Showing papers on "Rarefaction published in 2012"

Quantum vortex reconnections

Abstract: We study reconnections of quantum vortices by numerically solving the governing Gross-Pitaevskii equation. We find that the minimum distance between vortices scales differently with time before and after the vortex reconnection. We also compute vortex reconnections using the Biot-Savart law for vortex filaments of infinitesimal thickness, and find that, in this model, reconnection are time-symmetric. We argue that the likely cause of the difference between the Gross-Pitaevskii model and the Biot-Savart model is the intense rarefaction wave which is radiated away from a Gross-Pitaeveskii reconnection. Finally we compare our results to experimental observations in superfluid helium, and discuss the different length scales probed by the two models and by experiments.

Dust ion-acoustic solitary waves in a dusty plasma with nonextensive electrons.

Abstract: The dust-modified ion-acoustic waves of Shukla and Silin are revisited within the theoretical framework of the Tsallis statistical mechanics. Nonextensivity may originate from correlation or long-range plasma interactions. Interestingly, we find that owing to electron nonextensivity, dust ion-acoustic (DIA) solitary waves may exhibit either compression or rarefaction. Our analysis is then extended to include self-consistent dust charge fluctuation. In this connection, the correct nonextensive electron charging current is rederived. The Korteweg--de Vries equation, as well as the Korteweg--de Vries--Burgers equation, is obtained, making use of the reductive perturbation method. The DIA waves are then analyzed for parameters corresponding to space dusty plasma situations.

Differential marker protein expression specifies rarefaction zone-containing human Adark spermatogonia

Abstract: It is unclear whether the distinct nuclear morphologies of human A(dark) (Ad) and A(pale) (Ap) spermatogonia are manifestations of different stages of germ cell development or phases of the mitotic cycle, or whether they may reflect still unknown molecular differences. According to the classical description by Clermont, human dark type A spermatogonium (Ad) may contain one, sometimes two or three nuclear 'vacuolar spaces' representing chromatin rarefaction zones. These structures were readily discerned in paraffin sections of human testis tissue during immunohistochemical and immunofluorescence analyses and thus represented robust morphological markers for our study. While a majority of the marker proteins tested did not discriminate between spermatogonia with and without chromatin rarefaction zones, doublesex- and mab-3-related transcription factor (DMRT1), tyrosine kinase receptor c-Kit/CD117 (KIT) and proliferation-associated antigen Ki-67 (KI-67) appeared to be restricted to subtypes which lacked the rarefaction zones. Conversely, exosome component 10 (EXOSC10) was found to accumulate within the rarefaction zones, which points to a possible role of this nuclear domain in RNA processing.

Zero Dissipation Limit to Rarefaction Wave with Vacuum for One-Dimensional Compressible Navier–Stokes Equations

Abstract: It is well-known that one-dimensional isentropic gas dynamics has two elementary waves, i.e., shock wave and rarefaction wave. Among the two waves, only the rarefaction wave can be connected to a vacuum. Given a rarefaction wave with one-side vacuum state to the compressible Euler equations, we can construct a sequence of solutions to one-dimensional compressible isentropic Navier–Stokes equations which converge to the above rarefaction wave with vacuum as the viscosity tends to zero. Moreover, the uniform convergence rate is obtained. The proof consists of a scaling argument and elementary energy analysis based on the underlying rarefaction wave structures.

Effect of interacting rarefaction waves on relativistically hot jets

Abstract: The effect of rarefaction acceleration on the propagation dynamics and structure of relativistically hot jets is studied through relativistic hydrodynamic simulations. We emphasize the nonlinear interaction of rarefaction waves excited at the interface between a cylindrical jet and the surrounding medium. From simplified one-dimensional (1D) models with radial jet structure, we find that a decrease in the relativistic pressure due to the interacting rarefaction waves in the central zone of the jet transiently yields a more powerful boost of the bulk jet than that expected from single rarefaction acceleration. This leads to a cyclic in situ energy conversion between thermal and bulk kinetic energies, which induces radial oscillating motion of the jet. The oscillation timescale is characterized by the initial pressure ratio of the jet to the ambient medium and follows a simple scaling relation, τoscillation(P jet, 0/P amb, 0)1/2. Extended two-dimensional simulations confirm that this radial oscillating motion in the 1D system manifests as modulation of the structure of the jet in a more realistic situation where a relativistically hot jet propagates through an ambient medium. We find that when the ambient medium has a power-law pressure distribution, the size of the reconfinement region along the propagation direction of the jet in the modulation structure λ evolves according to a self-similar relation λt α/2, where α is the power-law index of the pressure distribution.

Solution to the Riemann problem in a one-dimensional magnetogasdynamic flow

Abstract: The Riemann problem for a quasilinear hyperbolic system of equations governing the one-dimensional unsteady flow of an inviscid and perfectly conducting compressible fluid, subjected to a transverse magnetic field, is solved approximately. This class of equations includes as a special case the Euler equations of gasdynamics. It has been observed that in contrast to the gasdynamic case, the pressure varies across the contact discontinuity. The iterative procedure is used to find the densities between the left acoustic wave and the right contact discontinuity and between the right contact discontinuity and the right acoustic wave, respectively. All other quantities follow directly throughout the (x, t)-plane, except within rarefaction waves, where an extra iterative procedure is used along with a Gaussian quadrature rule to find particle velocity; indeed, the determination of the particle velocity involves numerical integration when the magneto-acoustic wave is a rarefaction wave. Lastly, we discuss numeric...

Internal heat transfer coefficients in microporous media with rarefaction effects

Abstract: The internal heat transfer of different gases in microporous media was investigated experimentally and numerically. The experimental test section had a sintered bronze porous media with average particle diameters from 11 μm to 225 μm. The Knudsen numbers at the average inlet and outlet pressures of each test section varied from 0.0006 to 0.13 with porosities from 0.16 to 0.38. The particle-to-fluid heat transfer coefficients of air, CO2 and helium in the microporous media were determined experimentally. The results show that the Nusselt numbers for the internal heat transfer in the microporous media decrease with decreasing the particle diameter, dp, and increasing Knudsen number for the same Reynolds number. For Kn>0.01, the rarefaction affects the internal heat transfer in the microporous media. A Nusselt number correlation was developed that includes the influence of rarefaction. The computational fluid dynamics (CFD) numerical simulation was carried out to do the pore scale simulation of internal heat transfer in the microporous media considering the rarefaction effect. Pore scale three-dimensional numerical simulations were also used to predict the particle-to-fluid heat transfer coefficients. The numerical results without slip-flow and temperature jump effects for Kn<0.01 corresponded well with the experimental data. The numerical results with slip-flow and temperature jump effects for 0.01

Numerical modelling of rarefied gas flow through a slit at arbitrary pressure ratio based on the kinetic equation

Abstract: A rarefied gas flow through a thin slit at an arbitrary gas pressure ratio is calculated on the basis of the kinetic model equations (BGK and S-model) applying the discrete velocity method. The calculations are carried out for the whole range of the gas rarefaction from the free-molecular regime to the hydrodynamic one. Numerical data on the flow rate and distributions of density, bulk velocity and temperature are reported. Comparisons of the present results with those based on the direct simulation Monte Carlo method and on the linearized BGK kinetic equation are performed. The conditions of applicability of the linearized theory are discussed.

Magnetosonic cylindrical soliton in electron-positron-ion plasma

Abstract: Solutions in the form of cylindrical magnetosonic solitons of compression and rarefaction were obtained within the scope of the three-species electromagnetic gas-dynamic model of an electron-positron-ion plasma. These solutions can describe formation of cylindrical structures in accretion disks and jets in the vicinity of compact astrophysical objects.

Thin-foil expansion into a vacuum with a two-temperature electron distribution function.

Abstract: A kinetic theory of the expansion into a vacuum of a plasma thin foil with initially a hot and a cold Maxwellian electron population is examined with a one-dimensional kinetic code. Whereas hot electrons always lose energy to expanding ions, cold electrons can either gain or lose energy depending on the initial temperature and density ratios and on time. When the cold electrons' density is not too large, they experience initially an adiabatic compression by the electric field associated with the rarefaction wave. The corresponding temperature increase can be as large as a factor of a few tens. Later on, as expected, the cold electrons eventually lose energy to the expansion. When cold electrons are numerically dominant, a rarefaction shock appears during the first phase of the expansion. Hot electrons cool down faster than cold electrons, thus reducing the effective temperature ratio. Furthermore, the amplitude of the rarefaction shock and the dip that it causes on the ion velocity spectrum tend to be smoothed out by the expansion.

Nonlinear stability of combination of viscous contact wave with rarefaction waves for a 1Dradiation hydrodynamics model

Abstract: In this paper we consider the large-time behavior of solutions for the Cauchy problem to a compressible radiating gas model, where the far field states are prescribed. This radiating gas model is represented by the one-dimensional system of gas dynamics coupled with an elliptic equation for radiation flux. When the corresponding Riemann problem for the compressible Euler system admits a solution consisting of a contact wave and two rarefaction waves, it is proved that for such a radiating gas model, the combination of viscous contact wave with rarefaction waves is asymptotically stable provided that the strength of combination wave is suitably small. This result is proved by a domain decomposition technique and elementary energy methods.

Comprehensive computer model for magnetron sputtering. I. Gas heating and rarefaction

Abstract: The complex interaction between several variables in magnetron sputtering discharges is a challenge in developing engineering design tools for industrial applications. For instance, at high pressures, rarefaction and gas heating should no longer be neglected for determining several parameters of the process. In this article, we use a comprehensive 3D reactor-scale simulator that incorporates most phenomena of interest in a self-consistent manner to simulate the transport of sputtered particles over a wide range of pressures and powers. Calculations of aluminum deposition rates and metal vapor densities are in reasonable agreement with experiments over a wide range of pressures and powers. Of the elements investigated (Al, Ti, and Cu), copper showed the greatest rarefaction (30%) due to its higher sputtering yield. Titanium, despite a slightly lower sputtering yield than Al, shows a greater rarefaction than aluminum as more particles are reflected from the target as high energy neutrals. In this case, a mo...

Rarefaction pulses for the Nonlinear Schrodinger Equation in the transonic limit

Abstract: We investigate the properties of finite energy travelling waves to the nonlinear Schrodinger equation with nonzero conditions at infinity for a wide class of nonlinearities. In space dimension two and three we prove that travelling waves converge in the transonic limit (up to rescaling) to ground states of the Kadomtsev-Petviashvili equation. Our results generalize an earlier result of F. Bethuel, P. Gravejat and J-C. Saut for the two-dimensional Gross-Pitaevskii equation, and provide a rigorous proof to a conjecture by C. Jones and P. H. Roberts about the existence of an upper branch of travelling waves in dimension three.

The effects that changes in the diaphragm aperture have on the resulting shock tube flow

Abstract: In a conventional shock tube, the driver and the driven sections have similar (if not identical) cross-sectional area and the diaphragm opened area, upon rupturing, is practically equal to the tube cross-sectional area. Such geometry results in generating a well-formed shock wave in the tube’s driven section. The present experimental work checks the effects that changes in the diaphragm ruptured area have on the generated shock and rarefaction waves. Experiments were conducted in an 80 mm by 80 mm cross section shock tube generating incident shock waves having Mach numbers within the range from 1.06 to 1.25. In each run, pressure histories were recorded along the driven and the driver sections of the shock tube. The recorded pressures reveal that progressive reduction in the diaphragm open space resulted in a weaker shock and both longer time and distance until the compression waves generated close to the diaphragm coalesces into a shock wave. In addition, reducing the open space of the diaphragm resulted in a significant slow down in the high pressure reduction prevailing in the driver section.

Simulation of general relativistic shock wave interactions by a locally inertial Godunov method featuring dynamical time dilation

Abstract: We introduce the locally inertial Godunov method with dynamical time dilation, and use it to give a definitive numerical simulation of a point of shock wave interaction in general relativity starting from a new initial dataset. Prior work of Groah and Temple justifies meeting the Einstein constraint equations for the initial data only at the weak level of Lipshitz continuity in the metric. The forward time simulations, presented here, resolve the secondary wave in the Smoller–Temple shock wave model for an explosion into a static, singular, isothermal sphere. The backward time solutions indicate black hole formation from a smooth solution via collapse associated with an incoming rarefaction wave. A new feature is that space–time is approximated as locally flat in each grid cell so that Riemann problems and the Godunov method can be implemented. Clocks are then dynamically dilated to simulate effects of space–time curvature. Such points of shock wave interaction are more singular than points on single shock surfaces because the coordinate systems that make space–time locally flat on single shock surfaces (Gaussian normal coordinates), break down at points of shock wave interaction.

Computational Study on Micro Shock Tube Flows with Gradual Diaphragm Rupture Process

Abstract: Gas flows through micro shock tubes are widely used in many engineering applications such as micro engines, particle delivery devices etc. Recently, few studies have been carried out to explore the shock wave excursions through micro shock tubes at very low Reynolds number and at rarefied gas condition. But these studies assumed centered shock and expansion waves, which are generally produced by instantaneous diaphragm rupture process. But in real scenario, the diaphragm ruptures with a finite rupture time and this phenomenon will significantly alter the shock wave propagation characteristics. In the present research, numerical simulations have been carried out on a two dimensional micro shock tube model to simulate the effect of finite diaphragm rupture process on the wave characteristics. The rarefaction effect was simulated using Maxwell’s slip wall equations. The results show that shock wave attenuates rapidly in micro shock tubes compared to conventional macro shock tubes. Finite diaphragm rupture causes the formation of non-centered shock wave at some distance ahead of the diaphragm. The shock propagation distance is also drastically reduced by the rupture effects.

An Interaction of a Rarefaction Wave and a Transonic Shock for the Self-Similar Two-Dimensional Nonlinear Wave System

Abstract: We study a two dimensional Riemann problem for the self-similar nonlinear wave system which gives rise to an interaction of a transonic shock and a rarefaction wave. The interesting feature of this problem is that the governing equation changes its type from supersonic in the far field to subsonic near the origin. The subsonic region is then bounded above by the sonic line (degenerate) and below by the transonic shock (free boundary). Furthermore due to the rarefaction wave in the downstream, which interacts with the transonic shock, the problem becomes inhomogeneous and degenerate. We establish the existence result of the global solution to this configuration, and present analysis to understand the solution structure of this problem.

Experimental investigation of adiabatic evaporation waves in superheated refrigerants

Abstract: Propagation of adiabatic evaporation waves arising while refrigerants R-11 rapidly transit to metastable state due to depressurization in the rarefaction wave is experimentally investigated. New regularities of the interphase surface dynamics and the influence of interphase heat and mass transfer in propagation of adiabatic evaporation waves are obtained. It has been found that the phase transition in metastable liquid occurs in the conditions of developing multiscale turbulence in liquid and vapor phases under dynamic action of a vapor flow on the interphase surface and convective heat supply to the zone of high-intensity phase transition. The surface phase transition was visualized by a rapid video camera, its pulsating character is revealed and its properties are determined.

Evolution of axisymmetric weakly turbulent mixtures interacting with shock or rarefaction waves

Abstract: This paper deals with the interaction of a shock or a rarefaction wave with a weakly turbulent mixture of perfect gases. Assuming weak density-velocity fluctuations, Kovasznay decomposition applies and linear theories can be used to predict the evolution of the joint spectrum of density and velocity during the interaction. In this work, the upstream spectrum is restricted to axisymmetric fields free of acoustic perturbations, in order to comply with shock tube experimental conditions. Besides, spectral anisotropy is limited to a first order spherical harmonic decomposition. With these assumptions, transfer matrices can be obtained which relate the Reynolds stresses, turbulent mass flux and density variance after interaction to their counterparts before interaction. Results are given for both shock waves and rarefaction or compression waves; they are intended to help improve one-point statistical turbulence models applied to shock tube experiments.

Slip flow and heat transfer in rectangular and circular microchannels using hybrid FE/FV method

Abstract: SUMMARY Rarefied gas flows typically encountered in MEMS systems are numerically investigated in this study. Fluid flow and heat transfer in rectangular and circular microchannels within the slip flow regime are studied in detail by our recently developed implicit, incompressible, hybrid (finite element/finite volume) flow solver. The hybrid flow solver methodology is based on the pressure correction or projection method, which involves a fractional step approach to obtain an intermediate velocity field by solving the original momentum equations with the matrix-free, implicit, cell-centered finite volume method. The Poisson equation resulting from the fractional step approach is then solved by node based Galerkin finite element method for an auxiliary variable, which is closely related to pressure and is used to update the velocity field and pressure field. The hybrid flow solver has been extended for applications in MEMS by incorporating first order slip flow boundary conditions. Extended inlet boundary conditions are used for rectangular microchannels, whereas classical inlet boundary conditions are used for circular microchannels to emphasize on the entrance region singularity. In this study, rarefaction effects characterized by Knudsen number (Kn) in the range of 0 ⩽ Kn ⩽ 0.1 are numerically investigated for rectangular and circular microchannels with constant wall temperature. Extensive validations of our hybrid code are performed with available analytical solutions and experimental data for fully developed velocity profiles, friction factors, and Nusselt numbers. The influence of rarefaction on rectangular microchannels with aspect ratios between 0 and 1 is thoroughly investigated. Friction coefficients are found to be decreasing with increasing Knudsen number for both rectangular and circular microchannels. The reduction in the friction coefficients is more pronounced for rectangular microchannels with smaller aspect ratios. Effects of rarefaction and gas-wall surface interaction parameter on heat transfer are analyzed for rectangular and circular microchannels. For most engineering applications, heat transfer is decreased with rarefaction. However, for fluids with very large Prandtl numbers, velocity slip dominates the temperature jump resulting in an increase in heat transfer with rarefaction. Depending on the gas-wall surface interaction properties, extreme reductions in the Nusselt number can occur. Present results confirm the existence of a transition point below and above wherein heat transfer enhancement and reduction can occur. Copyright © 2011 John Wiley & Sons, Ltd.