforts in this direction have been made only recently, a number of distinct approaches to asymptotic solution techniques for finite element analysis have been put forward and are examined herein. Consideration is given to the differences and similarities of the approaches and the resulting methods of solution. Special characteristics regarding applicability, accuracy and efficiency are delineated.

Mallett, R. H.↗

NASA NTRS1973

Impedance of strip-traveling waves on an elastic half space - Asymptotic solution

The dynamic normal-load distribution across a strip that is required to maintain a plane progressive wave along its length is studied for the case where the strip is of infinite length and lies on the surface of a homogeneous isotropic elastic half space. This configuration is proposed as a preliminary idealized model for analyzing the dynamic interaction between soils and flexible foundations. The surface load distribution across the strip and the motion of the strip are related by a pair of dual integral equations. An asymptotic solution is obtained for the limiting case of small wavelength. The nature of this solution depends importantly on the propagation velocity of the strip-traveling wave in comparison with the Rayleigh wave speed, the shear wave speed and the dilatational wave speed. When the strip-traveling wave propagates faster than the Rayleigh wave speed, a pattern of trailing Rayleigh waves is shed from the strip. The limiting amplitude of the trailing waves is provided by the asymptotic solution.

Crandall, S. H.↗

NASA NTRS1974

The development of jet mixing toward the asymptotic similar solution

An analytic study of the development of an initially nonsimilar jet mixing velocity profile toward the final asymptotic, similar solution, is made. The corresponding incompressible boundary layer equations are solved for each of the streams above and below the dividing streamline by using Meksyn's asymptotic method of integration. The behavior of this flow development toward the final similar solution, as influenced by the initial condition, is properly described and discussed.

Brink, D. F.↗

NASA NTRS1976

Solution of the exact equations for three-dimensional atmospheric entry using directly matched asymptotic expansions

The problem of determining the trajectories, partially or wholly contained in the atmosphere of a spherical, nonrotating planet, is considered. The exact equations of motion for three-dimensional, aerodynamically affected flight are derived. Modified Chapman variables are introduced and the equations are transformed into a set suitable for analytic integration using asymptotic expansions. The trajectory is solved in two regions: the outer region, where the force may be considered a gravitational field with aerodynamic perturbations, and the inner region, where the force is predominantly aerodynamic, with gravity as a perturbation. The two solutions are matched directly. A composite solution, valid everywhere, is constructed by additive composition. This approach of directly matched asymptotic expansions applied to the exact equations of motion couched in terms of modified Chapman variables yields an analytical solution which should prove to be a powerful tool for aerodynamic orbit calculations.

Busemann, A.↗

NASA NTRS1977

Slender streams with gravity - Outer asymptotic expansions. I, II

The steady, three-dimensional, potential flow (neglecting surface tension) of a slender stream of fluid in the presence of gravity is considered and a description is presented of the first part of an asymptotic theory of such a flow. The theory will provide the ingredients for the construction of the solution to many flow problems involving slender streams. The flows and their boundaries are represented as asymptotic power series in the slenderness ratio of the stream. Attention is given to the formulation of the outer expansion problems, first approximations for a jet, a first approximation for pipe flow, and a first approximation for channel flow.

Geer, J.↗

NASA NTRS1979

Generalized quadratic weights for asymptotic regulator properties

The paper describes a generalized quadratic weight selection procedure based on asymptotic modal properties of linear-quadratic regulators as control weights tend to zero. Explicit formulas are developed for weighting matrices which produce an asymptotic eigenstructure consisting of p no greater than n - m finite modes, with the rest tending to infinity in selectable Butterworth patterns or determined by other secondary design considerations.

Stein, G.↗

NASA NTRS1979

Generalized quadratic weights for asymptotic regulator properties

This paper describes a generalized quadratic weight selection procedure based on asymptotic modal properties of linear-quadratic regulators as control weights tend to zero. Explicit formulas are developed for weighting matrices which produce an asymptotic eigen-structure consisting of p less than or equal to n-m finite modes, with the rest tending to infinity in selectable Butterworth patterns or determined by other secondary design considerations.

Stein, G.↗

NASA NTRS1980

Asymptotic Eigenstructures

The behavior of the closed loop eigenstructure of a linear system with output feedback is analyzed as a single parameter multiplying the feedback gain is varied. An algorithm is presented that computes the asymptotically infinite eigenstructure, and it is shown how a system with high gain, feedback decouples into single input, single output systems. Then a synthesis algorithm is presented which uses full state feedback to achieve a desired asymptotic eigenstructure.

Thompson, P. M.↗

NASA NTRS1981

Simple approximations for the asymptotic description of the interaction between a normal shock wave and a turbulent boundary layer at transonic speeds

The asymptotic description of the interaction between a normal shock wave and a turbulent boundary layer is reviewed. The layers necessary in a rational analysis of the interaction are discussed with emphasis on the differences from an interaction with a laminar boundary layer, the uncoupling of solutions for the distribution of pressure and skin friction at the wall, and the role of the Reynolds shear stress in these solutions. The accuracy of asymptotic solutions in flows at Reynolds numbers of technical interest is discussed. Solutions for the distribution of pressure and skin friction at the wall and the shape of the shock are considered for the case where the flow is near separation. For the pressure and skin friction, it is possible to write two simplified partial solutions, one valid at the beginning of the interaction and one valid somewhat downstream of the shock wave. A solution composed of these two parts and a linear interpolation between them appears to give good comparison with experiment; one unknown constant, independent of the parameters of the interaction, must be found from experiment. The simplified relations are presented. Comparison of numerical computations with experimental data indicates a possible value for the constant and shows quite satisfactory results.

Adamson, T. C., Jr.↗

NASA NTRS1980

Comparison of two leading uniform theories of edge diffraction with the exact uniform asymptotic solution

The diffraction of an arbitrary cylindrical wave by a half-plane has been treated by Rahmat-Samii and Mittra who used a spectral domain approach. In this paper, their exact solution for the total field is expressed in terms of a new integral representation. For large wave number k, two rigorous procedures are described for the exact uniform asymptotic expansion of the total field solution. The uniform expansions obtained are valid in the entire space, including transition regions around the shadow boundaries. The final results are compared with the formulations of two leading uniform theories of edge diffraction, namely, the uniform asymptotic theory and the uniform theory of diffraction. Some unique observations and conclusions are made in relating the two theories.

Boersma, J.↗

NASA NTRS1979

Asymptotic eigenstructures of filters

This paper describes relationships between Kalman-Bucy filter design parameters and the asymptotic eigenstructures of the resulting error dynamics. Simple, explicit formulas are developed which select noise intensity matrices to achieve pre-specified eigenstructures. The results also add basic understanding of the asymptotic properties of filters, particularly with respect to recently proposed robustness recovery processes.

Stein, G.↗

NASA NTRS1981

Application of adaptive grids to fluid-flow problems with asymptotic solutions

Coordinate system selection is an important consideration in the asymptotic numerical solution of any fluid-flow or heat transfer problem. This paper uses a new technique that provides a simple way of moving the mesh points in physical space in order to reduce the error in the computed asymptotic solution relative to that obtained using a fixed mesh. Applications to fluid-flow problems are presented, including boundary layer flow and inviscid supersonic flow over cylinders, and wedges with associated detached shocks. The treatment of curved boundaries, stationary and nonstationary boundaries, and systems of PDE's is discussed. Significant error reductions are demonstrated.

Rai, M. M.↗

NASA NTRS1981

An asymptotically stable damping enhancement controller for large space structures

A secondary controller which uses a number of Annular Momentum Control Devices (AMCD's) for enhancement of structural damping in large flexible space structures is investigated. The closed-loop secondary controller is shown to be equivalent to a certain closed-loop optimal linear regulator, and the necessary and sufficient conditions for asymptotic stability are obtained. Sufficient conditions for asymptotic stability are also obtained which are much less restrictive than those obtained in an earlier paper. Design of a robust stable primary controller is also discussed.

Joshi, S. M.↗

NASA NTRS1982

Solution of second-order linear system by matched asymptotic expansions

Matched asymptotic expansions (MAE) are used to obtain a first order approximation to the solution of a singularly perturbed second order system. A special case is considered in which the uniform asymptotic solution obtained by MAE is shown to converge to the exact solution. Ways in which the method can be used to sole higher-order linear systems, including those which are not singularly perturbed, are also discussed.

Ardema, M. D.↗

NASA NTRS1981

Theoretical quasar emission line ratios. IV - General asymptotic escape probabilities and the effects of linear Stark broadening

Established techniques permitting the evaluation of exact asymptotic forms of photon escape probabilities for a wide range of absorption coefficient profile types are used for QSO radiative transfer effect studies, and it is shown that the exact formulae are easily evaluated. It is found that some of the commonly used expressions overestimate the true value by a factor of about two, and a computationally expedient approximate expression is derived for the asymptotic form of the photon escape probability when linear Stark broadening contributes to the line absorption coefficient profile in hydrogenic lines. Attention is given to Lyman-alpha, for the case in which partial redistribution, over the linear Stark component of the line absorption coefficient profile, dominates single-flight photon escape.

Puetter, R. C.↗