Reduced Order Modeling of Low Mach Number Unsteady Microchannel Flows

Abstract

We present reducedorder models of unsteady lowMachnumber ideal gas flows in twodimensional rectangular microchannels subject to firstorder slipboundary conditions. The pressure and density are related by a polytropic process, allowing for isothermal or isentropic flow assumptions. The Navier–Stokes equations are simplified using lowMachnumber expansions of the pressure and velocity fields. Up to first order, this approximation results in a system that is subject to noslip condition at the solid boundary. The secondorder system satisfies the slipboundary conditions. The resulting equations and the subsequent pressureflowrate relationships enable modeling the flow using analog circuit components. The accuracy of the proposed models is investigated for steady and unsteady flows in a twodimensional channel for different values of Mach and Knudsen numbers.