Numerical investigation of axial flow effects on Taylor–Couette instability: influence of cylinder radius ratios and stabilization mechanisms

Abstract

The investigation of various instabilities in the fluid flow between two rotating cylinders, known as Taylor–Couette instability, has significant implications for the design of industrial equipment. One effective method of controlling flow instabilities is by introducing axial flow to Taylor–Couette flow. In this study, the impact of adding axial flow to Taylor–Couette at different radii ratios was numerically analyzed using the direct protocol approach. This involved creating Taylor vortex flow first, followed by introducing axial flow to eliminate the vortices and stabilize the flow. The research was conducted on seven radius ratios, ranging from 0.77 to 0.95. The shape of the vortices, as well as their formation and disappearance, were examined using vorticity contours and velocity levels. The axial Reynolds number of the flow stabilizer was calculated using velocity profiles and skin friction coefficient evolution on the inner cylinder for each case. The results indicate that decreasing the ratio of the inner and outer cylinder radii resulted in a significant reduction of the Axial Re-laminarization Reynolds Number (ARRN) of the flow. The skin friction coefficient value reaches its minimum value, and when the axial Reynolds number reaches ARRN, it remains constant along the length of the inner cylinder. Finally, a mathematical equation was formulated to forecast changes in the axial re-laminarized Reynolds number in relation to the radius ratio of the two cylinders.