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At least 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Fresh look at floating shock fitting

A fast implicit upwind procedure for the two-dimensional Euler equations is described that allows accurate computations of shocked flows on nonadapted meshes. Away from shocks, the second-order accurate upwinding is based on the split-coefficient-matrix (SCM) method. In the presence of shocks, the difference stencils are modified using a floating shock fitting technique. Rapid convergence to steady-state solutions is attained with a diagonalized approximate factorization (AF) algorithm. Results are presented for Riemann's problem, for a regular shock reflection at an inviscid wall, for supersonic flow past a cylinder, and for a transonic airfoil. All computed shocks are ideally sharp and in excellent agreement with other numerical results or 'exact' solutions. Most importantly, this has been accomplished on unusually crude meshes without any attempt to align grid lines with shock fronts or to cluster grid lines around shocks.

Hartwich, PETER-M.↗
NASA NTRS1989

Monte Carlo simulation of particle acceleration at astrophysical shocks

A Monte Carlo code was developed for the simulation of particle acceleration at astrophysical shocks. The code is implemented in Turbo Pascal on a PC. It is modularized and structured in such a way that modification and maintenance are relatively painless. Monte Carlo simulations of particle acceleration at shocks follow the trajectories of individual particles as they scatter repeatedly across the shock front, gaining energy with each crossing. The particles are assumed to scatter from magnetohydrodynamic (MHD) turbulence on both sides of the shock. A scattering law is used which is related to the assumed form of the turbulence, and the particle and shock parameters. High energy cosmic ray spectra derived from Monte Carlo simulations have observed power law behavior just as the spectra derived from analytic calculations based on a diffusion equation. This high energy behavior is not sensitive to the scattering law used. In contrast with Monte Carlo calculations diffusive calculations rely on the initial injection of supra-thermal particles into the shock environment. Monte Carlo simulations are the only known way to describe the extraction of particles directly from the thermal pool. This was the triumph of the Monte Carlo approach. The question of acceleration efficiency is an important one in the shock acceleration game. The efficiency of shock waves efficient to account for the observed flux of high energy galactic cosmic rays was examined. The efficiency of the acceleration process depends on the thermal particle pick-up and hence the low energy scattering in detail. One of the goals is the self-consistent derivation of the accelerated particle spectra and the MHD turbulence spectra. Presumably the upstream turbulence, which scatters the particles so they can be accelerated, is excited by the streaming accelerated particles and the needed downstream turbulence is convected from the upstream region. The present code is to be modified to include a better description of particle scattering (pitch-angle instead of hard-sphere) and as iterative procedure for treating the self-excitation of the MHD turbulence.

Campbell, Roy K.↗
NASA NTRS1991

Mass-loading and parallel magnetized shocks

Recent observations at comets Giacobini-Zinner and Halley suggest that simple nonreacting gas dynamics or MHD is an inappropriate description for the bow shock. The thickness of the observed (sub)shock implies that mass-loading is an important dynamical process within the shock itself, thereby requiring that the Rankine-Hugoniot conditions possess source terms. This leads to shocks with properties similar to those of combustion shocks. The paper considers parallel magnetized shocks subjected to mass-loading, describes some properties which distinguish them from classical MHD parallel shocks, and establishes the existence of a new kind of MHD compound shock. These results will be of importance both to observations and numerical simulations of the comet-solar wind interaction.

Zank, G. P.↗
NASA NTRS1990

Formation of slow shock pairs associated with coronal mass ejections

The formation of a forward-reverse slow shock pair in the solar corona is presently simulated by an MHD model that uses the Rankine-Hugoniot solution to calculate the flow-property jumps at all shock crossings. The shocks divide the solution-domain into several continuous flow regions whose respective governing characteristics are solved by the method of characteristics. The plasma impact compresses the plasma near the front of the coronal mass ejection (CME); as the CME-associated slow shock pair moves outwards in interplanetary space, it evolves into a pair of fast shocks. All three phenomena are eventually manifested in interplanetary space as a magnetic cloud accompanied by a fast shock pair, with a forward shock preceding the cloud and a reverse shock appearing either within or behind the cloud.

Whang, Y. V.↗
NASA NTRS1992

Influence of the preshock temperature on shock effects in quartz

Shock metamorphic features are the prime indicators for recognizing impact phenomena on Earth and other planetary bodies. Although the pressure dependence of shock features is well known, information about the influence of the preshock temperature is almost lacking. Especially in the case of large-scale impacts like Sudbury, it is expected that deep-seated crustal rocks were subjected to shock at elevated temperatures. Therefore, we continued to perform shock experiments at elevated temperatures on less than 0.5-mm thin disks of single crystal quartz cut parallel to the (1010) face. All recovered quartz samples were investigated by universal stage, spindle stage, and a newly developed density gradient technique. Errors of refractive index and density measurements are +/- 0.0005 and +/- 0.002 g/cu cm respectively. Our investigations indicate that shock metamorphic features are strongly dependent on the preshock temperature. This statement has far-reaching implications with respect to shock wave barometry that is based on data from recovery experiments at room temperature. These datasets might be applicable only to low-temperature target rocks. Moreover, this study demonstrates that shock recovery experiments are definitely required for understanding the complete pressure-temperature regime of shock metamorphism on planetary bodies.

Langenhorst, F.↗
NASA NTRS1991

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

We present the first results of time dependent, two-fluid, cosmic-ray (CR) modified, MHD shock simulations. The calculations were carried out with a new numerical code for 1-D 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 appear to have converged to dynamical steady states. We also present results from an initial time dependent simulation which extend 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 timescale than parallel shocks.

Frank, Adam↗
NASA NTRS1992

Interaction of fast steady flow with slow transient flow - A new cause of shock pair and interplanetary B(z) event

The occurrence of the nonspiral magnetic field (high helium density) Cold Magnetic Enhancement and counterstreaming suprathermal electron flux in the slow flow around the forward shock indicates that the slow flow is a CME in interplanetary space (ICME). The characteristics of the field and plasma in the fast flow around the reverse shock is typical for a high speed stream. Thus the shock pair here appears to be caused by the interaction of a high speed stream with a slow ICME. The fact that a -B(z) event occurred in such a shock pair suggests that the slow ICME is disconnected from the sun. It is shown that compression alone appears to be adequate to explain the large southward IMF component within the shocked plasma because of the large southward field component present in the ICME ahead of the forward shock. In addition, a new method to infer the shock angle and Mach number from the observed upstream plasma B and the jump ratios of proton density and total magnetic flux density across a shock is described.

Zhao, Xuepu↗
NASA NTRS1991

High-speed helicopter rotor noise - Shock waves as a potent source of sound

In this paper we discuss the problem of high speed rotor noise prediction. In particular, we propose that from the point of view of the acoustic analogy, shocks around rotating blades are sources of sound. We show that, although for a wing at uniform steady rectilinear motion with shocks the volume quadrupole and shock sources cancel in the far field to the order of 1/r, this cannot happen for rotating blades. In this case, some cancellation between volume quadrupoles and shock sources occurs, yet the remaining shock noise contribution is still potent. A formula for shock noise prediction is presented based on mapping the deformable shock surface to a time independent region. The resulting equation is similar to Formulation 1A of Langley. Shock noise prediction for a hovering model rotor for which experimental noise data exist is presented. The comparison of measured and predicted acoustic data shows good agreement.

Farassat, F.↗
NASA NTRS1993

Venus bow shocks at unusually large distances from the planet

Recent analysis of data from the Pioneer Venus Orbiter (PVO) has shown that the bow shock often travels to unusually large distances from the planet when the solar wind magnetosonic Mach number is near unity. We suggest that distant bow shocks can be explained as an integral part of the response of the global solar wind/Venus interaction to the anomalous local solar wind conditions that existed during the time of these observations. The lower-than-normal plasma beta and magnetosonic Mach number are in a parameter regime for which the usual fast-mode bow shock close to the planet may not provide the necessary compression and deflection of the solar wind. Using MHD simulations we show that, for these conditions, the usual fast shock is replaced by a bow shock consisting of an intermediate shock near the Sun-Venus line and a fast shock at large distances from the Sun-Venus line. This composite bow shock propagates upstream away from the planet at a low speed and appears to be approaching a new equilibrium stand-off location at a large distance from the planet.

Steinolfson, R. S.↗
NASA NTRS1991

Calculation of hypersonic shock structure using flux-split algorithms

There exists an altitude regime in the atmosphere that is within the continuum domain, but wherein the conventional Navier-Stokes equations cease to be accurate. The altitude limits for this so called continuum transition regime depend on vehicle size and speed. Within this regime the thickness of the bow shock wave is no longer negligible when compared to the shock stand-off distance and the peak radiation intensity occurs within the shock wave structure itself. For this reason it is no longer valid to treat the shock wave as a discontinuous jump and it becomes necessary to compute through the shock wave itself. To accurately calculate hypersonic flowfields, the governing equations must be capable of yielding realistic profiles of flow variables throughout the structure of a hypersonic shock wave. The conventional form of the Navier-Stokes equations is restricted to flows with only small departures from translational equilibrium; it is for this reason they do not provide the capability to accurately predict hypersonic shock structure. Calculations in the continuum transition regime, therefore, require the use of governing equations other than Navier-Stokes. Several alternatives to Navier-Stokes are discussed; first for the case of a monatomic gas and then for the case of a diatomic gas where rotational energy must be included. Results are presented for normal shock calculations with argon and nitrogen.

Eppard, W. M.↗
NASA NTRS1993

Thermal shock resistance of ceramic matrix composites

The experimental and analytical investigation of the thermal shock phenomena in ceramic matrix composites is detailed. The composite systems examined were oxide-based, consisting of an aluminosilicate matrix with either polycrystalline aluminosilicate or single crystal alumina fiber reinforcement. The program was divided into three technical tasks; baseline mechanical properties, thermal shock modeling, and thermal shock testing. The analytical investigation focused on the development of simple expressions for transient thermal stresses induced during thermal shock. The effect of various material parameters, including thermal conductivity, elastic modulus, and thermal expansion, were examined analytically for their effect on thermal shock performance. Using a simple maximum stress criteria for each constituent, it was observed that fiber fracture would occur only at the most extreme thermal shock conditions and that matrix fracture, splitting parallel to the reinforcing fiber, was to be expected for most practical cases. Thermal shock resistance for the two material systems was determined experimentally by subjecting plates to sudden changes in temperature on one surface while maintaining the opposite surface at a constant temperature. This temperature change was varied in severity (magnitude) and in number of shocks applied to a given sample. The results showed that for the most severe conditions examined that only surface matrix fracture was present with no observable fiber fracture. The impact of this damage on material performance was limited to the matrix dominated properties only. Specifically, compression strength was observed to decrease by as much as 50 percent from the measured baseline.

Carper, D. M.↗
NASA NTRS1991

Interaction of two glancing, crossing shock waves with a turbulent boundary-layer at various Mach numbers

A preliminary experimental investigation was conducted to study two crossing, glancing shock waves of equal strengths, interacting with the boundary-layer developed on a supersonic wind tunnel wall. This study was performed at several Mach numbers between 2.5 and 4.0. The shock waves were created by fins (shock generators), spanning the tunnel test section, that were set at angles varying from 4 to 12 degrees. The data acquired are wall static pressure measurements, and qualitative information in the form of oil flow and schlieren visualizations. The principle aim is two-fold. First, a fundamental understanding of the physics underlying this flow phenomena is desired. Also, a comprehensive data set is needed for computational fluid dynamic code validation. Results indicate that for small shock generator angles, the boundary-layer remains attached throughout the flow field. However, with increasing shock strengths (increasing generator angles), boundary layer separation does occur and becomes progressively more severe as the generator angles are increased further. The location of the separation, which starts well downstream of the shock crossing point, moves upstream as shock strengths are increased. At the highest generator angles, the separation appears to begin coincident with the generator leading edges and engulfs most of the area between the generators. This phenomena occurs very near the 'unstart' limit for the generators. The wall pressures at the lower generator angles are nominally consistent with the flow geometries (i.e. shock patterns) although significantly affected by the boundary-layer upstream influence. As separation occurs, the wall pressures exhibit a gradient that is mainly axial in direction in the vicinity of the separation. At the limiting conditions the wall pressure gradients are primarily in the axial direction throughout.

Hingst, Warren R.↗
NASA NTRS1993

Hybrid simulations of the effects of interstellar pickup hydrogen on the solar wind termination shock

Hybrid (kinetic ions/fluid electrons) plasma simulations are used to study the effects of a population of energetic interstellar pickup hydrogen ions on the solar wind termination shock. The pickup hydrogen is treated as a second ion species in the simulations, and thus the effects of the pick-ups on the shock, as well as the effects of the shock on the pickups, are treated in a fully self-consistent manner. For quasi-perpendicular shocks with 10-20 percent pickup hydrogen the pickup ions manifest themselves in a small foot ahead of the shock ramp caused by pickup ion reflection. For oblique shocks with smaller angles between the field and the shock normal, a large fraction of the pickup ions are reflected and move back upstream where they excite large amplitude magnetosonic waves which steepen into shocklets. These backstreaming pickup ions may provide advance warning of a spacecraft encounter with the termination shock.

Liewer, P. C.↗
NASA NTRS1993

Termination shock - Solar cycle variations of location and speed

Plasma and magnetic field data from Voyagers 1 and 2 over an 11-year period (1978-1988) together with a one-fluid MHD model are used to study the motion of the termination shock. The observed large fluctuations in solar wind parameters cause variations in the speed, in the jump conditions, and in the location of the termination shock. If the interstellar stagnation pressure is equivalent to a magnetic field of 0.5 nT plus draping enhancements, the termination shock moves between 88 AU and 102 AU. The location of the termination shock is anticorrelated with the sunspot number. The termination shock is very strong with pressure ratios of a few thousands, the fast Mach number is about 12, and the plasma beta ratio jumps from about 0.1 to about 14. During the declining phase of the solar cycle, the shock speed is often greater than or comparable to the spacecraft speed. If the crossing of the termination shock by a spacecraft occurs during the declining phase, the spacecraft will cross the termination shock 3 or more times over a period of about 4 years.

Whang, Y. C.↗
NASA NTRS1994

Floating shock fitting via Lagrangian adaptive meshes

In recent works we have formulated a new approach to compressible flow simulation, combining the advantages of shock-fitting and shock-capturing. Using a cell-centered Roe scheme discretization on unstructured meshes, we warp the mesh while marching to steady state, so that mesh edges align with shocks and other discontinuities. This new algorithm, the Shock-fitting Lagrangian Adaptive Method (SLAM) is, in effect, a reliable shock-capturing algorithm which yields shock-fitted accuracy at convergence. Shock-capturing algorithms like this, which warp the mesh to yield shock-fitted accuracy, are new and relatively untried. However, their potential is clear. In the context of sonic booms, accurate calculation of near-field sonic boom signatures is critical to the design of the High Speed Civil Transport (HSCT). SLAM should allow computation of accurate N-wave pressure signatures on comparatively coarse meshes, significantly enhancing our ability to design low-boom configurations for high-speed aircraft.

Vanrosendale, John↗
NASA NTRS1995

Molecular dynamics simulation of a piston driven shock wave in a hard sphere gas

Molecular dynamics simulation is used to study the piston driven shock wave at Mach 1.5, 3, and 10. A shock tube, whose shape is a circular cylinder, is filled with hard sphere molecules having a Maxwellian thermal velocity distribution and zero mean velocity. The piston moves and a shock wave is generated. All collisions are specular, including those between the molecules and the computational boundaries, so that the shock development is entirely causal, with no imposed statistics. The structure of the generated shock is examined in detail, and the wave speed; profiles of density, velocity, and temperature; and shock thickness are determined. The results are compared with published results of other methods, especially the direct simulation Monte-Carlo method. Property profiles are similar to those generated by direct simulation Monte-Carlo method. The shock wave thicknesses are smaller than the direct simulation Monte-Carlo results, but larger than those of the other methods. Simulation of a shock wave, which is one-dimensional, is a severe test of the molecular dynamics method, which is always three-dimensional. A major challenge of the thesis is to examine the capability of the molecular dynamics methods by choosing a difficult task.

Woo, Myeung-Jouh↗
NASA NTRS1994

Time-dependent evolution of cosmic-ray-modified shock structure: Transition to steady state

Steady state solutions to the two-fluid equations of cosmic-ray-modified shock structure were investigated first by Drury and Volk (1981). Their analysis revealed, among other properties, that there exist regions of upstream parameter space where the equations possess three different downstream solutions for a given upstream state. In this paper we investigate whether or not all these solutions can occur as time-asymptotic states in a physically realistic evolution. To do this, we investigate the time-dependent evolution of the two-fluid cosmic-ray equations in going from a specified initial condition to a steady state. Our results indicate that the time-asymptotic solution is strictly single-valued, and it undergoes a transition from weakly to strongly cosmic-ray-modified at a critical value of the upstream cosmic ray energy density. The expansion of supernova remnant shocks is considered as an example, and it is shown that the strong to weak transition is in fact more likely. The third intermediate solution is shown to influence the time-dependent evolution of the shock, but it is not found to be a stable time-asymptotic state. Timescales for convergence to these states and their implications for the efficiency of shock acceleration are considered. We also investigate the effects of a recently introduced model for the injection of seed particles into the shock accelerated cosmic-ray population. The injection is found to result in a more strongly cosmic-ray-dominated shock, which supports our conclusion that for most classes of intermediate and strong cosmic-ray-modified shocks, the downstream cosmic-ray pressure component is at least as large as the thermal gas pressure, independent of the upstream state. As a result, cosmic rays almost always play a significant role in determining the shock structure and dissipation and they cannot be regarded as test particles.

Donohue, D. J.↗
NASA NTRS1994

Computing unsteady shock waves for aeroacoustic applications

The computation of unsteady shock waves, which contribute significantly to noise generation in supersonic jet flows, is investigated. The paper focuses on the difficulties of computing slowly moving shock waves. Numerical error is found to manifest itself principally as a spurious entropy wave. Calculations presented are performed using a third-order essentially nonoscillatory scheme. The effect of stencil biasing parameters and of two versions of numerical flux formulas on the magnitude of spurious entropy are investigated. The level of numerical error introduced in the calculation is quantified as a function of shock pressure ratio, shock speed, Courant number, and mesh density. The spurious entropy relative to the entropy jump across a static shock decreases with increasing shock strength and shock velocity relative to the grid, but is insensitive to Courant number. The structure of the spurious entropy wave is affected by the choice of flux formulas and algorithm biasing parameters. The effect of the spurious numerical waves on the calculation of sound amplification by a shock wave is investigated. For this class of problem, the acoustic pressure waves are relatively unaffected by the spurious numerical phenomena.

Meadows, Kristine R.↗