Rarefaction

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

Reshocks, rarefactions, and the generalized Layzer model for hydrodynamic instabilities

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 ...

Rarefied gas flows through a curved channel: Application of a diffusion-type equation

Abstract: Rarefied gas flows through a curved two-dimensional channel, caused by a pressure or a temperature gradient, are investigated numerically by using a macroscopic equation of convection-diffusion type. The equation, which was derived systematically from the Bhatnagar–Gross–Krook model of the Boltzmann equation and diffuse-reflection boundary condition in a previous paper [K. Aoki et al., “A diffusion model for rarefied flows in curved channels,” Multiscale Model. Simul. 6, 1281 (2008)], is valid irrespective of the degree of gas rarefaction when the channel width is much shorter than the scale of variations of physical quantities and curvature along the channel. Attention is also paid to a variant of the Knudsen compressor that can produce a pressure raise by the effect of the change of channel curvature and periodic temperature distributions without any help of moving parts. In the process of analysis, the macroscopic equation is (partially) extended to the case of the ellipsoidal-statistical model of the ...

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.

A two-dimensional blast wave in relativistic magnetohydrodynamics

Abstract: The blast wave produced by a star-like object in a magnetic field is studied numerically in the approximation of ideal, fully relativistic magnetohydrodynamics (MHD). Waves of this type are observed to evolve along three episodes. At early time an outgoing shock front and an ingoing rarefaction wave is established. The ingoing rarefaction wave steepens, and gives rise to dust formation in the core. The steep rarefaction wave front becomes an ingoing shock. An annular region of high magnetic pressure about the equatorial plane deforms this shock front radially, whereby it becomes prolate along the axis of symmetry. The core is subsequently refilled as this shock front converges. Subsequent collapse in the center gives rise to high pressures, familiar from the well-known converging shock problem in nonrelativistic hydrodynamics, and high densities unique to the relativistic description. The results are compared with spherical blast waves in relativistic hydrodynamics, where a similar three episodes can be found and where collapse of the interior shock at the center constitutes a fluid singularity. It remains an open question whether such fluid singularity persists in the full MHD problem. The computations employ the covariant equations of constraint-free MHD in divergence form introduced in earlier work. The magnetic field is kept divergence free to within machine round-off error.