Showing papers on "Rarefaction published in 2000"

Navier-Stokes simulations of gas flow in micro devices

Abstract: A numerical study of flow in micro channels and micro pipes is described. The simulations are performed by solving Navier-Stokes equations with a slip velocity boundary condition, using the LU-TVD implicit algorithm. A second-order slipping model incorporating pressure gradient is proposed and investigated. The numerical results obtained using the new slipping model are presented and found to compare well with available experimental data and numerical results from other references.Our computations also show that compressibility and the rarefied effects of gas flows are present in both micro channel and micro pipe flows. It is also found that the effect of rarefaction tends to mitigate the negative curvature of pressure distribution that can be attributed to compressibility.

Global asymptotics toward the rarefaction wave for solutions of viscous p -system with boundary effect

Abstract: The initial-boundary value problem on the half-line R+ = (0, oo) for a system of barotropic viscous flow vt — ux = 0, ut + p(v)x = n{y^)x is investigated, where the pressure p(v) = v~y (7 > 1) for the specific volume v > 0. Note that the boundary value at x = 0 is given only for the velocity u, say u_, and that the initial data (vq,ilq)(x) have the constant states (u+,w+) at x = +00 with vq(x) > 0, v+ > 0. If < u+, then there is a unique i>_ such that (f+,u+) G (the 2-rarefaction curve) and hence there exists the 2-rarefaction wave uf)(x/t) connecting (u_,u_) with (v+,u+). Our assertion is that, if w_ < u+, then there exists a global solution (v,u)(t,x) in C°([0,00); Jcf1(R+)), which tends to the 2-rarefaction wave (v?,u§)(x/t) I x>o as t —>■ 00 in the maximum norm, with no smallness condition on |u+ — U-1 and ||(«o — v+,uq — u+) ||//1) nor restriction on 7 (> 1). A similar result to the corresponding Cauchy problem is also obtained. The proofs are given by an elementary L2-energy method. Received February 15, 1998. 2000 Mathematics Subject Classification. Primary 35B40, 35L65, 76N10. Research by the second author was supported in part by Waseda University Grant for Special Research Project 97A-242. ©2000 Brown University 69 70 AKITAKA MATSUMURA and KENJI NISHIHARA

Molecular-dynamics simulation of rarefaction waves in media that can undergo phase transitions

Abstract: The expansion of an instantly heated planar layer of condensed matter into a vacuum is investigated. It is shown that, as the result of a phase transition, a liquid shell characterized by a constant density and filled with matter in a two-phase state is formed in a rarefaction wave. By measuring the velocity of the shell and its density and mass, it is possible to obtain important information about the behavior of matter in the near-critical region of the phase diagram, where both experimental and theoretical investigations are complicated. Problems associated with the kinetics of the phase transition in rarefaction waves are investigated in detail. This investigation is based on a direct computer simulation of the dynamics of atoms and is free from any assumptions usually used in phenomenologically describing the fluctuation kinetics of the liquid-vapor transition.

Structural properties of solutions arising from a nonequilibrium traffic flow theory

Abstract: This paper analyzes the structural properties of the shock and rarefaction wave solutions of a nonequilibrium theory of vehicular traffic flow. It shows that this nonequilibrium theory has two families of characteristics: one is slower and the other is faster than vehicular speed. Corresponding to the slower characteristic arise 1-shock and 1-rarefaction waves, whose behavior is similar to that of the shock and rarefaction waves in the LWR theory; corresponding to the faster characteristic there are 2-shocks (and 2-rarefaction waves) that behave as bores in rivers. The latter behavior does not accord with the generally held view that traffic is an anisotropic fluid. It is shown, however, those 2-shocks and 2-rarefactions in the studied nonequilibrium theory are transitory and their influence on traffic flow decays exponentially. It is further argued that as long as the 2-shocks and 2-rarefactions do not persist, they can be allowed in a nonequilibrium theory. Apart from the behavioral aspects, the paper also derives the formulae for solving the Riemann problem associated with the nonequilibrium theory. Most of the results carry over directly to other nonequilibrium theories of the same kind, including the PW theory.

A Model for the Static Sealing Performance of Compliant Metallic Gas Seals Including Surface Roughness and Rarefaction Effects

Abstract: The static sealing performance of compliant metallic gas seals is analyzed, accounting for both surface roughness and rarefaction effects. This is accomplished by a simultaneous solution of the contact and the flow problems for rough surfaces of which the compliant one is curved. A simplified semi-empirical model is developed and its accuracy is established for a wide range of practical applications. The effects of various design parameters and operating conditions on the sealing performance, are investigated using this model. It is found that the most important parameters to obtain “gas tight” sealing are the hardness of the softer component, the composite RMS roughness of the two mating faces, and the seal curvature at the contact zone. Presented at the 54th Annual Meeting Las Vegas, Nevada May 23–27, 1999

Successive generation of sounds by shock–strong vortex interaction

Abstract: The development of a flow field and the generation of sound due to the interaction between a vortex ring and a shock wave are studied numerically. The axisymmetric, unsteady, compressible Navier–Stokes equations are solved by a finite difference method. The results show that, when the vortex ring moves in the opposite direction to the shock wave, the interaction produces reflected shock waves, first. Then, the reflected shock waves interact with the vortex ring, and new rarefaction and compression waves are produced. The new compression waves interact with the vortex ring again, resulting in the further generation of rarefaction and compression waves. As the strength of the vortex ring is increased, this process is repeated and the pressure waves are generated successively.

Sonic rarefaction wave recoilless gun system

Abstract: A low recoil and low bore heat gun system provides a delayed pressure release mechanism for fired propellant charges in the rear gun barrel section. The delayed pressure release of the exhaust gases causes a sonic rarefaction wave along the length of the barrel bore to arrive at the exist end of the gun barrel at a predetermined time, generally coincident with the fired projectile.

Rarefaction waves in nonequilibrium-boiling fluid flows

Abstract: The depressurization of a high-pressure vessel initially filled with water heated to below the saturation point is investigated. After depressurization, the pressure in the vessel drops and the boiling fluid flows out into the atmosphere. The experiments [1–3] showed that, when the first rarefaction wave passes through the fluid and the pressure falls below the saturation point, a two-phase mixture with a small steam volume fraction (below 20%) is formed in the vessel. Intense boiling starts only after the arrival of a rarefaction wave traveling at a speed ∼ 10 m/s called the "boiling shock" in [4]. To explain the specific features of this process we developed a mathematical model which takes the difference in the phase velocities into account. Although in bubbly flows this difference is only ∼ 1 m/s, it is enough to cause bubble fragmentation. The calculation showed that the fragmentation proceeds like a chain reaction, i. e. one fragmentation event creates the conditions for the succeeding events. The avalanche-like bubble number growth leads to sharp boiling intensification and the rapid transition of the non-equilibrium mixture to the equilibrium state. This process occurs in a narrow region, namely, in a slow boiling wave which, in the numerical calculations, looks like a shock. The model developed has made it possible to obtain numerical solutions which agree well with the experimental data, to study the wave structure, and to explain the wave mechanism.

Influence of the shock-induced α-ε transition in Fe on its post-shock substructure evolution and mechanical behavior

Abstract: The effect of shock-prestraining high-purity Fe, above and below the 13 GPa phase transition, on post-shock compressive stress-strain behavior and substructure evolution is presented. The degree of shock hardening in Fe is higher for shock strength above the transition than below it. The substructure also displayed more deformation twinning for shocks above the phase transition than below. The shock hardening in Fe varied with propagation distance. Modeling shock propagation in Fe revealed that for the geometry used, the transition wave was overtaken and quenched by the rarefaction release explaining the gradient in shock hardening.

Turbulent adiabatic shock waves and diffusive particle acceleration

Abstract: We investigate the properties of turbulent adiabatic shock waves resulting from the self-consistent inclusion of finite Alfven-wave pressure in the shock balance equations. We demonstrate (i) the absence of a switch-on shock; (ii) the existence of two separated domains where the Mach number is greater than unity that have gas compression, and an associated domain where the gas compression ratio is less than unity (i.e. a rarefaction domain); (iii) the difference between the scattering-centre compression ratio and the gas compression ratio for all upstream wave cross-helicity values except for the isolated case of zero helicity; (iv) the presence of anomalous domains where the cosmic-ray particle spectral index can be negative. All of these results are brought about by including the upstream and downstream turbulent wave energies in the shock balance structure. Without the waves, none of the effects persists.

Characterization of showerhead performance at low pressure

Abstract: The performance of showerheads used in semiconductor processing applications has been examined over a wide range of Knudsen number and Reynolds number. Both computational fluid dynamics and direct simulation Monte Carlo techniques have been used to characterize the showerhead flow with the intent of developing correlations between the upstream velocity and the pressure drop across the showerhead. Empirical correlations developed to account for entrance effects and rarefaction are also examined. Recommendations are made concerning boundary conditions and, when appropriate, correlations for given pressures and flow rates.

Formation conditions for bubble suspensions upon shock-wave loading of liquids

Abstract: The conditions of development of bubble cavitation in liquid media upon shock-wave loading are found. It is s shown that, for the development of an unbounded cavitation, the bubbles should grow to certain critical sizes sufficient for their transition to a nonequilibrium state owing to the elastic energy transferred by a rarefaction wave to a liquid sample (at the stage of unloading). In contrast to low-viscosity liquids, in high-viscosity ones (such as glycerin) these conditions cannot be satisfied for any really attainable parameters of shock waves.

Generalized smooth and weak-discontinuous unsteady waves

Abstract: A theorem of equivalence regarding the weak discontinuity of the solutions (ũ(1),ũ(2),…,ũ(n),ũ) of an underdetermined system of n quasi-linear partial differential equations in one spatial dimension is proven The theorem demonstrates the theoretical existence of a smooth wave and a weak-discontinuous wave in a generalized unsteady wave, which consists of a shock wave, new (n+1) elementary waves, and a rarefaction wave A ũ(j)−ũ(i) path has anomalous characteristics such as a peak, an inflection, and a discontinuity in slope

Phase Transitions in Nonequilibrium Traffic Theory

Abstract: This paper uses the center difference scheme of Lax-Friedichs to numerically solve a newly developed continuum traffic flow theory and the kinematic theory of Lighthill and Whitham (1955) and Richards (1956) (the LWR theory), and it studies the flow-concentration phase transitions in flow containing both shock and rarefaction waves. A homogeneous road with finite length was modeled by both theories. Numerical simulations show that both theories yield nearly identical results for two representative Riemann problems: one has a shock solution and the other a rarefaction wave solution. Their phase transition curves, however, are different: those derived from the new theory have two branches--one for acceleration flow and one for deceleration flow--whereas those derived from the LWR theory comprise a single curve--the equilibrium curve. The phase transition curves in the shock case agree well with certain experimental observations but disagree with others. This disagreement may be resolved by studying transitions among nonequilibrium states, which awaits further development of a more accurate finite difference approximation of the nonequilibrium theory.

Study on Properties of Pressure Waves Generated by Steady Flames in a Duct

Abstract: One dimensional unsteady equations and Richtmyer Lax Wendroff scheme were used to study the influences of compression and rarefaction waves, combustion speed, flame out and length of tube to the pressure waves generated by steady propagating flames The results indicate that the traveling flames are accelerated by compression waves traveling in the same direction or rarefaction waves traveling in the opposite direction with respect to the flame front Otherwise, flames are decelerated Increasing combustion speed increases the pressure and temperature on both sides of the flame front The flame front is transformed into an interface as soon as the flame is extinguished, and the interface is almost stopped Also, the rarefaction waves propagates into the unburned and burned gases Increased tube length will contribute to the deflagration to detonation transition

Reduction of effects of rarefaction in ionized physical vapour deposition discharges

Abstract: Ionized physical vapour deposition (IPVD) is of current interest to the semiconductor industry for the deposition of thin metal films as diffusion barriers and seed layers in high aspect ratio features. One of the aims of IPVD is to collimate depositing particle fluxes by ionizing a significant fraction of the incident metal vapour and applying an electric potential bias to the substrate. A system consisting of a dc-powered, 15 cm diameter copper sputter source and a RF induction plasma powered by a single-turn, 36 cm diameter, loop antenna internal to the vacuum chamber has been examined. Measurements made with a biased quartz crystal microbalance in an argon background of 10-90 mTorr demonstrate that, at low magnetron sputtering levels of 100 W, ionized metal flux fractions (IMFFs) as high as 90% can be observed. However, further measurements of the IMFFs and plasma density indicate rarefaction of the background argon gas as the metal flux to the plasma increases. Results are presented from an experimental investigation of methods to reduce the gas rarefaction. These include the modulation of the metal flux on the timescale of the process gas residence time and increasing the target-to-substrate height.

Supersonic rarefied gas flow behind the trailing edge of a smooth plate

Abstract: A numerical analysis of the flow is based on a solution of a kinetic equation by a finite-difference method. The effect of rarefaction on the interaction between two uniform supersonic flows originating at the trailing edge of a semiinfinite plate of zero thickness is examined. The gas is treated as monatomic. When the pressures in the unperturbed flows far behind the trailing edge are equal, a mixing layer develops, with heat release in the initial tangential discontinuity and acoustic waves at the layer boundaries. When the downstream pressures are different, an interaction involving deflection of the flows developing behind the plate takes place. Special emphasis is placed on accurate computation of the flow in the neighborhood of the plate's edge. The kinetic equation was integrated with the use of schemes allowing for discontinuities in the distribution function and second-order accurate schemes outside the domains of substantial influence of discontinuities.

Nonsteady condensation and evaporation waves

Abstract: We study the motion of a phase transition (PT) front at a constant temperature between stable and metastable states in fluids with the van der Waals equation of state. We focus on a case of relatively large metastability and low viscosity, when no steadily moving PT front exists. Simulating the one-dimensional hydrodynamic equations, we find that the PT front generates acoustic shocks in forward and backward directions. Through this mechanism, the nonsteady PT front drops its velocity and eventually stops. The shock wave may shuttle between the PT front and the system's edge, rarefaction waves appearing in the shuttle process. If the viscosity is below a certain threshold, a turbulent state sets in.

Analysis and Validation of One-Dimensional Models for Gaseous Flows in Micro-Channels

Abstract: We present three one-dimensional models to simulate gaseous flows in micro-channels. These include no-slip flow, simple fully-developed, and locally fully-developed models. The locally fully-developed model provides a more accurate prediction when both rarefaction and gas acceleration need to be considered in micro-flows. Furthermore, the effects of rarefaction and gas acceleration on the locally dimensionless pressure ratio are specified on the basis of the three models

Shock wave propagation in porous ice

Abstract: We present data on shock wave propagation in porous ice under conditions applicable to the outer solar system. The equation of state of porous ice under low temperature and low pressure conditions agrees well with measurements under terrestrial conditions implying that data on terrestrial snow may be applicable to the outer solar system. We also observe rarefaction waves from small regions of increased porosity and calculate release wave velocities.

Evolution of the glow of an aerogel irradiated with a high-power pulse electron beam

Abstract: The evolution of the glow of the energy-release zone in porous transparent aerogel, with a density of 0.03–0.25 g/cm3, which is irradiated by a high-power pulse electron beam, is studied experimentally. In addition to a fast (τ≤τbeam) and a luminescent (τ≈10−6 s) glow components, a slow glow component (τ≈2×10−5 s) has been revealed. The appearance of this slow component is associated with an aerogel rarefaction wave and its destruction (cracking) arising after its isochoric bulk heating by electron radiation, which may occur due to an electrostatic field induced under irradiation. The discovered glow is utilized to visually determine the current position of the rarefaction wave front. The sound velocity measured as a function of the density of SiO2 aerogels with porosities of 10–100 allowed us to experimentally determine the percolation parameter of the aerogel equation of state.

Electrodynamic Effects Accompanying the Propagation of Current–Carrying Shock Waves in a Transverse Magnetic Field

Abstract: This paper considers the shock–wave compression of a magnetic field by waves capable of trapping a certain current and transferring it within the shock front. It is shown that this current screens the electromagnetic radiation of the shock front and lowers the efficiency of magnetic compression. An analytical model is proposed that allows one to obtain the spatial distribution and magnitude of shock–induced current for both conducting materials and materials with a shock–induced transition from a nonconducting to a conducting state. It is shown that the current magnitude in conductors is determined primarily by the compressibility of the material, and the magnitude of trapped current is determined by the shock–wave structure and depends primarily on the conductivity of the material, the thickness of the shock front, and the location of the phase transition point within the wave front. In materials with dielectric—conductor transitions, current is entirely concentated inside the shock front, and the current magnitude is determined only by the shock–front structure. It is shown that shock–induced current is accompanied by an anticurrent of the same strength and opposite direction, which spreads over the conducting material surface adjacent to the shock wave, leading to a number of new electrodynamic effects. Decay of a current–carrying shock wave at the interface of materials, which accompanies classical decay of shock–wave discontinuity, is considered. An analysis of the magnetic moments of shock–induced currents shows that for compression of a homogenous magnetic field, the electromagnetic–energy radiation from high–conducting materials is insignificant. However, failure of a conductor involving loss of conductivity in a properly organized rarefaction wave can lead to radiation of a considerable amount of the magnetic field energy accumulated in the conducting material during shock–wave cumulation of the magnetic field.

Pump device for system maintaining evaporation of fuel and system using such device

Abstract: mechanical engineering; internal combustion engines. SUBSTANCE: proposed device is furnished with valves designed for building rarefaction which are made so that, with regenerating valve open and cutoff valve closed, low resistance to flow is provided owing to sufficiently large cross- section of flow Aschutz. Thanks to it possibility of fuel tank damage caused by rise of rarefaction is excluded. EFFECT: improved reliability of systems maintaining fuel evaporation within preset limits by excluding possibility of fuel tank damage. 8 cl, 1 dwg

Unit for study of protective properties of individual protection complex

Abstract: units for testing devices for tightness by means of liquid or gaseous media or vacuum. SUBSTANCE: unit is provided with dummy with contractions located inside it for taking air from under-suit and under-mask spaces, air lines for taking samples of air for analysis, electric heaters with contact thermometers and rarefaction compensators placed in hermetic chamber, breathing simulating device (artificial lungs), air supply devices and gaseous chromatograph. EFFECT: enhanced efficiency. 2 dwg, 1 tbl

Experimental study of interaction between oblique detonation wave and rarefaction wave around a hypersonic free projectile

Abstract: Hypersonic projectiles whose speed was beyond the Chapman-Jouguet (C-J) detonation speed, were fired into stoichiometric hydrogen-oxygen premixed gases The flowfield around the projectile was visualized using a gated CCD camera A steady-state detonation wave was generated around the projectile With respect to the flow Mach number behind the wave front, the whole detonation-wave was partitioned into four parts; (i) strong overdriven detonation wave, (ii) weak overdriven detonation wave, (iii) quasi C-J detonation wave, and (iv) C-J detonation wave It has been found that a rarefaction wave generated at the projectile shoulder has a significant effect on the structure of the detonation wave