Flow in curved ducts. Part 2. Rotating ducts

Abstract

When a coiled tube is rotated about the coil axis, the effects of rotation interact with centrifugal and viscous effects to complicate the flow characteristics beyond those seen in stationary curved ducts. The phenomena encountered are examined for steady, fully developed Newtonian flow in circular tubes of small curvature. The governing equations are solved using orthogonal collocation, and the results presented cover both the nature of the flow and the bifurcation structure. When rotation is in the same direction as the axial flow imposed by a pressure gradient, the flow structure remains similar to that seen in stationary ducts, i.e. with two- or four-vortex secondary flows in addition to the axial flow. There are, however, quantitative changes, which are due to the Coriolis forces resulting from rotation. The bifurcation structure also shows only quantitative changes from that for stationary ducts at all values of Taylor number examined. More complex behaviour is possible when rotation opposes the flow due to the pressure gradient. In particular, the direction of the secondary flow may be reversed at higher rotational strengths, and the mechanism of the flow reversal is explored. The flow reversal occurs smoothly at low Taylor numbers, but at higher rotational strengths a cusp appears in the primary solution branch in the vicinity of the flow reversal.