Oscillatory flows in wavy-walled tubes

Abstract

The problem of oscillatory viscous flow in a tube with rigid sinusoidal walls of large amplitude is solved numerically, for Reynolds numbers up to 300 and Strouhal numbers in the range 10−4–1. Flow visualization photographs have confirmed qualitatively many of the predictions. Results analogous to those of Sobey (1980, 1983) for the two-dimensional problem have been obtained for regions of the parameter space studied in detail by that author. However, new flow structures are found in the previously neglected Strouhal number range of 0.02–0.1. These flows are characterized by significant interaction of flow events in successive half-cycles, due to the persistence of strong shed vortices. Bifurcation of the solution structure can then occur for Strouhal numbers between about 0.025 and 0.045, with the development of time-asymmetric flows: thus the velocity field at some instant of a positive-flow half-cycle may not be equal to minus the velocity field at the corresponding instant of a negative-flow half-cycle.