Dutcher C S, Muller S J
Department of Chemical Engineering, University of California at Berkeley, Berkeley, California 94720, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Apr;75(4 Pt 2):047301. doi: 10.1103/PhysRevE.75.047301. Epub 2007 Apr 3.
In this study, existing primary stability boundary data for flow between concentric cylinders, for the broad range of radius and rotation ratios examined, were found to be self-similar in a properly chosen parameter space. The experimental results for the primary transitions to both Taylor vortex flow and spiral vortex flow collapsed onto a single curve using a combination of variables technique, for both counter-rotating and co-rotating cylinders. The curves were then empirically fit, yielding explicit analytic formulas for the critical Reynolds number for any radius ratio (eta) and rotation ratio (micro) . For counter-rotating flows, the primary critical Reynolds number is determined by a single variable: the ratio of the nodal gap fraction to a known function of the radius ratio. The existence and influence of a nodal surface is shown experimentally for micro approximately equal -1.7. For co-rotating flows, the important scaled variable was found to be the radius ratio divided by the nodal radius ratio. Comparisons of the resulting explicit stability formulas were made to existing analytic stability expressions and experimental data. Excellent quantitative agreement was found with data across the entire parameter space.
在本研究中，对于所考察的宽范围半径和旋转比，发现同心圆柱间流动的现有初始稳定性边界数据在适当选择的参数空间中是自相似的。使用变量组合技术，对于反向旋转和同向旋转圆柱，向泰勒涡旋流和螺旋涡旋流的初始转变的实验结果都汇聚到一条单一曲线上。然后对这些曲线进行经验拟合，得出了针对任何半径比（η）和旋转比（μ）的临界雷诺数的显式解析公式。对于反向旋转流动，初始临界雷诺数由单个变量确定：节点间隙分数与半径比的已知函数的比值。实验表明，对于μ约等于 -1.7 的情况，存在节点表面及其影响。对于同向旋转流动，发现重要的缩放变量是半径比除以节点半径比。将所得的显式稳定性公式与现有的解析稳定性表达式和实验数据进行了比较。在整个参数空间中与数据发现了极好的定量一致性。
