Numerical simulation and experimental verification of cavity flows

Abstract

Cavity flows in cylindrical and spherical geometry are investigated numerically on the basis of a finite element calculation and are compared with experimental results which were gained by a photochemical, nearly disturbance-free visualization technique. The onset of secondary flows in the axial region is analysed according to the parameters which describe the moving boundaries and the geometry of the cavity. For the cylindrical geometry the influence of an independently co- or counterrotating bottom is investigated while the lid of the cylinder is rotating at different angular velocities leading to a recirculating zone in the axial region. The aspect ratio of the cylinder and the ratio of the angular velocities of top and bottom determine the region of existence of recirculation zones in the container. The analysis of the experimental results shows the existence of stationary and even space- and time-periodic solutions of the recirculating type of axial flows.

For the spherical gap flow the numerical analysis predicts clearly for different gap sizes the existence of recirculation regions between the south poles of the spherical boundaries. In the experiments such a type of secondary flow could be observed for the concentrical and the eccentrical position of the two spherical boundaries. In the eccentrical case also a time-periodic motion in axial direction could be detected experimentally. For the spherical geometry only the inner sphere is assumed to be in motion. The outer boundary is kept at rest. The penalty finite element calculations were performed using coarse grids.

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