On the effect of surface roughness in transonic high Reynolds number flow through slender channels

In the present study transonic weakly three‐dimensional flows at high Reynolds numbers in slender channels, as they are found e.g. in micro nozzles and turbo‐machines of micro‐electromechanical‐ systems (MEMS), are considered. The channel height is taken to be so small that the viscous layers forming at the channel walls start to interact strongly rather than weakly with the predominantly inviscid core flow and, therefore, the classical boundary layer approach fails. The resulting viscous‐inviscid interaction problem is formulated using matched asymptotic expansions and found to be governed by a triple deck structure. As a consequence, the properties of the inviscid core region and the viscous wall layers have to be calculated simultaneously in the interaction region. Weakly three‐dimensional effects caused by surface roughness, upstream propagating flow perturbations and boundary layer separation are discussed. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)