Contribution of wall-attached momentum transfer structures to the skin friction in slip channel flows

Abstract

Reducing the skin-friction drag in wall turbulence is crucial for minimizing energy consumption in various industrial applications. Although numerous studies have proposed strategies for skin-friction reduction, their effectiveness generally degrades at high Reynolds numbers (Re) owing to the multiscale nature of wall turbulence. To address this challenge, it is necessary to understand coherent structures that span a wider range at high Re, particularly those that extend down to the wall. Hence, we explore wall-attached momentum transfer structures in drag-reduced flows and investigate the associated Re effects on the skin-friction reduction. We perform direct numerical simulations of drag-reduced flows at two bulk Re of 10,000 and 20,000 by employing the Navier slip boundary condition. For comparison, we conduct no-slip cases at the same bulk Re. We extract clusters of intense ejections and sweeps responsible for momentum transfer in instantaneous flow fields. We observe that wall-attached momentum transfer structures play a dominant role in the turbulent skin friction quantified through the FIK identity (Fukagata et al., 2002). These structures are classified into buffer-layer, self-similar, and non-self-similar ones according to their height. The self-similar structures not only exhibit geometrical self-similarity but also maintain their Reynolds shear stress distribution relative to the local Reynolds shear stress under slip conditions. Moreover, these self-similar structures show nearly identical skin-friction reduction across all heights. In contrast, the non-self-similar structures exhibit a significant difference under slip conditions, especially at a high Re. The reduced area fraction and volume of non-self-similar structures, along with decreased wall-normal transport under slip conditions, result in a greater skin-friction reduction compared to that observed at the low Re. Our findings advance the understanding of the scale-dependent behavior of wall-attached structures in drag-reduced flows, paving the way for the development of new drag-reduction methods through the strategic manipulation of these structures.