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NASA NTRS1995

Evaluation of numerical schemes for the analysis of sound generation by blade-gust interaction

In this investigation three different numerical algorithms have been utilized to compute the flow about a flat plate in the presence of a transverse gust described by a sinusoidal disturbance. The three schemes include the MacCormack explicit finite difference scheme which is second order accurate in both time and space, the Gottlieb and Turkel modification of MacCormack's scheme which is fourth order accurate in space and second order accurate in time, (referred to as the 2-4 scheme), and a two step scheme developed by Bayliss et al. which has second order temporal accuracy and sixth order spatial accuracy (a 2-6 scheme). The flow field results are obtained with these schemes by using the same code with the only difference being the implementation of the respective solution algorithms. The problem is set up so that the sinusoidal disturbance is imposed at the surface of the flat plate as a surface boundary condition. Thus the problem is treated as scattering problem. The computed results include the time average of the acoustic pressure squared along grid lines five points away from the boundaries; distribution throughout the computational domain is monitored at various times. The numerical results are compared with an exact solution obtained by Atassi, Dusey, and Davis.

Scott, J. N.↗
NASA NTRS1993

Numerical simulation of shock/turbulent boundary layer interaction

Most flows of aerodynamic interest are compressible and turbulent. However, our present knowledge on the structures and mechanisms of turbulence is mostly based on incompressible flows. In the present work, compressibility effects in turbulent, high-speed, boundary layer flows are systematically investigated using the Direct Numerical Simulation (DNS) approach. Three-dimensional, time-dependent, fully nonlinear, compressible Navier-Stokes equations were numerically integrated by high-order finite-difference methods; no modeling for turbulence is used during the solution because the available resolution is sufficient to capture the relevant scales. The boundary layer problem deals with fully-turbulent compressible flows over flat geometries. Apart from its practical relevance to technological flows, turbulent compressible boundary layer flow is the simplest experimentally realizable turbulent compressible flow. Still, measuring difficulties prohibit a detailed experimental description of the flow, especially in the near-wall region. DNS studies provide a viable means to probe the physics of compressible turbulence in this region. The focus of this work is to explore the paths of energy transfer through which compressible turbulence is sustained. The structural similarities and differences between the incompressible and compressible turbulence are also investigated. The energy flow patterns or energy cascades are found to be directly related to the evolution of vortical structures which are generated in the near-wall region. Near-wall structures, and mechanisms which are not readily accessible through physical experiments are analyzed and their critical role on the evolution and the behavior of the flow is documented extensively.

Biringen, Sedat↗
NASA NTRS1995

Numerical solution of the full potential equation using a chimera grid approach

A numerical scheme utilizing a chimera zonal grid approach for solving the full potential equation in two spatial dimensions is described. Within each grid zone a fully-implicit approximate factorization scheme is used to advance the solution one interaction. This is followed by the explicit advance of all common zonal grid boundaries using a bilinear interpolation of the velocity potential. The presentation is highlighted with numerical results simulating the flow about a two-dimensional, nonlifting, circular cylinder. For this problem, the flow domain is divided into two parts: an inner portion covered by a polar grid and an outer portion covered by a Cartesian grid. Both incompressible and compressible (transonic) flow solutions are included. Comparisons made with an analytic solution as well as single grid results indicate that the chimera zonal grid approach is a viable technique for solving the full potential equation.

Holst, Terry L.↗
NASA NTRS1995

An efficient numerical procedure for thermohydrodynamic analysis of cavitating bearings

An efficient and accurate numerical procedure to determine the thermo-hydrodynamic performance of cavitating bearings is described. This procedure is based on the earlier development of Elrod for lubricating films, in which the properties across the film thickness are determined at Lobatto points and their distributions are expressed by collocated polynomials. The cavitated regions and their boundaries are rigorously treated. Thermal boundary conditions at the surfaces, including heat dissipation through the metal to the ambient, are incorporated. Numerical examples are presented comparing the predictions using this procedure with earlier theoretical predictions and experimental data. With a few points across the film thickness and across the journal and the bearing in the radial direction, the temperature profile is very well predicted.

Vijayaraghavan, D.↗
NASA NTRS1995

Numerical simulation of heat and mass transport during space crystal growth with MEPHISTO

The MEPHISTO space experiments are collaborative United States and French investigations aimed at understanding the fundamentals of crystal growth. Microgravity experiments were conducted aboard the USMP-1 and -2 missions on STS-52 and 62 in October 1992 and March 1994 respectively. MEPHISTO is a French designed and built Bridgman type furnace which uses the Seebeck technique to monitor the solid/liquid interface temperature and Peltier pulsing to mark the location and shape of the solid/liquid interface. In this paper the Bridgman growth of Sn-Bi and Bi-Sn under terrestrial and microgravity conditions is modeled using the finite element code, FIDAP*. The numerical model considers fully coupled heat and mass transport, fluid motion and solid/liquid phase changes in the crystal growth process. The primary goals of this work are: to provide a quantitative study of the thermal buoyancy-induced convection in the melt for the two flight experiments; to compare the vertical and horizontal growth configurations and systematically evaluate the effects of various gravity levels on the solute segregation. Numerical results of the vertical and horizontal Bridgman growth configurations are presented.

Yao, Minwu↗
NASA NTRS1994

A satellite observational and numerical study of precipitation characteristics in western North Atlantic tropical cyclones

Special Sensor Microwave/Imager (SSM/I) observations were used to examine the spatial and temporal changes of the precipitation characteristics of tropical cyclones. SSM/I observations were also combined with the results of a tropical cyclone numerical model to examine the role of inner-core diabatic heating in subsequent intensity changes of tropical cyclones. Included in the SSM/I observations were rainfall characteristics of 18 named western North Atlantic tropical cyclones between 1987 and 1989. The SSM/I rain-rate algorithm that employed the 85-GHz channel provided an analysis of the rain-rate distribution in greater detail. However, the SSM/I algorithm underestimated the rain rates when compared to in situ techniques but appeared to be comparable to the rain rates obtained from other satellite-borne passive microwave radiometers. The analysis of SSM/I observations found that more intense systems had higher rain rates, more latent heat release, and a greater contribution from heavier rain to the total tropical cyclone rainfall. In addition, regions with the heaviest rain rates were found near the center of the most intense tropical cyclones. Observational analysis from SSM/I also revealed that the greatest rain rates in the inner-core regions were found in the right half of fast-moving cyclones, while the heaviest rain rates in slow-moving tropical cyclones were found in the forward half. The combination of SSM/I observations and an interpretation of numerical model simulations revealed that the correlation between changes in the inner core diabetic heating and the subsequent intensity became greater as the tropical cyclones became more intense.

Rodgers, Edward B.↗
NASA NTRS1994

Regional-scale flows in mountainous terrain. Part 1: A numerical and observational comparison

This study uses observed data and a numerical simulation to examine the generation of thermally driven flows across the Colorado mountain barrier on meso-beta to meso-alpha scales. The observations were collected from remote surface observing systems at exposed mountaintop locations throughout the state of Colorado, over the summers of 1984-88, as part of the Rocky Mountain Peaks Experiment (ROMPEX). The data show the development of a recurrent circulation system across the Colorado mountain barrier, operating on a diurnal timescale. From the observations, the basic structure of the flow system appears as a daytime inflow toward the highest terrain, and a nocturnal outflow away from it. However, when examined in detail, the flow system exhibits more unusual behavior, especially west of the barrier crest. Here, winds in the early evening are occasionally observed to onset abruptly from an easterly direction, generally counter to the upper-level winds. Observations from ROMPEX for 26 August 1985 are used to provide comparison data for a numerical simulation with the Regional Atmospheric Modeling System (RAMS). This three-dimensional case study experiment is initialized with data from the National Meteorological Center and incorporates two-way interactive grid nesting. From the observed data and case study simulation, four distinct phases of the regional-scale circulation system have been identified. In the development phase, a deep mountain-plains solenoid is generated through terrain heating along the Front Range. This circulation system transforms in the late afternoon transition phase into a westward-propagating density current (WPDC). The third phase, called the 'density-current propagation phase,' occurs as the WPDC moves westward across the mountains, leaving in its wake strong southeasterly flow at the mountaintop level. This current appears to be the cause of the peculiar easterly component winds found in the ROMPEX mountaintop observations along the western slope. In the final late-night adjustment phase, the WPDC dissipates near the western edge of the Colorado mountains and steady southerly flow evolves over the high mountain terrain. This southerly flow is the steady response to the differential heating that develops between the low-lying plains and the intermountain region.

Bossert, James E.↗
NASA NTRS1994

Oblique magnetohydrodynamic cosmic-ray-modified shocks: Two-fluid numerical simulations

We present the first results of time-dependent two-fluid cosmic-ray (CR) modified magnetohydrodynamic (MHD) shock simulations. The calculations were carried out with a new numerical code for one-dimensional ideal MHD. By coupling this code with the CR energy transport equation we can simulate the time-dependent evolution of MHD shocks, including the acceleration of the CR and their feedback on the shock structures. We report tests of the combined numerical method including comparisons with analytical steady state results published earlier by Webb, as well as internal consistency checks for more general MHD CR shock structures after they apppear to have converged to dynamical steady states. We also present results from an initial time-dependent simulation which extends the parameter space domain of previous analytical models. These new results support Webb's suggestion that equilibrium oblique shocks are less effective than parallel shocks in the acceleration of CR. However, for realistic models of anisotropic CR diffusion, oblique shocks may achieve dynamical equilibrium on shorter timescales than parallel shocks.

Frank, Adam↗
NASA NTRS1995

Improvements of an ice-phase microphysics parameterization for use in numerical simulations of tropical convection

It is important to properly simulate the extent and ice water content of tropical anvil clouds in numerical models that explicitly include cloud formation because of the significant effects that these clouds have on the radiation budget. For this reason, a commonly used bulk ice-phase microphysics parameterization was modified to more realistically simulate some of the microphysical processes that occur in tropical anvil clouds. Cloud ice growth by the Bergeron process and the associated formation of snow were revised. The characteristics of graupel were also modified in accord with a previous study. Numerical simulations of a tropical squall line demonstrate that the amount of cloud ice and the extent of anvil clouds are increased to more realistic values by the first two changes.

Krueger, Steven K.↗
NASA NTRS1994

Numerical simulation of incidence and sweep effects on delta wing vortex breakdown

The structure of the vortical flowfield over delta wings at high angles of attack was investigated. Three-dimensional Navier-Stokes numerical simulations were carried out to predict the complex leeward-side flowfield characteristics, including leading-edge separation, secondary separation, and vortex breakdown. Flows over a 75- and a 63-deg sweep delta wing with sharp leading edges were investigated and compared with available experimental data. The effect of variation of circumferential grid resolution grid resolution in the vicinity of the wing leading edge on the accuracy of the solutions was addressed. Furthermore, the effect of turbulence modeling on the solutions was investigated. The effects of variation of angle of attack on the computed vortical flow structure for the 75-deg sweep delta wing were examined. At moderate angles of attack no vortex breakdown was observed. When a critical angle of attack was reached, bubble-type vortex breakdown was found. With further increase in angle of attack, a change from bubble-type breakdown to spiral-type vortex breakdown was predicted by the numerical solution. The effects of variation of sweep angle and freestream Mach number were addressed with the solutions on a 63-deg sweep delta wing.

INCIDENCE↗
NASA NTRS1994

Five years' central Pacific sea level from in situ array, satellite altimeter and numerical model

Temporal and spatial fetures of central equatorial Pacific Ocean sea-level variation appear similar, in measurements from two very different systems (one in the ocean and one carried on a satellite), and in results from a numerical model of the region. In particular, there is an interannual cycle: during El Nino, Kelvin waves appear at the equator, and the sea-surface ridge associated with the equatorial current system shifts southward; in non-El Nino years, instability waves appear at 6 deg N (strongest around the end of each calendar year), and the ridge shifts to the north. This three-way comparison gives support to both measurement systems and to the numerical model.

Donohue, Kathleen A.↗
NASA NTRS1994

Numerical simulations of catastrophic disruption: Recent results

Numerical simulations have been used to study high velocity two-body impacts. In this paper, a two-dimensional Largrangian finite difference hydro-code and a three-dimensional smooth particle hydro-code (SPH) are described and initial results reported. These codes can be, and have been, used to make specific predictions about particular objects in our solar system. But more significantly, they allow us to explore a broad range of collisional events. Certain parameters (size, time) can be studied only over a very restricted range within the laboratory; other parameters (initial spin, low gravity, exotic structure or composition) are difficult to study at all experimentally. The outcomes of numerical simulations lead to a more general and accurate understanding of impacts in their many forms.

Benz, W.↗
NASA NTRS1995

Numerical magetohydrodynamics in astronphysics: Algorithm and tests for one-dimensional flow`

We describe a numerical code to solve the equations for ideal magnetohydrodynamics (MHD). It is based on an explicit finite difference scheme on an Eulerian grid, called the total variation diminishing (TVD) scheme, which is a second-order-accurate extension of the Roe-type upwind scheme. We also describe a non-linear Riemann solver for ideal MHD, which includes rarefractions as well as shocks. The numerical code and the Riemann solver have been used to test each other. Extensive tests encompassing all the possible ideal MHD structures with planar symmetries (i.e., one-dimensional flows) are presented. These include those for which the field structure is two dimensional (i.e., those flows often called '1 + 1/2 dimensional') as well as those for which the magnetic field plane rotates (i.e., those flows often called '1 + 1/2 + 1/2 dimensional'). Results indicate that the code can resolve strong fast, slow, and magnetosonic shocks within two to four cells, but more cells are required if shocks become weak. With proper steepening, we could resolve rotational discontinuities within three to five cells. However, without successful implementation of steepening, contact discontinuities are resolved with approximately 10 cells and tangential discountinuities are resolved with approximately 15 cells. Out tests confirm that slow compound structures with tow-dimensional magnetic fields are composed of intermediate shocks (so-called 2-4 intermediate shocks) followed by slow rarefaction waves. Finally, tests demostrate that in two-dimensional magnetohydrodynamics, fast compound structures, which are composed of intermediate shocks (so-called 1-3 intermediate shocks) preceeded by fast rarefaction waves, are also possible.

Ryu, Dongsu↗
NASA NTRS1994

Numerical study of the wave-vector dependence of the electron interband impact ionization rate in bulk GaAs

Ensemble Monte Carlo calculations of the electron interband impact ionization rate in bulk GaAs are presented using a wave-vector (k)-dependent formulation of the ionization transition rate. The transition rate is evaluated through the use of numerically generated wavefunctions determined via a k-p calculation within the first two conduction bands at numerous points within a finely spaced three-dimensional grid in k space. The transition rate is determined to be greatest for states within the second conduction band. Is is found that the interband impact ionization transition rate in bulk GaAs is best characterized as having an exceedingly soft threshold energy. As a consequence, the dead space, defined as the distance over which the ionization probability for a given carrier is assumed to be zero, is estimated to be much larger than that estimated using a harder threshold. These results have importance in the design of the multiquantum-well avalanche photodiodes.

Wang, Yang↗
NASA NTRS1994

Charged dust in planetary magnetospheres: Hamiltonian dynamics and numerical simulations for highly charged grains

We use a combination of analytical and numerical methods to investigate the dynamics of charged dust grains in planetary magnetospheres. Our emphasis is on obtaining results valid for particles that are not necessarily dominated either by gravitational or electromagnetic forces. A Hamiltonian formulation of the problem yields exact results, for all values of charge-to-mass ratio, when we introduce two constraints: particles remain in the equatorial plane and the magnetic field is taken as axially symmetric. In particular, we obtain locations of equilibrium points, the frequencies of stable periodic orbits, the topology of separatrices in phase space, and the rate of longitudinal drift. These results are significant for specific applications: motion in the nearly aligned dipolar field of Saturn, and the trajectories of arbitrarily charged particles in complex magnetic fields for limited periods of time after ejection from parent bodies. Since the model is restrictive, we also use numerical integrations of the full three-dimensional equations of motion and illustrate under what conditions the constrained problem yields reasonable results. We show that a large fraction of the intermediately charged and highly charged (gyrating) particles will always be lost to a planet's atmosphere within a few hundred hours, for motion through tilted-dipole magnetic fields. We find that grains must have a very high charge-to-mass ratio in order to be mirrored back to the ring plane. Thus, except perhaps at Saturn where the dipole tilt is very small, the likely inhabitants of the dusty ring systems are those particles that are either nearly Keplerian (weakly charged) grains or grains whose charges place them in the lower end of the intermediate charge zone. Fianlly, we demonstrate the effect of plasma drag on the orbits of gyrating particles to be a rapid decrease in gyroradius followed by a slow radial evolution of the guiding center.

Schaffer, L.↗
NASA NTRS1994

Post-Gondwana geomorphic evolution of southwestern Africa: Implications for hte controls on landscape development from observations and numerical experiments

The relationship between morphology and surficial geology is used to quantify the denudation that has occurred across southwestern Africa sicne the fragmentation of Gondwana during the Early Mesozoic. Two main points emerge. Signficant denudation, of the order of kilometers, is widespread except in the Kalahari region of the continental interior. The denudation is systematically distributed so that the continental exterior catchment, draining directly to the Cape basin, is denuded to a greater depth than the interior catchment inland of the Great Escarpment. The analysis also implies tha the majority of the denudation occurred before the beginning of the Cenozoic for both teh exerior and interior catchments. Existing models of landscape development are reviewed, and implications of the denudation chronology are incorporated into a revised conceptual model. This revision implies tha thte primary effect of rifting on the subsequent landscape evolution is that it generates two distinct drainage regimes. A marginal upwarp, or rift flank uplift, separates rejuvenated rivers that drain into the subsiding rift from rivers in the continetal interior that are deflected but not rejuvenated. The two catchments evolve independently unless they are integrated by breaching of hte marginal upwarp. If this occurs, the exterior baselevel is communicated to the interior catchment that is denuded accordingly. Denudation rates generally decrease as the margin evolves, and this decrease is reinforced by the exposure of substrate that is resistant to denudation and/or a change to a more arid climate. The observations do not reveal a particular style of smaller-scale landscape evolution, sucha s escarpment retreat, that is responsible for the differential denudation across the region. It is proposed that numerical model experiments, which reflect the observational insights at the large scale, may identify the smaller-scale controls on escarpment development if the model and natural systems are analogous. Four numerical experiments are presented in which the roles of antecedent topography, resistant substrate, climte change, and lowering the baselevel of the interior catchment are investigated for an initially high elevation margin bordered by an escarpment. The model results suggest several styles of landscape evolution that are compatible with the observations. Escarpments may retreat in a regular manner, but they also degrade and are destroyed, only to reform at the drainage divide between exterior and interior catchments.

Gilchrist, Alan R.↗
NASA NTRS1994

Numerical simulation of three-dimensional self-gravitating flow

The three-dimensional flow of a self-gravitating fluid is numerically simulated using a Fourier pseudospectral method with a logarithmic variable formulation. Two cases with zero total angular momentum are studied in detail, a 32(exp 3) simulation (Run A) and a 64(exp 3) simulation (Run B). Other than the grid size, the primary differences between the two cases are that Run A modeled atomic hydrogen and had considerably more compressible motion initially than Run B, which modeled molecular hydrogen. ('Compressible motion' is that part of the velocity which has zero curl, but non-zero divergence). The numerical results indicate that gravitational collapse can proceed in a variety of ways. In Run A, collapse led to an elongated tube-like structure, while in Run B, collapse led to a flatter, disk-like structure.

Shebalin, J. V.↗
NASA NTRS1994

Experimental and numerical study of swept ramp injection into a supersonic flowfield

Time-averaged measurements of pressure, temperature, velocity, and injectant mole fraction are presented using the planar laser-induced iodine fluorescence technique in the complex three-dimensional compressible flowfield around a swept ramp fuel injector. Within the range of thermodynamic conditions present in the test case studied, the technique's accuracy is estimated to be 4% for pressure, temperature, and velocity and 3% for injectant mole fraction. Comparisons with numerical simulations using the SPARK three-dimensional Navier-Stokes computer code with an algebraic turbulence model are made at the centerplane of the flowfield as well as on three crossflow planes downstream of the injector. Calculations and measurements are in good agreement throughout the flowfield, with deviations on the order of 5%; however, in specific regions, such as in the base of the ramp, deviations are larger. A weak asymmetry in the incoming flowfield appears to be amplified by boundary-layer separation occurring when the ramp-generated shock reflects off the tunnel walls. Ramp-generated vortices are weaker in the calculated results due to the effects of numerical viscosity in the vortex cores. This leads to less turning and mixing of the jet plume than observed in the experiments. The rate of decay of the maximum injectant mole fraction with streamwise distance is greater for the present ramp injection scheme than for previously measured transverse injection schemes. In this recirculation region at the base of the injector, laminar calculations show better agreement with the measurements than turbulent calculations.

Donohue, James M.↗