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.
Highlights
Gas rarefaction leads to the occurrence of phenomena such as velocity slip and temperature jump at boundaries, Knudsen layers in front of boundaries, transpiration flow, thermal stresses, or heat transfer without temperature gradients, all of which are reproduced by solutions of the regularized 13 moment (R13) equations
Proper modeling of boundary conditions (BCs) is essential to obtain a meaningful description of rarefied flows, and below we develop and test conditions for liquid-vapor boundaries with condensation and evaporation
The regularized 13 moment equations arise from an alternative closure,1 which accounts for parts of, but not the complete, transport equations for mijk, ∆, Rij
Summary
The regularized 13 moment (R13) equations are a macroscopic model to describe rarefied gas flows for not too large Knudsen numbers in good approximation to the Boltzmann equation. Gas rarefaction leads to the occurrence of phenomena such as velocity slip and temperature jump at boundaries, Knudsen layers in front of boundaries, transpiration flow, thermal stresses, or heat transfer without temperature gradients, all of which are reproduced by solutions of the R13 equations. The regularized 13 moment (R13) equations are a macroscopic model to describe rarefied gas flows for not too large Knudsen numbers in good approximation to the Boltzmann equation.. After deriving the full set of boundary conditions, as a first application, we solve two simple one-dimensional evaporation problems: a half-space problem for pressure driven evaporation and condensation and evaporation of a vapor between two liquid surfaces at different interface temperatures.. After deriving the full set of boundary conditions, as a first application, we solve two simple one-dimensional evaporation problems: a half-space problem for pressure driven evaporation and condensation and evaporation of a vapor between two liquid surfaces at different interface temperatures.31–35 For both cases, the R13 and NSF equations can be analytically solved, and their solutions are compared with DSMC simulations. Some preliminary results were published before; the present contribution gives all required details for the derivation of the boundary conditions, corrects several errors, and expands on the results presented and discussed
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