Numerical models of gas flow and heat transfer in microscale channels: capturing rarefaction behaviour using a constitutive scaling approach

In this paper we discuss the physics of rarefied gas flows at the micro-scale, including discontinuities of momentum and energy at solid boundaries, and the Knudsen layer (a region within one to two mean free paths of any solid surface where non-equilibrium flow features are dominant.) We describe how scaling the constitutive relations of the Navier-Stokes-Fourier equation set can capture key rarefaction behaviour observed in gas microsystems, and how a new implementation of this approach in fully compressible, non-isothermal CFD facilitates the analysis of "real-world" engineering problems. Details of our implementation are given, as are the results of a compressible Couette flow case study, successfully validated against available data sources. We also discuss the relative merits of two published constitutive scaling models, comparing their micro-flow predictions for half-space problems, and contrasting their individual means of application. Some practical implications of using constitutive-relation scaling are explained, and some advantages of the technique compared to alternative methods are outlined. To conclude, we examine some limitations of the method, and outline avenues of research that could potentially broaden the scope of what is a flexible and efficient approach to gas microsystem design using CFD.