ON THE STABILITY OF LAMINAR FLOW OF A DUSTY GAS
ON THE STABILITY OF LAMINAR FLOW OF A DUSTY GAS
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DOI：
10.1017/s0022112062000555
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发表时间：
1962-01-01
影响因子：
3.7
通讯作者：
SAFFMAN, PG
中科院分区：
文献类型：
--
作者：
SAFFMAN, PG
给出了描述携带小尘粒的气体运动的方程，并导出了稳定层流的小扰动所满足的方程。灰尘的影响由两个参数描述；灰尘的浓度和弛豫时间 τ 测量灰尘颗粒的速度根据气体速度的变化进行调整的速率，并且取决于单个颗粒的尺寸。结果表明，如果灰尘足够细，使得 τ 与与流动相关的特征时间尺度相比很小，那么灰尘的添加就会使气流不稳定；对于平面平行流，结果表明，含尘气体的稳定特性仍然由Orr-Sommerfeld方程的解决定，但用一般复杂的修正剖面代替基本速度剖面。使用一个简单但不切实际的例子来说明灰尘作用的一些特征。它的目的是在后面的论文中描述平面泊肃叶流的修正奥尔-索末菲方程的解。
The equations describing the motion of a gas carrying small dust particles are given and the equations satisfied by small disturbances of a steady laminar flow are derived. The effect of the dust is described by two parameters; the concentration of dust and a relaxation time τ which measures the rate at which the velocity of a dust particle adjusts to changes in the gas velocity and depends upon the size of the individual particles. It is shown that if the dust is fine enough for τ to be small compared with a characteristic time scale associated with the flow, then the addition of dust destabilizes a gas flow; whereas if the dust is coarse so that τ is relatively large, then the dust has a stabilizing action.For plane parallel flow, it is shown that the stability characteristics for a dusty gas are still determined by solutions of the Orr-Sommerfeld equation, but with the basic velocity profile replaced by a modified profile which is in general complex. A simple, although unrealistic, example is used to illustrate some features of the action of dust. It is intended to describe the solution of the modified Orr-Sommerfeld equation for plane Poiseuille flow in a later paper.