边界层稳定性的非平行性问题研究

采用抛物化稳定性方程的新方法研究稳定性的非平行问题，其控制方程从涡量形式的N－S方程导出，为提高计算精度和收敛速度，在法向采用高精度的高阶谱方法，结合边界层特征安排边界条件的方程，以及对无限区域数值问题作高效的代数变换处理，通过对预估校正迭代过程中推进步长有效的控制，以满足正规化条件，研究了不同类型压力梯度对稳定性的作用，由系列算例得到的增长率变化曲线和扰动中性曲线等，精确地给出了非平行性对流动稳定性的影响，计算的结果与相关数据符合甚好。

Studies on Nonparallelism of Boundary Layer Stability

The Orr Sommerfeld equation is adopted to study parallel stability problem. The effect of nonparallelism of the basic flow should be considered. A new method of the parabolic stability equations (PSE) is used to study the nonparallelism of the boundary layer stability. Because the velocity profiles, wavelengths and growth rates of the disturbance change slowly in boundary layer along the stream wise direction, this method takes a hypothesis: the second derivatives and products of first derivatives of these quantities are sufficiently small to be negligible. With this hypothesis, the governing equations are directly derived from N S equations. During the numerical calculation process, the precision of the calculation and the convergence velocity are improved by spectral collocation method and the way to collocate the boundary point based on the characteristic of the boundary layer, and a special effective algebraic mapping to deal with the problem of infinite region. The iteration of predictor corrector is used in the marching procedure and the normalization is satisfied. The effects of the pressure gradients on the stability are investigated. From different curves computed by the examples, the effects of the nonparallelism are accurately given. Results are quite consistent with available data. It has been proved that PSE method is effective to study the non parallelism of the boundary layer stability. It indicates that the non parallelism of two dimensional disturbance is week, but for three dimensional disturbance the non parallelism is strong, even change the stable flow in parallel basic flow into unstable flow. Favorable pressure gradient can delay the instability and retard the occurrence of transient. But the adverse pressure gradient included accelerates the instability and promotes the transient of boundary layer.