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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.↗

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 NTRS1994

Mass-loss rates, ionization fractions, shock velocities, and magnetic fields of stellar jets

In this paper we calculate emission-line ratios from a series of planar radiative shock models that cover a wide range of shock velocities, preshock densities, and magnetic fields. The models cover the initial conditions relevant to stellar jets, and we show how to estimate the ionization fractions and shock velocities in jets directly from observations of the strong emission lines in these flows. The ionization fractions in the HH 34, HH 47, and HH 111 jets are approximately 2%, considerably smaller than previous estimates, and the shock velocities are approximately 30 km/s. For each jet the ionization fractions were found from five different line ratios, and the estimates agree to within a factor of approximately 2. The scatter in the estimates of the shock velocities is also small (+/- 4 km/s). The low ionization fractions of stellar jets imply that the observed electron densities are much lower than the total densities, so the mass-loss rates in these flows are correspondingly higher (approximately greater than 2 x 10(exp -7) solar mass/yr). The mass-loss rates in jets are a significant fraction (1%-10%) of the disk accretion rates onto young stellar objects that drive the outflows. The momentum and energy supplied by the visible portion of a typical stellar jet are sufficient to drive a weak molecular outflow. Magnetic fields in stellar jets are difficult to measure because the line ratios from a radiative shock with a magnetic field resemble those of a lower velocity shock without a field. The observed line fluxes can in principle indicate the strength of the field if the geometry of the shocks in the jet is well known.

Hartigan, Patrick↗

NASA NTRS1994

On the sources of interplanetary shocks at 0.72 AU

In order to understand the solar cycle variation of interplanetary shocks and their driving source at 0.72 AU, a survey of Pioneer Venus Orbiter (PVO) magnetometer and plasma data from 1979-1988 has been conducted. Known shock drivers at 1.0 AU include coronal mass ejections (CMEs) and fast/slow stream interactions. In our analysis, CMEs were identified by a decrease in plasma temperature to background or below accompanied by an increase in plasma density and dynamic pressure. It was also required that the magnetic field exhibit a coherent rotation over about a day and an increase and decline in magnitude on a timescale of hours to days. Stream interactions were identified by a characteristic increase in ion temperature and velocity coincident with a decrease in density and a coincident increase in the total magnetic field magnitude. These signatures were usually preceded within 24 hours by a change in flow angle. In all, 45 shocks were identified: 36 driven by CMEs, 6 resulting from fast/slow stream interactions, and 3 with sources that could not be defined. The shocks driven by CMEs show a solar cycle variation that roughly follows the sunspot number. These shocks all have normals consistent with radial propagation of the shock fronts from the sun. In contrast, the few stream interaction related shocks show a tendency to occur later in the solar cycle and have a broader distribution of shock normals.

Lindsay, G. M.↗

NASA NTRS1995

Neptune inbound bow shock

Voyager 2 crossed the inbound or upstream Neptunian bow shock at 1430 spacecraft event time on August 24 in 1989 (Belcher et al., 1989). The plasma and magnetic field measurements allow us to study the solar wind interaction with the outermost gas giant. To fully utilize all of the spacecraft observations, an improved nonlinear least squares, 'Rankine-Hugoniot' magnetohydrodynamic shock-fitting technique has been developed (Szabo, 1994). This technique is applied to the Neptunian data set. We find that the upstream bow shock normal points nearly exactly toward the Sun consistent with any reasonable large-scale model of the bow shock for a near subsolar crossing. The shock was moving outward with a speed of 14 +/- 12 km/s. The shock can be characterized as a low beta, high Mach number, strong quasi-perpendicular shock. Finally, the shock microstructure features are resolved and found to scale well with theoretical expectations.

Szabo, Adam↗

NASA NTRS1993

Magnetospheric response to solar wind dynamic pressure variations: Interaction of interplanetary tangential discontinuities with the bow shock

Some magnetic impulse events observed in the polar region are related to vortices associated with plasma convection in the ionosphere. Recent analyses of satellite and ground data suggest that the interaction of solar wind dynamic pressure pulses and the magnetosphere may lead to the formation of velocity vortices in the magnetopause boundary layer region. This can in turn lead to the presence of vortices in the polar ionosphere. However, before reaching the Earth's magnetopause, these interplanetary pressure pulses must interact with and pass through the bow shock. A variation of the solar wind dynamic pressure may be associated with shocks, magnetic holes, or tangential discontinuities (TDs) in the interplanetary medium. We study the interaction of interplanetary TDs with the Earth's bow shock (BS) using both theoretical analysis and MHD computer simulations. It is found that as a result of the collision between a TD and the BS, the jump in the solar wind dynamic pressure associated with the TD is significantly modified, the bow shock moves, and a new fast shock or fast rarefaction wave, which propagates in the downstream direction, is excited. Our theoretical analysis shows that the change in the plasma density across the interplanetary TD plays the most important role in the collision process. In the case with an enhanced dynamic pressure behind the interplanetary TD, the bow shock is intensified in strength and moves in the earthward direction. The dynamic pressure jump associated with the transmitted TD is generally reduced from the value before the interaction. A fast compressional shock is excited ahead of the transmitted TD and propagates toward the Earth's magnetosphere. For the case in which the dynamic pressure is reduced behind the interplanetary TD, the pressure jump across the transmitted TD is substantially weakened, the bow shock moves in the sunward direction, and a rarefaction wave which propagates downstream is excited. We also simulate and discuss the interaction of a pair of tangential discontinuities, which may correspond to a magnetic hole, with the BS.

Wu, Bor-Han↗