来流马赫数对叶栅吸力面可压边界层稳定性影响研究

The Effect of Inlet Mach Number to Stability Analysis in Compressible Boundary Layers of Blade Cascade Suction Surface

针对叶栅高速流动稳定性预测及转捩问题,采用理论分析与实验测量相接合的方法。首先推导出正交曲线坐标系下三维扰动波的抛物化稳定性方程(PSE),在风洞实验中,采用叶栅表面压力测孔测量了设计叶栅表面静压分布。根据表面静压分布测量值,通过求解Falkner-Skan方程以获得不同来流马赫数下边界层内速度、压力、密度等参数的分布。将以上结果作为边界层平均流动值,结合数值离散化的正交曲线坐标系非线性抛物化稳定性方程(PSE)对流动的稳定性进行特征值分析。数值离散采用六阶精度差分格式,采用大步长隐格式法求解方程以保证求解的稳定性。计算结果表明本文所选用的实验叶栅由于加工量较小并采用后部加载叶型设计,边界层流动相对稳定。来流马赫数增加对边界层稳定性有微弱影响,会导致流动趋于不稳定。

Compressible boundary layers stability on blade cascade suction surface was discussed by wind tunnel experiment and numerical solution. Three dimensional disturbance wave parabolized stability equation （PSE） of orthogonal curvilinear coordinates in compressible flow was deducted. The surface pressure of blade in wind tunnel experiment was measured. The Falkner - Skan equation was solved under the boundary conditions of experiment result, and velocity, pressure and temperature of average flow were obtained. Substituted this result to discretization of the PSE eigenvalue problem, the stability problem can be solved. Implicit scheme and a large enough marching step size in the streamwise direction were used to obtain a stable solution. It is shown in result that the cascade in this experiment boundary flow is stability, and the increase of inlet mach number weakly effect flow, but lead to instability.