Oscillatory flow in a corrugated curved channel

Abstract

Unsteady flow through a curved channel with roughness in the form of sinusoidal corrugations is examined. The flow is generated by a time periodic pressure gradient. The fluid velocity is both time and space periodic, as a result of the oscillatory pressure gradient and the geometry of the curved channel. The effects of the inherent parameters; physical and geometrical, on the velocity field and the volumetric flow rate are determined analytically. For low frequency of the oscillatory pressure gradient, the flow is essentially similar in characteristics to that of the steady flow driven by a constant pressure gradient, but for high frequency, the flow is substantially modified, when compared with the steady flow. The corrugations increase the total flow rate for small corrugation wavenumber, and further enhancement is obtained when the phase difference between the corrugated curved walls is increased. For large corrugation wavenumber, a contrary effect of the corrugations is found; the flow rate decreases irrespective of the phase difference. However, we have shown that for sufficiently high corrugation wavenumber and oscillation frequency, the effect of the phase difference would be negligible.