Slow flows of a vapor-gas mixture with large density and temperature variations in the near-continuum regime

Abstract

A binary mixture of a vapor and a noncondensable gas in contact with the boundary made of the condensed phase ͑liquid or solid͒ of the vapor is considered in the following situation: the amount of the noncondensable gas contained in the system is of the same order of magnitude as that of the vapor; the temperature variation along the boundary may be large; the boundary is at rest, and there is no flow at infinity when an infinite domain is considered; and the Knudsen number is small ͑i.e., near-continuum regime͒. Slow steady flows ͑with Mach number of the order of Knudsen number, or equivalently, with Reynolds number of the order of unity͒ of the mixture, mainly caused by evaporation and condensation of the vapor on the boundary, are investigated on the basis of kinetic theory. The basic system used in this work is the fluid-dynamic-type system that was derived systematically from the Boltzmann system in a previous paper ͓S. Takata and K. Aoki, Transp. Theor. Stat. Phys. 30, 205 ͑2001͒; erratum, ibid. 31, 289 ͑2002͔͒ in connection with the ghost effect, and it is solved numerically by a finite-volume method. Some additional computation using the direct simulation Monte Carlo method, based on the original Boltzmann system, is also performed for comparison. The behavior of the mixture in the continuum limit in which the Knudsen number vanishes is discussed with special interest in the ghost effect.

Computer simulation of slightly rarefied gas flows driven by significant temperature variations and their continuum limit

“…The present results were obtained using the special-purpose solver of the SNIT flow equations (12)- (14). It has been developed on the open-source CFD platform OpenFOAM R [15], based on the finite-volume approach for evaluating partial derivatives.…”

“…The continuity equation (12), along with the momentum equation (13), is solved using the implicit conservative SIMPLE algorithm [23]. A detailed description of the similar scheme for gas mixtures can be found in [14]. According to the naming convention adopted in OpenFOAM R , the introduced solver can be called as snitSimpleFoam.…”

“…The Navier-Stokes equations with any slip boundary conditions have a trivial solution u i = 0, which is, however, not valid for (12)- (14). As stated above, even under such boundary conditions, the nonlinear thermal-stress flow can emerge due to nonparallelism of the isothermal surfaces (27).…”

“…As noted above, p ij2 is determined up to the constant factor from the system (12)- (14). This constant factor makes no contribution to the total force acting on a body, but to evaluate a force per unit area, we have to impose an additional condition on p ij2 , for example, the following one:…”

“…The pioneering solutions are based on the finite-difference methods [8,11,12]. The finite-volume method is applied in some recent works [13,14].…”