Taylor vortex instability and annulus length effects
Taylor vortex instability and annulus length effects
复制标题
泰勒涡不稳定性和环空长度效应
作者：
J. A. Cole
旋转气缸间流动的稳定性具有基础性和技术意义。G.I.Taylor1对周向层流稳定性的经典分析涉及长度为L的无限长、径向间隙c=R2−r1的同轴圆柱体，但随后的工作2已消除了小间隙近似的需要。流动一旦不稳定，就会表现为轴对称环状涡的形式，而这些泰勒涡又可以随着非轴对称波状涡的开始而变得不稳定。早期对这种不稳定性的分析再次局限于无限长和小间隙的同轴圆柱体，但Eagles4已经给出了避免小间隙近似的稳定性分析，并将其应用于圆柱体半径比r1/r2=0.951。对于有限长度的环空似乎不存在稳定性分析，大多数实验工作者选择使用长圆柱体，尽管在工程应用中更有可能遇到短圆柱体。最近，我描述了一些在短环形间隙中观察到的涡旋大小，我注意到这些实验中明显没有波状涡：现在我有了更多的确凿证据，证明环隙长度对波状涡临界速度有相当大的影响。
THE stability of the flow between rotating cylinders has both fundamental and technological significance. The classical analysis by G. I. Taylor1 of the stability of the circumferential laminar flow deals with coaxial cylinders for which the length L is infinite and the radial clearance c=R2−R1, is small, but subsequent work2 has eliminated the need for the small clearance approximation. The flow, once unstable, takes the form of axisymmetric toroidal vortices and these Taylor vortices can in turn become unstable with the onset of non-axisymmetric wavy vortices. Early analysis of this instability3 was again restricted to coaxial cylinders of infinite length and small clearance, but Eagles4 has produced a stability analysis avoiding the small clearance approximation and has applied it to a cylinder radius ratio R1/R2=0.951. No stability analyses seem to exist for an annulus of finite length and most experimental workers choose to work with long cylinders even though short cylinders are more likely to be encountered in engineering applications. Recently I described some observations5 of vortex sizes in short annular clearances and I noticed the apparent absence of wavy vortices in those experiments: now I have more positive evidence of the considerable effect of annulus length on the wavy vortex critical speed.