Stability of swirling flows with radius-dependent density
Stability of swirling flows with radius-dependent density
复制标题
密度依赖于半径的旋流流的稳定性
DOI：
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发表时间：
1975
影响因子：
3.7
通讯作者：
U. Kurzweg
中科院分区：
文献类型：
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作者：
Y. Fung;U. Kurzweg
研究了具有半径依赖密度的非均质旋流的无粘不稳定性，并从控制方程的显式解中得到了几种不同流型的不稳定性增长率的长期关系。与先前得到的流动稳定性的充分性条件一致，当密度是半径的单调递增函数时，它们在轴对称和非轴对称无穷小模态下都是稳定的，同时角速度分量和轴向速度分量的径向变化都很小。这些流动的不稳定机制既有离心的，也有剪切的，经典的瑞利- synge准则是离心稳定的一个条件。通过几个反例表明，当考虑非轴对称扰动或流中存在大剪切时，旋流稳定性的瑞利- synge判据一般既不是充分条件也不是必要条件。当角速度和轴向速度分量没有径向变化，同时密度随半径增加时，就会发生非常稳定的流动，这是典型离心机的情况。
The inviscid instability of heterogeneous swirling flows with radius-dependent density is investigated and secular relations for the instability growth rates for several different flow configurations are obtained from explicit solutions of the governing equations. It is found, in agreement with a sufficiency condition for the stability of such flows obtained earlier, that they are stable to both axisymmetric and non-axisymmetric infinitesimal modes whenever the density is a monotonic increasing function of radius and at the same time the radial variations in both the angular and axial velocity components remain small. The instability mechanisms present in these flows are both of centrifugal and of shear origin, the classical Rayleigh–Synge criterion being a condition for centrifugal stability. It is shown, via several counter examples, that the Rayleigh–Synge criterion for the stability of swirling flows is generally neither a necessary nor a sufficient condition when non-axisymmetric disturbances are considered or large shears exist in the flow. Very stable flows occur when the angular and axial velocity components have no radial variation and simultaneously the density increases with radius as is the case in a typical centrifuge.