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AN ANALYTICAL MODEL OF THE KNUDSEN LAYER WITH THERMAL CONDUCTION

DOI: 10.1615/ICHMT.2008.CHT.1890
12 pages

Leonid Pekker
Edwards AFRL

Jean-Luc Cambier
Propulsion Directorate - Aerophysics Branch, Air Force Research Laboratory, Edwards Air Force Base, 10 E. Saturn Blvd., California 93524, USA

Abstrakt

This work motivation is formulation of the boundary condition for numerical simulation of fluid dynamic with ablative boundaries. In this paper we develop an analytical model of the Knudsen layer by considering a kinetic formulation that takes into account the gas temperature gradient at a flat gas-wall interface. The main focus of this research is to study the effect of the thermal conductivity on the Knudsen layer formed near an ablating surface. This analysis is based on the premise that the thermal conductivity (the temperature gradient) in the bulk gas can be taken into account in the velocity distribution function at the outer boundary of the Knudsen layer. We use such a function obtained by Chapman-Enskog expansion method, based on the assumption that the molecular mean-free path is much smaller than the characteristic length scale of the temperature gradient. The model uses a bimodal velocity distribution function in the Knudsen layer which preserves the laws of conservation of mass, momentum and energy and converges to the Chapman-Enskog velocity distribution function at the outer boundary of the layer. The model allows obtaining the boundary conditions at the interface between the ablative surface and the bulk gas avoiding “micro” modeling of the evaporation process at the mean free path scale. Thus, our Knudsen layer model can be used as a “constructor” for boundary conditions between the bulk gas and ablative surface that is important for numerical simulation of evaporation processes and for fluid dynamics in general.

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