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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Theoretical paper discusses physical significance of vanishing of hyperbolic coefficients in equations of elastodynamics. Paper presents generalized approach to structural elastodynamics as part of continuing effort to develop mathematical stability criteria for structures and simulate postinstabilty behavior of elastics in general.
The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme.
An analytical and computer study of the dynamic energy equations that describe the physical phenomena that occurs in a Stirling cycle engine. The basic problem is set up in terms of a set o hyperbolic partial differential equations. The characteristic lines are determined. The equations are then transformed to ordinary differential equations that are valid along characteristic lines. Computer programs to solve the differential equations and to plot pertinent factors are described.
The generation of the Advanced X-ray Astrophysics Facility/TMA hyperbolic and parabolic optical mirror blanks, the process used, and the final measurements are described.
Explicit forms for the six coefficients of a generalized quadric surface are given in terms of the parameters of a tilted and displaced elliptical or hyperbolic surface. The parent conic parameters, together with the values for its tilt and displacement, are then related to the physical conic concentrators. The parent conic parameters are related to the concentrator's large and small aperture sizes and the angle of the limiting ray.
The relationships between beam attenuation spectra, chlorophyll and pheophytin pigment concentrations, and particle size distributions are examined for a coastal region believed to have negligible concentrations of terrestrially derived dissolved organic compounds but large quantities of phytoplankton and resuspended sediments. It was found that the slope of the beam attenuation spectra increases when the hyperbolic slope of the size distribution increases. The magnitude of this increase in slope was consistent with calculations based on a range of particle diameters from 0.5 to 30 microns so that it would be possible to predict the slope of the particle size distribution if the slope of the beam attenuation spectra is known. The ratio of chlorophyll and pheophytin pigments to suspended volume concentrations affected the beam attenuation spectra to a lesser degree and in a more complex manner. Because of the strong effect of slope, it was concluded that the chlorophyll and pheophytin pigment content of suspended particles could not be efficiently predicted by means of beam attenuation measurements.
Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.
A practical method for efficiently analyzing the two-phase flow field in the supersonic region of an axisymmetric rocket nozzle is presented. The governing hyperbolic equations for the gas- and particle-phases are simultaneously integrated downstream using a space-marching procedure. Both one- and two-phase flow computations are performed for the JPL axisymmetric nozzle. The results show the nonequilibrium effects which are due to the existence of particles in the flow. The comparisons with the experimental data and other numerical solutions are made to examine the accuracy of the present method.
A miniaturized Cassegrainian concentrator solar array concept is under development to reduce the cost of multi-kW spacecraft solar arrays. A primary parabolic reflector directs incoming solar energy to a secondary, centrally mounted inverted hyperbolic reflector and down onto a solar cell mounted on an Mo heat spreader on a 0.25 mm thick Al heat fin. Each unit is 12.7 mm thick, which makes the concentrator assembly roughly as thick as a conventional panel. The output is 100 W/sq and 20 W/kg, considering 20% efficient Si cells at 100 suns. A tertiary light catcher is mounted around the cell to ameliorate optic errors. The primary reflector is electroformed Ni with protective and reflective coatings. The cells have back surface reflectors and a SiO antireflective coating. An optical efficiency of 80% is projected, and GaAs cells are being considered in an attempt to raise cell efficiencies to over 30%.
A comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given. Some general mathematical framework and error analysis common to such coordinate systems is also included. The general categories of generating systems are those based on conformal mapping, orthogonal systems, nearly orthogonal systems, systems produced as the solution of elliptic and hyperbolic partial differential equations, and systems generated algebraically by interpolation among the boundaries. Also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation. Dynamically adaptive coordinate systems, coupled with the physical solution, and time-dependent systems that follow moving boundaries are treated. References reporting experience using such coordinate systems are reviewed as well as those covering the system development.
Papers presented in this volume provide an overview of recent work on numerical boundary condition procedures and multigrid methods. The topics discussed include implicit boundary conditions for the solution of the parabolized Navier-Stokes equations for supersonic flows; far field boundary conditions for compressible flows; and influence of boundary approximations and conditions on finite-difference solutions. Papers are also presented on fully implicit shock tracking and on the stability of two-dimensional hyperbolic initial boundary value problems for explicit and implicit schemes.
The class of one-dimensional stretching functions used in finite-difference calculations is studied. For solutions containing a highly localized region of rapid variation, simple criteria for a stretching function are derived using a truncation error analysis. These criteria are used to investigate two types of stretching functions. One an interior stretching function, for which the location and slope of an interior clustering region are specified. The simplest such function satisfying the criteria is found to be one based on the inverse hyperbolic sine. The other type of function is a two-sided stretching function, for which the arbitrary slopes at the two ends of the one-dimensional interval are specified. The simplest such general function is found to be one based on the inverse tangent. Previously announced in STAR as N80-25055
The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme. Previously announced in STAR as N83-23085
The 'Osher' scheme was introduced by Osher (1981). It represents an upwind finite-difference method for hyperbolic systems of conservation laws, including the Euler equations. In studies conducted by Osher (1981) and Osher and Solomon (1982), the method was applied to the nonisentropic form of the Euler equations in one dimension and the isentropically restricted form in two spatial dimensions, both in Cartesian coordinates. Chakravarthy and Osher (1982) have shown an approach for extending the Osher scheme to the Euler equations written for general geometries, taking into account the use of mappings to arbitrary curvilinear coordinate systems. The present investigation is concerned with the high resolution extension of the Osher scheme to second-order accuracy. Results are presented for several example problems, giving attention to quasi-one-dimensional Laval nozzle flow, a one-dimensional shock tube problem, and supersonic flow over a cylinder.
Vibrational characteristics are determined for a previously unsolved class of problems, that of doubly-curved shallow shells having rectangular planforms, clamped along one edge and free on the other three. The solution procedure uses the Ritz method with algebraic polynomial trial functions. Convergence studies are made, and accurate frequencies and contour plots of mode shapes are presented for various curvature ratios, including spherical, circular cylindrical and hyperbolic paraboloidal shells. Particular emphasis is given to the effect of adding spanwise curvature to shells having chordwise curvature; numerous published references already exist for the case of zero spanwise curvature. The effects of changing aspect ratio, thickness ratio and Poisson's ratio are also studied.
Single pass aerocapture and aeroassisted orbital transfer designs are discussed for modifying spacecraft orbits using planetary atmospheres. Aerodynamic drag can be used to shift a hyperbolic flyby trajectory to a planetary orbit by having the spacecraft altering its in-plane L/D ratio to maintain constant drag until the desired velocity is attained. The spacecraft would then move out of the atmosphere, sometimes with a small propulsive assist. Sample missions to Uranus, Jupiter, and Titan are mentioned, with mission scenarios commencing with a Shuttle launch. Biconic-shaped spacecraft are cited as having the best L/D for insertion accuracy, a low hypersonic ballistic coefficient, and volumeric efficiency. Aeroassisted orbital transfer involves atmospheric braking in order to shed velocity on a return trip from higher orbits. No decision has yet been made as to the spacecraft shape, but calculations indicate that aeroassist braking before return to LEO for rendezvous with the Shuttle has the potential for the lowest cost/mass to GEO of any delivery system currently under consideration.
Approximation schemes employing cubic splines in the context of a linear semigroup framework are developed for both parabolic and hyperbolic second-order partial differential equation parameter estimation problems. Convergence results are established for problems with linear and nonlinear systems, and a summary of numerical experiments with the techniques proposed is given.
The present investigation shows that a finite element scheme with a weighted least squares variational principle is applicable to the problem of transonic flow around a harmonically oscillating airfoil. For the flat plate case, numerical results compare favorably with the exact solution. The obtained numerical results for the transonic problem, for which an exact solution is not known, have the characteristics of known experimental results. It is demonstrated that the performance of the employed numerical method is independent of equation type (elliptic or hyperbolic) and frequency. The weighted least squares principle allows the appropriate modeling of singularities, which such a modeling of singularities is not possible with normal least squares.