Showing papers on "Rarefaction published in 2013"

The Limit of the Boltzmann Equation to the Euler Equations for Riemann Problems

Abstract: The convergence of the Boltzmann equation to the compressible Euler equations when the Knudsen number tends to zero has been a long-standing open problem in kinetic theory. In the setting of a Riemann solution that contains the generic superposition of shock, rarefaction wave, and contact discontinuity to the Euler equations, we succeed in justifying this limit by introducing hyperbolic waves with different solution backgrounds to capture the extra masses carried by the hyperbolic approximation of the rarefaction wave and the diffusion approximation of contact discontinuity.

The characteristic shape of emission profiles of plasma spokes in HiPIMS: the role of secondary electrons

Abstract: A time resolved analysis of the emission of HiPIMS plasmas reveals inhomogeneities in the form of rotating spokes. The shape of these spokes is very characteristic depending on the target material. The localized enhanced light emission has been correlated with the ion production. Based on these data, the peculiar shape of the emission profiles can be explained by the localized generation of secondary electrons, resulting in an energetic electron pressure exceeding the magnetic pressure. This general picture is able to explain the observed emission profile for different target materials including gas rarefaction and second ionization potential of the sputtered elements.

A lattice Boltzmann study of gas flows in a long micro-channel

Abstract: In this paper, the pressure-driven flow in a long micro-channel is studied via a lattice Boltzmann equation (LBE) method. With the inclusion of the gas-wall collision effects, the LBE is able to capture the flow behaviors in the transition regime. The numerical results are compared with available data of other methods. Furthermore, the effects of rarefaction and compressibility on the deviation of the pressure distribution from the linear one are also investigated.

Crossover distributions at the edge of the rarefaction fan

Abstract: We consider the weakly asymmetric limit of simple exclusion process with drift to the left, starting from step Bernoulli initial data with ρ−<ρ+ so that macroscopically one has a rarefaction fan. We study the fluctuations of the process observed along slopes in the fan, which are given by the Hopf–Cole solution of the Kardar–Parisi–Zhang (KPZ) equation, with appropriate initial data. For slopes strictly inside the fan, the initial data is a Dirac delta function and the one point distribution functions have been computed in [Comm. Pure Appl. Math. 64 (2011) 466–537] and [Nuclear Phys. B 834 (2010) 523–542]. At the edge of the rarefaction fan, the initial data is one-sided Brownian. We obtain a new family of crossover distributions giving the exact one-point distributions of this process, which converge, as T↗∞ to those of the Airy A2→BM process. As an application, we prove moment and large deviation estimates for the equilibrium Hopf–Cole solution of KPZ. These bounds rely on the apparently new observation that the FKG inequality holds for the stochastic heat equation. Finally, via a Feynman–Kac path integral, the KPZ equation also governs the free energy of the continuum directed polymer, and thus our formula may also be interpreted in those terms.

Dense plasma heating and Gbar shock formation by a high intensity flux of energetic electrons

Abstract: Process of shock ignition in inertial confinement fusion implies creation of a high pressure shock with a laser spike having intensity of the order of a few PW/cm2. However, the collisional (Bremsstrahlung) absorption at these intensities is inefficient and a significant part of laser energy is converted in a stream of energetic electrons. The process of shock formation in a dense plasma by an intense electron beam is studied in this paper in a planar geometry. The energy deposition takes place in a fixed mass target layer with the areal density determined by the electron range. A self-similar isothermal rarefaction wave of a fixed mass describes the expanding plasma. Formation of a shock wave in the target under the pressure of expanding plasma is described. The efficiency of electron beam energy conversion into the shock wave energy depends on the fast electron energy and the pulse duration. The model is applied to the laser produced fast electrons. The fast electron energy transport could be the dominant mechanism of ablation pressure creation under the conditions of shock ignition. The shock wave pressure exceeding 1 Gbar during 200–300 ps can be generated with the electron pulse intensity in the range of 5–10 PW/cm2. The conclusions of theoretical model are confirmed in numerical simulations with a radiation hydrodynamic code coupled with a fast electron transport module.

Vacuum Behaviors around Rarefaction Waves to 1D Compressible Navier--Stokes Equations with Density-Dependent Viscosity

Abstract: In this paper, we study the large time asymptotic behavior toward rarefaction waves for solutions to the one-dimensional compressible Navier--Stokes equations with density-dependent viscosities for general initial data whose far fields are connected by a rarefaction wave to the corresponding Euler equations with one end state being vacuum. First, a global-in-time weak solution around the rarefaction wave is constructed by approximating the system and regularizing the initial data with general perturbations, and some a priori uniform-in-time estimates for the energy and entropy are obtained. Then it is shown that the density of any weak solution satisfying the natural energy and entropy estimates will converge to the rarefaction wave connected to vacuum with arbitrary strength in sup-norm time-asymptotically. Our results imply, in particular, that the initial vacuum at far field will remain for all the time, which is in sharp contrast to the case of nonvacuum rarefaction waves studied in [Q. S. Jiu, Y. Wan...

Caveats for Using Shock Tube in Blast-Induced Traumatic Brain Injury Research

Abstract: Blast-induced traumatic brain injury (TBI) is currently an important and very “hot” research topic because it has been acknowledged to be a significant source of morbidity and disability during the wars in Iraq and Afghanistan, among blast victims. A total of 545 academic articles about blast TBI research have been published since 1946, of which 82% (447 articles) have been published since 2003, and 57% (312 articles) were published from 2010 to 2013. A number of experimental models are currently implemented to investigate the mechanisms of blast-induced TBI in rodents and larger animals such as rabbits and swine. As the fundamental shock wave generator, shock tubes (either compressed air-driven or detonation-driven) are generally employed in these experimental models. The compressed air-driven shock tube is a horizontally mounted, circular steel tube, in which a gas at low pressure (the driven gas) and a gas at high pressure (the driver gas) are separated using diaphragms (such as polyester Mylar membrane). After the diaphragm suddenly ruptures at predetermined pressure thresholds (e.g., 126–147 kPa), shock waves are generated and propagate through the low pressure section (the driven section) toward the mouth of the shock tube. The detonation-driven shock tube is a cylindrical metal tube that is closed at one end. The blast, causing the shock waves, is generated by detonation of an explosive charge in the closed end of the tube. Both compressed air-driven and detonation-driven shock tubes can produce blast shock waves to induce blast injuries in animals. However, because of their designs and structures, both shock tubes are not able to generate the Friedlander wave (an ideal form of a primary blast wave) that occurs when a powerful explosive detonates in a free field, without nearby surfaces that can interact with the wave. A series of complex shock waves are then generated following the lead shock wave (the original shock front), including reflected shock waves, a Mach stem, an unsteady turbulent jet, and rarefaction waves. These waves can cause sudden compression or rarefaction effects upon any object encountered in their motion path, and transfer kinetic energy to the object. Therefore, if an experimental animal is placed inside the shock tube, these complex pressure waves will cause more severe and complex injuries that are rarely observed in blast victims, thus leading to false-positive results in the studies of blast TBI mechanism.

Busemann functions and the speed of a second class particle in the rarefaction fan

Abstract: In this paper we will show how the results found in [Probab. Theory Related Fields 154 (2012) 89–125], about the Busemann functions in last-passage percolation, can be used to calculate the asymptotic distribution of the speed of a single second class particle starting from an arbitrary deterministic configuration which has a rarefaction fan, in either the totally asymetric exclusion process or the Hammersley interacting particle process. The method will be to use the well-known last-passage percolation description of the exclusion process and of the Hammersley process, and then the well-known connection between second class particles and competition interfaces.

Computational study of the unsteady flow characteristics of a micro shock tube

Abstract: Micro shock tubes are widely employed in many micro instruments which require high speed and high temperature flow field. The small flow dimension introduces additional flow physics such as rarefaction effects, viscous effects etc, which makes the micro shock tube different from conventional macro shock tubes. In the present study, a numerical investigation of the flow physics associated with shock propagation and reflection inside micro shock tubes was carried out using unsteady Navier Stokes equations. Maxwell’s slip boundary conditions were incorporated to simulate the rarefaction effects produced due to low pressure and very small length scale. The effect of initial pressures on the shock propagation was investigated keeping the pressure ratio constant. The dependency of the shock tube diameter on shock propagation was also investigated. The results show that shock strength attenuates drastically in a micro shock tube compared to macro shock tubes. The viscous boundary layer becomes a governing parameter in controlling micro shock tube wave propagations. The implementation of slip velocity to model rarefaction effects increases the shock strength and aids in shock wave propagation. The simulation with slip wall exhibits a wider hot zone (shock-contact distance) compared to no-slip simulation. The contact surface propagation distance reduces under the slip effects. A drastic attenuation in shock propagation distance was observed with reduction in diameter. The shock wave when reflected from the end wall inhibits the rarefaction effects, generally happening at very low pressure micro shock tubes, and the associated slip effect vanishes for the post reflected shock flow field.

Orion Aerodynamics for Hypersonic Free Molecular to Continuum Conditions

Abstract: Numerical simulations are performed for the Orion Crew Module, previously known as the Crew Exploration Vehicle (CEV) Command Module, to characterize its aerodynamics during the high altitude portion of its reentry into the Earth's atmosphere, that is, from free molecular to continuum hypersonic conditions. The focus is on flow conditions similar to those that the Orion Crew Module would experience during a return from the International Space Station. The bulk of the calculations are performed with two direct simulation Monte Carlo (DSMC) codes, and these data are anchored with results from both free molecular and Navier-Stokes calculations. Results for aerodynamic forces and moments are presented that demonstrate their sensitivity to rarefaction, that is, for free molecular to continuum conditions (Knudsen numbers of 111 to 0.0003). Also included are aerodynamic data as a function of angle of attack for different levels of rarefaction and results that demonstrate the aerodynamic sensitivity of the Orion CM to a range of reentry velocities (7.6 to 15 km/s).

Simulation of the transient heat transfer between two coaxial cylinders

Abstract: The transient heat flux between two coaxial cylinders is studied on the basis of the numerical solution of the nonlinear unsteady S-model kinetic equation. A large range of the gas rarefaction and two temperature ratios between the cylinders' walls are considered. The time evolutions of the averaged over the distance between the cylinders heat flux, pressure, and bulk velocity are analyzed. The steady state time, as a time of steady state flow establishment, is introduced. This time depends on the characteristic time of the system and on the gas rarefaction. It is found that this steady state time for the averaged heat flux varies approximately 18 times from the near free molecular to the hydrodynamic flow regime. In the slip flow regime, the analytical expression for the steady state temperature distribution between two cylinders is obtained. It is found that the transient heat flux evolution derived from the energy balance allows to estimate the time of steady state flow establishment in the slip flow regime.

Rarefaction acceleration in magnetized gamma-ray burst jets

Abstract: Submitted by Ρένια Βασιλeιάδου (irenevasiliades@ekt.gr) on 2016-04-27T07:28:50Z No. of bitstreams: 1 1.5_ΑΝ_15_7_13.pdf: 848087 bytes, checksum: cbaf3cd44cc694bd57bd6e2bcfc4c828 (MD5)

Direct simulation Monte Carlo investigation of mixed supersonic–subsonic flow through micro-/nano-scale channels

Abstract: The main goal in this study is to provide deep physical descriptions on the behaviour of supersonic micro-/nano-channel flow using the direct simulation Monte Carlo method. We found some unique physical aspects of micro-/nano-flows including mixed supersonic–subsonic regimes in constant-area ducts. This mixed regime is due to the formation of entrance shocks and their reflection from the thick boundary layer developed in a rarefied medium. We studied the effects of Mach number, channel aspect ratio and flow rarefaction on the channel inflow condition. The effects of wall thermal state on flow behaviour and shock wave structures were also investigated.

On gaseous microflows under isothermal conditions

Abstract: Flow processes of gases and related heat and mass transfer properties in smallest channels or porous structures are of utmost interest for many technical application in engineering science. This so-called microflows occur for instance in geometrically defined microchannels which are parts of Micro/Nano Electro Mechanical Systems (MEMS/NEMS) or in porous catalysts or filters. In such applications the heat transfer or the yield in gas phase reactions is crucially dependent on the flow behavior. In microflows the fluid gas phase is in a state called rarefied, when the distance of solid boundaries (e.g. pore diameter) is on the same order of magnitude as the gaseous mean free path λ. The ratio of λ to a characteristic length is defined as the Knudsen number which is reciprocally proportional to and the pressure of the bulk gas. Hence, also gases in larger structures can be rarefied if the pressure is sufficiently low. For instance in vacuum applications or high altitude aerodynamics gaseous rarefaction has to be taken into account. Depending on the dimensionless quantified rarefaction it is commonly known that continuum fluid dynamics fail for modeling gas flows in (and around) very small geometries. Rarefied flows behave totally different as continuum flows. Hence research on gaseous microflows can contribute to the general understanding of rarefaction effects. Central aspect of the current thesis is the modeling of integral quantities of gaseous flows in micro structures with uniform and alongside varying cross section. A microchannel is the simplest geometry in which rarefaction effects can be observed and can as well be considered as a model for more complex geometries. A mathematical model which allows for the predictive and non-empirical calculation of integral flow properties (e.g. pressure loss or mass flow rate) is not only a useful tool for design of MEMS/NEMS devices, but also bears the chance of gaining new, basic insights. Consequently, a basic aspect of the current work is the review and analysis of existing approaches in modeling gas microflows. General weaknesses of commonly used transport models are revealed and critically discussed. This analysis simultaneously represents the motivation for development of an alternative approach. In the framework of this PhD thesis a transport model is developed which is based on the superposition of transport mechanisms and is unrestrictively valid over the whole range of rarefaction. The model is developed by means of a raised hypothesis on a rarefied flow in a slightly tapered duct. The derived mathematical formulation is twofold evaluated. First, comparison is carried out of measured values found in literature to analytically and predictively calculated curves, where a strikingly good accordance of data and model is found. Further, own measurements on microchannels with slightly varying cross section are performed. The presentation of manufactured microstructures and the experimental set-up is another central aspect of the current thesis. Even for measured values on these asymmetric ducts, the prediction of the model is thoroughly accurate which does surprise due to the simplicity of the mathematical formulation.

Hyperbolic-hyperbolicrelaxation limit for a 1d compressible radiation hydrodynamics model: superpositionof rarefaction and contact waves

Abstract: In this paper we consider a hyperbolic-hyperbolic relaxation limit problem for a 1D compressible radiation hydrodynamics (RHD) system. The RHD system consists of the full Euler system coupled with an elliptic equation for the radiation flux. The singular relaxation limit process we consider corresponds to the physical problem of letting the Bouguer number become infinite. We prove for appropriate initial datum that the solution of the initial value problem for the RHD system converges for vanishing reciprocal Bouguer number to a weak solution of the limit system which is the Euler system. The initial data are chosen such that the limit solution is composed by a $1$-rarefaction wave, a contact discontinuity and a $3$-rarefaction wave. Moreover we give the convergence rate in terms of the physical parameter.

The Riemann problem for a hyperbolic model of incompressible fluids

Abstract: The aim of the present paper is to investigate shock and rarefaction waves in a hyperbolic model of incompressible fluids. To this aim, we use the so-called extended-quasi-thermal-incompressible (EQTI) model, recently proposed by Gouin and Ruggeri (H. Gouin, T. Ruggeri, International Journal of Non-Linear Mechanics 47 (2012) 688–693). In particular, we use as constitutive equation a variant of the well-known Boussinesq approximation in which the specific volume depends not only on the temperature but also on the pressure, leading to a hyperbolic system of differential equations. The limit case of ideal incompressibility, namely when the thermal expansion coefficient and the compressibility factor vanish, is also considered. The results show that the propagation of shock waves in an EQTI fluid is characterized by small jump in specific volume and temperature, even when the jump in pressure is relevant, and rarefaction waves originating from a general Riemann problem are characterized by a very steep profile. The knowledge of the loci of the states that can be connected to a given state by a shock wave or a rarefaction wave allows also to completely solve the Riemann problem. The obtained results are confirmed by means of numerical calculations.

Flows of rarefied gaseous mixtures in networks of long channels

Abstract: A method is presented to calculate the steady flows of rarefied gaseous mixtures in networks of long channels. The approach is based on the kinetic level. First, the McCormack linearized kinetic model is solved to obtain the local flow properties in the channels in a wide range of gaseous rarefaction and mole fraction. Second, the global flow properties including the flow rates and the distribution of the pressure and the mole fraction are deduced. An integral equation is introduced in order to determine the flow rates as functions of the differences of the partial pressures between the two ends of each channel. The conservation of mass at the nodes of the network results into a system of linear algebraic equations. The overall mathematical problem is solved iteratively. Pressure driven flows of He/Xe and He/Ar through an example network of circular tubes are calculated at intermediate values of the gaseous rarefaction. The results of the flow rates and the pressures and the mole fractions at the nodes in the whole system and the representative distributions of the pressure and the mole fraction along the channels are presented and commented on.

Intervals of radial interplanetary magnetic fields at 1 au, their association with rarefaction regions, and their apparent magnetic foot points at the sun

Abstract: We have examined 226 intervals of nearly radial interplanetary magnetic field orientations at 1 AU lasting in excess of 6 hr. They are found within rarefaction regions as are the previously reported high-latitude observations. We show that these rarefactions typically do not involve high-speed wind such as that seen by Ulysses at high latitudes during solar minimum. We have examined both the wind speeds and the thermal ion composition before, during and after the rarefaction in an effort to establish the source of the flow that leads to the formation of the rarefaction. We find that the bulk of the measurements, both fast- and slow-wind intervals, possess both wind speeds and thermal ion compositions that suggest they come from typical low-latitude sources that are nominally considered slow-wind sources. In other words, we find relatively little evidence of polar coronal hole sources even when we examine the faster wind ahead of the rarefaction regions. While this is in contrast to high-latitude observations, we argue that this is to be expected of low-latitude observations where polar coronal hole sources are less prevalent. As with the previous high-latitude observations, we contend that the best explanation for these periods of radial magnetic field is interchange reconnection between two sources of different wind speed.

Extensions of Dorfman’s Theory

Abstract: Economic impact of composite sampling is investigated in the realistic framework of tests with positive probability of false positive and of false negative results. Sensitivity and specificity when pooling samples are also discussed, using rarefaction as a framework.

Expansion of a plasma into vacuum with a bi-Maxwellian electron distribution function

Abstract: A comprehensive theory is developped to describe the expansion of a plasma into a vacuum with a two-temperature electron distribution function. The characteristics of the rarefaction shock which occurs in the plasma when the hot- to the cold-electron temperature ratio is larger than 9.9 are investigated with a semi-infinite plasma. Furthermore by using a finite plasma foil, a possible heating of the cold electrons population is evidenced, for a sufficiently large hot- to the cold-electron density ratio.

Analysis of Rarefaction Effects in the Hypersonic Rarefied Wind Tunnel

Abstract: A hypersonic rarefied wind tunnel (HRWT) has lately been developed at Japan Aerospace Exploration Agency. Flow characteristics of hypersonic rarefied flows have been investigated experimentally and numerically in this work. By conducting experiments of a pendulous sphere model and pitot tubes, we have probed flow characteristics in the test section. We have improved the understandings of the hypersonic rarefied flows by integrating a numerical approach with the HRWT measurement. Moreover, rarefaction effects on the impact pressure measurement have been analyzed by carrying out particle simulations, and good agreement was obtained between the measured and computed impact pressure. Finally, a method for the determination of surface accommodation parameters in HRWT has been proposed by utilizing a three degree-of-freedom measurement system with a plate model.

The Effect of the Pre-Detonation Stellar Internal Velocity Profile on the Nucleosynthetic Yields in Type Ia Supernova

Abstract: A common model of the explosion mechanism of Type Ia supernovae is based on a delayed detonation of a white dwarf. A variety of models differ primarily in the method by which the deflagration leads to a detonation. A common feature of the models, however, is that all of them involve the propagation of the detonation through a white dwarf that is either expanding or contracting, where the stellar internal velocity profile depends on both time and space. In this work, we investigate the effects of the pre-detonation stellar internal velocity profile and the post-detonation velocity of expansion on the production of alpha-particle nuclei, including Ni56, which are the primary nuclei produced by the detonation wave. We perform one-dimensional hydrodynamic simulations of the explosion phase of the white dwarf for center and off-center detonations with five different stellar velocity profiles at the onset of the detonation. We observe two distinct post-detonation expansion phases: rarefaction and bulk expansion. Almost all the burning to Ni56 occurs only in the rarefaction phase, and its expansion time scale is influenced by pre-existing flow structure in the star, in particular by the pre-detonation stellar velocity profile. We find that the mass fractions of the alpha-particle nuclei, including Ni56, are tight functions of the empirical physical parameter rho_up/v_down, where rho_up is the mass density immediately upstream of the detonation wave front and v_down is the velocity of the flow immediately downstream of the detonation wave front. We also find that v_down depends on the pre-detonation flow velocity. We conclude that the properties of the pre-existing flow, in particular the internal stellar velocity profile, influence the final isotopic composition of burned matter produced by the detonation.