Two- and three-dimensional flows in nearly rectangular cavities driven by collinear motion of two facing walls

摘要

Two- and three-dimensional flows in nearly cuboidal cavities are investigated experimentally. A tight cavity is formed in the gap between two long and parallel cylinders of large radii by adding rigid top, bottom, and end walls. The cross-section perpendicular to the axes of the cylinders is nearly rectangular with aspect ratio Gamma. The axial aspect ratio Lambda > 10 is large to suppress end-wall effects. The fluid motion is driven by independent and steady rotation of the cylinders about their axes which defines two Reynolds numbers Re (1,2). Stability boundaries of the nearly two-dimensional steady flow have been determined as functions of Re (1,2) for Gamma = 0.76 and Gamma = 1. Up to six different three-dimensional supercritical modes have been identified. The critical thresholds for the onset of most of the three-dimensional modes, three of which have been observed for the first time, agree well with corresponding linear-stability calculations. Particular attention is paid to the flow for Gamma = 1 under symmetric and parallel wall motion. In that case the basic flow consists of two mirror symmetric counter-rotating parallel vortices. They become modulated in span-wise direction as the driving increases. Detailed LDV measurements of the supercritical three-dimensional velocity field and the bifurcation show an excellent agreement with numerical simulations.