Detachment phenomena in low Reynolds number flows through sinusoidally constricted tubes

Abstract

We examine the nature of detachment experimentally and numerically in steady axisymmetric flows through sinusoidally constricted tubes with Re varying from 10−4 to 102. Various regions can be distinguished, including flow detachment at the lowest Re used. Further, the transition in the pressure drop from a linear Poiseuille-like behaviour to a nonlinear pressure-drop–velocity relationship is not generally related to the appearance of detachment regions but rather to their form and to the nature of their growth. For the geometries considered here, the relationship between the start of nonlinearity in the pressure drop and incipient detachment depends on whether detachment is symmetric (detachment point at the bottom of a trough): for flow geometries with symmetric incipient detachment kinematic changes occur at Re lower than or the same as that at which dynamic changes can be detected, whereas for those with asymmetric incipient detachment they occur at higher Re. We look at various possible criteria for determining the transition from the viscous to the inertial range. Finally, we discuss the effect of elongational terms in the energy dissipation on flow through periodically constricted tubes and compare this flow with flow through porous media.