Numerical Investigation of Rough Surfaces: Coupling Approach

Abstract

A numerical analysis of the flow field in rough microchannel is carried out decomposing the computational physical domain into kinetic and continuum sub-domains. Each domain size is determined by the value of a proper threshold parameter, based on the local Knudsen number and local gradients of macro-parameters. This switching parameter is computed from a preliminary Navier–Stokes solution throughout the whole physical domain. The solution is then advanced in time simultaneously in both kinetic and continuum domains: the coupling is achieved by matching half fluxes at the interface of the kinetic and Navier–Stokes domains, taking care of the conservation of momentum, energy and mass through the interface. The roughness geometry is modeled as a series of triangular obstructions with a relative roughness up to a maximum of 5% of the channel height. A wide range of Mach numbers is considered, from nearly incompressible to chocked flow conditions and a Reynolds number up to 100. Accuracy and discrepancies between full Navier Stokes, kinetic and coupled solutions are discussed, assessing the range of applicability of first order slip condition in rough geometries. The effect of the roughness is discussed via Poiseuille number as a function of local Knudsen and Mach numbers.