Influence of the amplitude of a solid wavy wall on a turbulent flow. Part 2. Separated flows

Abstract

A study has been carried out of turbulent flow over a sinusoidally shaped solid boundary of large enough amplitude that the flow separates from the downstream side of the wave. Measurements are presented of the conditions under which separated flows exist, the extent of the separated region and the variation of the pressure and shear stress along and the velocity profile above the wavy surface. The results are consistent with the model D turbulent solution of the linear momentum equations discussed in Zilker, Cook & Hanratty (1977, hereafter referred to as I) in that reversed flows are possible for wave height to wavelength ratios 2a/λ > 0·033 and in that the range of flow rates for which reversed flows exist increases with increasing 2a/λ. For non-separated flows and for flows with thin separated regions the amplitude of the pressure variation changes linearly with wave height; however, for very large amplitude waves with thick separated regions it is much less sensitive to variations in wave height since the external flow that controls the pressure variation sees a wave profile consisting of a composite of the solid wave and the separated region. The variation of the velocity field along the wave surface in the non-separated region is similar to that predicted by linear theory for small amplitude waves. The flow separates in a region of increasing pressure and reattaches in the region where the pressure on the wave surface is a maximum. A large increase in the wall shear stress is noted immediately downstream of reattachment.