Showing papers on "Rarefaction published in 2009"
TL;DR: An experimental and numerical systematic study of the growth of the Richtmyer-Meshkov instability-induced mixing following a re-shock is made, where the initial shock moves from the light fluid to the heavy one, over an incident Mach number range of 1.15-1.45 as discussed by the authors.
Abstract: An experimental and numerical systematic study of the growth of the Richtmyer–Meshkov instability-induced mixing following a re-shock is made, where the initial shock moves from the light fluid to the heavy one, over an incident Mach number range of 1.15–1.45. The evolution of the mixing zone following the re-shock is found to be independent of its amplitude at the time of the re-shock and to depend directly on the strength of the re-shock. A linear growth of the mixing zone with time following the passage of the re-shock and before the arrival of the reflected rarefaction wave is found. Moreover, when the mixing zone width is plotted as a function of the distance travelled, the growth slope is found to be independent of the re-shock strength. A comparison of the experimental results with direct numerical simulation calculations reveals that the linear growth rate of the mixing zone is the result of a bubble competition process.
127 citations
TL;DR: In this paper, the second-order slip velocity model derived from kinetic theory can provide relatively accurate velocity profiles up to a Knudsen (Kn) number of around 0.5; however, its mass flow rate accuracy decreases as knudsen number approaches the upper bound.
Abstract: The kinetic-theory-based numerical schemes, such as direct simulation Monte Carlo (DSMC) and information preservation (IP), can be readily used to solve transition flow regimes. However, their high computational cost still promotes the researchers to extend the Navier–Stokes (NS) equations beyond the slip flow and to the transition regime applications. Evidently, a suitable extension would accurately predict both the local velocity profiles and the mass flow rate magnitude as well as the streamwise pressure distribution. The second-order slip velocity model derived from kinetic theory can provide relatively accurate velocity profiles up to a Knudsen (Kn) number of around 0.5; however, its mass flow rate accuracy decreases as Knudsen number approaches the upper bound. One remedy is to consider the rarefaction effects in calculating the NS viscosity coefficient. In this work, we use the shear stress distribution derived from our IP simulations, extend an analytical expression for the viscosity coefficient, ...
94 citations
TL;DR: The rarefaction acceleration as mentioned in this paper is specific to relativistic jets because their energy budget can still be dominated by magnetic energy even in highly super-fast magnetosonic regime.
Abstract: When a magnetically-dominated super-fast magnetosonic GRB jet leaves the progenitor star the external pressure support may drop and the jet may enter the regime of ballistic expansion during which its magnetic acceleration becomes highly ineffective. However, recent numerical simulations suggested that the transition to this regime is accompanied by a sudden "burst" of acceleration. We confirm this finding and attribute the acceleration to the sideways expansion of the jet - the magnetic energy is converted into the kinetic one in the strong magnetosonic rarefaction wave, which is launched when the jet loses its external support. This type of acceleration, the rarefaction acceleration, is specific to relativistic jets because their energy budget can still be dominated by magnetic energy even in highly super-fast magnetosonic regime. Just like the collimation acceleration of externally confined magnetized jets, it is connected with the geometry of magnetic flux sufaces. In both cases, in the acceleration zone the poloidal field lines diverge faster than in the monopolar configuration. On the other hand, whereas the collimation acceleration keeps the product of jet opening angle and Lorentz factor somewhat below unity, the rarefaction acceleration allows to make it significantly larger, in agreement with the standard model of jet breaks in afterglow light curves.
62 citations
TL;DR: The asymptotic stability of not only the single contact wave but also the superposition of the subsonic boundary layer solution, the contact wave, and the rarefaction wave to the inflow problem are investigated under some smallness conditions.
Abstract: The inflow problem of full compressible Navier–Stokes equations is considered on the half-line $(0,+\infty)$. First, we give the existence (or nonexistence) of the boundary layer solution to the inflow problem when the right end state $(\rho_+,u_+,\theta_+)$ belongs to the subsonic, transonic, and supersonic regions, respectively. Then the asymptotic stability of not only the single contact wave but also the superposition of the subsonic boundary layer solution, the contact wave, and the rarefaction wave to the inflow problem are investigated under some smallness conditions. Note that the amplitude of the rarefaction wave is not necessarily small. The proofs are given by the elementary energy method.
54 citations
TL;DR: In this article, a sound propagation through a rarefied gas is investigated on the basis of the linearized kinetic equation taking into account the influence of receptor, and the kinetic equation is solved via a discrete velocity method with a numerical error of 0.1%.
Abstract: A sound propagation through a rarefied gas is investigated on the basis of the linearized kinetic equation taking into account the influence of receptor. A plate oscillating in the normal direction to its own plane is considered as a sound source, while a stationary parallel plate is considered as being the receptor of sound. The main parameters determining the solution of the problem are the oscillation speed parameter, which is defined as the ratio of intermolecular collision frequency to the sound frequency, and the rarefaction parameter defined as the ratio of the distance between source and receptor to the molecular mean free path. The kinetic equation is solved via a discrete velocity method with a numerical error of 0.1%. The numerical calculations are carried out for wide ranges of the oscillation and rarefaction parameters. The concept of integral phase parameter is introduced to obtain the sound speed correctly in all regimes of the gas rarefaction and sound frequency. Analytical solutions are obtained in the limits of small and large parameters of frequency and rarefaction.
54 citations
TL;DR: In this paper, an extension of the Graetz problem to include the rarefaction effect, viscous dissipation term and axial conduction with constant-wall-heat-flux thermal boundary condition is presented.
51 citations
TL;DR: It is shown that during the expansion the bulk of the distribution function evolves towards a top-hat distribution, and while the electrons globally lose energy in favor of the ions, the rarefaction wave accelerates until it reaches the center of the foil.
Abstract: The collisionless expansion into a vacuum of a thin plasma foil adiabatically cooling down is studied with a particular emphasis on the evolution of the electron distribution function. It is shown that during the expansion the bulk of the distribution function evolves towards a top-hat distribution. As a result, while the electrons globally lose energy in favor of the ions, the rarefaction wave accelerates until it reaches the center of the foil. The electron temperature becomes strongly inhomogeneous, with a maximum in the center of the foil, a strong dip in the outer part of the foil, and a constancy of the initial temperature in the far corona.
45 citations
TL;DR: In this article, the authors solved the Riemann problem for the deceleration of an arbitrarily magnetized relativistic flow injected into a static unmagnetized medium in one dimension, and found that for the same initial Lorentz factor, the reverse shock becomes progressively weaker with increasing magnetization σ (the Poynting-to-kinetic energy flux ratio), and the shock becomes a rarefaction wave when σ exceeds a critical value, defined by the balance between the magnetic pressure in flow and the thermal pressure in the forward shock.
Abstract: We solve the Riemann problem for the deceleration of an arbitrarily magnetized relativistic flow injected into a static unmagnetized medium in one dimension. We find that for the same initial Lorentz factor, the reverse shock becomes progressively weaker with increasing magnetization σ (the Poynting-to-kinetic energy flux ratio), and the shock becomes a rarefaction wave when σ exceeds a critical value, σ c , defined by the balance between the magnetic pressure in the flow and the thermal pressure in the forward shock. In the rarefaction wave regime, we find that the rarefied region is accelerated to a Lorentz factor that is significantly larger than the initial value. This acceleration mechanism is due to the strong magnetic pressure in the flow. We discuss the implications of these results for models of gamma-ray bursts and active galactic nuclei.
39 citations
TL;DR: An analytical nonlinear gasdynamic theory of ion-acoustic waves in an e-p-i plasma is developed for the case in which all the plasma components in the wave undergo polytropic compression and rarefaction as mentioned in this paper.
Abstract: An analytical nonlinear gasdynamic theory of ion-acoustic waves in an e-p-i plasma is developed for the case in which all the plasma components in the wave undergo polytropic compression and rarefaction. An exact solution to the basic equations is found and analyzed by the Bernoulli pseudopotential method. The parameter range in which periodic waves can propagate and the range in which solitary waves (solitons) exist are determined. It is shown that the propagation velocity of a solitary is always higher than the linear ion sound velocity. The profiles of all the physical quantities in both subsonic and supersonic waves are calculated. The results obtained agree well with both the data from other papers and particular limiting cases.
37 citations
TL;DR: Interactions of dispersive shock waves (DSWs) and rarefaction waves (RWs) associated with the Korteweg-de Vries equation are shown to exhibit multiphase dynamics and isolated solitons.
Abstract: Interactions of dispersive shock waves (DSWs) and rarefaction waves (RWs) associated with the Korteweg-de Vries equation are shown to exhibit multiphase dynamics and isolated solitons. There are six canonical cases: one is the interaction of two DSWs that exhibit a transient two-phase solution but evolve to a single-phase DSW for large time; two tend to a DSW with either a small amplitude wave train or a finite number of solitons, which can be determined analytically; two tend to a RW with either a small wave train or a finite number of solitons; finally, one tends to a pure RW.
36 citations
TL;DR: Knudsen boundary layers, which present non-Newtonian stress and non-Fourier heat flow, are predicted as the dominant rarefaction effects in the linear theory and a set of second-order boundary conditions for velocity slip and temperature jump are derived for the NSF system.
Abstract: Microscale gas flows between two rotating coaxial circular cylinders of infinite length with different temperatures are investigated. Navier-Stokes-Fourier (NSF) and regularized 13-moment (R13) equations in their linear form are used to independently analyze velocity and temperature fields in shear-driven rotary flows, i.e., cylindrical Couette flows. Knudsen boundary layers, which present non-Newtonian stress and non-Fourier heat flow, are predicted as the dominant rarefaction effects in the linear theory. We show that the R13 system yields more accurate results for this boundary value problem by predicting the Knudsen boundary layers, which are not accessible for NSF equations. Furthermore, a set of second-order boundary conditions for velocity slip and temperature jump are derived for the NSF system. It is shown that the proposed boundary conditions effectively improve the classical hydrodynamics. The accuracy of NSF and R13 equations is discussed based on their comparison with available direct simulation Monte Carlo data.
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TL;DR: In this paper, the authors considered the inflow problem of full compressible Navier-Stokes equations on the half line and gave the existence (or non-existence) of the boundary layer solution when the right end state was in the subsonic, transonic and supersonic regions respectively.
Abstract: The inflow problem of full compressible Navier-Stokes equations is considered on the half line $(0,+\infty)$. Firstly, we give the existence (or non-existence) of the boundary layer solution to the inflow problem when the right end state $(\rho_+,u_+,\theta_+)$ belongs to the subsonic, transonic and supersonic regions respectively. Then the asymptotic stability of not only the single contact wave but also the superposition of the boundary layer solution, the contact wave and the rarefaction wave to the inflow problem are investigated under some smallness conditions. Note that the amplitude of the rarefaction wave can be arbitrarily large. The proofs are given by the elementary energy method.
TL;DR: In this paper, a rarefied gas flow through a thin slit into vacuum is studied on the basis of the direct simulation Monte Carlo method, and the mass flow rate and flow field are calculated over the whole range of the gas rarefaction from the free-molecular regime to the viscous one.
Abstract: A rarefied gas flow through a thin slit into vacuum is studied on the basis of the direct simulation Monte Carlo method. The mass flow rate and flow field are calculated over the whole range of the gas rarefaction from the free-molecular regime to the viscous one. A comparison to other results on the same problem available in literature is performed. An interpolating formula for the reduced flow rate is obtained.
TL;DR: In this paper, the Kadomtsev-Petviashvili-Burger equation for pair-ion plasmas is derived using the small amplitude expansion method.
Abstract: Nonlinear electrostatic waves are studied in unmagnetized, dissipative pair-ion plasmas in the presence of weak transverse perturbations. The dissipation in the system is taken into account by incorporating the kinematic viscosity of both positive and negative ions in plasmas. The Kadomtsev–Petviashvili–Burger equation is derived using the small amplitude expansion method. The Kadomtsev–Petviashvili equation for pair-ion plasmas is also presented by ignoring the dissipative effects. Both compressive and rarefactive shocks and solitary waves are found to exist in pair-ion plasmas. The dependence of compression and rarefaction on the temperature ratios between the ion species is numerically shown. The present study may have relevance to the understanding of the formation of electrostatic shocks and solitons in laboratory produced pair-ion plasmas.
TL;DR: In this article, the effects of rarefaction, aspect ratio and a parameter representing the fluid/wall interaction on thermal and hydrodynamic character of flow in trapezoidal microchannels are explored.
TL;DR: In this paper, the authors studied the unsteady motion of a rarefied gas between two parallel plates, one of which is oscillating in its plane, based on the linearized Boltzmann equation for a hard sphere molecular gas.
TL;DR: The main motivation for the study is to overcome the intense computational effort required by the large computational domain and the slow downstream variation and convergence in this problem, and to address some of the existing concerns with current models.
Abstract: This article addresses some analytical and numerical modeling issues regarding the simulation of pressure-driven nitrogen slip flow in long microchannels. The main motivation for the study is to overcome the intense computational effort required by the large computational domain and the slow downstream variation and convergence in this problem, and to address some of the existing concerns with current models. A parallel solver is developed and used along with a serial version to obtain the steady state solution. This approach is found to provide an efficient and accurate solution to the problem. A comparison with earlier results is used for validation, as well as for justifying this hybrid approach. Some implemental issues related to the parallel algorithm are discussed and solved. The effects of variable properties, rarefaction, and the source terms in energy equation are determined and are found to be significant, particularly for the case of uniform wall heat flux boundary condition.
TL;DR: In this paper, the effects of the relativistic ponderomotive force and trapped particles in the presence of ponderOMotive force on the rarefaction shock waves are investigated.
Abstract: The effects of the relativistic ponderomotive force and trapped particles in the presence of ponderomotive force on the rarefaction shock waves are investigated. The ponderomotive force alters the electron density distribution. This force and relativistic mass affect the plasma frequency. These physical parameters modify the total pressure and the existence condition of the rarefaction shock wave. Furthermore, the trapping of particles by the high frequency electromagnetic field considerably changes the existence condition of the rarefaction shock wave. The total pressure and Hugoniot curve are obtained by considering the relativistic ponderomotive force and trapped particles.
TL;DR: In this article, a theoretical model is proposed to describe the mechanism of laser-induced plasma shock wave evolution in air, and an optical beam deflection technique is employed to track the plasma wave evolution process.
Abstract: A theoretical model is proposed to describe the mechanism of laser-induced plasma shock wave evolution in air. To verify the validity of the theoretical model, an optical beam deflection technique is employed to track the plasma shock wave evolution process. The theoretical model and the experimental signals are found to be in good agreement with each other. It is shown that the laser-induced plasma shock wave undergoes formation, increase and decay processes; the increase and the decay processes of the laser-induced plasma shock wave result from the overlapping of the compression wave and the rarefaction wave, respectively. In addition, the laser-induced plasma shock wave speed and pressure distributions, both a function of distance, are presented.
TL;DR: In this article, numerical simulations and analytic modeling of shock tube experiments on Rayleigh-Taylor and Richtmyer-Meshkov instabilities are presented, where the incident shock is initiated in A and the transmitted shock proceeds into B. They compare their simulation results with a generalized Layzer model for two fluids with time-dependent densities and derive a new freeze-out condition whereby accelerating...
Abstract: We report numerical simulations and analytic modeling of shock tube experiments on Rayleigh–Taylor and Richtmyer–Meshkov instabilities. We examine single interfaces of the type A/B where the incident shock is initiated in A and the transmitted shock proceeds into B. Examples are He/air and air/He. In addition, we study finite-thickness or double-interface A/B/A configurations such as air/SF6/air gas-curtain experiments. We first consider conventional shock tubes that have a “fixed” boundary: A solid endwall which reflects the transmitted shock and reshocks the interface(s). Then we focus on new experiments with a “free” boundary—a membrane disrupted mechanically or by the transmitted shock, sending back a rarefaction toward the interface(s). Complex acceleration histories are achieved, relevant for inertial confinement fusion implosions. We compare our simulation results with a generalized Layzer model for two fluids with time-dependent densities and derive a new freeze-out condition whereby accelerating ...
TL;DR: In this paper, an extended model of the reactive magnetron sputtering that assumes the non-uniform discharge current density and which accommodates the gas rarefaction effect is presented.
Abstract: The majority of current models of the reactive magnetron sputtering assume a uniform shape of the discharge current density and the same temperature near the target and the substrate. However, in the real experimental set-up, the presence of the magnetic field causes high density plasma to form in front of the cathode in the shape of a toroid. Consequently, the discharge current density is laterally non-uniform. In addition to this, the heating of the background gas by sputtered particles, which is usually referred to as the gas rarefaction, plays an important role. This paper presents an extended model of the reactive magnetron sputtering that assumes the non-uniform discharge current density and which accommodates the gas rarefaction effect. It is devoted mainly to the study of the behaviour of the reactive sputtering rather that to the prediction of the coating properties. Outputs of this model are compared with those that assume uniform discharge current density and uniform temperature profile in the deposition chamber. Particular attention is paid to the modelling of the radial variation of the target composition near transitions from the metallic to the compound mode and vice versa. A study of the target utilization in the metallic and compound mode is performed for two different discharge current density profiles corresponding to typical two pole and multipole magnetics available on the market now. Different shapes of the discharge current density were tested. Finally, hysteresis curves are plotted for various temperature conditions in the reactor.
TL;DR: In this article, the authors studied the convergence rate of solutions to the initial-boundary value problem for scalar viscous conservation laws on the half line and showed that the solution tends toward a linear superposition of the stationary solution and the rarefaction wave.
Abstract: We study the convergence rate of solutions to the initial-boundary value problem
for scalar viscous conservation laws on the half line Especially, we deal with the case where the
Riemann problem for the corresponding hyperbolic equation admits transonic rarefaction waves In
this case, it is known that the solution tends toward a linear superposition of the stationary solution
and the rarefaction wave We show that the convergence rate is (1 + t)1
2 (1 1
p ) log2(2 + t) in Lp
norm (1 p < 1) and (1 + t)1
2+ in L1 norm if the initial perturbation from the corresponding
superposition is located in H1 \ L1 The proof is given by a combination of the weighted Lp energy
method and the L1 estimate
TL;DR: In this paper, the Riemann problem for two-dimensional isentropic Euler equations is considered and the initial data are three constants in three fan domains forming different angles.
Abstract: The Riemann problem for two-dimensional isentropic Euler equations is considered. The initial data are three constants in three fan domains forming different angles. Under the assumption that only a rarefaction wave, shock wave or contact discontinuity connects two neighboring constant initial states, it is proved that the cases involving three shock or rarefaction waves are impossible. For the cases involving one rarefaction (shock) wave and two shock (rarefaction) waves, only the combinations when the three elementary waves have the same sign are possible (impossible).
TL;DR: In this paper, the dynamic performance of the herringbone groove journal bearings (HGJBs) with the effects of gas rarefaction taken into account is considered for applications in microsystems.
Abstract: The dynamic performance of the herringbone groove journal bearings (HGJBs) with the effects of gas rarefaction taken into account is considered for applications in microsystems. Two important parameters (the Knudsen number Kn and the tangential momentum accommodation coefficients, TMACs or the accommodation coefficients, ACs) that affect gas rarefaction significantly are considered. Small variations in film thickness and pressure from the equilibrium state are substituted into the transient modified molecular gas lubrication (MMGL) equation, which considers effects of gas rarefactions with the Poiseuille and Couette flow rate correctors. The gas film in the rotor-bearing system is modeled as stiffness and damping elements with coefficients dependent on the exciting frequency. The dynamic coefficients are then obtained by solving the linearized MMGL equations. The equations of motion of the rotor as well as the dynamic coefficients are performed for the present linear stability analysis. Due to the exciting frequency-dependent nature of the dynamic coefficients, an iterative method with the golden section technique is introduced in the linear stability analysis of rotor-bearing systems. The critical mass parameters and the related threshold speed are computed and discussed. The results of this study prove that HGJBs in microsystems can operate at concentric conditions at very high speeds.
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TL;DR: In this paper, various shock and rarefaction-type similarity solutions of the third-order nonlinear dispersion equation in 1D are constructed and blow-up of some solutions are proved by different techniques.
Abstract: Various shock and rarefaction-type similarity solutions of the third-order nonlinear dispersion equation in 1D are constructed Blow-up of some solutions are proved by different techniques
TL;DR: The Riemann problem for a two-dimensional pressure-gradient system is considered and it is proved that the cases involving three rarefaction waves are impossible.
TL;DR: A more realistic model of a spherical blast wave of moderate strength, which, however, does not involve a secondary shock, and the theory developed for the spherical blasts is also extended to cylindrical blasts.
TL;DR: In this paper, a gas-dynamic model is used to study the conditions for the existence of large-amplitude ion acoustic solitons in a plasma with negative ions.
Abstract: A gas-dynamic model is used to study the conditions for the existence of large-amplitude ion acoustic solitons in a plasma with negative ions. It is shown that the limiting Mach number—the upper boundary of the region of existence of compression solitons—depends nonmonotonically on the temperature of the positive ions. The result is that, for certain fixed densities of the negative ions, there are one or two temperature boundaries between the regions where solitons can and cannot exist. It is found that, for rarefaction solitons, it is fundamentally important to take into account electron inertia and that the Mach number of such solitary waves is restricted not by the complete decompression of electrons within the wave (as thought previously), but by the fact that the electrons at the center of the wave reach the acoustic speed, above which the thermal-pressure-induced action cannot be transferred back to the electron flow and smooth continuous solutions are impossible.
01 Jun 2009
TL;DR: In this paper, a modified molecular gas lubrication (MMGL) equation is utilized as the governing equation for the gas film to include the effect of gas rarefaction. And the dynamic coefficients (stiffness and damping coefficients) are obtained by integrating the dynamic pressure over the bearing surfaces.
Abstract: The performance of grooved air bearings in microsystems is analysed and discussed. The modified molecular gas lubrication (MMGL) equation is utilized as the governing equation for the gas film to include the effect of gas rarefaction. The gas rarefaction is significantly affected by two important parameters (Knudsen numbers (Kn) and accommodation coefficients (ACs)). The Poiseuille and Couette flowrate correctors (QP and QC) are introduced in the MMGL equation to extend the lubrication theory (compressible Reynolds equation) for arbitrary Kn and tangential momentum accommodation coefficients or ACs. At a specific operating condition, the transient MMGL equation is linearized by small variations in film thickness and pressure. The linearized MMGL equation is then solved by finite-element method to obtain the dynamic pressure distributions. Therefore, the dynamic coefficients (stiffness and damping coefficients) are obtained by integrating the dynamic pressure over the bearing surfaces.
TL;DR: In this article, non-selfsimilar elementary waves of the conservation laws in another kind of view, which is different from the usual self-similar transformation, are obtained by the interactions between different elementary waves, and will continue to interact with other states.