Evaluating constitutive scaling models for application to compressible microflows

Abstract

We demonstrate here, for the first time, the constitutive scaling approach applied to simulate a fully compressible, non-isothermal micro gas flow within a mainstream computational physics framework. First, the physics underlying these new constitutive-relation scaling models for rarefied gas flows at the microscale, in particular, the Knudsen layer, is discussed. Results for Couette-type flows in microchannels, including heat transfer effects due to rarefaction, are then reported and we show comparisons with both traditional Navier-Stokes-Fourier solutions and independent numerical studies. We discuss the limitations of the constitutive scaling process, such as the breakdown of the model as the Knudsen number increases and the influence of the wall interaction model on the numerical results. Advantages of the constitutive scaling technique are described, with particular reference to the practicality of using it for microscale engineering design.

The Importance of Mean Free Path in Determining Gas Micro Flow Behaviour

“…Lockerby et al [4] and O'Hare et al [5] developed walldistance scaling models for the constitutive relationship for shear stress in planar flows. The applicability of these models is limited to relatively low-Kn flows.…”

Perspectives on the Simulation of Micro Gas and Nano Liquid Flows

“…However, there are still issues surrounding the correct implementation of non-equilibrium boundary conditions. To illustrate, we confine our attention here to models for calculating the slip-velocity to be imposed on hydrodynamic simulations of gas flows at solid bounding surfaces, although calculation of the temperature-jump at surfaces also requires careful consideration [11]. Copyright c 2011 by ASME While there has been recent interest in using a Langmuir adsorption model of the gas/surface interaction to retrieve rarefied flow boundary conditions [12,13], for flows of Kn > 0.001 Maxwell's phenomenological expression [14] remains the most often-used expression for the tangential slip-velocity, u slip :…”

Natural convection slip flow in a vertical microchannel heated at uniform heat flux

“…Particularly for air, it assumes typical values quasi-unity [33,34]. This means that the case of diffuse reflection is considered (s v ¼ 1.0 and s T ¼ 1.0 [9,35]). …”