平面槽流的二次失稳分析

Secondary Instability Analysis of Plane Channel Flow

本文以得自二维直接数值模拟的稳定的二维平衡态解,或将其中的扰动部分乘一小的系数所得到的准定常解取作基本流,考察它们对三维小扰动的不稳定性。导出了只包含二个未知函数的封闭的扰动运动方程组,与齐次边条件一起构成了一个常微分方程组的特征值问题。采用Chebyshev—τ方法将问题转化为一个代数特征值问题。对三维基本波与亚谐波失稳两种情形数值求解获得了三维扰动增长率随二维扰动幅值、雷诺数与展向波数的变化关系。结果表明在各种情况下三维扰动的增长率都远高于二维TS波的增长率,较好地解释了实验观测到的槽流转捩现象。

Taken the stable 2-D equilibrium solution obtained from 2-D direct numerical simulation, or the quasi-steady solutions obtained by multiplied its perturbation part by a small coefficient as a basic flow, their instability to 3-D small perturbation is examined. A closed perturbation equation set including only two unknown functions is derived, which with the homogeneous boundary conditions together constitutes an eigenvalue problem of an ordinary differential equation system. Chebyshev-r method is used to transform the above problem into an algebraic eigenvalue problem. For 3-D fundamental and subharmonic modes, the growing rates of 3-D perturbations on the amplitude values of 2-D perturbations, Reynolds numbers and spanwise wavenumbers is obtained numeriscally. Results indicate that m all cases the growing rates of 3-D Perturbations are much greater than those of 2-D T-S waves, so the transition phenomena in channel flow observed in wxperiments are better explained.