Numerical investigation of gaseous heat and mass transfer: the effect of rarefaction

Abstract

Recent advances in micro-scale fabrication have uncovered the limitations of classical uid dynamics analysis techniques. The current status of numerical techniques for micro-ows is found to be highly varied with no accepted best-practice. This situation encourages investigation of new and improved methods in the eld. In this work a new numerical method based upon the solution of the model Boltzmann equation using arbitrary order polynomials is presented. The S-model is solved by a discrete ordinate method with velocity space discretized with a truncated Hermite polynomial expansion. Physical space is discretized according to the Conservative Flux Approximation scheme with extension to allow non-uniform grid spacing. This approach, which utilizes Legendre polynomials, allows the spatial representation and ux calculation to be of arbitrary order. High order boundary conditions are implemented. Various results are shown to demonstrate the utility and limitations of the method with comparison to solutions of the Euler and Navier-Stokes equations and from the Direct Simulation Monte Carlo and Uni ed Gas Kinetic schemes. The e ect of both the velocity space discretization and Knudsen number on the convergence properties of the scheme are also investigated.Due to limitations in the geometric adaptability of the new method an implementation of the Uni ed Gas Kinetic Scheme with a variety of enhancements is also presented. These enhancements include internal degree of freedom handling and advanced gas-surface interaction mechanisms including a model of the adsorption and desorption of gas molecules by a surface.The numerical methods developed are used to investigate physical ow phenomena including rare ed e ects such as thermal creep. Pressure gradient inducing thermal creep driven ows in microchannels, commonly referred to as Knudsen pumps, are investigated across a range of rarefaction with particular focus on the e ects of realistic gas coe cients and geometric con guration on performance.A range of geometries are investigated consisting of a previously proposed curved-straight channel and three newly developed channels including a novel two dimensional matrix pump arrangement and classical linear designs. Use of the S-model kinetic equations enables investigation with realistic values of the Prandtl number and viscosity index for argon and nitrogen as well as for Maxwell molecules. The pumping performance and ow structure of each geometry is investigated for a range of channel aspect ratios and Knudsen numbers where the Knudsen numbers are nely spaced between 0.1 and 2.0 to allow approximate performance extrema to be identi ed. The in uence of Prandtl number is found to be signi cant with increased maximum mass ow rates for argon and nitrogen of 5.5-6% when compared to a gas with Maxwellian molecular model. The impact of speci c heat ratio is found to be comparatively minor with a di erence of 0.5% between the argon and nitrogen. The two new channel designs are found to lie between the classical and existing ...