Showing papers on "Rarefaction published in 2001"

Compact damping models for laterally moving microstructures with gas-rarefaction effects

Abstract: Compact models for the viscous damping coefficient in narrow air gaps between laterally moving structures are reported. In the first part of the paper, a simple frequency-independent first-order slip-flow approximation for the damping coefficient is derived and compared with a more accurate expression obtained from the linearized Boltzmann equation. The simple approximation is slightly modified and fitted to match the accurate model. The resulting simple approximation has a maximum relative error of less than /spl plusmn/6% at arbitrary Knudsen numbers in viscous, transitional and free molecular regions. In the second part of the paper, dynamic models for the damping force are derived, considering again gas rarefaction, by applying various boundary conditions. The damping admittance of the first-order slip-flow model is implemented also as an electrical equivalent admittance, constructed of RC sections, to allow both frequency and time domain simulations with a circuit simulator. The dependence of the damping admittance on pressure and gap displacement is demonstrated with model simulations. The accuracy and validity range of the model are verified with comparative numerical simulations of the Navier-Stokes equation. Finally, the damping coefficient in a lateral resonator is calculated using the compact model and compared with measured data with good agreement.

Distortion of the Wave Profiles in an Elastoplastic Body upon Spalling

Abstract: The distortion of wave profiles in measuring the spall strength of elastoplastic materials is analyzed. An expression for the velocity of an elastic compression wave that overtakes a plastic rarefaction wave is obtained. It is shown that, depending on the ratio between the stress gradients in the plastic rarefaction wave and the overtaking compression wave, the front velocity of the compressive wave varies in the limits between the velocities of the longitudinal perturbations and the perturbations of volume expansion or compression.

Growth rate of the Richtmyer–Meshkov instability when a rarefaction is reflected

Abstract: A model is presented that calculates the asymptotic growth rate of the linear Richtmyer–Meshkov instability when a rarefaction is reflected at the contact surface. The result is valid for any value of the incident shock Mach number and initial fluids parameters. There is very good agreement with previous numerical simulations and experiments done at high compressions. The technique developed in the model is seen to be highly accurate and allows us a fast evaluation of the asymptotic normal velocity at the interface.

Mapping subsurface fractures using nonlinearity measurements

Abstract: This Patent describes a method for determining the location and orientation of the open natural fractures in an earth formation by analyzing the interaction of the two seismic signals. One is a low frequency signal transmitted from the earth's surface and the other a high frequency signal transmitted from a wellbore. The compressional and the rarefaction cycles of the lower frequency signal are used to modulate the width of the open fractures, which changes their transmission characteristics. As a result, the amplitude of the high frequency signal gets modulated as it propagates through the open fractures. The result of the interaction of the high and low frequency seismic signals is recorded in another wellbore. The spectral analysis of the modulated signal that is recorded during compression and rarefaction cycles of the lower frequency surface generated signal is used to determine the location and the orientation of the open natural fractures.

Chapter 3.4 - Theory of Shock Waves: 3.4 Rarefaction Shocks

Abstract: This chapter focuses mainly on the conditions under which rarefaction shocks may form in single-phase fluids and on the local properties of discontinuities. One of the main issues in the theory of gasdynamic shocks is the question of the type of shocks, that is, compression or rarefaction shocks, which can be sustained by a given fluid. The second law of thermodynamics provides a powerful tool to eliminate shocks that are physically impossible. This chapter concentrates on shock formation in the dense gas regime of Bethe-Zel'dovich-Thompson (BZT) fluids. The properties of BZT fluids and the role of the second law in ruling out impossible shocks are treated in discussed. Further, restrictions resulting from the stability condition that requires that the wave speeds immediately upstream/downstream of the shock front must not be larger/smaller than the shock speed is considered. The main emphasis is on rarefaction shocks, the properties of compression shocks is also addressed, the reason being twofold. First, it is found that embedded regions of negative that are a necessary ingredient for the existence of rarefaction shocks strongly affect the behavior of compression shocks. Second, when dealing with general initial and/or boundary value problems, rarefaction and compression shocks may be generated simultaneously and even interact.

History of Shock Waves

Abstract: A shock wave is a surface of discontinuity propagating in a gas at which density and velocity experience abrupt changes. One can imagine two types of shock waves: (positive) compression shocks which propagate into the direction where the density of the gas is a minimum, and (negative) rarefaction waves which propagate into the direction of maximum density. 1 Gyozy Zemplen University of Budapest 1905

Oblique solitons in a cold magnetized plasma

Abstract: A fully nonlinear theory for stationary waves, propagating obliquely to the ambient magnetic field in a cold plasma, has been developed. Soliton solutions, representing both compressions and rarefactions in the magnetic field, exist for sub-fast flow conditions and in certain cones of magnetic obliquity. The soliton is explicitly characterized, in terms of the wave speed and its obliquity, by a parameter m (the “soliton number”). Compressive (“bright”) solitons are found to have a maximum attainable compression amplitude of three, corresponding to the condition m=1. Rarefactive (“dark”) solitons attain complete rarefaction when m=4. The properties of these stationary waves are described both in terms of magnetic hodographs, and of a spatial structure equation, whose equilibrium points yield the maximum compression and rarefaction at the center of the waves. An analytic solution, in terms of elementary transcendental functions, is also presented and highlights the role played by the soliton number m in det...

Rarefaction shock wave: formation under short pulse laser ablation of solids.

Abstract: We investigate formation, dynamics, and decay of the rarefaction shock wave under the conditions of ultrashort pulse laser ablation of solids. On the basis of the Euler equation and the van der Waals equation, we consider the planar and spherical expansion into vacuum matter heated instantaneously above the thermodynamic critical temperature. When the expansion occurs along an abnormal adiabat, in a part of which ( partial differential(2)p/ partial differentialv(2))/(S)<0, a rarefaction shock wave moving toward the target is formed. After its reflection from the nonvaporized material of the target, a thin dense layer of the expanding material is found to be formed. We suggest that this is the explanation for interference patterns observed experimentally above laser ablated surfaces. It has been speculated that the rarefaction shock wave may be formed on nova outbursts.

Three-dimensional singularities of a thin plasma slab.

Abstract: The three-dimensional (3D) nonlinear development of the interchange-like (Rayleigh-Taylor) instability of a thin slab of plasma exhibits interesting features with respect to its two-dimensional (2D) limit investigated by Bulanov, Pegoraro, and Sakai [Phys. Rev. E 59, 2292 (1999)]. We show that, contrary to the 2D case, the 3D evolution equations remain nonlinear when Lagrangian variables are adopted. Explicit solutions are found by the use of a generalized hodograph transformation. Both compression and rarefaction singularities are formed. Local solutions in the neighborhood of the singular points have a generic 2D character.

Rarefaction Wave Gun Propulsion

Abstract: : A new species of gun propulsion that dramatically reduces recoil momentum imparted to the gun is presented. First conceived by the author on 18 March 1999, the propulsion concept is explained, a methodology for the design of a reasonable apparatus for experimental validation using NATO standard 35mm TP anti-aircraft ammunition is developed, and the experimental results are presented. The firing results are juxtaposed by a simple interior ballistic model to place the experimental findings into a context within which they may better be understood. Rarefaction wave gun (RAVEN) propulsion is an original contribution to the field of armament engineering. No precedent is known, and no experimental results of such a gun have been published until now. Recoil reduction in excess of 50% was experimentally achieved without measured loss in projectile velocity. RAVEN achieves recoil reduction by means of a delayed venting of the breech of the gun chamber that directs the high enthalpy propellant gases through an expansion nozzle to generate forward thrust that abates the rearward momentum applied to the gun prior to venting. The novel feature of RAVEN, relative to prior recoilless rifles, is that sufficiently delayed venting results in a rarefaction wave that follows the projectile through the bore without catching it. Thus, the projectile exits the muzzle without any compromise to its propulsion performance relative to guns that maintain a sealed chamber.

Several questions in research of micro scale flow

Abstract: This paper gives the review of the recent research of micro scale flows. Some problems different from those of the macro scale flows are discussed. Some important facts in the research of micro scale flows, for example, scaling and the valid range of the continuum model, effects of surface,rarefaction, compressibility and the wall of the flow channel, are analysized.

Shock Tube Studies on Recombination Kinetics of Sodium Ion with Electron

Abstract: The ionization kinetics of sodium diluted in argon is studied in a shock tube, in which the test gas mixture is ionized by a reflected shock wave and subsequently quenched by a strong rarefaction wave. A Langmuir electrostatic probe is used to monitor the variation of the ion number density at the reflection shock wave region. The working state of the probe is in the near free fall region and a correction for reduction of the probe current due to elastic scattering in the probe sheath is introduced. At the temperature range of 800 to 2600 K and in the ambience of argon gas, the three-body recombination rate coefficient of the sodium ion with electron is determined: 3.43×10-14T-3.77cm6s-1.

A test facility for hypervelocity rarefied flows

Abstract: This paper describes a rarefied hypervelocity test facility producing gas speeds greater than 7 km/s. The X1 expansion tube at The University of Queensland has been used to produce nitrogen flows at 8.9 and 9.5 km/s with test flow durations of 50 and 40 μs respectively. Rarefied flow is indicated by values of the freestream breakdown parameter >0.1 (Cheng’s rarefaction parameter <10) and freestream Knudsen numbers up to 0.038, based on a model size of 9 mm. To achieve this, the test gas is expanded from the end of the acceleration tube into a dump tank. Nominal conditions in the expansion are derived from CFD predictions. Measured bar gauge (Pitot) pressures show that the flow is radially uniform when the Pitot pressure has decreased by a factor ten. The measured bar gauge pressures are an increasing fraction of the expected Pitot pressure as the rarefaction parameters increase.

Shock Compression of a Plate on a Wedged–Shaped Target

Abstract: Problems of compression of a plate on a wedge–shaped target by a strong shock wave and plate acceleration are studied using the equations of dissipationless hydrodynamics of compressible media. The state of an aluminum plate accelerated or compressed by an aluminum impactor with a velocity of 5—15 km/sec is studied numerically. For a compression regime in which a shaped–charge jet forms, critical values of the wedge angle are obtained beginning with which the shaped–charge jet is in the liquid or solid state and does not contain the boiling liquid. For the jetless regime of shock–wave compression, an approximate solution with an attached shock wave is constructed that takes into account the phase composition of the plate material in the rarefaction wave. The constructed solution is compared with the solution of the original problem. The temperature behind the front of the attached shock wave was found to be considerably (severalfold) higher than the temperature behind the front of the compression wave. The fundamental possibility of initiating a thermonuclear reaction is shown for jetless compression of a plate of deuterium ice by a strong shock wave.

Measurement of the slope of shock velocity-particle velocity Hugoniot curve for polymers

Abstract: In case of shock waves in polymers in the stress range of less than 1 GPa, a strategy to measure the slope of shock velocity-particle velocity Hugoniot curve is proposed. The method is based on the measurement of sound velocity at the shocked state as well as shock and particle velocity. The slope of Hugoniot can be evaluated by combining these values with the shock thermodynamic equation. Experiments were conducted for two kinds of polyethylene samples exhibiting peculiar shape of Hugoniot curve. An in-material PVDF gauge detects both a plane shock wave in polyethylene target induced by impact with a flyer plate and a rarefaction wave reflected from free surface of the flyer. Slope of the Hugoniot analyzed at several Hugoniot points for the polyethylene samples are consistent with their peculiar shape of the Hugoniot curves.

Shock wave interactions and propagation

Abstract: VOLUME 1: Theoretical, Experimental and Numerical Techniques History of Shock Waves General Laws for Propagation of Shock Waves Through Matter Theory of Shock Waves Shock Tubes and Tunnels: Facilities, Instrumentation Techniques Measurement Techniques and Diagnostics Numerical Methods VOLUME 2: Shock Wave Interactions and Propagation One-Dimensional Interactions Two-Dimensional Interactions Axi-Symmetric Shock Wave Reflections The Propagation of Shock Waves in Channels Application of Shock Waves in Medicine Spherical Shock Waves Shock Induced Instabilities of Interfaces Shock Wave Propagation in Multi-Phase Media VOLUME 3: Chemical Reactions in Shock Waves and Detonations Chemical and Combustion Kinetics Combustion, Detonation and Deflagration

Effects of lateral rarefaction wave on phase transition of PZT-95/5 ceramics under shock wave

Abstract: The results of research of effects of lateral rarefaction waves on phase transitions in PZT-95/5 ceramics under shock wave by shock experiments are reported. The experimental results indicate that the depolarization electric current linearly decreases with the shock-wave propagation distance in z direction. Based on Fluid Elastic-Plastic Model[1,2], a three-dimensional numerical simulation was performed, which explains the experimental results very well.

Rarefaction Waves and Bubbly Cavitation in Real Liquid

Abstract: The paper presents the short review of two stages of cavitating liquid fracture at the explosive loading. The problems of the real liquid state (with view point of its inhomogeneity) and limit tensile stress, as well as the mechanics of the cavitation development excited by intense rarefaction waves and the dynamic feature of breaking of a spherical liquid drop under the action of ultra-short shock wave are considered.

The Structure of Solitons Propagating Obliquely to the Magnetic Field

Abstract: A fully non-linear theory for stationary waves, propagating obliquely to an ambient magnetic field in a cold plasma, is developed. In the cold case soliton solutions, representing both compressions and rarefactions in the magnetic field, exist if the flow is sub-fast and sufficiently oblique, but in the case of compressions not too oblique. The maximum attainable compression is 3 (when the soliton number m is unity) and there is a complete rarefaction when m = 4. The properties of these stationary waves are described both in terms of magnetic hodographs and a spatial structure equation, whose equilibrium points yield the maximum compression and rarefaction at the centre of the waves. The existence of an analytic solution in terms of elementary transcendental functions highlights the role played by the soliton number m in determining the speed, strength and width of the solitons. The effects of thermal pressure on solitons structures is briefly described. In general pressure effects weaken the fast soliton, but give rise to a new slow soliton.

J/Psi suppression in colliding nuclei: statistical model analysis

Abstract: We consider the $J/\Psi$ suppression at a high energy heavy ion collision. An ideal gas of massive hadrons in thermal and chemical equilibrium is formed in the central region. The finite-size gas expands longitudinally in accordance with Bjorken law. The transverse expansion in a form of the rarefaction wave is taken into account. We show that $J/\Psi$ suppression in such an environment, when combined with the disintegration in nuclear matter, gives correct evaluation of NA38 and NA50 data in a broad range of initial energy densities.

Asymptotic Towards Rarefaction Wave of the Jin-Xin Relaxation Model for the p System

Abstract: We study the asymptotic equivalence of the Jin-Xin relaxation model to its formal limit of genuinely nonlinear 2 by 2 conservation laws (isentropic Euler equation in Lagrangian coordinate). We consider the case where the initial data are allowed to have jump discontinuities such that the corresponding solutions to the Euler equation contain centered rarefaction waves. In particular, Riemann data connected by rarefaction curves are included. We show that, as long as the initial data is a small perturbation of a non-vacuum constant state, the solution for the relaxation system exists globally in time and converges, as e —> 0, to the solution of the corresponding Euler equation uniformly except for an initial layer whose width is essentially of order O(e).

Non-Equilibrium Stationary Solitons

Abstract: Semi-analytical investigations using the orientation-free discrete gas-kinetic theory are performed in order to link the non-equilibrium but stationary solitons found in the randomly and approximately boundary treatment for the interactions between gases and solid-surfaces with vorticity at the pseudo-flat walls. The stationary solitons thus obtained from the integrable system of partial differential equations are subjected to different but limited dissipations depending on the intrinsic parameter of rarefaction. We also address the linear stability of our results in brief.

Numerical Studies on Effect of Nozzle Geometry and of Flow Continuity on Thrust Performance

Abstract: IEPC-01-193 Numerical studies have been conducted in order to investigate the effects of nozzle geometry and rarefaction on the thrust performance. For the estimation, ratio of mean free path to calculation grid size, grid Knudsen number is newly installed and evaluated. Based on the grid Knudsen number, wide range of nozzle flow is considered to be rarefied gas. Thus, continuum flow is solved by N-S equation and rarefied gas region is solved by DSMC. The results show that the rarefaction have some effect on velocity distribution.

Decompressive (cooling rarefaction) shock in optically thin radiative plasma

Abstract: It is shown that the decompressive shock, i.e., a shock where the pressure behind the front is smaller than the pressure ahead of it, is possible in a radiative plasma; this is in contrast to the situation in classic gas dynamics. An example of a steady state decompressive shock wave for a simple, but realistic model for radiative losses is presented. It is shown that it satisfies the Landau stability criteria.