Streaming flows generated by high-frequency small-amplitude oscillations of arbitrarily shaped cylinders

Abstract

Small-amplitude harmonic oscillations of arbitrarily shaped cylinders are considered both experimentally and theoretically. For the theoretical model, the flow regime is separated into inner and outer regions. In the inner region, the flow is governed by the classical Stokes boundary layer equation. In the outer region, the full Navier–Stokes equation for the steady streaming flow is solved numerically by using a finite difference method coupled with conformal mapping techniques. Numerical results of streaming, a nonlinear response to harmonic motion, show complicated flow schemes. Experimental results confirm the existence of such flows. Streaming flow around a sharp corner of a square cylinder is investigated through numerical calculation and experimental flow visualization. The absence of any vortex shedding on the time scale of the streaming flow is noted. These results suggest that in the limit of a small amplitude of oscillation, or equivalently large Strouhal numbers, sharp-edged bodies experience attached flow in the mean sense.