Stability of Taylor-Couette Flow with Axial Flow

This paper describes an investigation, which uses a torquemeasurement technique, of effects of axial flow on the stability of Taylor-Couette flow. Two radius ratios, 0.846 and 0.956, are used. The preliminary results show that the critical Taylor number for the onset of Taylor vortices increases monotonically with the Reynolds number of the axial flow and asymptotes to a constant value. Although our findings are in good agreement with previously published results, which were obtained with either flow visualization or pressure measurements, there are some noticeable differences with earlier studies. Introduction Flow between two rotating concentric cylinders, also known as Taylor-Couette flow, has long been the subject of theoretical and experimental investigation. These studies originated with the work of Couette [6] and Mallock [12], but Taylor [17] made the most significant advances in describing this flow in his 1923 classical paper “Stability of a viscous liquid between two rotating concentric cylinders”. Since then, hundreds of papers on the subject have been published with most studies utilising a rotating inner cylinder and a stationary outer cylinder. Here, as the rotational speed of the inner cylinder is slowly increased from rest, the laminar axisymmetric flow (also known as Couette flow) becomes unstable. This leads to a series of flow transitions with the following flow modes: Circular Couette Flow (CCF), TaylorVortex Flow (TVF), Wavy Vortex Flow (WVF), Modulated Wavy Vortex Flow (MWVF) and Turbulent Taylor Vortex Flow (TTVF). Imposing an axial flow on a Taylor-Couette flow has been shown to delay the transition to TVF, thus increasing the stability of the flow. Cornish [5] was the first to study this phenomenon. He determined the critical angular velocity of the inner cylinder for the onset of TVF for different axial flow rates. Also, he found that the beginning of TVF is accompanied by a sudden increase in the axial pressure drop across the annular region between the inner and outer cylinders. The same phenomenon was analytically investigated by Goldstein [9] for axial Reynolds numbers of 0 ≤ Rex ≤ 25. In contrast to the results of [5], he found that for 0 ≤ Rex ≤ 15, the axial flow has a stabilizing effect, but for 15 < Rex ≤ 25 it has a destabilizing effect. Many of the discrepancies between the early works of the 1930s were clarified by studies conducted in the 1960s (see Chandrasekhar [3], Di Prima [7], Krueger and Di Prima [10] and Sparrow, Munro and Jonsson [15]). Chandrasekhar [3] published a monumental paper covering a more complete stability theory for the Couette-Poiseuille flow. He reported that an axial flow tends to stabilize rotational flow and, criter work simil were show mono and S