Showing papers on "Rarefaction published in 2014"

A Numerical Investigation of Blast Loading and Clearing on Small Targets

Abstract: When a blast wave strikes a finite target, diffraction of the blast wave around the free edge causes a rarefaction clearing wave to propagate along the loaded face and relieve the pressure acting at any point it passes over. For small targets, the time taken for this clearing wave to traverse the loaded face will be small in relation to the duration of loading. Previous studies have not shown what happens in the late-time stages of clearing relief, nor the mechanism by which the cleared reflected pressure decays to approach the incident pressure. Current design guidance assumes a series of interacting clearing waves propagate over the target face - this assumption is tested in this article by using numerical analysis to evaluate the blast pressure acting on small targets subjected to blast loads. It is shown that repeat propagations of the rarefaction waves do not occur and new model is proposed, based on an over-expanded region of air in front of the loaded face of the target.

Distinct temporal phases of microvascular rarefaction in skeletal muscle of obese Zucker rats

Abstract: Evolution of metabolic syndrome is associated with a progressive reduction in skeletal muscle microvessel density, known as rarefaction. Although contributing to impairments to mass transport and exchange, the temporal development of rarefaction and the contributing mechanisms that lead to microvessel loss are both unclear and critical areas for investigation. Although previous work suggests that rarefaction severity in obese Zucker rats (OZR) is predicted by the chronic loss of vascular nitric oxide (NO) bioavailability, we have determined that this hides a biphasic development of rarefaction, with both early and late components. Although the total extent of rarefaction was well predicted by the loss in NO bioavailability, the early pulse of rarefaction developed before a loss of NO bioavailability and was associated with altered venular function (increased leukocyte adhesion/rolling), and early elevation in oxidant stress, TNF-α levels, and the vascular production of thromboxane A2 (TxA2). Chronic inhibition of TNF-α blunted the severity of rarefaction and also reduced vascular oxidant stress and TxA2 production. Chronic blockade of the actions of TxA2 also blunted rarefaction, but did not impact oxidant stress or inflammation, suggesting that TxA2 is a downstream outcome of elevated reactive oxygen species and inflammation. If chronic blockade of TxA2 is terminated, microvascular rarefaction in OZR skeletal muscle resumes, but at a reduced rate despite low NO bioavailability. These results suggest that therapeutic interventions against inflammation and TxA2 under conditions where metabolic syndrome severity is moderate or mild may prevent the development of a condition of accelerated microvessel loss with metabolic syndrome.

Shock structure and temperature overshoot in macroscopic multi-temperature model of mixtures

Abstract: The paper discusses the shock structure in macroscopic multi-temperature model of gaseous mixtures, recently established within the framework of extended thermodynamics. The study is restricted to weak and moderate shocks in a binary mixture of ideal gases with negligible viscosity and heat conductivity. The model predicts the existence of temperature overshoot of heavier constituent, like more sophisticated approaches, but also puts in evidence its non-monotonic behavior not documented in other studies. This phenomenon is explained as a consequence of weak energy exchange between the constituents, either due to large mass difference, or large rarefaction of the mixture. In the range of small Mach number it is also shown that shock thickness (or equivalently, the inverse of Knudsen number) decreases with the increase of Mach number, as well as when the mixture tends to behave like a single-component gas (small mass difference and/or presence of one constituent in traces).

Single-phase gas flow in microchannels

Abstract: The role of rarefaction and its consequences on the behavior of gas flows in microchannels are discussed in this chapter. Heat transfer in microchannels and thermally driven gas microflows are particularly interesting for vacuum generation, using microsystems without moving parts. The main micro-effect that results from shrinking down the devices' size is rarefaction. In microchannels, the main effects are those of rarefaction, essentially quantified by the Knudsen number. Rarefaction affects steady microflows and modifies the behavior of unsteady microflows. The case of pulsed flows is of particular interest because such flows are encountered in many applications. Theoretical knowledge for gas flows is currently more advanced than that for liquid flows in microchannels. The regime of gas flow in a macrochannel refers to viscosity and compressibility effects quantified by the Reynolds number and the Mach number and depends on the rarefaction regime. Generating vacuum by means of microsystems concerns various applications such as the taking of biological or chemical samples, or the control of the vacuum level in the neighborhood of some specific microsystems during working. However, there is still a need for accurate experimental data, both for steady or unsteady gas microflows, with or without heat transfer.

Coherent Cavitation in the Liquid of Light

Abstract: We study the cubic- (focusing-)quintic (defocusing) nonlinear Schr\"odinger equation in two transverse dimensions. We discuss a family of stationary traveling waves, including rarefaction pulses and vortex-antivortex pairs, in a background of critical amplitude. We show that these rarefaction pulses can be generated inside a flattop soliton when a smaller bright soliton collides with it. The fate of the evolution strongly depends on the relative phase of the solitons. Among several possibilities, we find that the dark pulse can reemerge as a bright soliton.

Thermal transpiration flow through a single rectangular channel

Abstract: A thermal transpiration flow through a single rectangular micro-channel was studied experimentally for various gas species, including all rare gases, in order to investigate the influence of gas species on the flow properties. The final equilibrium flow characteristics and relaxation time of the pressure variation were evaluated as functions of the rarefaction parameter. The thermal molecular pressure difference was well fitted by the log-normal distribution function, and its magnitude was found to be strongly dependent on the gas species: a larger pressure difference was obtained for molecules of smaller diameter. However, for the thermal molecular pressure ratio and the thermal molecular pressure exponent, which are dimensionless quantities, the dependence on the gas species was negligible. The relaxation time of the pressure variation was well normalized by the characteristic time of the system. The influence of the geometry was evaluated by comparing the present results, obtained for the case of a rectangular channel, with already published data obtained for the case of a circular cross-section tube. The comparison showed that these two geometrical configurations influence the fluid flow in equal manner, if appropriate geometrical parameters are used for their representation.

A stochastic jump process applied to traffic flow modelling

Abstract: The paper presents the main aspects of a stochastic conservative model of the evolution of the number of vehicles per road section. The model, defined in continuous time on a discrete space, follows a misanthrope Markovian process. It is a mesoscopic traffic model in the following sense: the vehicles are individually considered, but their dynamics are aggregated per section. The model parameters are supply and demand functions in equilibrium (i.e. a fundamental diagram). In order to model flows on a traffic network, different schemes of junction dynamics are proposed. The model properties in transient and stationary states are investigated analytically in simple cases and by simulation. The results show that the process presents classical properties of deterministic macroscopic model such as the propagation of shock or rarefaction wave for Riemann initial condition. On the other hand, one observes phenomena usually related to high order models, such as a wide scattering of the flow performances or the pro...

NDCX-II target experiments and simulations

Abstract: The ion accelerator NDCX-II is undergoing commissioning at Lawrence Berkeley National Laboratory (LBNL). Its principal mission is to explore ion-driven High Energy Density Physics (HEDP) relevant to Inertial Fusion Energy (IFE) especially in the Warm Dense Matter (WDM) regime. We have carried out hydrodynamic simulations of beam-heated targets for parameters expected for the initial configuration of NDCX-II. For metal foils of order one micron thick (thin targets), the beam is predicted to heat the target in a timescale comparable to the hydrodynamic expansion time for experiments that infer material properties from measurements of the resulting rarefaction wave. We have also carried out hydrodynamic simulations of beam heating of metallic foam targets several tens of microns thick (thick targets) in which the ion range is shorter than the areal density of the material. In this case shock waves will form and we derive simple scaling laws for the efficiency of conversion of ion energy into kinetic energy of fluid flow. Geometries with a tamping layer may also be used to study the merging of a tamper shock with the end-of-range shock. This process can occur in tamped, direct drive IFE targets.

Solution of the Riemann Problem in magnetogasdynamics

Abstract: In the present paper, the Riemann Problem for a quasilinear hyperbolic system of equations, governing the one dimensional unsteady flow of an inviscid and perfectly conducting gas, subjected to transverse magnetic field, is solved analytically without any restriction on the initial states. This class of equations includes, as a special case, the Euler equation of gasdynamics. The elementary wave solutions of the Riemann problem, that is, shock waves, rarefaction waves and contact discontinuities are derived and their properties are discussed. It is noticed that although the magnetogasdynamics system is more complex than the corresponding gasdynamics system, all the parallel results remain identical. It is also assessed as to how the presence of magnetic field influences the variation of velocity and density across the shock wave, rarefaction wave and contact discontinuities.

High energy gain in three-dimensional simulations of light sail acceleration

Abstract: The dynamics of radiation pressure acceleration in the relativistic light sail regime are analysed by means of large scale, three-dimensional (3D) particle-in-cell simulations Differently to other mechanisms, the 3D dynamics leads to faster and higher energy gain than in 1D or 2D geometry This effect is caused by the local decrease of the target density due to transverse expansion leading to a “lighter sail” However, the rarefaction of the target leads to an earlier transition to transparency limiting the energy gain A transverse instability leads to a structured and inhomogeneous ion distribution

A large time step Godunov scheme for free-surface shallow water equations

Abstract: An algorithm for simulating free surface flows is presented using large time step based on the wave-propagation method proposed by LeVeque, and an exact Riemann solver is used. A multiple wave approximation approach was suggested for eliminating the discontinuities found in the rarefaction fans of dam-breaking flows. In addition, we use the random choice method to reduce non-physical oscillations. Applications demonstrate that the algorithm proposed in this paper can considerably increase the CFL number up to 25 when modeling dam-break flows, while retaining satisfactory accuracy and efficiency. This suggests that our algorithm has the potential to be applied to modeling free surface flows.

Regularization of a sharp shock by the defocusing nonlinear Schr\"odinger equation

Abstract: The defocusing nonlinear Schrodinger (NLS) equation is studied for a family of step-like initial data with piecewise constant amplitude and phase velocity with a single jump discontinuity at the origin. Riemann-Hilbert and steepest descent techniques are used to study the long time/zero-dispersion limit of the solution to NLS associated to this family of initial data. We show that the initial discontinuity is regularized in the long time/zero-dispersion limit by the emergence of five distinct regions in the $(x, t)$ half-plane. These are left, right, and central plane waves separated by a rarefaction wave on the left and a slowly modulated elliptic wave on the right. Rigorous derivations of the leading order asymptotic behavior and error bounds are presented

Rarefaction Pulses for the Nonlinear Schrödinger 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.

On the damping effect of gas rarefaction on propagation of acoustic waves in a microchannel

Abstract: We consider the response of a gas in a microchannel to instantaneous (small-amplitude) non-periodic motion of its boundaries in the normal direction. The problem is formulated for an ideal monatomic gas using the Bhatnagar, Gross, and Krook (BGK) kinetic model, and solved for the entire range of Knudsen (Kn) numbers. Analysis combines analytical (collisionless and continuum-limit) solutions with numerical (low-variance Monte Carlo and linearized BGK) calculations. Gas flow, driven by motion of the boundaries, consists of a sequence of propagating and reflected pressure waves, decaying in time towards a final equilibrium state. Gas rarefaction is shown to have a “damping effect” on equilibration process, with the time required for equilibrium shortening with increasing Kn. Oscillations in hydrodynamic quantities, characterizing gas response in the continuum limit, vanish in collisionless conditions. The effect of having two moving boundaries, compared to only one considered in previous studies of time-periodic systems, is investigated. Comparison between analytical and numerical solutions indicates that the collisionless description predicts the system behavior exceptionally well for all systems of the size of the mean free path and somewhat larger, in cases where boundary actuation acts along times shorter than the ballistic time scale. The continuum-limit solution, however, should be considered with care at early times near the location of acoustic wavefronts, where relatively sharp flow-field variations result in effective increase in the value of local Knudsen number.

A modified gas-kinetic scheme for turbulent flow

Abstract: The implementation of a turbulent gas-kinetic scheme into a finite-volume RANS solver is put forward, with two turbulent quantities, kinetic energy and dissipation, supplied by an allied turbulence model. This paper shows a number of numerical simulations of flow cases including an interaction between a shock wave and a turbulent boundary layer, where the shock-turbulent boundary layer is captured in a much more convincing way than it normally is by conventional schemes based on the Navier-Stokes equations. In the gas-kinetic scheme, the modeling of turbulence is part of the numerical scheme, which adjusts as a function of the ratio of resolved to unresolved scales of motion. In so doing, the turbulent stress tensor is not constrained into a linear relation with the strain rate. Instead it is modeled on the basis of the analogy between particles and eddies, without any assumptions on the type of turbulence or flow class. Conventional schemes lack multiscale mechanisms: the ratio of unresolved to resolved scales – very much like a degree of rarefaction – is not taken into account even if it may grow to non-negligible values in flow regions such as shocklayers. It is precisely in these flow regions, that the turbulent gas-kinetic scheme seems to provide more accurate predictions than conventional schemes.

On the Asymmetric Zero-Range in the Rarefaction Fan

Abstract: We consider one-dimensional asymmetric zero-range processes starting from a step decreasing profile leading, in the hydrodynamic limit, to the rarefaction fan of the associated hydrodynamic equation. Under that initial condition, and for totally asymmetric jumps, we show that the weighted sum of joint probabilities for second class particles sharing the same site is convergent and we compute its limit. For partially asymmetric jumps, we derive the Law of Large Numbers for a second class particle, under the initial configuration in which all positive sites are empty, all negative sites are occupied with infinitely many first class particles and there is a single second class particle at the origin. Moreover, we prove that among the infinite characteristics emanating from the position of the second class particle it picks randomly one of them. The randomness is given in terms of the weak solution of the hydrodynamic equation, through some sort of renormalization function. By coupling the constant-rate totally asymmetric zero-range with the totally asymmetric simple exclusion, we derive limiting laws for more general initial conditions.

Two-phase flow numerical simulation with real-gas effects and occurrence of rarefaction shock waves

Abstract: A discrete equation method (DEM) for the simulation of compressible multiphase flows including real-gas effects is illustrated. A reduced five equation model is obtained starting from the semi-discrete numerical approximation of the two-phase model. A simple procedure is then proposed for using a more complex equation of state, thus improving the quality of the numerical prediction. Classical test-cases well-known in literature are performed featuring a strong importance of thermodynamic complexity for a good prediction of temperature evolution. Finally, a computational study on the occurrence of rarefaction shock waves (RSW) in a two-phase shock tube is presented, with dense vapors of complex organic fluids. Since previous studies have shown that a RSW is relatively weak in a single-phase (vapor) configuration, its occurrence and intensity are investigated considering the influence of the initial volume fraction, initial conditions and the thermodynamic model.