Oscillatory viscous flow in symmetric wavy-walled channels

Abstract

Oscillating flow in furrowed channels with symmetric sinusoidal and arc-shaped walls of a large amplitude was studied experimentally. We observed the deformation of dye streaks within a transparent channel during piston induced, volume-cycled oscillations. The experiments were carried out under the following conditions: 5< Re<200, 0.06< St<0.3. The wall geometries have little effect on fundamental characteristics of oscillatory flow. The observed steady streaming was compared to finite element solutions of Navier—Stokes equations. Both the experimental and computational results show diverse structures dependent on the value of the Womersley number, α 2 = StRe. For small values of α 2, e.g. α 2 < 4, the steady streaming consists of a symmetrical pair of recirculations within each furrow on the walls, i.e. two-vortex systems. When α 2 exceeds about 4, a new secondary counter-rotating pair of recirculations appears near the centerline of the maximum cross section, in addition to primary recirculations observed for values of α 2 < 4, i.e. four-vortex system.