A Hybrid Method for the Computation of a Rarefied Gas Jet Efflux through a Very Long Channel into Vacuum

Abstract

On the basis of the kinetic model, the steady efflux of monatomic gas from a high pressure camera (the Knudsen number $${\text{Kn}} \ll 1$$ ) 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.