Showing papers on "Shock wave published in 1985"

Errors for calculations of strong shocks using an artificial viscosity and an artificial heat flux

Abstract: The artificial viscosity (Q) method of von Neumann and Richtmyer is a tremendously useful numerical technique for following shocks wherever and whenever they appear in the flow. We show that it must be used with some caution, however, as serious Q-induced errors (on the order of 100%) can occur in some strong shock calculations. We investigate three types of Q errors: 1. Excess Q heating, of which there are two types: (a) excess wall heating on shock formation and (b) shockless Q heating; 2. Q errors when shocks are propagated over a nonuniform mesh; and 3. Q errors in propagating shocks in spherical geometry. As a basis of comparison, we use as our standard the Lagrangian formulation with Q = C/sup 2//sub 0/rhol/sup 2/(u/sub x/)/sup 2/. This standard Q is compared with Noh's (Q and H) shock-following method, which employs an artificial heat flux (H) in addition to Q, and with the (non-Q) piecewise-parabolic method (PPM) of Colella and Woodward. Both the (Q and H) method and PPM (particularly when used with an adaptive shock-tracking mesh) give superior results for our test problems. In spherical geometry, Schulz's and Walen's tensor Q formulations of the hydrodynamic equations prove to be moremore » accurate than the standard Q formulation, and when Schulz's formulation is combined with Noh's (Q and H) method, superior results are achieved. Copyright 1987 Academic Press, Inc.« less

Shock acceleration of electrons and ions in solar flares

Abstract: The simultaneous first-order Fermi shock acceleration of electrons, protons, and alpha particles are compared to observations of solar energetic particle events. For each event, a unique shock compression ratio in the range of approximately 1.6-3 produces spectra in good agreement with observation. The range in compression ratios predicts that the more than five orders of magnitude spread in electron-to-proton intensity ratios observed at MeV energies is compressed to about three orders of magnitude at an assumed injection energy of 100 keV. The remaining spread can be accounted for with a modest range of injection conditions. The model predicts that the acceleration time to a given energy will be approximately equal for electrons and protons, and for reasonable solar parameters, can be on the order of 1 s to approximately 100 MeV. 37 references.

Shock viscosity and the prediction of shock wave rise times

Abstract: The present study is focused on viscouslike behavior of solids during large‐amplitude compressive stress‐wave propagation. Maximum strain rate in the plastic wave has been determined for 30 steady‐ or near steady‐wave profiles obtained with velocity interferometry methods. The materials include six metals, aluminum, beryllium, bismuth, copper, iron, and uranium, and two insulating solids, magnesium oxide and fused silica. A plot of Hugoniot stress versus maximum strain rate for each material is adequately described by η=aσmh. The exponent m is approximately 4 for all materials while the coefficient a is material dependent. A model is developed which incorporates the observed trends of the shock viscosity data in a three‐dimensional framework. Finite‐difference calculations using the model reproduce the experimental wave profile data.

On convergence of computation of chemically reacting flows

Abstract: The computational problems associated with high-temperature flows undergoing finite-rate ionization reactions is investigated. The conservation equations governing chemical species and vibrational and electron energies are solved simultaneously with those for overall mass, momentum, and energy for a one-dimensional subsonic flow, through a constant-area duct, originating behind a normal shock wave, using an implicit time-marching technique. Boundary conditions are imposed in the form of characteristic wave variables accounting for the effects of chemical reactions on the speed of sound. Converging solutions are obtained for cases in which chemical reactions are weak, but difficulty is encountered in other cases. The cause of the difficulty is investigated and shown to be the sharp pressure disturbances produced by such reactions.

Coupling of newborn ions to the solar wind by electromagnetic instabilities and their interaction with the bow shock

Abstract: The process by which the solar wind assimilates newly ionized atoms is important for understanding the presence of planetary or interstellar helium in the solar wind, the dynamics of the Active Magnetospheric Particle Tracer Explorers (AMPTE) lithium releases in front of the earth's bow shock, and the formation of cometary tails. In this paper we examine how newborn ions can be coupled to the solar wind in the direction parallel to the magnetic field by means of electromagnetic instabilities driven by the distribution of newborn ions. The linear properties of three instabilities are analyzed and compared with numerical solutions of the linear dispersion equation, while their nonlinear behavior is followed by means of computer simulation to obtain the characteristic time for the pickup process. With a primary emphasis on the AMPTE lithium releases, various degrees of realism are introduced into the calculations to model the upstream conditions and the intersection of the lithium with the bow shock. It is shown that a time-dependent shock model is needed to correctly reproduce the amount of lithium which is transmitted through the shock and that the resulting lithium ion distribution is still likely to be subject to the same type of instabilities in the magnetosheath. Application of these results to comets, in particular the artificial comet expected to be generated by the AMPTE barium release in the magnetosheath, is also briefly discussed.

Collisionless shocks in the heliosphere: Reviews of current research

Abstract: The present conference on heliospheric collisionless shocks considers such macrostructure-, microstructure-, and particle acceleration-related topics as interplanetary shock phenomena near and within 1 AU, as well as beyond, planetary bow shocks, shock formation and evolution in the solar atmosphere, MHD and gasdynamic theories for planetary bow waves, and subcritical collisionless shock waves. Also discussed are ion reflection, gyration, and dissipation at supercritical shocks, the numerical simulation of quasi-perpendicular collisionless shocks, electron distributions near collisionless shocks, the microtheory of collisionless shock current layers, plasma waves and instabilities, the electron foreshock, upstream suprathermal ions, and both diffusive and shock drift acceleration.

Acceleration of >47 keV Ions and >2 keV electrons by interplanetary shocks at 1 AU

Abstract: We present initial results from a survey of the effects of interplanetary shocks on energetic ≥2 keV electrons and ≥47 keV ions, as observed by the field, plasma, and energetic particle experiments on the ISEE 3 spacecraft. Shock normals, velocities, Mach numbers, and upstream and downstream plasma parameters were determined for 37 forward shocks out of a total of 55 shocks observed between August 1978 and November 1979. We find that a minimum shock velocity along the upstream magnetic field of ∼250 km/s is required for an interplanetary shock to have a significant effect on acceleration of ≥2 keV electrons or ≥47 keV ions. Shocks with no effect on the energetic particle populations also had relatively small ratios of downstream to upstream magnetic field magnitudes. These results suggest that magnetostatic reflection off the shock itself is a significant mechanism in the acceleration process. Both energetic electron and ion flux variations associated with shocks can be classified into four general types: (1) no significant variation at all, (2) a spike of a few minutes duration at or near the shock, (3) a steplike postshock increase, and (4) a slow rise beginning several hours before the shock (energetic storm particle event). Essentially, every quasi-perpendicular shock with θBn ≳ 70° produced a shock spike in the proton fluxes, while every quasi-parallel shock (θBn ≲ 50°) produced a proton energetic storm particles event, provided the shock velocity was greater than the above stated threshold. Electron spikes were also observed for most, but not all, shocks with θBn ≳ 70°. The most common effect observed in the electron fluxes was a steplike postshock increase of a factor of ∼2. These had no obvious dependence on θBn, but were found for every shock with speed greater than ∼175 km/s. Shock effects in the electron fluxes were about as common as for protons, but were limited to the 2–10 keV energy range except for 3 events which extended up to ∼50 keV. We find that significant ambient populations of both ≥2 keV electrons and ≳47 keV ions are present in the interplanetary medium prior to every shock. These particles could be the “seed” particles for the shock acceleration.

Unsteadiness of the shock wave structure in attached and separated compression ramp flows

Abstract: Wall pressure fluctuations have been measured upstream of the corner-line in several two dimensional, adiabatic, compression ramp flows. The nominal freestream Mach number was 3 and the Reynolds number, based on boundary layer thickness, was 1.4 million. The measurements show that the shockwave structure is unsteady in both separated and attached flows, resulting in a region in which the wall pressure signal is intermittent. Statistical properties of this intermittent region, and of the separated flow, are presented and correlated with results from other studies.

Ion and electron heating at collisionless shocks near the critical Mach number

Abstract: The present study has the objective to document more fully a somewhat surprising heating pattern for 10 of the bow shock crossings investigated by Russell et al. (1982). A description of the detailed evolution of the actual distribution functions across the subcritical shocks is also provided. It is pointed out that the shocks examined are all very near the theoretical one-fluid critical Mach number. None of the shocks has a significant magnetic foot or overshoot. It is argued that the observed heating is not due to reflected ions but rather to physical processes characteristic of subcritical shocks.

A multiple-scales model of the shock-cell structure of imperfectly expanded supersonic jets

Abstract: The present investigation is concerned with the development of an analytical model of the quasi-periodic shock-cell structure of an imperfectly expanded supersonic jet. The investigation represents a part of a program to develop a mathematical theory of broadband shock-associated noise of supersonic jets. Tam and Tanna (1982) have suggested that this type of noise is generated by the weak interaction between the quasi-periodic shock cells and the downstream-propagating large turbulence structures in the mixing layer of the jet. In the model developed in this paper, the effect of turbulence in the mixing layer of the jet is simulated by the addition of turbulent eddy-viscosity terms to the momentum equation. Attention is given to the mean-flow profile and the numerical solution, and a comparison of the numerical results with experimental data.

Surface reactions of metal clusters I: The fast flow cluster reactor

Abstract: A new fast flow device for the study of metal cluster reactions in the gas phase is described and characterized. The new device utilizes metal clusters made by laser vaporization of an appropriate metal target mounted in the throat of a supersonic nozzle which exhausts into a fast‐flow reaction tube. Reactants are injected into the flowing helium–metal cluster mixture at a point in the flow tube where shock waves have reheated the gas to roughly 320 K. Turbulence in the wake of these shock waves produces efficient mixing of the reactants. Measurement of the flow properties of this reaction tube indicate a residence time of 150–200 μs with an average density of helium buffer gas equivalent to 50–100 Torr at room temperature. Subsequent free expansion of this reaction mixture into a large vacuum chamber produces a supersonic beam with extensive cooling of the various constituents in the mixture (pyrazine was measured to be rotationally cooled to 10 K). The new cluster reaction device is, therefore, an excellent source for future studies of the jet‐cooled metal cluster reaction products themselves.

Preionization-dependent families of radiative shock waves

Abstract: Radiation shock waves are shown to be organizable into families within which the spectra are very similar. A high-velocity shock into neutral material is spectrally similar to a somewhat slower shock in fully ionized material. The similarities should allow the identification of the family to which an observed spectrum belongs, while spectral details permit subsequent identification of the separate values of shock velocity and preionization. By calculating shock spectra for the various families at constant recombination zone density, rather than constant preshock density, it is possible to separate the effects of 'velocity' (by which is meant postionization enthalpy per atom) from those of 'density' (by which is meant the degree of collisional deexcitation in the optical lines).

The unsteadiness of shock waves propagating through gas-particle mixtures

Abstract: A shock wave which is incident onto a gas-particle mixture or initiated within such a mixture needs a certain distance to reach a constant velocity. This effect is due to the inertia and the heat capacity of the particles. In general the shock wave is decelerated and the frozen pressure jump is decaying.

Strong ion acceleration by a collisionless magnetosonic shock wave propagating perpendicularly to a magnetic field

Abstract: A 2 1/2 ‐dimension, fully relativistic, fully electromagnetic particle code is used to study the time evolution of a nonlinear magnetosonic pulse propagating in a direction perpendicular to a magnetic field. The pulse is excited by an instantaneous piston acceleration, and evolves in a totally self‐consistent manner. A large amplitude pulse traps some ions and accelerates them parallel to the wave front. They are detrapped when their velocities become of the order of the sum of the E×B drift velocity and the wave phase velocity, where E is the electric field in the direction of the wave propagation. The pulse develops into a quasishock wave in a collisionless plasma because of dissipation caused by the resonant ion acceleration. A simple nonlinear wave theory for a cold plasma describes the shock properties observed in the simulation except for the effects of resonant ions. In particular, the magnitude of an electric potential across the shock region is derived analytically and is found to be in good agreement with our simulations. The potential jump is proportional to B2, and hence the E×B drift velocity of the trapped ions is proportional to B.

A simplified model for timing the arrival of solar flare‐initiated shocks

Abstract: The solar flare-initiated shock can be considered to be an initially driven shock that converts into a blast wave as it propagates through the interplanetary medium In our simplified shock modeling, to estimate the time of the shock arrival at a specified position in space we assume that the shock is initially driven from the flare position at the velocity indicated by the type II solar radio burst We assume the shock is driven until the initiating solar flare energy is somewhat expended After this initially driven phase, the shock front then propagates with the characteristic speed expected of the shock front of a blast wave In the interplanetary medium with its 1/r² density dependence, the blast wave shock front speed should be proportional to r−05 We find that this r−05 speed dependence is a general characteristic of the shock front speed when the speeds are determined in the solar wind reference frame The blast wave “rides over” the preexisting solar wind so that the disturbance speed of the shock front at any instant of time is the speed of the shock front added vectorially to the solar wind speed Application of these principles enables a consistent “timing” of solar flare-initiated shock waves that is event independent We show that this concept is consistent with the time position profile derived from the analysis of kilometric type II events that are associated with interplanetary shocks

Characteristics of energetic particle events associated with interplanetary shocks

Abstract: We present observations of the 35- to 1600-keV proton intensity-time profiles and the three-dimensional 35- to 56-keV anisotropy distributions recorded during two interplanetary shock events on ISEE 3, and discuss these in the light of current particle acceleration models. The large April 5, 1979, event associated with a quasi-parallel shock shows an extended foreshock region with a strong increase of the upstream proton flux, a downstream plateaulike profile, upstream flow from the shock, and downstream isotropy in the solar wind frame of reference. The small March 9, 1979, event has a structured intensity-time profile, a narrow shock spike, and anisotropic angular distributions both upstream and downstream, the anisotropies immediately behind the shock exhibiting an intensity peak at pitch angles around 90°. The April event, representative for a class of large energetic storm particle events, shows many observational features which are in agreement with predictions made by diffusive shock acceleration models. The March event, representative for a class of events with irregular profiles and mainly associated with quasi-perpendicular shocks, exhibits features which are characteristic of shock drift acceleration. We conclude that both acceleration models are operative in association with interplanetary shocks.

Shock wave tube for the fragmentation of concrements

Abstract: In a shock wave tube for concrement fragmentation in a patient the coil is formed as a plane flat coil A tubular connecton leads from the region between the flat coil and a diaphragm disposed before it to the suction side of a vacuum pump During operation of the shock wave tube, the diaphragm is sucked against the flat coil The arrangement has the advantage that a pressure chamber for pressing the diaphragm from the outside is eliminated Therefore the shock waves need not pass through any exit windows, owing to which malfunctions due to cracks in the exit window are obviated The shock wave tube can be designed in a very compact form in conjunction with reflectors The reflectors preferably have a parabolic form with a focus at which the concrement of the patient is positioned

Modeling short pulse duration shock initiation of solid explosives

Abstract: The chemical reaction rate law in the ignition and growth model of shock initiation and detonation of solid explosives is modified so that the model can accurately simulate short pulse duration shock initiation The reaction rate law contains three terms to model the ignition of hot spots by shock compression, the slow growth of reaction from these isolated hot spots, and the rapid completion of reaction as the hot spots coalesce Comparisons for PBX 9404 between calculated and experimental records are presented for the electric gun mylar flyer plate system, the minimum priming charge test, embedded manganin pressure and particle velocity gauges, and VISAR particle velocity measurements for a wide variety of input pressures, rise times and pulse durations The ignition and growth model is now a fully developed phenomenological tool that can be applied with confidence to almost any hazard, vulnerability or explosive performance problem 27 refs, 16 figs, 2 tabs

Conical similarity of shock/boundary-layer interactions generated byswept and unswept fins

Abstract: A parametric experimental investigation has been made of the class of three-dimensional shock wave/turbulent boundary layer interactions generated by swept and unswept leading-edge fins. The fin sweepback angles were 0-65 deg at 5, 9, and 15 deg angles of attack. Two equilibrium two-dimensional turbulent boundary layers with a freestream Mach number of 2.95 and a Reynolds number of 6.3 x 10 to the 7th/m were used as incoming flow conditions. All of the resulting interactions were found to possess conical symmetry of the surface flow patterns and pressures outside of an initial inception zone. Further, these interactions were found to obey a simple conical similarity rule based on inviscid shock wave strength, irrespective of fin sweepback or angle of attack. This is one of the first demonstrations of similarity among three-dimensional interactions produced by geometrically dissimilar shock generators.

Cylindrical sound wave generated by shock-vortex interaction

Abstract: The passage of a columnar vortex broadside through a shock is investigated. This has been suggested as a crude, but deterministic, model of the generation of 'shock noise' by the turbulence in supersonic jets. The vortex is decomposed by Fourier transform into plane sinusoidal shear waves disposed with radial symmetry. The plane sound waves produced by each shear wave/shock interaction are recombined in the Fourier integral. The waves possess an envelope that is essentially a growing cylindrical sound wave centered at the transmitted vortex. The pressure jump across the nominal radius R = ct attenuates with time as 1/(square root of R) and varies around the arc in an antisymmetric fashion resembling a quadrupole field. Very good agreement, except near the shock, is found with the antisymmetric component of reported interferometric measurements in a shock tube. Beyond the front r approximately equals R is a precursor of opposite sign, that decays like 1/R, generated by the 1/r potential flow around the vortex core. The present work is essentially an extension and update of an early approximate study at M = 1.25. It covers the range (R/core radius) = 10, 100, 1000, and 10,000 for M = 1.25 and (in part) for M = 1.29 and, for fixed (R/core radius) = 1000, the range M = 1.01 to infinity.

A theory for the 2fp radiation upstream of the Earth's bow shock

Abstract: The mechanism responsible for the radiation observed near the earth bow shock at twice the plasma frequency f(p) is investigated theoretically. A model comprising two three-wave steps and involving Langmuir (L), ion-sound (S), and EM (t) waves is proposed: L + or - S yields L-prime; L + L-prime yields t. This model is shown to be consistent with observations of low-frequency S-like waves (Anderson et al., 1981), and further observational tests are suggested. A critical examination of the theory of Fung et al. (1982) is included, and it is found that an important term in the absorption coefficient was neglected. Correcting this error leads to an intrinsic theoretical brightness-temperature limit of 3 x 10 to the 9th K, well below the observed brightness temperature of the 2 f(p) radiation, about 10 to the 11th K.

Simulation of the Effects of Shock Wave Passing on a Turbine Rotor Blade

Abstract: The unsteady effects of shock waves and wakes shed by the nozzle guide vane row on the flow over a downstream turbine rotor have been simulated in a transient cascade tunnel. At conditions representative of engine flow, both wakes and shock waves are shown to cause transient turbulent patches to develop in an otherwise laminar (suction-surface) boundary layer. The simulation technique employed, coupled with very high-frequency heat transfer and pressure measurements, and flow visualization, allowed the transition initiated by isolated wakes and shock waves to be studied in detail. On the profile tested, the comparatively weak shock waves considered do not produce significant effects by direct shock-boundary layer interaction. Instead, the shock initiates a leading edge separation, which subsequently collapses, leaving a turbulent patch that is convected downstream. Effects of combined wake- and shock wave-passing at high frequency are also reported.

Simulations of high-Mach-number collisionless perpendicular shocks in astrophysical plasmas.

Abstract: A problem of critical importance to space physics and astrophysics is the existence and properties of high-Mach-number shocks. Preliminary results of a simulation of a perpendicular shock with Alfven Mach number 22 are reported. It is shown that for sufficiently small electron resistivity the dissipation for this shock is provided by a periodic rather than time-stationary reflection of ions. The problem of electron heating and the extension to higher Mach numbers are discussed.

Doppler scintillation observations of interplanetary shocks within 0.3 AU

Abstract: It is pointed out that more definitive shock velocity observations near the sun are needed for an improved determination of the extent of shock deceleration from the sun to earth. Woo and Armstrong (1981) have demonstrated the use of radio scattering and scintillation observations, using spacecraft signals, for measuring interplanetary shock waves near the sun. Woo and Armstrong provided the first near-sun profiles of solar wind speed and electron density fluctuation for a shock wave produced by a solar flare. The present investigation has the objective to demonstrate the use of Doppler or phase scintillations for monitoring and observing interplanetary shocks. It is also shown that Doppler noise, a parameter which is routinely observed and recorded by the NASA Deep Space Network, is essentially a measure of Doppler scintillations.

On the initial phase of interaction between expanding stellar envelopes and surrounding medium

Abstract: The initial stages of deceleration in the circumstellar medium of a stellar envelope, thrown off by a shock wave, are investigated. The equations of spherical-symmetric adiabatic hydrodynamics are shown to have a similarity solution in the case of the density of the expanding envelope being approximated by a reasonable power law. The overall flow pattern has such a form that the stellar material is decelerated in the internal shock wave while another shock propagates through the circumstellar matter. Between the shocks there is a contact discontinuity separating the circumstellar and stellar matter. The characteristics of the similarity solution are calculated for various exponents in the density laws of an expanding envelope and circumstellar matter and for two values of the adiabatic index (γ=5/3, 4/3). Some parts of the flow exhibit Rayleigh-Taylor instability.