The existence of Taylor vortices and wide-gap instabilities in spherical Couette flow
The existence of Taylor vortices and wide-gap instabilities in spherical Couette flow
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DOI：
10.1007/bf01376924
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发表时间：
1995-09
期刊：
影响因子：
2.7
通讯作者：
C. Egbers;H. Rath
中科院分区：
文献类型：
--
作者：
C. Egbers;H. Rath
研究了粘性不可压缩流体在内球转动而外球静止的情况下，在两同心球之间的差距中的流动。为了确定层流-湍流转捩过程中的不稳定性以及相应的临界雷诺数随展弦比的变化，在较宽的雷诺数（Re = 2·105）和展弦比（0.08 <$β <$0.5）范围内进行了流动显示研究。研究发现，层流基流在稳定性阈值处以不同的方式失去稳定性。不稳定性的发生强烈地依赖于纵横比和初始条件。对于小的和中等的展弦比（0.08 <$β <$0.25），进行了作为雷诺数的函数的实验，以确定基本流、泰勒涡流、超临界基本流的存在区域，并进一步给出作为展弦比的函数的泰勒涡对的最大数目的最佳拟合。然而，对于宽间隙（0.33 <$β <$0.5），无法检测到泰勒涡。第一个不稳定性表现为空间对称性的破坏和非轴对称的二次波与螺旋臂出现取决于雷诺数。当β=0.33时，发现了方位波数n = 6、5和4的次级波，而在宽高比β=0.5的差距中，发现了n = 5、4和3个旋臂的次级波。测量了这些二次波的频率，得到了相应的临界雷诺数和向湍流过渡的过渡雷诺数，在极点处出现的流动模式与两旋转圆盘间流动的模式非常相似。非唯一性和滞后的影响被确定为加速度的函数。
The flow of a viscous incompressible fluid in the gap between two concentric spheres was investigated for the case where only the inner sphere rotates and the outer one is stationary. Flow visualization studies were carried out for a wide range of Reynolds numbers (Re≦2·105) and aspect ratios (0.08≦β≦0.5) to determine the instabilities during the laminar-turbulent transition and the corresponding critical Reynolds numbers as a function of the aspect ratio. It was found that the laminar basic flow loses its stability at the stability threshold in different ways. The instabilities occurring depend strongly on the aspect ratio and the initial conditions. For small and medium aspect ratios (0.08≦β≦0.25), experiments were carried out as a function of the Reynolds number to determine the regions of existence for basic flow, Taylor vortex flow, supercritical basic flow and furthermore, to give the best fit for the maximum number of pairs of Taylor vortices as a function of aspect ratio. For wide gaps (0.33≦β≦0.5), however, Taylor vortices could not be detected. The first instability manifests itself as a break of the spatial symmetry and non-axisymmetric secondary waves with spiral arms appear depending on the Reynolds number. For β=0.33, secondary waves with an azimuthal wave numbern=six, five and four were found, while in the gap with an aspect ratio of β=0.5 secondary waves withn=five, four and three spiral arms exist. Frequencies of these secondary waves were measured, the corresponding critical Reynolds numbers and the transition Reynolds numbers during the transition to turbulence were found. The flow modes occurring at the poles look very similar to those found in the flow between two rotating disks. Effects of non-uniqueness and hysteresis were determined as a function of the acceleration rate.