基于线性抛物化稳定性方程的后掠翼边界层内横流稳定性研究

Investigation on Cross-flow Instabilities in Swept-wing Boundary Layers with Linear Parabolized Stability Equations

采用有限差分法求解考虑模型曲率的线性抛物化稳定性方程(LPSE),分析无限展长后掠翼边界层内的横流驻波不稳定,并与实验结果进行对比,研究LPSE方法的模拟效果及其适用范围.研究表明,在横流驻波扰动增长的初期,LPSE能够准确的预测扰动的eN曲线,较好地描述边界层内的流动结构和扰动形态;当扰动增长到足够大时,扰动的高阶项不能再被忽略,LPSE的线性假设不再成立,需要采用非线性的方法(NPSE)来分析该状态.计算分析发现,模型曲率和边界层非平行性对后掠翼边界层内横流驻波的稳定性分析影响很大,影响程度与雷诺数无关.对于本文研究的模型,曲率对边界层内的横流扰动起着稳定的作用,而非平行性对扰动起不稳定的影响.

Linear parabolized stability equations （LPSE） considering model curvature are solved with finite difference method. Stationary cross-flow instabilities in boundary layers of an infinite swept-wing are analyzed. LPSE and experimental results are compared. It is shown that at early development of stationary cross-flow disturbances, LPSE simulates flow structure and disturbance profiles well and predicts the N-factors accurately. When disturbances are amplified enough, high order terms can not be omitted and linearization assumption of LPSE is no longer suitable. Moreover, effects of model curvature and boundary layer non-parallelism are investigated. It shows that curvature and non-parallel terms have significant effects on stability analysis of stationary cross-flow instabilities on a swept-wing, and the effects are independent of Reynolds numbers. In the model investigated, inclusion of curvature has a stabilizing effect and non-parallelism shows destabilizing effects on disturbances.