Rarefaction

About: Rarefaction is a research topic. Over the lifetime, 1852 publications have been published within this topic receiving 26943 citations.

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.

Self-diffusivity of dense confined fluids

Abstract: Molecular transport through tight porous media is crucial to shale gas exploration, but deeper insights of the elemental physics are still required, particularly under high pressures and nanoscale confinements, where Navier–Stokes and Boltzmann solutions are no longer valid. In this work, we carry out a fundamental and systematic study of self-diffusion using event-driven molecular dynamics simulations, varying fluid rarefaction, confinement, and surface friction. We differentiate between fluid–fluid and fluid-wall collisions to identify the interplay of the underpinning diffusive mechanisms, namely, molecular and Knudsen diffusion. We find that the Bosanquet formula, which has been used for describing rarefied gases, is also able to provide a good semi-analytical description of self-diffusivities in confined dense fluids, as long as the pore height is not smaller than five molecular diameters. Importantly, this allows us to predict the self-diffusion coefficient, regardless of the fluid rarefaction, confinement state, and surface roughness, in a wide range of Knudsen numbers that were not possible before. Often as a source of debate, we prove here that despite strong fluid inhomogeneities arising in these conditions, the Einstein self-diffusivity can still be used within Fick's law, provided boundary effects are considered when using Fick's setup. Finally, we notice that a previously identified linear scaling of self-diffusivities with confinement is only valid in the limit of low densities and frictionless walls, which is not representative of shale reservoirs. This work will serve as a foundation for investigating the anomalous gas transport behavior observed in the recent work of dense, confined fluids.

Formation of fast magnetosonic shock waves during a two-current-loop collision in solar flares

Abstract: We present a numerical simulation of the fast magnetosonic shock wave formation during a two-current-loop collision by using a magnetohydrodynamical model. It is shown that the rarefaction waves are generated in the initial stage when the two current loops start to collide. After the rarefaction waves propagate away from the excited region, the fast magnetosonic waves with density enhancement can be produced for the simulation when the current strength of the loop is weak. As the current becomes strong enough, the magnetosonic shock waves can be generated in the direction perpendicular to that of the two-loop collision.

Binary gas mixture outflow into vacuum through an orifice

Abstract: The results of a numerical study of a binary gas mixture outflow from a source with specified stagnation parameters into vacuum through a round orifice are presented. Silver and helium atoms (with a mass ratio of 26.95) are selected as a mixture species. The near free-molecular, transitional, and near-continuum regimes of the flow are considered with the direct simulation Monte Carlo method used for the computations. The results of simulations show that the rarefaction degree and the mole composition of the mixture have a significant impact on the spatial variation of flow parameters and the flow rates through the orifice. At all degrees of rarefaction, the variation in the dimensionless flow rate (related to the free-molecular flow rate) of the mixture is a non-monotonic function of the mole fraction of the species with a maximum/minimum (for the mass/particle flux). The presence of a light carrier gas (helium) leads to the acceleration, axial focusing, and increase in the flow rate of the heavy species (silver). The velocity slip of light and heavy species is observed at all degrees of rarefaction under consideration. The effect of the increasing density of heavy species near the orifice plane is revealed. The spatial variation of mole fractions of species on the degree of rarefaction is studied. The results of the study are compared to available analytical and experimental data, and the simulation results of pure gas outflow obtained by other authors.

Zero‐viscosity‐capillarity limit to rarefaction waves for the 1D compressible Navier–Stokes–Korteweg equations

Abstract: In this paper, we study the zero viscosity and capillarity limit problem for the one-dimensional compressible isentropic Navier–Stokes–Korteweg equations when the corresponding Euler equations have rarefaction wave solutions. In the case that either the effects of initial layer are ignored or the rarefaction waves are smooth, we prove that the solutions of the Navier–Stokes–Korteweg equation with centered rarefaction wave data exist for all time and converge to the centered rarefaction waves as the viscosity and capillarity number vanish, and we also obtain a rate of convergence, which is valid uniformly for all time. These results are showed by a scaling argument and elementary energy analysis. Copyright © 2016 John Wiley & Sons, Ltd.