Showing papers on "Rarefaction published in 1993"

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.

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.

Zero dissipation limit to rarefaction waves for the one‐dimensional navier‐stokes equations of compressible isentropic gases

Abstract: We study the zero dissipation limit problem for the one-dimensional Navier-Stokes equations of compressible, isentropic gases in the case that the corresponding Euler equations have rarefaction wave solutions. We prove that the solutions of the Navier-Stokes equations with centered rarefaction wave data exist for all time, and converge to the centered rarefaction waves as the viscosity vanishes, uniformly away from the initial discontinuities. In the case that either the effects of initial layers are ignored or the rarefaction waves are smooth, we then obtain a rate of convergence which is valid uniformly for all time. Our method of proof consists of a scaling argument and elementary energy analysis, based on the underlying wave structure. © 1993 John Wiley & Sons, Inc.

On slow‐mode waves in an anisotropic plasma

Abstract: The properties of small-amplitude waves propagating in a homogeneous anisotropic plasma are investigated using an MHD double-polytropic model that incorporates the CGL double-adiabatic model in one extreme and the isothermal model in the other. It is found that the properties of fast and intermediate mode waves remain qualitatively the same as in ordinary MHD but that, in certain parameter regimes, three inversions occur for slow-mode waves: (1) their phase speed exceeds that of intermediate waves; (2) they behave like fast-mode waves in that, across them, the plasma density and magnetic field increase or decrease together; (3) rarefaction waves rather than compression waves steepen.

Hypersonic blunt body wake computations using DSMC and Navier-Stokes solvers

Abstract: Numerical results obtained with direct simulation Monte Carlo (DSMC) and Navier-Stokes methods are presented for Mach 20 nitrogen flow about a 70-deg blunted cone. The flow conditions simulated are those that can be obtained in existing low-density hypersonic wind tunnels. Three sets of flow conditions are considered with freestream Knudsen numbers ranging from 0.03 to 0.001. The focus is on the wake structure: how does the wake structure change as a function of rarefaction, what are the afterbody levels of heating, and to what limits are continuum models realistic as rarefaction in the wake is progressively increased. Calculations are made with and without an afterbody sting. Results for the afterbody sting are emphasized in anticipation of an experimental study for the current flow conditions and model configuration. The Navier-Stokes calculations were made with and without slip boundary conditions. Comparisons of the results obtained with the two simulation methodologies are made for both flowfield structure and surface quantities.

Sheath dynamics induced by ion‐acoustic rarefaction wave

Abstract: A simple analytical model is presented to describe the sheath dynamics, when a stationary slab plasma with a uniform density n0 faces a negatively biased wall with a voltage φ0. The dynamics strongly depends on the sheath thickness s. If s is less than a well‐defined distance se, which is given by n0, φ0, and the electron temperature Te, then the sheath front advances supersonically. On the contrary, if s is greater than se, the sheath front moves subsonically, and a rarefaction wave is launched ahead of the sheath. In this case, the ion sheath and the rarefaction flow are continuously matched throughout the process. The model is applied to evaluate the ion collection time, and gives a good agreement with experiments over a wide region of plasma density. Rapid heating of electrons up to temperatures in the order of 10 eV is required for applications to atomic vapor laser isotope separation (AVLIS).

Particle motion through an oblique shock wave

Abstract: The authors describe the behavior of particles (connected with Laser Doppler Anemometry measurements) in high velocity flows. The different flow regimes are exposed, as well as the associated usual drag laws for a sphere. A unique relation is proposed for high velocities and for all flow regimes. Calculated values obtained with this law and experimental results are compared in the case of particle motion through an oblique shock wave. They are found in good agreement. Different effects due to rarefaction, compressibility and high relative Reynolds number are discussed.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Melting phenomenon in laser-induced shock waves.

Abstract: The melting fraction in laser-induced shock waves in aluminum was estimated as a function of the shock pressure. The results show that partial melting can begin during the relaxation of a shock pressure of 680 kbar. It is also suggested that for very short laser pulses (femtoseconds) a supercooling phenomenon may occur without melting during the rarefaction wave.

Analysis of unsteady wave processes in a rotating channel

Abstract: The impact of passage rotation on the gas dynamic wave processes is analyzed through a numerical simulation of ideal shock-tube flow in a closed rotating-channel. Initial conditions are prescribed by assuming homentropic solid-body rotation. Relevant parameters of the problem such as wheel Mach number, hub-to-tip radius ratio, length-to-tip radius ratio, diaphragm temperature ratio, and diaphragm pressure ratio are varied. The results suggest possible criteria for assessing the consequences of passage rotation on the wave processes, and they may therefore be applicable to pressure-exchange wave rotors. It is shown that for a fixed geometry and initial conditions, the contact interface acquires a distorted three-dimensional time-dependent orientation at non-zero wheel Mach numbers. At a fixed wheel Mach number, the level of distortion depends primarily on the density ratio across the interface as well as the hub-to-tip radius ratio. Rarefaction fronts, shocks, and contact interfaces are observed to propagate faster with increasing wheel Mach number.

The Riemann Problem for Two-Dimensional Gas Dynamics

Abstract: The Riemann problem for two-dimensional gas dynamics with isentropic and poly-tropic gas is considered. The initial data is constant in each quadrant and chosen so that only a rarefaction or shock wave connects two neighboring constant initial states. With this restriction the existence of five (resp. four) genuinely different wave combinations for isentropic (resp. polytropic) gas is proved. For each configuration the relations for the initial data and the symmetry properties of the solution are given.

Decay of an ion temperature discontinuity in a collisionless plasma

Abstract: The decay of an ion temperature discontinuity in a collisionless plasma is considered. Theoretical analysis and simulation are used. A shock is formed in the cold plasma region and a rarefaction wave is formed in the hot plasma region. Profiles of density and potential are presented. A comparison of the theoretical dependence on the initial hot ion temperature of the hot ion density, temperature, velocity, current and energy flux at the plateau region and the shock speed with the simulation data shows good agreement.

Mathematical modeling of the head‐disk interface (abstract)

Abstract: State‐of‐the‐art theoretical and numerical techniques required to simulate the head‐disk interface (HDI) of future magnetic storage devices is presented. The severity of operating conditions (i.e., attempts to achieve flying heights as low as 40 nm) pose several challenges. Large transient pressure gradients can be established within air bearing leading to numerical oscillations as well as to increased program execution times. Enhanced gaseous rarefaction effects must also be incorporated into the analysis. In the present study, accurate nonoscillatory air bearing pressure distributions were obtained using a high resolution finite element algorithm to solve the generalized Reynolds equation. Higher order gaseous rarefaction effects are incorporated into generalized Reynolds equations using the total mass flow rate coefficient predicted from the linearized Boltzmann equation. The form of the generalized Reynolds equation that is presented in this paper is an improved version of the continued fraction approximation previously proposed by Crone et al.1 A simple scaling analysis, which is based upon the results of the linearized Boltzmann equation, will also be presented to study the effect of slider miniaturization, as well as to obtain a novel interpretation of accelerated wear and accelerated flyability test results.

Melting phenomenton in laser-induced shock waves

Abstract: The melting fraction in laser-induced shock waves in aluminum was estimated as a function of the shock pressure. The results show that partial melting can begin during the relaxation of a shock pressure of 680 kbar. It is also suggested that for very short laser pulses (femtoseconds) a supercooling phenomenon may occur without melting during the rarefaction wave

Nonlinear reflection of divergent acoustic rarefaction waves in the atmosphere

Abstract: It is shown that the propagation velocity of a divergent rarefaction wave in an isothermal exponential atmosphere decays to zero at a certain critical height, which decreases as the initial pressure amplitude of the wave increases, and at which the Mach number attains its maximum possible negative value. The latter depends only on the isentropy exponent of the air. It is found that any further increase in the absolute value of the Mach number in the rarefaction wave above the critical height is limited by the onset of total reflection,which is characterized by a change of sign of the velocity of the corresponding part of the rarefaction waveform

Exploring Dense Plasma by Laser Compression. A simulation study

Abstract: A series of hydrodynamic simulations is presented, related to laser compression of matter. In particular, low entropy compression of hydrogen is studied in order to reach the metallic phase transition. Anomalous hydrodynamic phenomena like shock splitting and rarefaction shocks occuring in the neighbourhood of the phase transition are investigated for a special configuration.

Cavitation‐induced seismic events caused by small explosions in boreholes

Abstract: An electrolytically recharged sleeve exploder was fired at depths between 15.2 m and 51.8 m in a 200-mm diameter, steel‐cased, water‐filled shallow borehole in Hopkins County, Texas. Oxy‐hydrogen explosive gas charges were varied between 30 and 170 kJ. Seismic traces revealed three distinct, delayed, anomalous arrivals. Two of these moved out nonlinearly with increasing charge. The fact that the anomalies were not peculiar to gaseous sleeve explosions was confirmed by repeating part of the experiment using small high explosive charges. The anomalies appear to stem from the collapse of cavities that are created by shock waves. A model is advanced, in which up‐ and downgoing shock fronts sweep away from the explosion at the tube wave velocity. They reflect from the free and plugged ends of the borehole. Reflection at the free end transforms an upgoing overpressure into a downgoing rarefaction. Momentum transfer surges the fluid. Surges accumulate. Two rarefaction shocks eventually collide at the shot point....