Abstract
The stability of viscous flow between concentric rotating cylinders with an axial flow due to an axial pressure gradient is considered. The governing equations with respect to three-dimensional disturbances are derived and solved by a direct numerical procedure. Results are given for the case of small-gap approximation. Three typical cases μ=−1,0 and 0.5 are studied, where μ represents the ratio of angular velocity of the outer cylinder to that of the inner cylinder. The value of the axial Reynolds numberR is up to 100. It is found that the critical disturbance is a non-axisymmetric mode when the value ofR is sufficiently large, and the transition of the onset mode withR is demonstrated in detail. Results for the critical Taylor number, wave number, vortex incline angle, and relative wave velocity are also determined. The present stability analysis is found to be in agreement with previous experimental studies and particularly reveals the stability characteristics with the variation of μ.
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