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NASA NTRS1987

Acoustic propagation in a thermally stratified atmosphere

Acoustic propagation in an atmosphere with a specific form of temperature profile has been investigated by analytical means. The temperature profile used is representative of an actual atmospheric profile and contains three free parameters. Both lapse and inversion cases have been considered. Although ray solution have been considered the primary emphasis has been on solutions of the acoustic wave equation with point force where the sound speed varies with height above the ground corresponding to the assumed temperature profile. The method used to obtain the solution of the wave equation is based on Hankel transformation of the wave equation, approximate solution of the transformed equation for wavelength small compared to the scale of the temperature (or sound speed) profile, and approximate or numerical inversion of the Hankel transformed solution. The solution displays the characteristics found in experimental data but extensive comparison between the models and experimental data has not been carried out.

Vanmoorhem, W. K.↗

NASA NTRS1987

Composite box beam analysis - Theory and experiments

Beam theory is widely used as a first approximation in numerous structural applications. When applied to composite beams, the accuracy of beam theory becomes questionable because (1) the shearing and warping deformations become significant, as the shearing stiffness of composite laminates is often very low, and (2) several elastic couplings can occur that strongly influence the behavior of composite beams. The torsional behavior of thin-walled composite beams has important implications for aeronautical structures and is deeply modified by the above nonclassical effects. This paper presents two comprehensive analysis methodologies for composite beams and describes experimental results obtained from a thin-walled, rectangular cross-sectional beam. The theoretical predictions are found in good agreement with the observed twist and strain distributions. Out-of-plane torsional warping of the cross-section is found to be the key factor for an accurate modeling of the torsional behavior of such structures.

Bauchau, O. A.↗

NASA NTRS1987

Structure and propagation of supersonic singularities from helicoidal sources

An asymptotic analysis of the acoustic field radiated by a supersonic helicoidal line source distribution is given. The asymptotic results are valid in the vicinity of the Mach surfaces associated with the moving sources. Particular attention is paid to the singular nature of the field on the Mach surfaces, which the analysis describes exactly. In addition, it is found that the asymptotic approximation predicts numerical values of the pressure with considerable accuracy. Some details on the field of a single source are derived as a special case.

Myers, M. K.↗

NASA NTRS1988

Acoustic propagation in a thermally stratified atmosphere

Acoustic propagation in an atmosphere with a specific form of a temperature profile has been investigated by analytical means. The temperature profile used is representative of an actual atmospheric profile and contains three free parameters. Both lapse and inversion cases have been considered. Although ray solutions have been considered, the primary emphasis has been on solutions of the acoustic wave equation with point source where the sound speed varies with height above the ground corresponding to the assumed temperature profile. The method used to obtain the solution of the wave equation is based on Hankel transformation of the wave equation, approximate solution of the transformed equation for wavelength small compared to the scale of the temperature (or sound speed) profile, and approximate or numerical inversion of the Hankel transformed solution. The solution displays the characteristics found in experimental data but extensive comparison between the models and experimental data has not been carried out.

Vanmoorhem, W. K.↗

NASA NTRS1989

CSM research: Methods and application studies

Computational mechanics is that discipline of applied science and engineering devoted to the study of physical phenomena by means of computational methods based on mathematical modeling and simulation, utilizing digital computers. The discipline combines theoretical and applied mechanics, approximation theory, numerical analysis, and computer science. Computational mechanics has had a major impact on engineering analysis and design. When applied to structural mechanics, the discipline is referred to herein as computational structural mechanics. Complex structures being considered by NASA for the 1990's include composite primary aircraft structures and the space station. These structures will be much more difficult to analyze than today's structures and necessitate a major upgrade in computerized structural analysis technology. NASA has initiated a research activity in structural analysis called Computational Structural Mechanics (CSM). The broad objective of the CSM activity is to develop advanced structural analysis technology that will exploit modern and emerging computers, such as those with vector and/or parallel processing capabilities. Here, the current research directions for the Methods and Application Studies Team of the Langley CSM activity are described.

Knight, Norman F., Jr.↗

NASA NTRS1988

Element-by-element and implicit-explicit finite element formulations for computational fluid dynamics

Preconditioner algorithms to reduce the computational effort in FEM analyses of large-scale fluid-dynamics problems are presented. A general model problem is constructed on the basis of the convection-diffusion equation and the two-dimensional vorticity/stream-function formulation of the Navier-Stokes equations; this problem is then analyzed using element-by-element, implicit-explicit, and adaptive implicit-explicit approximation schemes. Numerical results for the two-dimensional advection and rigid-body rotation of a cosine hill, flow past a circular cylinder, and driven cavity flow are presented in extensive graphs and shown to be in good agreement with those obtained using implicit methods.

Tezduyar, T. E.↗

NASA NTRS1988

An approximation technique for computing optimal fixed-order controllers for infinite-dimensional systems

The finite-dimensional approximation of the infinite-dimensional Bernstein/Hyland optimal projection theory is investigated analytically. The approach yields fixed-finite-order controllers which are optimal with respect to high-order approximating finite-dimensional plant models. The technique is illustrated by computing a sequence of first-order controllers for a one-dimensional SISO parabolic (heat/diffusion) system using a spline-based Ritz-Galerkin finite-element approximation. The numerical studies indicate convergence of the feedback gains with less than 2-percent performance degradation over full-order LQG controllers.

Bernstein, Dennis S.↗

NASA NTRS1990

Navier-Stokes computations of vortex asymmetries controlled by small surface imperfections

Navier-Stokes analyses are employed to explore the driving mechanisms controlling asymmetric vortical flows with Re(D) = 0.8 million (Reynolds number based on maximum diameter) over a 3.5 caliber tangent-ogive cylinder at large angles of attack (alpha = 20, 30, and 40 degrees). All flowfield results are steady-state solutions to the three-dimensional, incompressible Navier-Stokes equations in the thin-layer approximation. The numerical results are temporally and spatially fully converged, and are in good agreement with experimental data. The major findings are: (1) for alpha not less than 30 degrees, the vortex flows are genuinely asymmetric yet recurrent; (2) asymmetric vortex patterns are highly sensitive toward such parameters as machine accuracy, grid topology, etc., unless triggered by a slight deformation (similar to an out-of-round nose tip) in the neighborhood of the apex; and (3) for alpha = 20 degrees, the flow is symmetric for both circular and elliptic cross-sectional shapes of the nose tip.

Hartwich, PETER-M.↗

NASA NTRS1990

Resonant decay of global MHD modes at 'thick' interfaces

A global surface mode can exist on a 'surface' which is not a true discontinuity, but without sufficient dissipation it is not a normal mode and it decays in time via resonance absorption. The decay rate can be calculated analytically when the 'surface' is thin. The goal of this paper is to numerically estimate the decay rate when the surface is not thin. A cold plasma in a uniform magnetic field is considered in which density varies linearly across the 'surface'. In this linearized calculation, the global surface mode is driven in steady state by an antenna located in one of the uniform regions external to the surface. The frequency is a free parameter, and resonance curves are computed numerically without approximations. The widths of the resonance curves are used to estimate the free decay times of undriven surface modes, via the uncertainty principle. When applied to the active solar corona, the decay rates are large enough to account for the coronal heating, but it should be kept in mind that the role of nonlinearity in resonance absorption is still undetermined.

Hollweg, Joseph V.↗

NASA NTRS1990

Spherically symmetric near-critical accretion onto neutron stars

Numerical and approximate analytic solutions for time-independent, spherically symmetric, radiation pressure-dominated accretion flows are presented. For flows with luminosities at infinity, L-infinity, sufficiently close to the Eddington limit L-crit, the flow velocity profile is qualitatively different from the modified free-fall profile v(r) = (1 - L-infinity/L-crit)exp 1/2 (2GM/r)exp 1/2. Advective contributions to the comoving radiation flux decelerate the flow within a criical radius, and, in this settling region, the velocity of the flow decreases linearly with decreasing radius.

Miller, Guy S.↗

NASA NTRS1991

Transpiration Cooling Of Hypersonic Blunt Body

Results on analytical approximation and numerical simulation compared. Report presents theoretical study of degree to which transpiration blocks heating of blunt, axisymmetric body by use of injected air. Transpiration cooling proposed to reduce operating temperatures on nose cones of proposed hypersonic aerospace vehicles. Analyses important in design of thermal protection for such vehicles.

Henline, William D.↗

NASA NTRS1992

Experimental measurement of the orbital paths of particles sedimenting within a rotating viscous fluid as influenced by gravity

Measurements were taken of the path of a simulated typical tissue segment or 'particle' within a rotating fluid as a function of gravitational strength, fluid rotation rate, particle sedimentation rate, and particle initial position. Parameters were examined within the useful range for tissue culture in the NASA rotating wall culture vessels. The particle moves along a nearly circular path through the fluid (as observed from the rotating reference frame of the fluid) at the same speed as its linear terminal sedimentation speed for the external gravitational field. This gravitationally induced motion causes an increasing deviation of the particle from its original position within the fluid for a decreased rotational rate, for a more rapidly sedimenting particle, and for an increased gravitational strength. Under low gravity conditions (less than 0.1 G), the particle's motion through the fluid and its deviation from its original position become negligible. Under unit gravity conditions, large distortions (greater than 0.25 inch) occur even for particles of slow sedimentation rate (less than 1.0 cm/sec). The particle's motion is nearly independent of the particle's initial position. Comparison with mathematically predicted particle paths show that a significant error in the mathematically predicted path occurs for large particle deviations. This results from a geometric approximation and numerically accumulating error in the mathematical technique.

Wolf, David A.↗

NASA NTRS1992

Computation of unsteady flows over airfoils

Two methods are described for calculating unsteady flows over rapidly pitching airfoils. The first method is based on an interactive scheme in which the inviscid flow is obtained by a panel method. The boundary layer flow is computed by an interactive method that makes use of the Hilbert integral to couple the solutions of the inviscid and viscous flow equations. The second method is based on the solution of the compressible Navier-Stokes equations. The solution of these equations is obtained with an approximately factorized numerical algorithm, and with single block or multiple grids which enable grid embedding to enhance the resolution at isolated flow regions. In addition, the attached flow region can be computed by the numerical solution of compressible boundary layer equations. Unsteady pressure distributions obtained with both methods are compared with available experimental data.

Ekaterinaris, J. A.↗

NASA NTRS1994

Analysis of the early spectra and light curve of SN 1987A

Numerical modeling of supernova spectra, light curves, and hydrodynamics requires physical inputs, numerical techniques, approximations, and assumptions which must be thoroughly understood in order to study the details of supernova explosions. Here, we discuss some of these in the context of the early evolution of supernova 1987A. Gray radiation-hydrodynamics is used to calculate the bolometric light curve and the hydrodynamic evolution of the supernova. Synthetic spectra are then obtained for the resulting density and velocity structure. The spectrum calculations are performed using a special-relativistic treatment of the radiative transfer equation in the comoving frame, line blanketing by about 10(exp 5) spectral lines, and departures from local thermodynamic equilibrium (LTE) for H I, He I, Mg II, and Ca II. We find that we are able to simultaneously fit the early light curve and spectra reasonably well, using a progenitor model from Arnett (1991a), without fine-tuning the free parameters. Temperature structures and radiative equilibrium, non-LTE effects, homologous expansion, and mean opacities are discussed.

Hauschildt, Peter H.↗

NASA NTRS1994

A Numerical Comparison of Barrier and Modified Barrier Methods for Large-Scale Bound-Constrained Optimization

When a classical barrier method is applied to the solution of a nonlinear programming problem with inequality constraints, the Hessian matrix of the barrier function becomes increasingly ill-conditioned as the solution is approached. As a result, it may be desirable to consider alternative numerical algorithms. We compare the performance of two methods motivated by barrier functions. The first is a stabilized form of the classical barrier method, where a numerically stable approximation to the Newton direction is used when the barrier parameter is small. The second is a modified barrier method where a barrier function is applied to a shifted form of the problem, and the resulting barrier terms are scaled by estimates of the optimal Lagrange multipliers. The condition number of the Hessian matrix of the resulting modified barrier function remains bounded as the solution to the constrained optimization problem is approached. Both of these techniques can be used in the context of a truncated-Newton method, and hence can be applied to large problems, as well as on parallel computers. In this paper, both techniques are applied to problems with bound constraints and we compare their practical behavior.

Nash, Stephen G.↗

NASA NTRS2000

Giant Impacts and the Distribution of Planetary Obliquities

We have conducted a set of approximately 200 numerical experiments to test the hypothesis that a giant impact leading to the formation of Earth's Moon could have occurred tens of millions of years after most of the small debris in the inner Solar System had been incorporated into terrestrial planets or been removed from the region. More than half of these simulations ended with a giant impact between two of the five terrestrial planets that were initially present. Neglecting any rotational angular momentum prior to the collision, the merged planet typically has a rotation period of less than five hours. The mean planetary obliquity is 91.7 degrees, and the median is 87.9 degrees; thus, there is no statistically significant difference between the number of bodies with prograde rotation and the number with retrograde rotation. There is a paucity of planets with obliquity close to 90 degrees, but the total number of impacts was too small for this result to be of much significance. Several encounters leading to collisions are dominated by three-body effects, with the velocity at impact being slightly less than the free-space escape velocity of the two bodies; the obliquity distribution produced by these impacts appears to be random.

Lissauer, Jack J.↗

NASA NTRS2001

Studies of Fundamental Particle Dynamics in Microgravity

This work summarizes theoretical and experimental concepts used to design the flight experiment mission for SHIVA - Spaceflight Holography Investigation in a Virtual Apparatus. SHIVA is a NASA project that exploits a unique, holography-based, diagnostics tool to understand the behavior of small particles subjected to transient accelerations. The flight experiments are designed for testing model equations, measuring g, g-jitter, and other microgravity phenomena. Data collection will also include experiments lying outside of the realm of existing theory. The regime under scrutiny is the low Reynolds number, Stokes regime or creeping flow, which covers particles and bubbles moving at very low velocity. The equations describing this important regime have been under development and investigation for over 100 years and yet a complete analytical solution of the general equation had remained elusive yielding only approximations and numerical solutions. In the course of the ongoing NASA NRA, the first analytical solution of the general equation was produced by members of the investigator team using the mathematics of fractional derivatives. This opened the way to an even more insightful and important investigation of the phenomena in microgravity. Recent results include interacting particles, particle-wall interactions, bubbles, and Reynolds numbers larger than unity. The Space Station provides an ideal environment for SHIVA. Limited ground experiments have already confirmed some aspects of the theory. In general the space environment is required for the overall experiment, especially for cases containing very heavy particles, very light particles, bubbles, collections of particles and for characterization of the space environment and its effect on particle experiments. Lightweight particles and bubbles typically rise too fast in a gravitational field and heavy particles sink too fast. In a microgravity environment, heavy and light particles can be studied side-by-side for long periods of time.

Rangel, Roger↗

NASA NTRS2001

SHIVA-(Spaceflight Holography in a Virtual Apparatus)

SHIVA (Spaceflight Holography Investigation in a Virtual Apparatus) will expand our understanding of the fundamental physics of particle movement in fluids by exploiting the power of holography in a spaceflight experiment'. In addition, the study will exploit the movement of particles in fluids to observe and quantify microgravity phenomena that are extremely important in materials sciences with applications both in space and on earth. The regime under scrutiny is the low Reynolds number, Stokes regime or creeping flow, which covers particles and bubbles moving at very low velocity. The equations describing this important regime have been under development and investigation for over 100 years and yet a complete analytical solution of the general equation had remained elusive yielding only approximations and numerical solutions. In the course of the ongoing NASA NRA, the first analytical solution of the general equation was produced by members of the investigator team using the mathematics of fractional derivatives. This opened the way to an even more insightful and important investigation of the phenomena in microgravity.

Trolinger, James D.↗