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NASA NTRS1990

Numerical simulations of the decay of Martian global dust storms

The decay of Martian global (great) dust storms is investigated. One-dimensional (vertical, static atmosphere) and two-dimensional (latitude-height, steady state circulation) simulations carried out with an aerosol transport-microphysical model indicate that atmospheric motions play a significant role in the observed decay of global dust storms. Spacecraft observations (Mariner 9, Viking) of the 1971 and the two 1977 planet-encircling dust storms have provided suggestions about some characteristics of storm decay. Specifically, the dust particle size distribution is inferred to have remained essentially unchanged for particles with radii between 1 and 10 microns during decay of the 1971 storm, and surface visible opacity declined quasi-exponentially with time in northern midlatitudes during the decay of the two 1977 storms. The results from this investigation indicate that two- and three-dimensional dynamical processes play a significant role the observed decay features of Martian global dust storms. The most important processes are the lofting of dust by vertical motions in the dust source region of the Southern Hemisphere subtropics and a continuing advective resupply of atmospheric dust into the dust sink regions of the Northern Hemisphere. This work has implications for Viking data analyses and future Mars observer observations and requires that the particle size distribution be treated as a time and latitude dependent quantity.

Murphy, James R.↗
NASA NTRS1990

Hypersonic vehicle simulation model: Winged-cone configuration

Aerodynamic, propulsion, and mass models for a generic, horizontal-takeoff, single-stage-to-orbit (SSTO) configuration are presented which are suitable for use in point mass as well as batch and real-time six degree-of-freedom simulations. The simulations can be used to investigate ascent performance issues and to allow research, refinement, and evaluation of integrated guidance/flight/propulsion/thermal control systems, design concepts, and methodologies for SSTO missions. Aerodynamic force and moment coefficients are given as functions of angle of attack, Mach number, and control surface deflections. The model data were estimated by using a subsonic/supersonic panel code and a hypersonic local surface inclination code. Thrust coefficient and engine specific impulse were estimated using a two-dimensional forebody, inlet, nozzle code and a one-dimensional combustor code and are given as functions of Mach number, dynamic pressure, and fuel equivalence ratio. Rigid-body mass moments of inertia and center of gravity location are functions of vehicle weight which is in turn a function of fuel flow.

Shaughnessy, John D.↗
NASA NTRS1991

Latitudinal dynamics of steady solar wind flows

In many previous studies, it has been assumed that the streamlines of the solar wind are in a purely radial direction beyond a few solar radii. Therefore, the nonradial modulations by the magnetic force and gas pressure is neglected at large heliocentric distances. The work reported in this paper includes a two-dimensional magnetohydrodynamic (MHD) study of the latitudinal structure of solar wind flows. The dynamical effects of the interplanetary magnetic field (IMF) are investigated by MHD solutions and by comparing them with both one-dimensional and two-dimensional hydrodynamic (HD) solutions. The corotational effect of the sun and the influence of transient events in the solar atmosphere are neglected. With such a simplification, the latitudinal structure of the steady solar wind is controlled by the dynamic balance of the magnetic force and the gas pressure. Several different patterns of the evolution of the solar wind latitudinal structure are exhibited in the calculation. The results indicate the existence of a proton number density maximum at the magnetic neutral line, whether or not there is a density maximum or minimum at the inner boundary. The drift motion of magnetic field lines toward the magnetic neutral line enhances the magnetic field strength around the neutral sheet, which may provide a possible explanation of the discrepancy between the measured IMF at 1 AU and that extrapolated from the photospheric magnetic field by the current source-surface modeling.

Yang, W.-H.↗
NASA NTRS1991

Nighttime reactive nitrogen measurements from stratospheric infrared thermal emission observations

IR thermal emission spectra of the earth's atmosphere in the 700-2000/cm region were obtained with a cryogenically cooled high-resolution interferometer spectrometer on a balloon flight from Palestine, Texas, on September 15-16, 1986. The observations exhibit spectral features of a number of stratospheric constituents, including important species of the reactive nitrogen family. An analysis of the observed data for simultaneously measured vertical distributions of O3, H2O, N2O, NO2, N2O5, HNO3, and ClONO2 is presented. These measurements permit the first direct determination of the nighttime total reactive nitrogen concentrations, and the partitioning of the important elements of the NO(x) family. Comparisons of the total reactive nitrogen budget are made with the measurements by the ATMOS experiment and with the predictions of one-dimensional and two-dimensional photochemical models.

Abbas, Mian M.↗
NASA NTRS1992

Progress in multi-dimensional upwind differencing

Multi-dimensional upwind-differencing schemes for the Euler equations are reviewed. On the basis of the first-order upwind scheme for a one-dimensional convection equation, the two approaches to upwind differencing are discussed: the fluctuation approach and the finite-volume approach. The usual extension of the finite-volume method to the multi-dimensional Euler equations is not entirely satisfactory, because the direction of wave propagation is always assumed to be normal to the cell faces. This leads to smearing of shock and shear waves when these are not grid-aligned. Multi-directional methods, in which upwind-biased fluxes are computed in a frame aligned with a dominant wave, overcome this problem, but at the expense of robustness. The same is true for the schemes incorporating a multi-dimensional wave model not based on multi-dimensional data but on an 'educated guess' of what they could be. The fluctuation approach offers the best possibilities for the development of genuinely multi-dimensional upwind schemes. Three building blocks are needed for such schemes: a wave model, a way to achieve conservation, and a compact convection scheme. Recent advances in each of these components are discussed; putting them all together is the present focus of a worldwide research effort. Some numerical results are presented, illustrating the potential of the new multi-dimensional schemes.

Vanleer, Bram↗
NASA NTRS1992

Formation and stability of the self-consistent one-dimensional tail current sheet

The paper investigates the formation, the structure, and the stability of self-consistent one-dimensional current sheets in which the ions carry most of the current and momentum (the occurrence of which was suggested by observations of Mitchell et al., 1990; and Sergeev et al., 1990). Results of the analysis showed that, for the case of a cold current sheet, the characteristic thickness lamba equals to about (Bz/B0) exp 4/3 c/omega(p0), where Bz is the normal field component, B0 is the asymptotic magnitude of the reversing field, and c/omega(p0)is the collisionless ion skin depth based on lobe density. A two-dimensional self-consistent dynamical simulation model is developed, which demonstrates that these idealized current sheets are unstable to kink perturbations driven by the anisotropic pressure distribution produced by the chaotic nature of the particle orbits in a field-reversal region.

Pritchett, P. L.↗
NASA NTRS1991

An experimental and analytical investigation on the response of GR/EP composite I-frames

Six-foot diameter, semicircular graphite/epoxy specimens representative of generic aircraft frames were loaded quasi-statically to determine their load response and failure mechanisms for large deflections that occur in an airplane crash. These frame-skin specimens consisted of a cylindrical skin section cocured with a semicircular I-frame. Various frame laminate stacking sequences and geometries were evaluated by statically loading the specimen until multiple failures occurred. Two analytical methods were compared for modeling the frame-skin specimens: a two-dimensional branched-shell finite element analysis and a one-dimensional, closed-form, curved beam solution derived using an energy method. Excellent correlation was obtained between experimental results and the finite element predictions of the linear response of the frames prior to the initial failure. The beam solution was used for rapid parameter and design studies, and was found to be stiff in comparison with the finite element analysis. The specimens were found to be useful for evaluating composite frame designs.

Moas, E., Jr.↗
NASA NTRS1993

High-resolution imaging gamma-ray spectroscopy with externally segmented germanium detectors

Externally segmented germanium detectors promise a breakthrough in gamma-ray imaging capabilities while retaining the superb energy resolution of germanium spectrometers. An angular resolution of 0.2 deg becomes practical by combining position-sensitive germanium detectors having a segment thickness of a few millimeters with a one-dimensional coded aperture located about a meter from the detectors. Correspondingly higher angular resolutions are possible with larger separations between the detectors and the coded aperture. Two-dimensional images can be obtained by rotating the instrument. Although the basic concept is similar to optical or X-ray coded-aperture imaging techniques, several complicating effects arise because of the penetrating nature of gamma rays. The complications include partial transmission through the coded aperture elements, Compton scattering in the germanium detectors, and high background count rates. Extensive electron-photon Monte Carlo modeling of a realistic detector/coded-aperture/collimator system has been performed. Results show that these complicating effects can be characterized and accounted for with no significant loss in instrument sensitivity.

Callas, J. L.↗
NASA NTRS1992

Helicopter response to atmospheric turbulence

A new time-domain method for simulating cyclostationary turbulence as seen by a translating and rotating blade element has recently been developed for the case of one-dimensional spectral distribution. This paper extends the simulation method to the cases of two- and three-dimensional spectral distributions and presents validation results for the two-dimensional case. The statistics of an isolated rigid blade flapping response to turbulence are computed using a two-dimensional spectral representation of the von Karman turbulence model, and the results are compared with those obtained using the conventional space-fixed turbulence analysis. The new turbulence simulation method is used for predicting the Black Hawk helicopter response to atmospheric turbulence.

Riaz, J.↗
NASA NTRS1993

Accurate upwind methods for the Euler equations

A new class of piecewise linear methods for the numerical solution of the one-dimensional Euler equations of gas dynamics is presented. These methods are uniformly second-order accurate, and can be considered as extensions of Godunov's scheme. With an appropriate definition of monotonicity preservation for the case of linear convection, it can be shown that they preserve monotonicity. Similar to Van Leer's MUSCL scheme, they consist of two key steps: a reconstruction step followed by an upwind step. For the reconstruction step, a monotonicity constraint that preserves uniform second-order accuracy is introduced. Computational efficiency is enhanced by devising a criterion that detects the 'smooth' part of the data where the constraint is redundant. The concept and coding of the constraint are simplified by the use of the median function. A slope steepening technique, which has no effect at smooth regions and can resolve a contact discontinuity in four cells, is described. As for the upwind step, existing and new methods are applied in a manner slightly different from those in the literature. These methods are derived by approximating the Euler equations via linearization and diagonalization. At a 'smooth' interface, Harten, Lax, and Van Leer's one intermediate state model is employed. A modification for this model that can resolve contact discontinuities is presented. Near a discontinuity, either this modified model or a more accurate one, namely, Roe's flux-difference splitting. is used. The current presentation of Roe's method, via the conceptually simple flux-vector splitting, not only establishes a connection between the two splittings, but also leads to an admissibility correction with no conditional statement, and an efficient approximation to Osher's approximate Riemann solver. These reconstruction and upwind steps result in schemes that are uniformly second-order accurate and economical at smooth regions, and yield high resolution at discontinuities.

Huynh, Hung T.↗
NASA NTRS1994

Active minimization of energy density in three-dimensional enclosures

The objective of this research project is to further investigate and develop a novel approach for actively controlling the sound field in enclosures. Typically the acoustic field in an enclosure has been controlled by minimizing the sum of the squared pressures from several microphones distributed throughout the enclosure. The approach being investigated in this project involves minimizing the acoustic energy density at the sensor locations, rather than the squared pressure. Previous research in a simple one-dimensional enclosure showed that improved global attenuation of the acoustic field is often obtained by minimizing the energy density, rather than the pressure. The current project builds on the previous research by extending the method of controlling the acoustic energy density to three-dimensional enclosures. The results will establish if improved control can still be expected in a more general enclosure. Pending successful results, the method could be applied to control problems such as attenuating the acoustic noise in an aircraft fuselage, an automobile cabin, or other general enclosures. The research project was set up as a two-year project designed to achieve both numerical and experimental results. The primary focus of the first year of research (now being completed) was on the analytical/numerical modeling of the method of controlling the acoustic energy density. During the second year, the research focuses on experimental verification of the approach and extending our understanding of the method.

Sommerfeldt, Scott D.↗
NASA NTRS1993

A generic efficient adaptive grid scheme for rocket propulsion modeling

The objective of this research is to develop an efficient, time-accurate numerical algorithm to discretize the Navier-Stokes equations for the predictions of internal one-, two-dimensional and axisymmetric flows. A generic, efficient, elliptic adaptive grid generator is implicitly coupled with the Lower-Upper factorization scheme in the development of ALUNS computer code. The calculations of one-dimensional shock tube wave propagation and two-dimensional shock wave capture, wave-wave interactions, shock wave-boundary interactions show that the developed scheme is stable, accurate and extremely robust. The adaptive grid generator produced a very favorable grid network by a grid speed technique. This generic adaptive grid generator is also applied in the PARC and FDNS codes and the computational results for solid rocket nozzle flowfield and crystal growth modeling by those codes will be presented in the conference, too. This research work is being supported by NASA/MSFC.

Mo, J. D.↗
NASA NTRS1993

Preconditioning for the Navier-Stokes equations with finite-rate chemistry

The extension of Van Leer's preconditioning procedure to generalized finite-rate chemistry is discussed. Application to viscous flow is begun with the proper preconditioning matrix for the one-dimensional Navier-Stokes equations. Eigenvalue stiffness is resolved and convergence-rate acceleration is demonstrated over the entire Mach-number range from nearly stagnant flow to hypersonic. Specific benefits are realized at the low and transonic flow speeds typical of complete propulsion-system simulations. The extended preconditioning matrix necessarily accounts for both thermal and chemical nonequilibrium. Numerical analysis reveals the possible theoretical improvements from using a preconditioner for all Mach number regimes. Numerical results confirm the expectations from the numerical analysis. Representative test cases include flows with previously troublesome embedded high-condition-number areas. Van Leer, Lee, and Roe recently developed an optimal, analytic preconditioning technique to reduce eigenvalue stiffness over the full Mach-number range. By multiplying the flux-balance residual with the preconditioning matrix, the acoustic wave speeds are scaled so that all waves propagate at the same rate, an essential property to eliminate inherent eigenvalue stiffness. This session discusses a synthesis of the thermochemical nonequilibrium flux-splitting developed by Grossman and Cinnella and the characteristic wave preconditioning of Van Leer into a powerful tool for implicitly solving two and three-dimensional flows with generalized finite-rate chemistry. For finite-rate chemistry, the state vector of unknowns is variable in length. Therefore, the preconditioning matrix extended to generalized finite-rate chemistry must accommodate a flexible system of moving waves. Fortunately, no new kind of wave appears in the system. The only existing waves are entropy and vorticity waves, which move with the fluid, and acoustic waves, which propagate in Mach number dependent directions. The nonequilibrium vibrational energies and species densities in the unknown state vector act strictly as convective waves. The essential concept for extending the preconditioning to generalized chemistry models is determining the differential variables which symmetrize the flux Jacobians. The extension is then straight-forward. This algorithm research effort will be released in a future version of the production level computational code coined the General Aerodynamic Simulation Program (GASP), developed by Walters, Slack, and McGrory.

Godfrey, Andrew G.↗
NASA NTRS1994

Nonaxisymmetric evolution in protostellar disks

We present a two-dimensional, multigridded hydrodynamical simulation of the collapse of an axisymmetric, rotating, 1 solar mass protostellar cloud, which forms a resolved, hydrotastic disk. The code includes the effects of physical viscosity, radiative transfer and radiative acceleration but not magnetic fields. We examine how the disk is affected by the inclusion of turbulent viscosity by comparing a viscous simulation with an inviscid model evolved from the same initial conditions, and we derive a disk evolutionary timescale on the order of 300,000 years if alpha = 0.01. Effects arising from non-axisymmetric gravitational instabilities in the protostellar disk are followed with a three-dimensional SPH code, starting from the two-dimensional structure. We find that the disk is prone to a series of spiral instabilities with primary azimulthal mode number m = 1 and m = 2. The torques induced by these nonaxisymmetric structures elicit material transport of angular momentum and mass through the disk, readjusting the surface density profile toward more stable configurations. We present a series of analyses which characterize both the development and the likely source of the instabilities. We speculate that an evolving disk which maintains a minimum Toomre Q-value approximately 1.4 will have a total evolutionary span of several times 10(exp 5) years, comparable to, but somewhat shorter than the evolutionary timescale resulting from viscous turbulence alone. We compare the evolution resulting from nonaxisymmetric instabilities with solutions of a one-dimensional viscous diffusion equation applied to the initial surface density and temperature profile. We find that an effective alpha-value of 0.03 is a good fit to the results of the simulation. However, the effective alpha will depend on the minimum Q in the disk at the time the instability is activated. We argue that the major fraction of the transport characterized by the value of alpha is due to the action of gravitational torques, and does not arise from inherent viscosity within the smoothed particle hydrodynamics method.

Laughlin, Gregory↗
NASA NTRS1994

Superconducting axisymmetric finite elements based on a gauged potential variational principle. Part 1: Formulation

The present work is part of a research program for the numerical simulation of electromagnetic (EM) fields within conventional Ginzburg-Landau (GL) superconductors. The final goal of this research is to formulate, develop and validate finite element (FE) models that can accurately capture electromagnetic thermal and material phase changes in a superconductor. The formulations presented here are for a time-independent Ginzburg-Landau superconductor and are derived from a potential-based variational principle. We develop an appropriate variational formulation of time-independent supercontivity for the general three-dimensional case and specialize it to the one-dimensional case. Also developed are expressions for the material-dependent parameters alpha and beta of GL theory and their dependence upon the temperature T. The one-dimensional formulation is then discretized for finite element purposes and the first variation of these equations is obtained. The resultant Euler equations contain nonlinear terms in the primary variables. To solve these equations, an incremental-iterative solution method is used. Expressions for the internal force vector, external force vector, loading vector and tangent stiffness matrix are therefore developed for use with the solution procedure.

Schuler, James J.↗
NASA NTRS1994

An analytical and experimental investigation of the response of the curved, composite frame/skin specimens

Six-foot diameter, semicircular graphite/epoxy specimens representative of generic aircraft frames were loaded quasi-statistically to determine their load response and failure mechanisms for large deflections that occur in airplanes crashes. These frame/skin specimens consisted of a cylindrical skin section co-cured with a semicircular I-frame. The skin provided the necessary lateral stiffness to keep deformations in the plane of the frame in order to realistically represent deformations as they occur in actual fuselage structures. Various frame laminate stacking sequences and geometries were evaluated by statically loading the specimen until multiple failures occurred. Two analytical methods were compared for modeling the frame/skin specimens: a two-dimensional shell finite element analysis and a one-dimensional, closed-form, curved beam solution derived using an energy method. Flange effectivities were included in the beam analysis to account for the curling phenomenon that occurs in thin flanges of curved beams. Good correlation was obtained between experimental results and the analytical predictions of the linear response of the frames prior to the initial failure. The specimens were found to be useful for evaluating composite frame designs.

Moas, Eduardo↗
NASA NTRS1995

Convergence properties of finite-difference hydrodynamics schemes in the presence of shocks

We investigate the asymptotic convergence of finite-difference schemes for the Euler equations when the limiting solution contains shocks. The Lax-Wendroff theorem guarantees that certain conservative schemes converge to correct, physically valid solutions. We focus on two one-dimensional operator-split schemes with explicit artificial-viscosity terms. One, an internal-energy scheme, does not satisfy the assumptions of Lax-Wendroff; the other, a conservative total-energy scheme, does. With viscous lengths chosen proportional to the grid size, we find that both schemes converge to their zero-grid-size limits at the theoretically expected rate, but only the conversative scheme converges toward correct solutions of the inviscid fluid equations. We show that the difference in their behaviors results directly from the presence of shocks in the limiting solution. Empirically, we find that when the viscous lenghts tend toward zero more slowly than the grid size, however the nonconservative scheme also converges toward correct solutions. We characterize the asymptotic behavior of the total-energy scheme in a particular problem in which a shock forms. As the grid is refined, a Cauchy error approaches the expected rate of change slowly. We show that the changes in the artificial viscosity alter the diffusion of small-amplitude waves. The differences associated with such waves make the dominant contribution to the Cauchy error. We formulate an analytic model to relate the rate of approach to the effect of varying diffusion in waves and find quantitative agreement with our numerical results.

Kimoto, Paul A.↗
NASA NTRS1994

VHF radar and rocket observations of equatorial spread F on Kwajalein

VHF radar data from the Summer 1990 Equatorial Spread F campaign on Kwajalein are presented. The Cornell 50 MHz portable radar interferometer (CUPRI) operated concurrently with the Altair UHF incoherent scatter radar throughout July and August and supported two sounding rocket flights on July 30 and August 2. This experiment provided the first opportunity to simultaneously diagnose equatorial spread F using the three prime experimental techniques: VHF/UHF coherent scatter, incoherent scatter, and in situ probe measurements of electric field and density fluctuations. The intensity of the coherent echoes observed was consistent with typical Jicamarca spread F observations, but chains of periodic, large-scale plasma upwellings were observed more often and for much longer durations on Kwajalein than have been seen over Peru. CUPRI also measured Doppler frequencies in one upwelling corresponding to 1200-m/s plasma drift velocities. This measurement agrees with recent observations of supersonic drift rates at the magnetic equator by spacecraft. Near the most active localized plasma upwellings, interferometer data reveal that the zonal drift rate of plasma irregularities can vary sharply in space, as one would expect for two-dimensional incompressible flow. We introduce a semiempirical model of the three-dimensional spectrum of F region irregularities that is consistent with the one-dimensional spectra of density fluctuations observed by sounding rockets and with the axial ratio of irregularities determined recently. Normalized to data from one of the rocket flights on Kwajalein, the model predicts the 3-m scattering cross-section measured by CUPRI to within a few decibels.

Hysell, D. L.↗