A Hybrid Method for the Computation of a Rarefied Gas Jet Efflux through a Very Long Channel into Vacuum
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ATICAL PHYSICS
A Hybrid Method for the Computation of a Rarefied Gas Jet Efflux through a Very Long Channel into Vacuum V. A. Titareva,* and E. M. Shakhova,** a
Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, Moscow, 119333 Russia *e-mail: [email protected] **e-mail: [email protected] Received April 16, 2020; revised May 20, 2020; accepted July 7, 2020
Abstract—On the basis of the kinetic model, the steady efflux of monatomic gas from a high pressure camera (the Knudsen number Kn 1) through a long channel between two parallel plates into a vacuum camera under a constant temperature on the bounding surfaces is studied. Using asymptotic estimates for relatively long channels, the flow domain is divided into three subdomains: (1) a neighborhood of the channel entry, (2) the main part of the flow in the channel that occupies almost all channel length, and (3) a neighborhood of the channel exit. The flow in subdomain (1) is not considered due to its low speed. In the main subdomain (2), the flow is slow and is driven by a low pressure gradient (the diffusion area). In subdomain (3), the flow gets faster, and the gas expands in the channel and in the vacuum camera. In subdomain (2), we have the continuum flow regime, and the well-known results of the linear one-dimensional theory of viscous gas flows in long channels (Poiseuille flow) are used. In the subdomain of fast flow, the full nonlinear kinetic equation (S-model) is used. The condition of asymptotic matching of solutions in two subdomains is replaced by the boundary condition of solution coupling in a certain section the position of which is chosen from the smoothness condition of the full solution of the problem. The kinetic equation is solved by the method of time marching to steady state using the conservative second-order scheme with respect to all variables implemented in Nesvetay software package. The proposed solution method can be considered as a hybrid one because the Navier–Stokes and kinetic equations are solved simultaneously. Keywords: rarefied gas, S-model, vacuum, asymptotic method, implicit scheme, Nesvetay, supercomputer computations DOI: 10.1134/S0965542520110135
INTRODUCTION The problem of gas efflux into vacuum through channels occurs in many applications. An important example is the gas diffusion through microcracks with the following gas efflux into vacuum. A simple model of a microcrack is a microchannel between two parallel plates. For the theoretical investigation of flows in microchannels and efflux into vacuum, the kinetic theory of gases that covers all flow regimes from the continuum flow regime to rarefied gas must be used. The flows of rarefied gas in channels and microchannels is studied in many works, including the seminal paper [1] and monograph [2]. The vast majority of these works are based on a linearized one-dimensional (with respect to the physical space) kinetic equation for long channels and pipes at small gradients of pressure and temperature. The possibility and conditions of local lin
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