Showing papers on "Shock wave published in 1993"

Review of chemical-kinetic problems of future NASA missions, II: Mars entries

Abstract: A number of chemical-kinetic problems related to phenomena occurring behind a shock wave surrounding an object flying in the earth atmosphere are discussed, including the nonequilibrium thermochemical relaxation phenomena occurring behind a shock wave surrounding the flying object, problems related to aerobraking maneuver, the radiation phenomena for shock velocities of up to 12 km/sec, and the determination of rate coefficients for ionization reactions and associated electron-impact ionization reactions. Results of experiments are presented in form of graphs and tables, giving data on the reaction rate coefficients for air, the ionization distances, thermodynamic properties behind a shock wave, radiative heat flux calculations, Damkoehler numbers for the ablation-product layer, together with conclusions.

Theory of Interstellar Shocks

Abstract: The interstellar medium is intermittently disturbed by violent events­ supernova explosions being but one example-which cause large increases in the local pressure. As the result of the pressure increase, the disturbed region will expand. If the pressure increase exceeds a minimum value, a "shock front" will develop at the leading edge of this expanding disturb­ ance, and the flow in the neighborhood of this front is referred to as a "shock" or "shock wave." Besides supernova explosions, interstellar shock waves may be driven by the pressure of photoionized gas, stellar winds, and collisions between fast-moving clumps of interstellar gas. A shock wave is an irreversible, pressure-driven fluid-dynamical dis­ turbance. The irreversible character is due to entropy generation as ordered kinetic energy is dissipated into heat. In neutral gas, the dissipation is due to molecular viscosity in the shock transition (where large velocity gradients and viscous stresses are present). In low-density plasmas, the dissipation may be collisionless, and due to collective motions of the charged particles and the resulting electromagnetic fields. In partially­ ionized gases, the dissipation may sometimes be primarily due to "friction"

Magma ocean formation due to giant impacts

Abstract: The thermal effects of giant impacts are studied by estimating the melt volume generated by the initial shock wave and corresponding magma ocean depths. Additionally, the effects of the planet's initial temperature on the generated melt volume are examined. The shock pressure required to completely melt the material is determined using the Hugoniot curve plotted in pressure-entropy space. Once the melting pressure is known, an impact melting model is used to estimate the radial distance melting occurred from the impact site. The melt region's geometry then determines the associated melt volume. The model is also used to estimate the partial melt volume. Magma ocean depths resulting from both excavated and retained melt are calculated, and the melt fraction not excavated during the formation of the crater is estimated. The fraction of a planet melted by the initial shock wave is also estimated using the model.

Numerical solution of the Riemann problem for two-dimensional gas dynamics

Abstract: The Riemann problem for two-dimensional gas dynamics with isentropic or polytropic gas is considered. The initial data is constant in each quadrant and chosen so that only a rarefaction wave, shock wave, or slip line connects two neighboring constant initial states. With this restriction sixteen (respectively, fifteen) genuinely different wave combinations for isentropic (respectively, polytropic) gas exist. For each configuration the numerical solution is analyzed and illustrated by contour plots. Additionally, the required relations for the initial data and the symmetry properties of the solutions are given. The chosen calculations correspond closely to the cases studied by T. Zhang and Y. Zheng [SIAM J. Math. Anal., 21 (1990), pp. 593–630], so that the analytical theory can be directly compared to our numerical study.

Applications of Shock-Induced Mixing to Supersonic Combustion

Abstract: Families of two-dimensional, unsteady shock-induced vortical flows are simulated numerically The flows consist of one or more regions of light gas, surrounded by heavy gas, being overtaken by a normal shock wave The interaction of the density gradient at each light/heavy interface with the pressure gradient from the shock wave generates vorticity This causes the light gas regions to roll up into one or more counter-rotating vortex pairs, which stir and mix the light and heavy gases The mixing is characterized by an asymptotic stretching rate The effects of shock strength, light/heavy gas density ratio, and geometry on the mixing are investigated These two-dimensional, unsteady flows are analogous to three-dimensional, steady flows that may be used in SCRAMJET combustors demanding rapid and efficient mixing of fuel and oxidizer For such applications, 1) the fuel injectors should be elongated in the direction of the shock; 2) multiple smaller injectors are preferable to a single larger injector; 3) injectors should be arranged in groups of closely spaced pairs, rather than uniformly; and 4) multiple shock waves should be utilized, if possible

Shock-wave propagation in a sonoluminescing gas bubble

Abstract: The motion of the bubble radius and of the air trapped inside the bubble during sonoluminescence are determined self-consistently by coupling the solution of the Rayleigh-Plesset equation governing the bubble radius to the solution of Euler's equations for the motion of air in the bubble. Results are presented for three slightly different conditions of excitation, in two of which shocks are formed during the collapse of the bubble, and in which such high temperatures are attained that the air is ionized. Estimates are made of the duration and intensity of the light then radiated by the plasma.

Direct numerical simulation of isotropic turbulence interacting with a weak shock wave

Abstract: Direct numerical simulations are used to investigate the interaction of isotropic quasi-incompressible turbulence with a weak shock wave. A linear analysis of the interaction is conducted for comparison with the simulations. Both the simulations and the analysis show that turbulence is enhanced during the interaction. Turbulent kinetic energy and transverse vorticity components are amplified, and turbulent lengthscales are decreased. It is suggested that the amplification mechanism is primarily linear. Simulations also showed a rapid evolution of turbulent kinetic energy just downstream of the shock, a behavior not reproduced by the linear analysis. Analysis of the budget of the turbulent kinetic energy transport equation shows that this behavior can be attributed to the pressure transport term. Multiple compression peaks were found along the mean streamlines at locations where the local shock thickness had increased significantly.

Generation of shock waves by laser‐induced plasma in confined geometry

Abstract: Confined plasmas induced by neodynium glass laser at 1.06 μm and pulse width of 3 and 30 ns are studied. The metallic target is covered with a dielectric layer, glass or water, transparent to the laser radiation. Experimental measurements of the pressure induced by the plasma have been performed. For a certain range of laser power density these measurements agree particularly well with an analytical model. At high power densities (10 GW/cm2), the dielectric breakdown appears to be the main limiting process of the confining method. It is observed that this breakdown induces a saturation of the pressure. It is shown that the use of a short‐rise‐time laser pulse is the only way to reduce the effects of the breakdown and to obtain much higher‐pressure shock waves. This is due to the dependence of the dielectric breakdown threshold on the laser pulse rise time.

Shock/boundary-layer interaction control with vortex generators and passive cavity

Abstract: This paper describes an experimental comparison of two passive approaches for controlling the shock interaction with a turbulent boundary layer: low-profile vortex generators and a passive cavity (porous wall with a shallow cavity underneath). This investigation is the first known direct comparison of the two methods wherein the advantages and disadvantages of both are revealed. The experiments were conducted with a normal shock wave in an axisymmetric wind tunnel. The shock strength (M = 1.56-1.65) was of sufficient magnitude to induce a large separation bubble, thus causing substantial boundary-layer losses. The low-profile vortex generators were found to significantly suppress the shock-induced separation and improve the boundary-layer characteristics downstream of the shock. However, the suppression of the separation bubble decreased the extent of the low total pressure loss region associated with the lambda foot shock system which results in a lower mass-averaged total pressure downstream of the shock. The passive cavity substantially reduced the total pressure loss through the shock system (and thus wave drag) by causing a more isentropic compression over a larger lateral extent. However, the boundary-layer losses downstream of the shock were significantly increased.

Kinks versus Shocks

Abstract: Localized phase transitions as well as shock waves can often be modeled by material discontinuities satisfying Rankine-Hugoniot (RH) jump conditions. The use of Maxwell, Gibbs-Thompson, Hertz-Knudsen, and similar (supplementary to RH) relations in the theory of dynamic phase changes suggest that the classical system of jump conditions is at least incomplete in the case of phase transitions. While the propagation of a shock wave is completely determined by the conservations laws, the boundary conditions of the problem and the condition that the entropy increases in the process, the same is not true for the propagation of phase boundaries. Additional condition must be added to the RH conditions in order to provide sufficient data for the unique determination of the transformation process. The necessity was tacitly assumed by those who attacked the calculation of the phase boundary velocity without even trying to determine this parameter from the conservation laws and boundary conditions alone.

Plasma Astrophysics: Kinetic Processes in Solar and Stellar Coronae

Abstract: Basic Concepts. Magnetohydrodynamics. Waves in a Cold, Collisionless Plasma. Kinetic Plasma and Particle Beams. Astrophysical Electron Beams. Ion Beams and Electromagnetic Instabilities. Electrons Trapped in Magnetic Fields. Electric Currents. Collisionless Shock Waves. Propagation of Radiation. Appendices: Mathematical Expressions Units Frequently Used Expressions Notation.

Flow in deformable porous media. Part 2 Numerical analysis - the relationship between shock waves and solitary waves

Abstract: Using numerical schemes, this paper demonstrates how viscous resistance to volume changes modifies the simplest shock wave solutions presented in Part 1. For an initial condition chosen to form a step-function shock, viscous resistance causes the shock to disperse into a rank-ordered wavetrain of solitary waves. Large obstructions in flux produce large-amplitude, slow-moving wavetrains while smaller shocks shed small-amplitude waves. While the viscous resistance term is initially important over a narrow boundary layer, information about obstructions in the flux can propagate over many compaction lengths through the formation of non-zero wavelength porosity waves. For large-amplitude shocks, information can actually propagate backwards relative to the matrix. The physics of dispersion is discussed and a physical argument is presented to parameterize the amplitude of the wavetrain as a function of the amplitude of the predicted shock. This quantitative relationship between the prediction of shocks and the development of solitary waves also holds when mass transfer between solid and liquid is included. Melting causes solitary waves to decrease in amplitude but the process is reversible and freezing can cause small perturbations in the fluid flux to amplify into large-amplitude waves. These model problems show that the equations governing volume changes of the matrix are inherently time dependent. Perturbations to steady-state solutions propagate as nonlinear waves and these problems demonstrate several initial conditions that do not relax to steady state. If these equations describe processes such as magma migration in the Earth, then these processes should be inherently episodic in space and time.

Shock Excitation of the Emission-Line Filaments in Centaurus A

Abstract: We present a self-consistent model for the excitation of the extranuclear emission line filaments in Centaurus A. Interaction of the northern radio jet of Centaurus A with a dense cloud of material at the location of the filaments causes shock waves with velocities ∼200-450 km s -1 . The shocks produce a strong flux of EUV and soft X-ray radiation which photoionize the visible knots. We show that the mechanical flux of a mildly supersonic low-density jet is sufficient to energize the shock waves through the production of supersonic turbulent velocities in the dense cloud via the Kelvin-Helmholtz instability

Review of chemical-kinetic problems of future NASA missions. I: Earth entries

Abstract: A number of chemical-kinetic problems related to phenomena occurring behind a shock wave surrounding an object flying in the earth atmosphere are discussed, including the nonequilibrium thermochemical relaxation phenomena occurring behind a shock wave surrounding the flying object, problems related to aerobraking maneuver, the radiation phenomena for shock velocities of up to 12 km/sec, and the determination of rate coefficients for ionization reactions and associated electron-impact ionization reactions. Results of experiments are presented in form of graphs and tables, giving data on the reaction rate coefficients for air, the ionization distances, thermodynamic properties behind a shock wave, radiative heat flux calculations, Damkoehler numbers for the ablation-product layer, together with conclusions.

Structure of normal shock waves: Direct numerical analysis of the Boltzmann equation for hard-sphere molecules

Abstract: The structure of normal shock waves is investigated on the basis of the standard Boltzmann equation for hard‐sphere molecules. This fundamental nonlinear problem in rarefied gas dynamics is analyzed numerically by a newly developed finite‐difference method, where the Boltzmann collision integral is computed directly without using the Monte Carlo method. The velocity distribution function, as well as the macroscopic quantities, is accurately obtained. The numerical results are compared with the Mott‐Smith and the direct simulation Monte Carlo results in detail. The analytical solution for a weak shock wave based on the standard Boltzmann equation is also presented up to the second order of the shock strength together with its explicit numerical data for hard‐sphere molecules.

Visual observations of supersonic transverse jets

Abstract: We present experimental results on penetration of round sonic and supersonic jets normal to a supersonic cross flow. It is found that penetration is strongly dependent on momentum ratio, weakly dependent on free-stream Mach number, and practically independent of jet Mach number, pressure ratio, and density ratio. The overall scaling of penetration is not very different from that established for subsonic jets. The flow is very unsteady, with propagating pressure waves seen emanating from the orifice of helium jets.

Detonations at nanometer resolution using molecular dynamics.

Abstract: We show that discrete detonation chemistry can be studied using molecular dynamics simulations. A model 2D semi-infinite energetic molecular solid described by reactive many-body potentials is shown to support a chemically sustained shock wave with properties that are consistent with experimental results and the classic continuum theory of planar detonations. These promising results demonstrate for the first time that simulations using reactive many-body potentials provide a powerful probe of the interplay between the continuum properties of shock waves and the atomic-scale chemistry they induce in condensed-phase detonations

Signatures of shock drivers in the solar wind and their dependence on the solar source location

Abstract: Solar wind and energetic ion observations following 40 interplanetary shocks with well-established solar source locations have been examined in order to determine whether signatures characteristic of the coronal material forming the shock driver are present. The signatures considered include magnetic-field-aligned bidirectional ion flows observed by the ISEE 3 and IMP 8 spacecraft; bidirectional solar wind electron heat fluxes; solar wind plasma proton and electron temperature depressions; low-beta plasma; enhanced, low-variance magnetic fields; and energetic ion depressions. Several shock driver signatures are commonly observed following shocks originating from within about 50 deg of central meridian, and are generally absent for other events. We conclude that shock drivers generally extend up to about 100 deg in longitude, centered on the solar source longitude. Since shocks from central meridian events are not usually associated with all the shock driver signatures examined, the absence of a driver cannot be confirmed from consideration of one of these signatures alone. We also find evidence that a few bidirectional energetic ion and solar wind electron heat flux events following shocks (in particular from far eastern sources) may occur on open field lines outside of shock drivers.

Classification of the Riemann problem for two-dimensional gas dynamics

Abstract: The Riemann problem for two-dimensional gas dynamics with isentropic and polytropic gas is considered. The initial data is constant in each quadrant and chosen so that only a rarefaction wave, shock wave or slip line connects two neighboring constant initial states. With this restriction, the existence of sixteen (respectively, fifteen) genuinely different wave combinations for isentropic (respectively, polytropic) gas is proved. For each configuration the relations for the initial data and the symmetry properties of the solution are given. This paper corrects the, conjectured classification presented in T. Zhang and Y. Zheng [SIAM J. Math. Anal., 21 (1990), pp. 593–630].

New mechanism for electron heating in shocks.

Abstract: Electron trajectories diverge exponentially in a sufficiently small-scale electrostatic field with a static external magnetic field. This electron trajectory instability results in the electron heating in field structure typical for the collisionless shock front ramp. The magnitude of the effect is sufficient to explain the observed heating at the Earth's bow shock and interplanetary shocks. The heating features are consistent with the observations.

The dynamics of shock accelerated light and heavy gas cylinders

Abstract: Experiments have been carried out in which a cylindrical volume of a gas, that is either lighter or heavier than its surroundings, is impulsively accelerated by a weak shock wave. Laminar jets of helium or sulphur hexafluoride (SF6) are used to produce the cylinders, and planar laser‐induced fluorescence is used to visualize the flow. It is found that the vorticity deposited on the boundary of the SF6 cylinder by the interaction with the shock wave, separates from the heavy gas to form a pair of vortices, which subsequently wrap the SF6 around them. This process is quite different from what is observed in the light gas experiments, which showed a small amount of helium to remain with the vorticity, eventually becoming part of the vortex cores. Centrifugal forces combined with differences in the rates of the diffusion of vorticity in the two gases are given as possible reasons for these differences. Measurement of the initial downstream velocity for a heavy gas cylinder is found to agree well with a theory based on two simple models. But, because diffusion causes the light gas jet density to be significantly greater than that of pure helium, the theory overpredicts the measured velocity of the light gas experiments. The final translational velocities for both light and heavy gas experiments are not accurately predicted by the model, and measurements of the vortex spacing are found to be significantly larger than those indicated by this theory. These differences are likely caused by the theory’s inability to accurately describe the viscous nonuniform flow.

Studies of acoustical and shock waves in the pulsed laser ablation of biotissue

Abstract: Quantitative studies are conducted into the absolute pressure values of the acoustical and shock waves generated and propagating in a biotissue under pulsed (tau p = 50 ns) UV (lambda = 308 nm) laser irradiation (below and above the ablation threshold). Powerful (several hundreds of bars in pressure) high-frequency (f approximately 10(7) Hz) acoustic compression and rarefaction pulses are found to be generated in the biotissue. The amplitudes and profiles of the acoustic pulses developing in atherosclerotic human aorta tissues and an aqueous CuCl2 solution under laser irradiation are investigated as a function of the laser pulse energy fluence. The results obtained point to the absence of the cold spallation of the objects of study by rarefaction waves. Based on experimental data, the rise rates, pressure gradients, and propagation velocities of shock waves in the biotissue are calculated. The experimental data are found to agree well with the theoretical estimates.

Interaction of lithotripter‐generated shock waves with air bubbles

Abstract: The shock wave‐induced collapse and jet formation of pre‐existing air bubbles at the focus of an extracorporeal shock wave lithotripter is investigated using high‐speed photography. The experimentally obtained collapse time, ranging from 1 to 9 μs for bubbles with an initial radius R0 of 0.15 to 1.2 mm, agrees well with numerical results obtained using the Gilmore model. The collapse time is not linearly dependent on the initial bubble diameter since the temporal profile of the lithotripter wave contains a stress wave. The bubbles, positioned below a thin plastic foil, show strong jet formation in the direction of wave propagation with peak velocities of up to 770 m/s at the moment of collapse. Bubbles of initial radii between 0.3 and 0.7 mm always induce perforation of the foil by the jet (hole diameter 80–300 μm). Averaging the jet flow speed over 5 μs immediately after the collapse results in velocities from nearly zero up to 210 m/s, depending on the initial bubble size, with a maximum at R0=550 μm. T...

Numerical solutions of Euler equations by using a new flux vector splitting scheme

Abstract: A new flux vector splitting scheme has been suggested in this paper. This scheme uses the velocity component normal to the volume interface as the characteristic speed and yields the vanishing individual mass flux at the stagnation. The numerical dissipation for the mass and momentum equations also vanishes with the Mach number approaching zero. One of the diffusive terms of the energy equation does not vanish. But the low numerical diffusion for viscous flows may be ensured by using higher-order differencing. The scheme is very simple and easy to be implemented. The scheme has been applied to solve the one dimensional (1D) and multidimensional Euler equations. The solutions are monotone and the normal shock wave profiles are crisp. For a 1D shock tube problem with the shock and the contact discontinuities, the present scheme and Roe scheme give very similar results, which are the best compared with those from Van Leer scheme and Liou–Steffen's advection upstream splitting method (AUSM) scheme. For the multidimensional transonic flows, the sharp monotone normal shock wave profiles with mostly one transition zone are obtained. The results are compared with those from Van Leer scheme, AUSM and also with the experiment.

Simulation of Thick Accretion Disks with Standing Shocks by Smoothed Particle Hydrodynamics

Abstract: We present results of numerical simulation of inviscid thick accretion disks and wind flows around black holes. We use Smoothed Particle Hydrodynamics (SPH) technique for this purpose. Formation of thick disks are found to be preceded by shock waves travelling away from the centrifugal barrier. For a large range of the parameter space, the travelling shock settles at a distance close to the location obtained by a one-and-a-half dimensional model of inviscid accretion disks. Occasionally, it is observed that accretion processes are aided by the formation of oblique shock waves, particularly in the initial transient phase. The post-shock region (where infall velocity suddenly becomes very small) resembles that of the usual model of thick accretion disk discussed in the literature, though they have considerable turbulence. The flow subsequently becomes supersonic before falling into the black hole. In a large number of cases which we simulate, we find the formation of strong winds which are hot and subsonic when originated from the disk surface very close to the black hole but become supersonic within a few tens of the Schwarzschild radius of the blackhole. In the case of accretion of high angular momentum flow, very little amount of matter is accreted directly onto the black hole. Most of the matter is, however, first squeezed to a small volume close to the black hole, and subsequently expands and is expelled as a strong wind. It is quite possible that this expulsion of matter and the formation of cosmic radio jets is aided by the shock heating in the inner parts of the accretion disks.

Wave propagation in gas-liquid media

Abstract: Acoustics and Shock Waves in Homogenous Gas- and Vapor-Liquid Mixtures. Dynamics of Gas and Vapor Bubbles. Wave Processes in Gas-Liquid Systems. Wave Propagation in a Liquid with Vapor Bubbles. Wave Processes on the Interface of Two Media. Wave Flow of Liquid Films. Survey of Basic Calculation Formulas and Relations of Wave Dynamics of Gas- and Vapor-Liquid Media. References.

Nonlinear growth of dynamical overstabilities in blast waves.

Abstract: The numerical gasdynamics code ZEUS-2D is used to directly model the dynamical overstabilities in blast waves. The linear analysis is confirmed by perturbing a blast wave with a low-amplitude eigenfunction of the overstability. The amplitude of the perturbations is increased in order to determine the nonlinear behavior of the overstabilities. The overstability is found to saturate due to weak transverse shocks in the shell. Transverse velocities in the dense shell reach the postshock sound speed, and high-density regions with sizes of the order of the shell thickness form. Transverse oscillations continue even after saturation. This confirms and explains the damping of the overstability experimentally discovered by Grun et al. (1991).