Showing papers on "Shock wave published in 1977"
01 Jun 1977
327 citations
TL;DR: In this paper, the sound speeds of water, air, steam, water-air mixtures, and water-steam mixtures are calculated. But the sound speed of a single component two-phase system depends on whether or not equilibrium between the phases on the saturation curve is maintained.
Abstract: The sound speed of a two-phase fluid, such as a magma-gas, water-air, or water-steam mixture, is dramatically different from the sound speed of either pure component. In numerous geologic situations the sound speed of such two-phase systems may be of interest: in the search for magma reservoirs, in seismic exploration of geothermal areas, in prediction of P wave velocity decreases prior to earthquakes, and in inversion of crustal and upper mantle seismic records. Probably most dramatically, fluid flow characteristics during eruptions of volcanoes and geysers are strongly dependent on the sound speed of erupting two-phase (or multiphase) fluids. In this paper the sound speeds of water, air, steam, water-air mixtures, and water-steam mixtures are calculated. It is demonstrated that sound speeds calculated from classical acoustic and fluid dynamics analyses agree with results obtained from finite amplitude ‘vaporization wave’ theory. To the extent that air and steam are represented as perfect gases with an adiabatic exponent γ, independent of temperature, their sound speeds vary in a simple manner directly with the square root of the absolute temperature. The sound speed of pure liquid water is a complex function of pressure and temperature and is given here to 8 kbar, 900°C. In pure water at all pressures the sound speed attains a maximum value near 100°C and decreases at higher temperatures; at high pressures the decrease is continuous, but at pressures below 1 kbar the sound speed reaches a minimum value in the vicinity of 500°–600°C, above which it again increases. The sound speed of a water-air mixture depends on the pressure, the void or mass fraction of air, the frequency of the sound wave, and, if surface tension effects are included, on bubble radius. The admixture of small volume fractions of air causes a dramatic lowering of the sound speed by nearly 3 orders of magnitude. The sound speeds of the pure liquid and gas end-members are nearly independent of pressure, but the sound speed of a mixture is highly dependent on pressure. Calculated values for water-air mixtures are in good agreement with measured values. The sound speed in a single-component two-phase system, such as a water-steam mixture, depends on whether or not equilibrium between the phases on the saturation curve is maintained. Heat and mass transfer which occur when equilibrium is maintained cause the sound speed to be much lower than under non-equilibrium conditions in which heat and mass transfer are absent. The sound speed in a water-steam mixture may be as low as 1 m s−1.
286 citations
TL;DR: In this article, it was shown that there is a scale radius approx30 kpc associated with the collapse of the most massive galaxies and that it may be possible to explain the original inability of the material of galactic disks to fragment in terms of this scale radius.
Abstract: A number of arguments lead one to consider the possibility that the first massive galaxies were formed after redshift 10 The formation of galaxies at small redshifts can only have occurred if the formation process was dissipative This paper is concerned with one theory of dissipative galaxy formation: the theory which arises from the supposition that a protogalactic cloud would not have fragmented very extensively during the first phase of its infall and thus that the collapse of the cloud would be halted by the formation of shock fronts around a caustic surface Detailed calculations of the formation and evolution of these shock fronts yield values for the physical conditions of the protogalactic gas and the rate of radiation of galactic binding energy by such shocks The adiabaticity or isothermality of these shock fronts is found to be dependent on the characteristic infall velocity and the surface density associated with the shock front but not on the shape of the initial density profile perpendicular to the incipient shock surfaces Protogalaxies which recollapsed at high z are more likely to have generated isothermal shocks than ones which collapsed at low z It is found that this binding energy release could makemore » collapsing protogalactic clouds very high surface brightness objects It appears that there is a scale radius approx30 kpc associated with the collapse of the most massive galaxies and that it may be possible to explain the original inability of the material of galactic disks to fragment in terms of this scale radius A similar theory of the origin of Magellanic irregulars, low surface brightness spheroidals, and dwarf ellipticals is suggested« less
263 citations
TL;DR: In this paper, the effect of spallation on the free surface velocity of a plate-impact target was studied. But the spall signal is a sensitive measure of the damage done to the target.
Abstract: We have studied spall by observing the effect of spallation on the free‐surface velocity of a plate‐impact target. We believe that the spall signal is a sensitive measure of the damage done to the target. We have formulated a simple theoretical model and incorporated it in a hydrodynamic computer code, to simulate the first few stress reverberations in the target as it spalls. The simple model successfully describes the principal features of our measurements in uranium and in a few other metals.
166 citations
TL;DR: In this article, the release and reshock behavior of aluminum from an initial shock stress of 2 GPa (20 kbar) has been examined, and it is found that a two-wave structure characterizes both release and recompression, although a definite elastic plastic structure is not obtained in either case.
Abstract: The release and reshock behavior of aluminum from an initial shock stress of 2 GPa (20 kbar) has been examined. It is found that a two‐wave structure characterizes both release and recompression, although a definite elastic‐plastic structure is not obtained in either case. The velocity of the initial disturbance for both recompression and release agrees with the extrapolated ultrasonic longitudinal velocity, which implies initial elastic response from the precompressed state. The present results are discussed in terms of a rate‐independent model which incorporates a distribution of yield states in the precompressed material. Reasonable agreement with experimental reshock and release wave profiles is obtained with this model. A brief discussion of rate effects estimated from an acceleration wave analysis is also presented.
113 citations
TL;DR: In this paper, a reasonably consistent model of steady-state magnetic-field-line reconnection in a collisionless plasma is constructed by incorporating ion-acoustic anomalous resistance into the hydromagnetic flow in the vicinity of the x-type neutral line.
Abstract: A reasonably consistent model of steady-state magnetic-field-line reconnection in a collisionless plasma is constructed by incorporating ion-acoustic anomalous resistance into the hydromagnetic flow in the vicinity of the x-type neutral line. The Petschek-Vasyliunas (1975) reconnection theory is applied, and properties of the ion-acoustic instability are reviewed for the case of comparable ion and electron temperatures. Nonlinear saturation of the instability is examined, the saturation wave intensity is determined as a function of electron drift speed and electron/ion temperature ratio, and the computed wave intensities are used to estimate the steady electric field in the neutral region. Ion-acoustic anomalous resistance is shown to limit the electron drift speed to slightly above the marginally stable value. A model for the resistive-diffusion region is constructed which incorporates the properties of ion-acoustic anomalous resistance, and an approximate solution for the external flow region is matched to the resistive-region solution. It is found that the two solutions are sensibly matched only for a restricted range of upstream plasma parameters. Limitations and possible extensions of the model are discussed.
88 citations
TL;DR: The principal Hugoniot of molybdenum has been determined at a pressure of 2.0 TPa by measuring directly both the shock velocity and the particle velocity behind the shock.
Abstract: The principal Hugoniot of molybdenum has been determined at a pressure of 2.0 TPa by measuring directly both the shock velocity and the particle velocity behind the shock. Neutrons from an underground nuclear explosion were used to generate a high‐pressure shock in a slab of molybdenum by rapidly fission heating an adjacent slab of enriched uranium. A shock velocity of 18.2 mm/μs (±5%) was obtained by determining the transit time of the planar shock between two points in the molybdenum separated by 9.87 mm. A particle velocity of 10.7 mm/μs (±5%) was obtained by observing the Doppler shifts of six neutron resonances in the energy region from 200 to 800 eV in the moving shocked molybdenum. The pressure and density derived from this pair of measurements are 2.0 TPa (20 Mbar) and 24.8 g cm−3, respectively. This experiment represents the first direct determination of a point on the Hugoniot of any material in this pressure region, and the resulting data point is in good agreement with theoretical estimates. This measurement was a successful demonstration that the Doppler‐shift technique can be used to obtain particle velocities in this pressure region. It appears that errors in both the shock velocity and the particle velocity can be reduced to approximately ±2% in an improved measurement, resulting in a well‐defined Hugoniot for molybdenum, which can be used as a standard in future impedance‐matching experiments.
83 citations
TL;DR: In this article, a mathematical analog for one-dimensional compressible flow in a chemically reacting fluid is constructed and used as a vehicle for a simplified introduction to such flows, with particular application to detonations.
Abstract: A mathematical analog for one‐dimensional compressible flow in a chemically reacting fluid is constructed and used as a vehicle for a simplified introduction to such flows, with particular application to detonations. The presentation includes a concise self‐contained introduction to the elements of nonreactive compressible flow.
81 citations
79 citations
TL;DR: The Helios search coil experiment provides accurate low background noise measurements of interplanetary magnetic fluctuation spectra from about 4 Hz to 2.2 kHz adjacent to the frequency band from 0 to 4 Hz of the Technical University of Braunschweig flux-gate magnetometer as discussed by the authors.
Abstract: The Helios search coil experiment provides accurate low background noise measurements of interplanetary magnetic fluctuation spectra from about 4 Hz to 2.2 kHz adjacent to the frequency band from 0 to 4 Hz of the Technical University of Braunschweig flux-gate magnetometer. Apart from a slowly varying fluctuation component ranging up to 100 Hz near 1 AU and beyond 500 Hz near 0.3 AU the following superposed ‘events’ can be discerned in the fluctuation spectra which also have a distinct signature in the slowly varying magnetic field: (1) directional discontinuities acting as wave guide boundaries, (2) directional discontinuities producing whistler wave fields because of instability, (3) reversible magnetic field variations, mostly dips of about 1 min duration associated with whistler wave fields, (4) interplanetary shocks, where, for example, the oblique shock of January 8, 1975, has a thickness of about 1 proton gyroradius and produces an increase in whistler wave fields by more than 2 orders o′ magnitude in power spectral density leading to a power spectrum of 1 γ²/Hz f−3.64 in the wake region.
TL;DR: From a matrix of models of plane-parallel radiating shocks with varying elemental abundances and shock conditions, a set of diagnostic diagrams analogous to those used for many years for H II regions has been computed as discussed by the authors.
Abstract: From a matrix of models of plane-parallel radiating shocks with varying elemental abundances and shock conditions, a set of diagnostic diagrams analogous to those used for many years for H II regions has been computed. This should enable abundances and shock conditions to be calculated for any reasonably evolved optical supernova remnant provided adequate spectrophotometric data are available.
TL;DR: In this article, the observed bow shock encounters at Mercury, Venus and Mars are least square fit using the same technique so that their sizes and shapes can be intercompared, and the shock front of Mercury most resembles the terrestrial shock in shape and the stand off distance is consistent with the observed moment.
Abstract: The observed bow shock encounters at Mercury, Venus and Mars are least square fit using the same technique so that their sizes and shapes can be intercompared. The shock front of Mercury most resembles the terrestrial shock in shape, and the shock stand off distance is consistent with the observed moment. The shapes of the Venus and Mars shock fronts more resemble each other than the earth's and the stand off distances are consistent with direct interaction of the solar wind with the ionosphere on the dayside. The Venus shock is closer to the planet than the Mars shock suggesting more absorption of the solar wind at Venus.
TL;DR: In this article, it was found that a generalized Grueneisen function dependent on temperature and volume is necessary for the self-consistent application of the Mie-Grueneisen equation at the physical conditions encountered in shock wave phenomena or in the interior of planets.
Abstract: Anharmonic models are used to describe the high temperatures and the electronic effects characteristic of shock wave phenomena and planetary interiors. It is found that a generalized Grueneisen function dependent on temperature and volume is necessary for the self-consistent application of the Mie-Grueneisen equation at the physical conditions encountered in shock wave phenomena or in the interior of planets. It is noted that at temperatures of a few thousand degrees Kelvin, by deriving the function in terms of anharmonic lattice dynamics, the difference between gamma and gamma(th) is of the same order of a magnitude as gamma. This leads to the conclusions that (1) gamma is not a function of temperature and (2) gamma?gamma(th) does not explain either the equation of state of planetary interiors or high-temperature shock wave phenomena.
01 Jan 1977
TL;DR: Shatter cones, a form of rock fracture in impact structures, apparently form as a shock front interacts with inhomogeneities or discontinuities in the rock as mentioned in this paper, and it is thought that shatter cones are produced within a limited range of shock pressures extending from about 20 to perhaps 250 kbar.
Abstract: Shatter cone characteristics are surveyed. Shatter cones, a form of rock fracture in impact structures, apparently form as a shock front interacts with inhomogeneities or discontinuities in the rock. Topics discussed include morphology, conditions of formation, shock pressure of formation, and theories of formation. It is thought that shatter cones are produced within a limited range of shock pressures extending from about 20 to perhaps 250 kbar. Apical angles range from less than 70 deg to over 120 deg. Tentative hypotheses concerning the physical process of shock coning are considered. The range in shock pressures which produce shatter cones might correspond to the range in which shock waves decompose into elastic and deformational fronts.
TL;DR: In this paper, the most likely mechanisms are collisional excitation behind a shock moving into a molecular cloud and near-ultraviolet pumping in the H2 Lyman and Werner bands and subsequent cascade.
Abstract: Physical mechanisms for producing vibrationally excited molecular hydrogen, such as has recently been detected toward the Orion Nebula, are discussed. The most likely mechanisms are collisional excitation behind a shock moving into a molecular cloud and near-ultraviolet pumping in the H2 Lyman and Werner bands and subsequent cascade. The absolute intensities of the Orion lines require either a 10-km/s shock moving into a cloud with a density of 300,000 per cu cm or an incident near-UV flux 1 million times the mean interstellar value. The shock model is favored because it matches the observed relative line intensities and because the near-UV source, Theta-1 Ori C, may be too weak to provide the required flux. Intensities of other H2 lines in the shock model are predicted as a further observational discriminant.
TL;DR: In this paper, a quasi-parallel bow shock structure was observed with field and particle detectors of both HEOS 1 and OGO 5 and the typical magnetic pulsation structure was at least 1 to 2 earth radii thick radially and was accompanied by irregular but distinct plasma distributions characteristic of neither the solar wind nor the magnetosheath.
Abstract: A thick, quasi-parallel bow shock structure was observed with field and particle detectors of both HEOS 1 and OGO 5. The typical magnetic pulsation structure was at least 1 to 2 earth radii thick radially and was accompanied by irregular but distinct plasma distributions characteristic of neither the solar wind nor the magnetosheath. Waves constituting the large pulsations were polarized principally in the plane of the nominal shock, therefore also in the plane perpendicular to the average interplanetary field. A separate interpulsation regime detected between bursts of large amplitude oscillations was similar to the upstream wave region magnetically, but was characterized by disturbed plasma flux and enhanced noise around the ion plasma frequency. The shock structure appeared to be largely of an oblique, whistler type, probably complicated by counterstreaming high energy protons. Evidence for firehose instability-based structure was weak at best and probably negative.
TL;DR: In this paper, a model for a supersonic blade row with two in-passage shock waves is developed, which accounts for three-dimensional effects in real flows by using an altered blade shape in a two-dimensional cascade.
Abstract: A model for a supersonic blade row with two in-passage shock waves is developed. It accounts for three-dimensional effects in real flows by using an altered blade shape in a two-dimensional cascade. There is enough flexibility in the choice of blade shape to accommodate a desired entrance angle, exit angle, boundary-layer thickness and stage pressure ratio at a given entrance Mach number. The model divides the mean flow into regions of uniform or one-dimensional flow in which the solutions for the unsteady flow may be formed successively. The analysis makes use of previous solutions for unsteady flow in cascades and over an oscillation wedge. Six flow conditions are chosen in the range of parameters for which the two-shock model is valid for studies of flutter in torsion and bending. It is found, in keeping with previous results from a single-shock model, that in each case there is increasing instability with decreasing frequency.
TL;DR: In this article, the authors derived general formulae for the damping and entropy production rate as functions of the shock strength, both in the limit of weak and strong shocks, and applied these results to entropy production and galaxy formation problems in the early universe.
Abstract: We study shock formations from one-dimensional simple waves in special relativity and Friedmann background universes. We derive general formulae for the damping and entropy production rate as functions of the shock strength, both in the limit of weak and strong shocks. These results are applicable to entropy production and galaxy formation problems in the early universe. We also give the hodograph method for solving the special one-dimensional relativistic flow problem.
TL;DR: In this article, a method and apparatus for recovering oil from an oil bearing soil by means of an electrohydraulic shock wave generated in a liquid by capacitor electrical discharge means is described.
Abstract: A method and apparatus are provided for recovering oil from an oil bearing soil by means of an electrohydraulic shock wave generated in a liquid by capacitor electrical discharge means.
TL;DR: In this paper, the authors used projectile impact techniques to introduce shocks into rectangular bars of the ferroelectric ceramic PZT 95/5, and the specimens were completely depoled and the permittivity was independent of both the stress and electric fields and had a value of 9 nF/m.
Abstract: Projectile impact techniques were used to introduce shocks into rectangular bars of the ferroelectric ceramic PZT 95/5. In these experiments the remanent polarization vector was perpendicular to the shock propagation vector. For shock amplitudes greater than 1.6 GPa the specimens were completely depoled, and the permittivity was independent of both the stress and electric fields and it had a value of 9 nF/m. These data indicate that a phase transformation to a nonferroelectric state had occurred. However, the characteristics of the high‐stress state are uncertain.
Patent•
17 May 1977
TL;DR: In this paper, a coupling unit is placed on the surface of the patient's body to locate and dissolve kidney stones, where the wall of the unit houses ultrasonic emitters and receivers whose axes intersect the axis of the shockwave source at the focal point of the accretion at an angle of 30 degrees.
Abstract: The system is used for locating and dissolving solid accretions e.g. kidney stones. A coupling unit is placed on the surface of the patient's body. The unit is elliptical with a circular cross-section and the shock wave source is situated at the focal point of the ellipsoid. The wall of the unit houses ultrasonic emitters and receivers, whose axes intersect the axis of the shockwave source at the focal point of the accretion (18) at an angle of 30 degrees. The emitter and receiver (2, 12) are arranged symmetrically on the circular cross-section and a B-scan is provided for preliminary location of the accretion.
TL;DR: In this paper, the early time history of hypervelocity impact effects can be simulated by requiring that the laser induced surface pressure equal the surface impact pressure, equating the laser pulse time to a particle/surface interaction time, and setting the focal spot diameter equal to the particle diameter.
Abstract: A theory is developed to determine the parameters for simulation of the hypervelocity impact of small particles on a surface by focusing a high power pulsed laser upon that surface. It is proposed that the early time history of hypervelocity impact effects can be simulated by requiring that the laser induced surface pressure equal the surface impact pressure, equating the laser pulse time to a particle/surface interaction time, and setting the focal spot diameter equal to the particle diameter. Calculations of impact pressure versus projectile velocity are performed using an idealized one dimensional model for shock wave propagation. A simplified theory for the interaction of a highly focused pulsed laser beam with a surface is developed to obtain the laser induced surface pressure. Results of a sample calculation for water droplets impacting a graphite surface between 3 and 6 km/sec indicate that laser intensities of 5×1010–5×1011 W/cm2 are required. The corresponding laser energies are strongly particle size and shape dependent and range from 0.01 J with a 5 nsec pulse time for 20 μ radius particles to 2 J with a 20 nsec pulse time for 80 μ radius particles. A qualitative comparison of data for high power laser produced craters and hypervelocity impact produced craters is also presented.
TL;DR: In this article, the linear dispersion relation for electromagnetic waves in a Vlasov plasma with unmagnetized ions and magnetized electrons undergoing an E × B drift is derived and studied.
Abstract: The linear dispersion relation for electromagnetic waves in a Vlasov plasma with unmagnetized ions and magnetized electrons undergoing an E × B drift is derived and studied. Results show that electromagnetic effects reduce the growth rate of the modified two-stream instability while they spread the region of instability in wave vector space. The possible contribution of this instability to two bow shock parameters, the ratio of electric to magnetic field wave energy densities and the shock width, is discussed.
TL;DR: In this paper, an interferometric system for continuously measuring specimen velocity is described, where the Doppler shift of a laser beam reflected from the free surface is transformed into a variation of the diameter of Fabry-Perot interference rings, and the evolution of diameter versus time is continuously recorded by a streak camera.
Abstract: An interferometric system for continuously measuring specimen velocity is described. The Doppler shift of a laser beam reflected from the specimen’s free surface is transformed into a variation of the diameter of Fabry–Perot interference rings, and the evolution of the diameter versus time is continuously recorded by a streak camera. Two examples of the use of this system for study of shock waves are given to show the accuracy of this device.
TL;DR: In this article, the authors compared numerical descriptions of shock wave induced flows obtained with a two-dimensional Lagrangian finite difference code with experimental data obtained via the lateral relaxation method for polycrystalline magnesium oxide (MgO) to a pressure of 360 kbar.
Abstract: Numerical descriptions of shock wave induced flows obtained with a two-dimensional Lagrangian finite difference code are compared in detail with experimental data obtained via the lateral relaxation method for polycrystalline magnesium oxide (MgO) to a pressure of 360 kbar. The equation of state used for MgO was assumed to be of the Mie-Gruneisen form, and detailed comparison of experimental and calculated data was used to obtain refined values of the shear strength and shear modulus of MgO at high pressures. The best fitting rheological model for MgO was characterized by a shear strength which decreased from a value of 26 kbar at 16.5-kbar mean stress to 13.5 kbar at 360-kbar mean stress along the principal Hugoniot curve. The first and second pressure derivatives of the shear modulus, when the shear modulus is evaluated as a quadratic function of pressure, yield (∂μ/∂P) = 2.44 and μ(∂^2μ/∂P^2) = 1.7±3.0. The uncertainties in the determination of μ(∂^2μ/∂P^2) have been reduced by a factor of 5 over previous estimates.
TL;DR: In this article, the locations of the bow shock encounters of Mariner 5 and 10 and Venera 4, 6, and 9 were examined and it was shown that the standoff distance of the nose of the shock is closer to the planet than the distance that one would obtain by simply scaling the solar wind Venus interaction under the assumption that Venus completely deflects the solar winds.
Abstract: Examination of the locations of the bow shock encounters of Mariner 5 and 10 and Venera 4, 6, and 9 suggests that the bow shock of Venus is on the average detached from the ionosphere. However, the standoff distance of the nose of the shock is closer to the planet than the distance that one would obtain by simply scaling the solar wind Venus interaction under the assumption that Venus completely deflects the solar wind. This fact implies that there is a significant influx of solar wind plasma into the Venus ionosphere. If the absorption of the solar wind by Venus is great enough, the shock may become attached to the ionosphere. The Mariner 10 bow shock encounter may have occurred during such a period. A rough estimate of the average fraction of the solar wind incident on the cross section of the planet that is absorbed is 29%.
TL;DR: In this paper, a photogrammetrical technique has been used to study the interaction of two identical explosively produced spherical shock waves and to compare this interaction with the reflexion of one of the spherical shocks from the ground.
Abstract: A photogrammetrical technique has been used to study the interaction of two identical explosively produced spherical shock waves and to compare this interaction with the reflexion of one of the spherical shocks from the ground. It is postulated that there was no energy loss in the interaction of the two shock waves and that the interaction therefore simulated the reflexion of a spherical shock from an ideal non-energyabsorbing surface. The ‘ideal’ reflexions were compared with real reflexions from two types of ground surface: one smooth and the other rough. Experiments were carried out with the centres of the spherical shocks at two separations so that observations could be made of the interaction of shocks of different strength. Significant differences were shown to exist in both the strengths of the Mach shocks and in the triple-point trajectories over the different surfaces. The results are intended to aid in the evaluation of computer codes being developed to simulate spherical-shock reflexions from real surfaces.
TL;DR: In this paper, a closed-form analytical "weak shock" solution for the subsequent propagation of such a wave has been obtained, which is in good agreement with the Kirkwood-Bethe theory, existing measurements, and the widely used experimentally based semi-empirical similarity formulas.
Abstract: The initial pressure wave measured at modest distances from an underwater explosion is often modeled as a spherical shock wave with an exponential decay. A closed‐form analytical ’’weak‐shock’’ solution for the subsequent propagation of such a wave has been obtained. The resulting simple formulas for peak pressure and decay constant as function of reduced range allow the prediction of the amplitude and initial slope of the wave given only the amplitude and decay constant of the original exponential shock and the density, sound speed, and parameter of nonlinearity of the water. The results are in good agreement with the Kirkwood–Bethe theory, existing measurements, and the widely used experimentally based semi‐empirical similarity formulas. An expression which gives a close approximation to the shape of the waveform as a function of distance is also derived.