混合层中的流向涡与Rayleigh离心不稳定

STREAMWISE VORTICES IN A PLANE MIXING LAYER AND RAYLEIGH'S CENTRIFUGAL INSTABILITY

摘要

摘要:用有限差分方法求解三维Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程和连续性方程，对时间发展的平面混合层中流向涡的产生原因进行了分析．将Ｒａｙｌｅｉｇｈ的轴对称无粘离心不稳定理论推广应用于分析混合层的二维基本流，并导出一无量纲量Ｒａｙ＝－（ｒ／νθ）νθ／ｒ，其中νθ为一流体质点相对于平均速度的速度，ｒ为该质点迹线的曲率半径．当Ｒａｙ＞１．０时就会发生离心不稳定．采用这一判别式后发现混合层中展向涡的周围，尤其是在辫带区，的确存在离心不稳定区域，而过去的实验结果也表明三维不稳定产生于展向涡之间的辫带区．因此有理由认为，除非雷诺数特别小，离心不稳定是流向涡产生和发展的主要原因

Abstract:A finite difference scheme is employed to solve the Navier Stokes and continuity equations for a 3 D temporally growing plane mixing layer. The physical mechanism for generation and development of streamwise vortices in the mixing layer is numerically investigated. Rayleigh's theory of centrifugal instability for inviscid axisymmetric flow is extended to analyze the two dimensional primary flows of the mixing layer. Accordingly, a dimensionless group Ray =-(r/υθ)/υθ/r is derived, where υθ is th...