Scattering and distortion of the unsteady motion on transversely sheared mean flows
Scattering and distortion of the unsteady motion on transversely sheared mean flows
复制标题
横向剪切平均流非定常运动的散射和畸变
DOI：
10.1017/s0022112079000379
复制
发表时间：
1979
影响因子：
3.7
通讯作者：
M. Goldstein
中科院分区：
文献类型：
--
作者：
M. Goldstein
结果表明，横向剪切平均流上非定常运动的压力和速度脉动可以完全用两个势函数的导数表示。其中之一是对流量（即它在流动中冻结），它可以被指定为边界条件，并与上游速度场的横向分量有关。另一个可以通过求解一个非齐次波动方程来确定，该方程的源项也是一个对流量，可以在任何给定的问题中指定为边界条件。后者与上游涡度场的旋度有关。结果被用来获得一个明确的表示的三维阵风或流体动力学运动的横向剪切平均流。由此表明，这种运动完全是由上面提到的两个对流量“驱动”的。本文用一般理论研究了非定常流与剪切层中的半无限平板的相互作用。在低频和高频范围内计算了这种相互作用产生的声场。结果与实验三分之一倍频程声压级辐射模式进行了比较。结果发现，一致性非常好，特别是在低频范围内，平均流动和对流效应对声音的方向性有很大影响。
It is shown that the pressure and velocity fluctuations of the unsteady motion on a transversely sheared mean flow can be expressed entirely in terms of the derivatives of two potential functions. One of these is a convected quantity (i.e. it is frozen in the flow) that can be specified as a boundary condition and is related to a transverse component of the upstream velocity field. The other can be determined by solving an inhomogeneous wave equation whose source term is also a convected quantity that can be specified as a boundary condition in any given problem. The latter is related to the curl of the upstream vorticity field. The results are used to obtain an explicit representation of the three-dimensional gust-like or hydrodynamic motion on a transversely sheared mean flow. It is thereby shown that this motion is ‘driven’ entirely by the two convected quantities alluded to above. The general theory is used to study the interaction of an unsteady flow with a scmi-infinite plate embedded in a shear layer. The acoustic field produced by this interaction is calculated in the limits of low and high frequency. The results are compared with experimental one-third octave sound pressure level radiation patterns. The agreement is found to be excellent, especially in the low frequency range, where the mean-flow and convective effects are shown to have a strong influence on the directivity of the sound.