Showing papers on "Shock (mechanics) published in 1999"

A Simple Model of Nonlinear Diffusive Shock Acceleration

Abstract: We present a simple model of nonlinear diffusive shock acceleration (also called first-order Fermi shock acceleration) that determines the shock modification, spectrum, and efficiency of the process in the plane-wave, steady state approximation as a function of an arbitrary injection parameter, η. The model, which uses a three-power-law form for the accelerated particle spectrum and contains only simple algebraic equations, includes the essential elements of the full nonlinear model and has been tested against Monte Carlo and numerical kinetic shock models. We include both adiabatic and Alfven wave heating of the upstream precursor. The simplicity and ease of calculation make this model useful for studying the basic properties of nonlinear shock acceleration, as well as providing results accurate enough for many astrophysical applications. It is shown that the shock properties depend upon the shock speed u0 with respect to a critical value u ηp, which is a function of the injection rate η and maximum accelerated particle momentum pmax. For u0 MA0, or by rtot ≈ 1.5M in the opposite case (MS0 is the sonic Mach number and MA0 is the Alfven Mach number). If u0 > u, the shock, although still strong, becomes almost unmodified and accelerated particle production decreases inversely proportional to u0.

Melt Production in Oblique Impacts

Abstract: Hydrocode modeling is a fundamental tool for the study of melt production in planetary impact events. Until recently, however, numerical modeling of impacts for melt production studies has been limited to vertical impacts. We present the first results of the investigation of melt production in oblique impacts. Simulations were carried out using Sandia's three-dimensional hydrocode CTH, coupled to the SESAME equation of state. While keeping other impact parameters constant, the calculations span impact angles (measured from the surface) from 90° (vertical impact) to 15°. The results show that impact angle affects the strength and distribution of the shock wave generated in the impact. As a result, both the isobaric core and the regions of melting in the target appear asymmetric and concentrated in the downrange, shallower portion of the target. The use of a pressure-decay power law (which describes pressure as function of linear distance from the impact point) to reconstruct the region of melting and vaporization is therefore complicated by the asymmetry of the shock wave. As an analog to the pressure decay versus distance from the impact point, we used a “volumetric pressure decay,” where the pressure decay is modeled as a function of volume of target material shocked at or above the given shock pressure. We find that the volumetric pressure decay exponent is almost constant for impact angles from 90° to 30°, dropping by about a factor of two for a 15° impact. In the range of shock pressures at which most materials of geologic interest melt or begin to vaporize, we find that the volume of impact melt decreases by at most 20% for impacts from 90° down to 45°. Below 45°, however, the amount of melt in the target decreases rapidly with impact angle. Compared to the vertical case, the reduction in volume of melt is about 50% for impacts at 30° and more than 90% for a 15° impact. These estimates do not include possible melting due to shear heating, which can contribute to the amount of melt production especially in very oblique impacts. Studies of melt production in vertical impacts suggest an energy scaling law in agreement with the point source limit. An energy scaling law, however, does not seem to hold for oblique impacts, even when the impact velocity is substituted by its vertical component. However, we find that for impact angles between about 30° and 90° (a range that includes 75% of impact events on planetary surfaces) the volume of melt is directly proportional to the volume of the transient crater generated by the impact.

Miscible displacement in a Hele-Shaw cell at high rates

Abstract: We study experimentally and theoretically the downward vertical displacement of one miscible fluid by another lighter one in the gap of a Hele-Shaw cell at sufficiently high velocities for diffusive effects to be negligible. Under certain conditions on the viscosity ratio, M , and the normalized flow rate, U , this results in the formation of a two-dimensional tongue of the injected fluid, which is symmetric with respect to the midplane. Thresholds in flow rate and viscosity ratio exist above which the two- dimensional flow destabilizes, giving rise to a three-dimensional pattern. We describe in detail the two-dimensional regime using a kinematic wave theory similar to Yang & Yortsos (1997) and we delineate in the ( M , U )-plane three different domains, characterized respectively by the absence of a shock, the presence of an internal shock and the presence of a frontal shock. Theoretical and experimental results are compared and found to be in good agreement for the first two domains, but not for the third domain, where the frontal shock is not of the contact type. An analogous treatment is also applied to the case of axisymmetric displacement in a cylindrical tube.

Shock detection from computational fluid dynamics results

Abstract: In complex flow regimes, it may be dimcult for an analyst to find the location of shock diecontinuities within a Computational Fluid Dynamics (CFD) solution. They do not correspond to locations where the math number is unity, and the high gradients associated with the discontinuity can be dimcult to detect because of numerical smoothing performed in order to obtain the solution. An algorithm is introduced that uses the flow physics to locate shocks in transient and steady state solutions. The test was validated with simple one and two dimensional models, then extended to more realistic three dimensional flows. A set of flltering algorithms was developed to remove any false shock indications. Results indicate that both the stationary and transient shock flnding algorithms accurately locate shocks, but need Altering to compensate for a lack of sharpness in C&‘D discontinuities.

The Nature of "Maskelymite" in Shocked Meteorites: Not Diaplectic Glass but Glass Quenched from Shock-induced Dense Melt at High Pressures

Abstract: Abstract Maskelynite, an important constituent of shocked meteorites, once thought to be diaplectic plagioclase glass formed by shock-induced solid-state transformation. Our systematic investigation of shocked L-chondrites and SNC meteorites indicates that maskelynite does not contain inherited fractures or cleavage, and shock-induced fractures. We found no evidence for models calling for melting that initiated in PDFs and affected the whole crystals. Maskelynite grains are smooth and display radiating cracks emerging from their surfaces into neighboring pyroxene. This is indicative of shock-induced melting and quenching of the dense melt at high pressure, thus erasing the inherited and shock-induced fractures. This was followed by relaxation of the dense plagioclase glass, which induced the expansion cracks in pyroxene and olivine. Enrichment in potassium, deviation from stoichiometry, degradation of igneous zoning, the presence of offshoots of maskelynite in pyroxene, the lack of vesiculation in the melt pockets, melt veins and molten mesostasis are clear evidence for melting and quenching under high pressure. Our investigations present unequivocal evidence that maskelynite in meteorites is not diaplectic plagioclase glass formed by solid-state transformation, but a dense quenched glass. The duration of the shock pulse in natural events can be several orders of magnitude longer than in shock experiments. Since kinetic effects are crucial factors in promoting phase transitions, vitrification and melting, experimentally induced solid-state vitrification of plagioclase produced in dynamic experiments is inadequate for calibration of peak shock pressures in maskelynite-bearing natural samples.

Accuracy of Shock Capturing in Two Spatial Dimensions

Abstract: An assessment of the accuracy of shock capturing schemes is made for two-dimensional steady flow around a cylindrical projectile. Both a linear fourth-order method and a nonlinear third-order method are used in this study. It is shown, contrary to conventional wisdom, that captured two-dimensional shocks are asymptotically first-order, regardless of the design accuracy of the numerical method. The practical implications of this finding are discussed in the context of the efficacy of high-order numerical methods for discontinuous flows.

Holographic Interferometric Visualization of the Richtmyer-Meshkov Instability Induced by Cylindrical Shock Waves

Abstract: Results of quantitative holographic interferometric flow visualization of cylindrical interface instability induced by converging cylindrical shock waves are reported. Experiments were conducted in an annular vertical co-axial diaphragmless shock tube, in which cylindrical soap bubbles filled with He, Ne, Air, Ar, Kr, Xe and SF_6 were co-axially placed in its test section. Pressure histories at different radii during the shock wave implosion and reflection from the center were measured. Diagnostic method base on double exposure holographic interferometry was applied for the measurement of turbulent mixing zone at the interface. The observed cylindrical interfaces were found to have a higher growth rate of turbulent mixing zone than that of the plane shock / plane interface.

Numerical Computation of Shock Waves in a Spherical Cloud of Cavitation Bubbles

Abstract: The nonlinear dynamics of a spherical cloud of cavitation bubbles have been simulated numerically in order to learn more about the physical phenomena occurring in cloud cavitation. A finite cloud of nuclei is subject to a decrease in the ambient pressure which causes the cloud to cavitate. A subsequent pressure recovery then causes the cloud to collapse. This is typical of the transient behavior exhibited by a bubble cloud as it passes a body or the blade of a ship propeller. The simulations employ the fully nonlinear continuum mixture equations coupled with the Rayleigh-Plesset equation for the dynamics of bubbles. A Lagrangian integral method is developed to solve this set of equations. It was found that, with strong bubble interaction effects, the collapse of the cloud is accompanied by the formation of an inward propagating bubbly shock wave, a large pressure pulse is produced when this shock passes the bubbles and causes them to collapse. The focusing of the shock at the center of the cloud produces a very large pressure pulse which radiates a substantial impulse to the far field and provides an explanation for the severe noise and damage potential in cloud cavitation.

Coupled hydromagnetic wave excitation and ion acceleration at interplanetary traveling shocks and Earth's bow shock revisited

Abstract: A revised version of the self-consistent theory of ion diffusive shock acceleration and the associated generation of hydromagnetic waves is presented. The theory generalizes and corrects the theory of Lee [1982, 1983]. Lee assumed a linear dependence of the anisotropic part of the ion distribution function on the cosine of the ion pitch angle. Here the wave growth or damping rate is again calculated using linear theory, but a more general ion anisotropy is calculated using the pitch angle diffusion equation. The wave intensity satisfies a wave kinetic equation, and the ion omnidirectional distribution function satisfies the energetic particle transport equation. These coupled equations are solved numerically and compared with an analytical approximation similar to that derived by Lee. The analytical approximation provides an accurate representation of both the proton distribution and the wave intensity. A comparison is made between the predicted wave magnetic power spectral density adjacent to the shock as a function of frequency and the wave spectrum measured by ISEE 3 at the November 11–12, 1978, interplanetary traveling shock. There is excellent agreement between the predicted and measured power spectral density in the frequency range of 0.03–0.3 Hz. A comparison is also made between the predicted total wave energy density and that observed upstream of Earth's bow shock by the AMPTE/IRM satellite for a statistical survey of ∼400 near-to nose events from late 1984 and 1985. This comparison revises the result presented by Trattner et al. [1994]. The correlation between the observed wave power and that predicted, based on the observed energetic proton energy density, is very good with a correlation coefficient of 0.92. However, the average observed wave magnetic energy density is ∼63% of that predicted, suggesting possible wave dissipation which is not included in the theory.

A mechanistic model for shock initiation of solid explosives

Abstract: This paper is devoted to the building of a model for the ignition and growth of a detonation in pressed solid explosives. The ignition model describes the various phenomena occurring at the microscopic scale during viscoplastic pore collapse. The growth stage is represented by a model combining inner combustion inside the pores and outer combustion on the surface of the grains. These microscopic models are incorporated into a macroscopic one. The macroscopic model reproduces waves propagation and takes into account the various couplings between the microscopic and macroscopic scales. Pores and grain size distributions are also considered. The governing equations are solved using a shock tracking high resolution scheme, in order to avoid numerical smearing of the shock front. The role of microscopic topology of the explosive is investigated. Results are validated on pressure gauge records and shock to detonation transition distance (Pop-plots).

Shock-resistive printed circuit board and electronic device including the same

Abstract: A printed circuit board has a layer including a resin material, which has a tensile breaking strain of approximately 1% or more at a tensile strain rate of 40%/sec at 25° C., and an Izod impact strength of approximately 1 kgf·cm/cm or more at 25° C. Otherwise, the resin material has a peak value of dynamic loss tangent of 0.05 or more in a range of −100° C. to −50° C. by β relaxation, and a peak value of dynamic loss tangent of 0.02 or more in a range of 0° C. to 100° C. by β′ relaxation in a dynamic viscoelasticity spectral measurement. Accordingly, thermal shock resistance and drop shock resistance of the printed circuit board can be improved.

Anode/cathode make and break phenomena in a model of defibrillation

Abstract: The goal of this simulation study is to examine, in a sheet of myocardium, the contribution of anode and cathode break phenomena in terminating a spiral wave reentry by the defibrillation shock. The tissue is represented as a homogeneous bidomain with unequal anisotropy ratios. Two case studies are presented in this article: tissue that can electroporate at high levels of transmembrane potential, and model tissue that does not support electroporation. In both cases, the spiral wave is initiated via cross-field stimulation of the bidomain sheet. The extracellular defibrillation shock is delivered via two small electrodes located at opposite tissue boundaries. Modifications in the active membrane kinetics enable the delivery of high-strength defibrillation shocks. Numerical solutions are obtained using an efficient semi-implicit predictor-corrector scheme that allows one to execute the simulations within reasonable time. The simulation results demonstrate that anode and/or cathode break excitations contribute significantly to the activity during and after the shock. For a successful defibrillation shock, the virtual electrodes and the break excitations restrict the spiral wave and render the tissue refractory so it cannot further maintain the reentry. The results also indicate that electroporation alters the anode/cathode break phenomena, the major impact being on the timing of the cathode-break excitations. Thus, electroporation results in different patterns of transmembrane potential distribution after the shock. This difference in patterns may or may not result in change of the outcome of the shock.

Method and apparatus for controlling write operations of a data storage system subjected to a shock event

Abstract: A method and apparatus for controlling write operations for a data storage system during and after a shock event is disclosed. A shock sensor measures the magnitude of a shock event and compares the magnitude of the shock event to at least two predetermined thresholds. Write operations are then inhibited based upon the comparison of the magnitude of the shock event and the at least two predetermined thresholds. When the shock event meets a first upper threshold, the write is inhibited until the write is requalified. The write is executed if the measured shock event does not meet a second lower threshold and the write is paused for a predetermined time period when the measured shock event meets the second lower threshold but does not meet the first upper threshold.

Relativistic Winds from Compact Gamma-Ray Sources: II. Pair Loading and Radiative Acceleration in Gamma-ray Bursts

Abstract: We consider the effects of rapid pair creation by an intense pulse of gamma-rays propagating ahead of a relativistic shock. Side-scattered photons colliding with the main gamma-ray beam amplify the density of scattering charges. The acceleration rate of the pair-loaded medium is calculated, and its limiting bulk Lorentz factor related to the spectrum and compactness of the photon source. One obtains, as a result, a definite prediction for the relative inertia in baryons and pairs. The deceleration of a relativistic shock in the moving medium, and the resulting synchrotron emissivity, are compared with existing calculations for a static medium. The radiative efficiency is increased dramatically by pair loading. When the initial ambient density exceeds a critical value, the scattering depth traversed by the main gamma-ray pulse rises above unity, and the pulse is broadened. These considerations place significant constraints on burst progenitors: a pre-burst mass loss rate exceeding 10^{-5} M_\odot per year is difficult to reconcile with individual pulses narrower than 10 s, unless the radiative efficiency is low. An anisotropic gamma-ray flux (on an angular scale \Gamma^{-1} or larger) drives a large velocity shear that greatly increases the energy in the seed magnetic field forward of the propagating shock.

Shock wave-inertial microbubble interaction: methodology, physical characterization, and bioeffect study.

Abstract: A method of generating in situ shock wave–inertial microbubble interaction by a modified electrohydraulic shock wave lithotripter is proposed and tested in vitro. An annular brass ellipsoidal reflector (thickness=28 mm) that can be mounted on the aperture rim of a Dornier XL-1 lithotripter was designed and fabricated. This ring reflector shares the same foci with the XL-1 reflector, but is 15 mm short in major axis. Thus, a small portion of the spherical shock wave, generated by a spark discharge at the first focus (F1) of the reflector, is reflected and diffracted by the ring reflector, producing a weak shock wave approximately 8.5 μs in front of the lithotripter pulse. Based on the configuration of the ring reflector (different combinations of six identical segments), the peak negative pressure of the preceding weak shock wave at the second focus (F2) can be adjusted from −0.96 to −1.91 MPa, at an output voltage of 25 kV. The preceding shock wave induces inertial microbubbles, most of which expand to a maximum size of 100–200 μm, with a few expanding up to 400 μm before being collapsed in situ by the ensuing lithotripter pulse. Physical characterizations utilizing polyvinylidene difluoride (PVDF) membrane hydrophone, high-speed shadowgraph imaging, and passive cavitation detection have shown strong secondary shock wave emission immediately following the propagating lithotripter shock front, and microjet formation along the wave propagation direction. Using the modified reflector, injury to mouse lymphoid cells is significantly increased at high exposure (up to 50% with shock number >100). With optimal pulse combination, the maximum efficiency of shock wave-induced membrane permeabilization can be enhanced substantially (up to 91%), achieved at a low exposure of 50 shocks. These results suggest that shock wave–inertial microbubble interaction may be used selectively to either enhance the efficiency of shock wave-mediated macromolecule delivery at low exposure or tissue destruction at high exposure.

Theoretical Solution of Dam-Break Shock Wave

Abstract: A mathematical model of dam-break shock waves, or flood waves, in channels of trapezoidal cross section is presented. When the model is applied to channels of rectangular cross section, a new theoretical solution expressed using one independent multinominal algebraic equation is derived. In the past, the solution had to be described using three interrelated equations. The new equation indicates that the hydraulic parameters of a shock wave—such as depth and velocity of flow, and velocity of discontinuity—are determined only by the ratio of initial downstream depth to initial upstream depth. The model shows that results from the new equation are completely equivalent to those of the set of old equations. In addition, the flood hydrograph produced by a dam break at any time or any site can be described by a single curve in terms of dimensionless variables.

Self-similar shocks in a dusty gas

Abstract: A group theoretic method is used to establish the entire class of self-similar solutions to the problem of shock wave propagation through a dusty gas. Necessary conditions for the existence of similarity solutions for shocks of arbitrary strength as well as for strong shocks are obtained. It is found that the problem admits a self-similar solution only when the ambient medium ahead of the shock is of uniform density. Collapse of imploding cylindrical and spherical shocks is worked out in detail to investigate as to how the shock involution is influenced by the mass concentration of solid particles in the medium, the ratio of the density of solid particles to that of initial density of the medium, the relative specific heat and the amplification mechanism of the flow convergence.

Fibre optic shock velocity sensor for solids

Abstract: This paper reports a fibre optic sensing technique for the measurement of shock velocity in solid materials. The shock-induced changes in the light transmission properties of an optical fibre are employed as the principal transduction mechanism. A polycarbonate flyer plate generated shock waves by impacting a perspex target. The shock velocity was determined from the difference in arrival times of the shock front at the spatially separated optical fibres embedded in the target. The main advantage of this sensor system lies in its simplicity and immunity to optical and radio frequency (RF) noise. Consideration is also given to the effect of release waves on the uniform shock pressure region generated by the ˚yer impact which can degrade the accuracy of the velocity measurement.

Transport and Acceleration of Energetic Charged Particles near an Oblique Shock

Abstract: We have developed a numerical simulation code that treats the transport and acceleration of charged particles crossing an idealized oblique, nonrelativistic shock within the framework of pitch angle transport using a finite-difference method. We consider two applications: (1) to study the steady state acceleration of energetic particles at an oblique shock and (2) to explain observed precursors of Forbush decreases of Galactic cosmic rays before the arrival of an interplanetary shock induced by solar activity. For the former, we find that there is a jump in the particle intensity at the shock, which is stronger for more oblique shocks. Detailed pitch angle distributions are also presented. The simple model of a Forbush decrease explains the key features of observed precursors, an enhanced diurnal anisotropy extending several mean free paths upstream of the shock and a depletion of particles in a narrow loss cone within ~0.1 mean free path from the shock. Such precursors have practical applications for space weather prediction.

Asymptotic particle spectra and plasma flows at strong shocks

Abstract: In a test-particle (linear) acceleration theory, the shock compression controls the particle spectrum We present a nonlinear self-similar solution in which the accelerated particles change the flow structure near the shock so strongly that the total shock compression r may become very high Despite this, the energy spectrum remains close to E-3/2 independent of r This result is valid for the particle diffusivity κ(p) growing with momentum faster than p1/2, which is believed to be the case

The structural response of cylindrical shells to internal shock loading

Abstract: The internal shock loading of cylindrical shells can be represented as a step load advancing at constant speed. Several analytical models are available to calculate the structural response of shells to this type of loading. These models show that the speed of the shock wave is an important parameter. In fact, for a linear model of a shell of infinite length, the amplitude of the radial deflection becomes unbounded when the speed of the shock wave is equal to a critical velocity. It is evident that simple (static) design formulas are no longer accurate in this case. The present paper deals with a numerical and experimental study on the structural response of a thin aluminum cylindrical shell to shock loading. Transient finite element calculations were carried out for a range of shock speeds. The results were compared to experimental results obtained with the GALCIT 6-in. shock tube facility. Both the experimental and the numerical results show an increase in amplitude near the critical velocity, as predicted by simple steady-state models for shells of infinite length. However, the finite length of the shell results in some transient phenomena. These phenomena are related to the reflection of structural waves and the development of the deflection profile when the shock wave enters the shell.

Flow Separation and Side-Load Behavior of the Vulcain Engine

Abstract: The Vulcain engine flow separation and side-load behavior observed and measured during thrust chamber tests is discudded in detail in this paper. It is shown by the test results and by comparison with numerical flow data that the parabolic Vulcain nozzle features a transition in separation behavior from free shock separation to restricted shock separation and vice versa during both engine start-up and shut-down. These highly transient phenomena are a major cause of side-loads. In addition, the side-load activities are measured during nozzle operation with pre free shock separation or pure restricted shock separation. By using results from numerical simulations, it is shown that a specific plume pattern, the cap-shock pattern, is responsible for the observed flow transition. Finally, a comparison of the flow behavior in the Vulcain nozzle during start-up and shut-down is compared with other published data for thrust-optimized or parabolic rocket nozzles with an internal shock emanating from the throat.