Evaporation boundary conditions for the R13 equations of rarefied gas dynamics

Abstract

The regularized 13 moment (R13) equations are a macroscopic model for the description of rarefied gas flows in the transition regime. The equations have been shown to give meaningful results for Knudsen numbers up to about 0.5. Here, their range of applicability is extended by deriving and testing boundary conditions for evaporating and condensing interfaces. The macroscopic interface conditions are derived from the microscopic interface conditions of kinetic theory. Tests include evaporation into a half-space and evaporation/condensation of a vapor between two liquid surfaces of different temperatures. Comparison indicates that overall the R13 equations agree better with microscopic solutions than classical hydrodynamics

Evaporation Boundary Conditions for the Linear R13 Equations Based on the Onsager Theory

“…derived from a Maxwell model for the interface, Struchtrup et al derived macroscopic evaporation boundary conditions (MBC) for the R13 equations [11]. In these, interface effects are described through the accommodation coefficient χ and the evaporation coefficient ϑ.…”

“…After non-dimensionalization and linearization around an equilibrium state, the MBC for evaporation [11]…”

“…corrected by adjusting the Onsager coefficients. In this context we simplify the linear R13 equations for one-dimensional and steady systems and solve them for two problems, previously dicussed in [11].…”

“…The configuration has been discussed in [11] and shall be outlined only briefly here. The interfaces are located at x = ± 1 2 with the normal vector n pointing from liquid into vapor and the superscripts 0 for x = − 1 2 and 1 for…”

“…The given solution for NSF is a simplification for χ = ϑ = 1, see Appendix D. The solution of the MBC for this system can be found in [11]. Results shall be compared in Sec.…”