The effects of eccentricity on torque and load in Taylor-vortex flow
The effects of eccentricity on torque and load in Taylor-vortex flow
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偏心率对泰勒涡流中扭矩和载荷的影响
DOI：
10.1017/s002211207800155x
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发表时间：
1978
影响因子：
3.7
通讯作者：
R. DiPrima
中科院分区：
文献类型：
--
作者：
P. M. Eagles;J. T. Stuart;R. DiPrima
本文推广了DiPrima&Stuart(1972b)首先计算临界泰勒数到ε2阶的临界泰勒数，其中偏心率ε与圆柱轴的位移成正比，第二次(1975)计算与泰勒涡非线性效应有关的扭矩和载荷到ε阶。在后一篇文章中，证明了对于ε阶，泰勒涡产生的力矩与由Davey(1962)首次用摄动法计算的同心问题的力矩是相同的。这一缺陷在本文中得到了改善，计算采用ε2阶。结果表明，当泰勒数高于依赖于ε的临界值的百分比保持不变时，随着ε的增加，与泰勒涡相关的扭矩略有下降。这一结果与Vohr(1967,1968)的实验观测结果一致。此外，还给出了与偏心几何形状有关的泰勒涡流发展压力场的计算结果，这比同心情况下雷诺润滑效应的压力场要大。还给出了内筒载荷的相关分量，但仅针对接近临界值的泰勒数。Vohr还观察到，对于间隙与内径之比平均为0.099的圆柱，当泰勒数高于临界值20%时，最大泰勒涡强度(ε=0.475)出现在最大间隙下游约50°处。在之前的两篇论文(1972b，1975)中的计算分别给出了该角度的90°和76°。请注意，在1975年的论文中包括了对ε阶的几何校正。在这里，由于流动而对ε阶作了额外的修正，通过所给出的扩展分析，这一结果被改进到49°，尽管“小”参数有点超出了微扰理论所期望的有效范围。
This paper extends two earlier papers in which DiPrima & Stuart calculated first (1972b) the critical Taylor number to order ε2, where the eccentricity ε is proportional to the displacement of the axes of the circular cylinders, and second (1975) the torque and load to order ε associated with nonlinear effects of Taylor vortices. In the latter paper, it was shown that to order ε the torque arising from the Taylor vortices is identical with that for the concentric problem, which was first calculated, by a perturbation method, by Davey (1962). This deficiency is remedied in the present paper, where the calculation is taken to order ε2. It is found that, as ε rises, the torque associated with the Taylor vortices falls slightly when we keep constant the percentage elevation of the Taylor number above the ε-dependent critical value. This result is in accordance with experimental observations by Vohr (1967, 1968). In addition, results of calculations of the pressure field developed by the Taylor-vortex flow in association with the eccentric geometry are presented; this is larger than in the concentric case owing to a Reynolds lubrication effect. Also given are the associated components of the load on the inner cylinder, but only for Taylor numbers close to the critical value. One additional observation by Vohr, for cylinders with a mean ratio of the gap to the inner radius of 0·099, was that the maximum Taylor-vortex strength with ε = 0·475 occurred some 50° downstream of the maximum gap for a 20% elevation of the Taylor number above the critical value. Calculations in the two earlier papers (1972b, 1975) gave 90 and 76°, respectively, for that angle. Note that in the 1975 paper a geometrical correction of order ε was included. Here, with an additional modification of order ε due to the flow, this result is improved to 49° by the extended analysis presented, although the ‘small’ parameters are somewhat outside the range for which perturbation theory is expected to be valid.