A numerical study on optimal rotation ratio and bottom shear stress in the counter-rotation mode of an annular flume

Abstract

In this study, the optimal rotation ratio that minimize both the secondary flow and the variation of the bottom shear stress in the radial direction in the annular flume was found from flow analysis using a computational fluid dynamics technique. The numerical model was verified from the measured data given in the literature. Forty-eight numerical calculations were carried out for the flow fields given with various rotation speed ratios of the top ring to the flume body. Some cases showed quite fluctuating non-uniform bottom shear stress profiles in the radial direction without any effective reduction of the secondary flow so that they were excluded in determining the optimal rotation ratio. It was found that the rotation ratio became optimal when both the maximum velocity ratio and the difference between the largest and smallest values of the stream function were minimal. Characteristically, in the range of relatively small top ring rotation speed (<10) the optimal, rotation ratio increased rapidly with it, but it converged to a fixed value as it became larger. The relationship between the optimal rotation ratio and the rotation speed of the top ring is presented. An equation for the averaged bottom shear stress under the optimal rotation ratios is also proposed as a function of the top ring rotation speed.