Showing papers on "Shock wave published in 1989"

The Riemann problem for fluid flow of real materials

Abstract: The Riemann problem for fluid flow of real materials is examined. An arbitrary equation of state is allowed, subject only to the physical requirements of thermodynamics. The properties of the isentropes and the shock Hugoniot loci that follow from conditions imposed on the equation of state are reviewed systematically. Important properties of these wave curves are determined by three dimensionless variables characterizing the equation of state: the adiabatic exponent $\ensuremath{\gamma}$, the Gr\"uneisen coefficient $\ensuremath{\Gamma}$, and the fundamental derivative $\mathcal{G}$. Standard assumptions on these variables break down near phase transitions. The result is an anomalous wave structure: either shock waves split into multiple waves, or composite waves form. Additional questions related to shock stability and nonuniqueness of the solution of the Riemann problem are discussed.

Neutron Star Accretion in a Supernova

Abstract: An estimate can be made of the effect of a central mass on an explosion through the study of self-similar blast waves in a medium having an inverse-square-of-r density profile, as is approximately the case in the inner core of the progenitor of SN 1987A; its parameters are such that the nucleon density is substantially constant within the shock front. In SN explosions with a massive envelopes, the core material is decelerated by its interaction with the envelope, and a reverse shock wave propagates back to the center. 42 refs.

Cosmic-ray transport and acceleration. I - Derivation of the kinetic equation and application to cosmic rays in static cold media. II - Cosmic rays in moving cold media with application to diffusive shock wave acceleration

Abstract: The propagation of energetic charged particles in a zero electric field and an ordered uniform magnetic field (B0) in a cold background medium is investigated theoretically, with a focus on the case where Alfven waves propagating parallel or antiparallel to B0 are superposed. The derivations of the governing equations of a quasi-linear theory for pitch-angle and momentum diffusion and for its applications to cosmic-ray protons in a cold medium at rest or in nonrelativistic motion parallel to B0 are given in great detail; numerical predictions are presented in tables and graphs and discussed with reference to published observational data. 83 references.

Standing Rankine-Hugoniot Shocks in the Hybrid Model Flows of the Black Hole Accretion and Winds

Abstract: This paper presents all the Rankine-Hugoniot shock solutions for the stationary, axially symmetric and rotating adiabatic flows of small transverse thickness in the black hole potential. The recently proposed hybrid model is used to treat the flows which include shocks. It is shown that, for given initial and final states of the flow, there can be as many as four formal shock locations in both the accretion and the winds. Only two (three) of these locations are acceptable for accretion onto black holes (neutron stars), and three of these locations are acceptable for winds. It is shown that the question of the multiplicity of the shocks cannot be resolved by local stability analysis of the shocks. In addition, the properties of the isentropic compression waves and the isothermal shocks are briefly studied. 17 refs.

The Riemann problem and interaction of waves in gas dynamics

Abstract: The initial-value problem constructed by Riemann (1860) to describe the motion of an ideal gas in a shock tube is investigated analytically, with an emphasis on the mathematical aspects Topics addressed include the simplest Riemann model and the interactions of elementary waves (shock waves, centered rarefaction waves, and contact discontinuities), one-dimensional isothermal flow, one-dimensional adiabatic flow, and two-dimensional flow Particular attention is given to the Riemann problem for a scalar conservation law, the interaction of a shock wave overtaking another in steady two-dimensional flow, and the diffraction of a planar shock along a compressive corner 92 refs

Cyclic behavior at quasi-parallel collisionless shocks

Abstract: Large scale one-dimensional hybrid simulations with resistive electrons have been carried out of a quasi-parallel high-Mach-number collisionless shock. The shock initially appears stable, but then exhibits cyclic behavior. For the magnetic field, the cycle consists of a period when the transition from upstream to downstream is steep and well defined, followed by a period when the shock transition is extended and perturbed. This cyclic shock solution results from upstream perturbations caused by backstreaming gyrating ions convecting into the shock. The cyclic reformation of a sharp shock transition can allow ions, at one time upstream because of reflection or leakage, to contribute to the shock thermalization.

Numerical simulations of magnetized jets

Abstract: The present axisymmetric numerical simulations of light hypersonic jets allow unmagnetized jets and jets carrying a dynamically important magnetic field to be contrasted. After decelerating a weakly magnetized jet through a series of weak, oblique shocks, a Mach disk and a strong annular shock are encountered near the outer edges of the contact discontinuity separating the shocked fluid from the shocked ambient gas. Upon passing the annular shock, the gas quickly expands and enters a backflowing cocoon surrounding the jet. The overall speed of advance of the jet is reduced; matter near the jet axis which passes through the terminal Mach disk accumulates in a plug, and gas is discharged into the cocoon by the intermittent shedding of vortices. When magnetic stresses dominate, however, the jet is rapidly decelerated via a Mach disk and strong annular shock.

The effects of target compliance on liquid drop impact

Abstract: When a liquid drop impacts a solid surface, the contact periphery at first expands more quickly than the compression wavefronts in either liquid or solid. The liquid behind the shock envelope is compressed and high pressures of order ρCV result, where ρ is the density of the liquid at ambient pressure, C the shock velocity in the liquid, and V the impact velocity. At a later stage, the shock envelope overtakes the contact periphery and a jetting motion, which releases the high pressures, commences. The magnitude and duration of the high pressures are critical in explaining the damage mechanisms and erosion processes caused by liquid impact. The experiments described in this paper use the two‐dimensional gel and photographic techniques developed for visualizing the shocks, recording the onset of jetting, and measuring jet velocities. This particular study is primarily concerned with the effect of target compliance on the early stages of impact. It is shown that the greater the target compliance, the longer...

Time-resolved measurements of picosecond optical breakdown

Abstract: Picosecond optical breakdown was investigated in order to assess its potential for performing highly localized incisions for laser surgery. Measurements of breakdown were performed using single 40-ps Nd: YAG laser pulses in distilled water. Novel optical pump-probe techniques were developed to characterize the transient spatial and temporal dynamics of the plasma, shock wave, and cavitation phenomena which are associated with the breakdown. The maximum cavity radius and the shock wave zone are shown to scale as the cube root of the pump pulse energy over almost three orders of magnitude. For pulse energies close to the threshold energy of 8 μJ, the shock range was ∼100–200 μm and the cavity radius was 140 μm. Complementary experiments were performed with 10-ns pulse durations. Since picosecond pulses have high peak intensities with low pulse energies, a significant enhancement in localizability may be achieved. The implications for ophthalmic microsurgery are discussed.

Experimental Shock-Wave Interference Heating on a Cylinder at Mach 6 and 8

Abstract: This paper presents the details of an experimental study of shock-wave interference heating on a cylindrical leading edge representative of the cowl of a rectangular hypersonic engine inlet. The study, which was conducted at Mach numbers of 6.3, 6.5, and 8.0, has provided 1) detailed pressure and heat-transfer-rate distributions for a two-dimensional shock-wave interference on a cylinder and 2) insight into the effects of temperature-d ependent specific heats on the phenomena. The peak pressure and heat-transfer rates were 2-25 times the undisturbed flow stagnation-point levels. The peak levels and their gradients increased with Mach number. Variation in specific heats and, hence, in the ratio of specific heats with temperature is manifested in slightly lower loads and amplification factors than for corresponding perfect-gas conditions.

Suprathermal electrons at Earth's bow shock

Abstract: Results are presented on electron measurements near the earth's bow shock, carried out with the fast-plasma experiments on ISEE 1 and 2, with emphasis placed on the suprathermal population of electrons present near the earth's bow shock. The pattern found for the suprathermal electrons at the bow shock suggests that a portion of the solar wind electron population is commonly accelerated to relatively high energy as the solar wind convects across quasi-perpendicular portions of the bow shock. The results are interpreted in terms of the global magnetic field geometry of the bow shock environment.

On the refraction of shock waves

Abstract: This paper discusses the refraction of plane shock waves in media with arbitrary equations of state. Previous work is reviewed briefly, then a rigorous definition of wave impedance is formulated. Earlier definitions are shown to be unsatisfactory. The impedance is combined with the boundary conditions at the media interface to study both head-on and oblique shock incidence. The impedance determines the nature of the reflected and transmitted waves, their intensities, and the fractions of energy and power that are reflected and transmitted. The refractive index is also defined and determines whether or not a wave will be refracted, and also helps determine whether the wave system will be regular or irregular. The fundamental law of refraction is derived and shown to be a consequence of the fact that an arbitrary point on a shock or an expansion wave follows a ray path of minimum time between any two points on the path. This is a generalization of Fermat's Principle to media that are deformed and convected by the waves propagating through them.

Ion distributions and thermalization at perpendicular and quasi‐perpendicular supercritical collisionless shocks

Abstract: Computer simulations and observations in laboratory and space plasmas have revealed that some incident ions are reflected at perpendicular and quasi-perpendicular high Mach number (i.e., supercritical) shocks. Moreover, these studies have established that the gyration and subsequent thermalization of these ions play a dominant role in the the shock dissipation process. We use a hybrid kinetic simulation in order to study the selection of an incoming ion as either reflected-gyrating or transmitted. We find that the reflected ions come from a limited region in the upstream velocity space distribution. None of the reflected ions come from the core of the distribution. Whether a particle becomes reflected depends on its energy in the upstream frame and its gyrophase as it encounters the shock. In the simulations we have carefully identified and separated the two subpopulations: transmitted and reflected. The transmitted ions do not heat appreciably in passing through the shock, although there may be wave-particle effects neglected in the hybrid simulation. There is a contribution to the total downstream pressure due to the gyration of the two subpopulations about their common center of mass, in addition to the pressure associated with the reflected component relative to its own center of mass.

Ion reflection and downstream thermalization at the quasi-parallel bow shock

Abstract: Using the results of ISEE 2 plasma and magnetic field measurements, two features related to the ion thermalization process at high-Mach-number (M above 2) quasi-parallel collisionless shocks are discussed. These are the presence of a coherent secondary beam of ions within the shock layer which is considered to be produced by reflection, and downstream ion distributions which contain both a relatively cold core of directly transmitted ions and a hotter 'shell' of ions, which appear to result from the disruption and scattering of ions initially reflected at the shock. Evidence is presented that coherent ion reflection is an important element of the ion energy dissipation process at high-Mach-number quasi-parallel shocks.

Subnanosecond x-ray diffraction from laser-shocked crystals.

Abstract: We have used single-shot sub-nanosecond x-ray diffraction to directly measure lattice parameters of crystals during the passage of laser-driven shock waves. Changes in the interatomic spacings can be measured with a temporal resolution better than 50 ps. We have studied shock-launching in single crystals and have directly measured dynamic tension during shock-breakout from a rear surface. In separate experiments we have directly observed the onset of shock-induced plasticity by diffracting from planes running perpendicular to the shock front. In addition to the single crystal work we have recently demonstrated that we can record x-ray powder patterns with sub-nanosecond exposure times; and are now in a position to laser-shock polycrystalline material simultaneously with the x-ray flash. The technique promises to be useful in the study of many fundamental problems in shock wave physics, including the behaviour of materials at the lattice level during plastic deformation and shock-induced polymorphic phase transitions.

Nonequilibrium molecular motion in a hypersonic shock wave

Abstract: Molecular velocities have been measured inside a hypersonic, normal shock wave, where the gas experiences rapid changes in its macroscopic properties. As first hypothesized by Mott-Smith, but never directly observed, the molecular velocity distribution exhibits a qualitatively bimodal character that is derived from the distribution functions on either side of the shock. Quantitatively correct forms of the molecular velocity distribution function in highly nonequilibrium flows can be calculated, by means of the Direct Simulation Monte Carlo technique.

On the Thermal Shock Wave Induced by a Moving Heat Source

Abstract: Analytical solutions for the temperature field around a moving heat source in a solid with finite speed of heat propagation are obtained via the method of Green's functions. When the speed of the moving heat source is equal to or faster than that of the thermal wave propagated in the solid, the thermal shock wave is shown to exist in the thermal field. The shock wave angle is obtained as sin{sup {minus}1} (1/M) for M {ge} 1. Orientation of crack initiation in the vicinity of the heat source is also estimated by considering the temperature gradient T,{sub {theta}} along the circumference of a continuum circle centered at the heat source. Such an orientation is established as a function of the thermal Mach number in the subsonic, transonic, and supersonic regimes, respectively.

Comparison of Burnett, super-Burnett and Monte Carlo solutions for hypersonic shock structure

Abstract: The continuum Navier-Stokes, Burnett, and super-Burnett equations are solved for one-dimensional shock structures in various monoatomic gases. Solutions for a hard sphere gas, argon, and a Maxwellian gas from Mach 1.3 to Mach 50 are obtained. A numerical method utilizing the complete time-dependent continuum equations and obtaining the steady-state shock structure by allowing the system to relax from arbitrary initial conditions is employed. Shock density, velocity, temperature, and entropy profiles are also obtained using the direct simulation Monte Carlo method, and these results are used as bases for comparison for continuum solution profiles. It is shown that the Burnett equations yield shock structure solutions in much closer agreement to both Monte Carlo and experimental results than do the Navier-Stokes equations. Solutions to the super-Burnett equations with coefficients as presently derived, however, are considered to be inferior to those of the Burnett equations.

Mixing augmentation technique for hypervelocity scramjets

Abstract: The paper discusses mixing problems in hypervelocity scramjet combustors. Techniques for providing turbulence and/or mixing enhancement are described. One such technique, the oscillating shock interaction, is studied numerically and options for producing oscillatory shock waves for mixing augmentation in scramjet combustors are discussed.

First plasma wave observations at neptune.

Abstract: The Voyager 2 plasma wave instrument detected many familiar plasma waves during the encounter with Neptune, including electron plasma oscillations in the solar wind upstream of the bow shock, electrostatic turbulence at the bow shock, and chorus, hiss, electron cyclotron waves, and upper hybrid resonance waves in the inner magnetosphere. Low-frequency radio emissions, believed to be generated by mode conversion from the upper hybrid resonance emissions, were also observed propagating outward in a disklike beam along the magnetic equatorial plane. At the two ring plane crossings many small micrometer-sized dust particles were detected striking the spacecraft. The maximum impact rates were about 280 impacts per second at the inbound ring plane crossing, and about 110 impacts per second at the outbound ring plane crossing. Most of the particles are concentrated in a dense disk, about 1000 kilometers thick, centered on the equatorial plane. However, a broader, more tenuous distribution also extends many tens of thousands of kilometers from the equatorial plane, including over the northern polar region.

Method and apparatus for dispersing a gas into a liquid

Abstract: The present invention relates to an improved method and apparatus for dispersing a gas into a liquid. Gas is injected into a liquid and the flowing gas-liquid mixture is accelerated by a flow area contraction to at least sonic flow velocity, and subsequently decelerated by a flow area expansion to subsonic velocity. The attendant shock waves disperse the gas in the liquid. Preferred embodiments include off-centering the gas injection direction from the centerline of the contracting flow area and controlling the pressure at the exit of the expanding flow area.

The velocity distributions of cometary protons picked up by the solar wind

Abstract: Velocity space distributions of picked up cometary protons were measured by the ion mass spectrometer on the Giotto spacecraft upstream of the Halley bow shock. Large pitch angle anisotropies were observed at all distances greater than 1.2 x 10 to the 6th km from the comet. As expected, pitch angle diffusion was much more rapid than energy diffusion. When the field was quasi-parallel to the solar wind velocity vector, it was possible to discern the effect of pitch angle scattering by sunward propagating, field-aligned hydromagnetic waves, but there is evidence for other scattering modes as well. For quasi-perpendicular geometries, the pitch angle distribution was very asymmetric with phase space density peaks near pitch angles of 180 deg. It is suggested that the asymmetric pitch angle distribution may be caused by global rather than local wave-particle interactions. Just outside the shock, the pitch angle distribution was nearly isotropic and the radius of the pickup shell increased significantly.

On the effect of a tangential discontinuity on ions specularly reflected at an oblique shock

Abstract: A study is conducted for the case of a tangential discontinuity (TD) that convects into a shock at some arbitrary angle, in order to clarify events observed in proximity to the earth's bow shock. Very different behavior is noted to result depending on the sense of ion gyration relative to the TD. The fact that particles can be injected into the TD's plane, so that they travel upstream close to the TD, implies that active current sheet (ACS) events thus far assumed to be generated by the solar wind's interaction with a large-density reflected component are actually detached from the bow shock. In other geometries, ions stay close to the shock after their TD interaction, implying that ACS events are modifications of the shock.

Shock-wave-induced mixing enhancement in scramjet combustors

Abstract: An experimental study of the interaction between a weak shock wave and a supersonic shear layer was carried out to determine the possibility of shock-induced mixing enhancement. A supersonic (Mach 2.5) stream of nitrogen was mixed with a sonic helium jet downstream of a rearward-facing step to simulate the mixing region in the vicinity of a SCRAMJET flameholder. A small wedge was used to generate an oblique shock wave that impinges on the mixing layer. Schlieren flow visualization and Rayleigh scattering concentration measurements were carried out. The results indicate that significant spreading of the shear layer may occur downstream of the shock/shear layer interaction region. Further study is required to determine the mechanism of the observed spreading and the extent of the increase in mixing efficiency. Since there are shock-induced losses, an optimum mixing enhancement configuration will have to be determined before the method can be validated and successfully implemented in a SCRAMJET combustor.

On the structure of resistive MHD intermediate shocks

Abstract: An overview is presented of the resistive steady state structure of intermediate MHD shocks, ie, shocks that effect a transition from super-alfvenic to sub-alfvenic flow The results are presented in terms of magnetic hodograms in which the two components of the magnetic field tangential to the shock surface are plotted against each other By performing fixed-point analysis in this plane, at the possible upstream and downstream states of these shocks, and by solving the one-dimensional, steady state, resistive, nonviscous MHD equations numerically, it is found that three basic types of hodogram topology exist, describing the resistive intermediate shock structure These topologies are characterized by the normal flow speed (in the shock frame) relative to the fast-wave speed and the sound speed at the upstream and downstream states Fast-mode and slow-mode shocks are contained within these hodograms as well In brief summary, it is found that all intermediate shocks that have an upstream normal flow speed, νx1, less than the local small-amplitude fast-mode wave speed, cf1, and a downstream normal flow speed, νx2, greater than the local small-amplitude slow-mode wave speed, cs2, have a unique magnetic structure consisting mainly of a rotation of the tangential magnetic field, accompanied by a more or less pronounced change in field magnitude This type of shock is called a subfast (νx1 cs2) intermediate shock A subfast strong intermediate shock has νx1 cf1) The structures of both weak (νx2>cs2) and strong (νx2 c1) to subsonic (νx2

Spallation studies in aluminum targets using shock waves induced by laser irradiation at various pulse durations

Abstract: The conditions of laser‐driven shock wave loading lead to the study of the dynamic fracture in an unusual range of stress and strain rates: 20–200 GPa and more than 107 s−1. A cumulative damage criterion for the spallation process has been included in a one‐dimensional finite difference hydrodynamic code. Numerical studies show the effect of different parameters: laser‐pulse duration, peak induced pressure related to the incident intensity, and target thickness. The simulation results are in agreement with spallation shock‐laser experiments on aluminum targets of various thicknesses irradiated by laser pulses of durations between 0.6 and 25 ns with an incident intensity of about 1012 W/cm2 .

Modeling two‐dimensional detonations with detonation shock dynamics

Abstract: One of the principal shortcomings of the computer models that are presently used for two‐dimensional explosive engineering design is their inadequate treatment of the explosive’s detonation reaction zone. Current methods lack the resolution to both calculate the broad gas expansion region and model the thin reaction zone with reasonable detail. Recently an alternative method for modeling the reaction zone has been developed. This method applies when the radius of curvature of the shock is large compared to the reaction‐zone length. In this limit, the dynamics of the interaction between the chemical heat release and the two‐dimensional flow in the reaction zone is quasisteady. It is summarized by a relation Dn(κ), between the local normal shock velocity Dn and shock curvature κ. When this relation is combined with the kinematic surface condition (an equation that describes how disturbances move along the shock), the two‐dimensional reaction‐zone calculation is reduced to a one‐dimensional calculation.

"Electron acceleration at nearly perpendicular collisionless shocks, 1, One-dimensional simulations without electron scale fluctuations""

Abstract: Under certain conditions electrons can be reflected and effectively energized at quasi-perpendicular shocks. This process is most prominent close to the point where the upstream magnetic field is tangent to the curved shock. A theoretical explanation of the underlying physical mechanism has been proposed which assumes conservation of magnetic moment and a static, simplified shock profile are performed. Test particle calculations of the electron reflection process in order to examine the results of the theoretical analysis without imposing these restrictive conditions. A one-dimensional hybrid simulation code generates the characteristic field variations across the shock. Special emphasis is placed on the spatial and temporal length scales involved in the mirroring process. The simulation results agree generally well with the predictions from adiabatic theory. The effects of the cross-shock potential and unsteadiness are quantified, and the influence of field fluctuations on the reflection process is discussed.