3:30 pm Thursday, October 4, 2007
ICES & Applied Mathematics Seminar: A Diffusion Model for Rarefied Gas Flows in a Curved Channel by Kazuo Aoki (Kyoto University, Department of Mechanical Engineering and Science ) in ACES 6.304
Abstract: A rarefied gas flow in a two-dimensional curved channel, driven by a pressure gradient imposed in the gas and/or by a temperature gradient imposed along the channel walls, is investigated on the basis of kinetic theory. Under the assumption that the width of the channel is much smaller than the length scales of variation of the pressure, temperature, and curvature of the channel walls along the channel, a one-dimensional convection-diffusion model is derived by a formal asymptotic analysis based on the BGK model of the Boltzmann equation with the diffuse-reflection boundary condition. The effect of channel curvature and that of gas rarefaction manifest themselves through the coefficients in the convection-diffusion model. A numerical database of these coefficients is constructed by solving basic flow problems along a circular ring. The connection conditions at the junction where the curvature is not continuous are also derived. As an application of the model, a pumping system (i.e., a variant of the Knudsen pump) using a snake-shaped channel with a periodic structure and a periodic temperature distribution along the channel walls is considered, and the compression ratio as well as the pressure distribution along the channel is obtained for the system with many (100) units. The accuracy of the model is confirmed by a full two-dimensional simulation based on the BGK model when the number of the unit is small. Submitted by
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