Ritz method for oscillatory flow in ducts

Abstract

Oscillatory viscous flow is solved by a Ritz integration method. The method is robust and efficient. The elliptic duct and the isosceles triangular duct are studied in detail. We find that the unsteady flow is dependent on a non-dimensional frequency s and the aspect ratio b. In general, for s=O(1) or lower, the flow may be considered quasi-steady, and the velocity is in phase with the applied pressure gradient. For large frequency, s=O(100), the maximum velocity occurs near the larger curvature ends and corners. Copyright © 2010 John Wiley & Sons, Ltd.