摘要
在高超声速边界层流动中,由于存在非平行效应以及激发Mack第二模态时的模态同步机制,因此在进行转捩预测研究时,中性曲线下支的确定需要考虑到这两方面的影响。全文针对高超声速平板边界层,首先采用线性抛物化稳定性方程(LPSE)对考虑感受性的中性曲线下支进行了求解,研究发现该方法存在两大难点:一是计算入口需要给定的离散模态在衰减区求解困难;二是由于存在快、慢模态的同步机制,所以在实际计算时,需要分别计算两次离散模态的演化以确定中性曲线下支,计算效率较低。基于以上问题,本文提出了一种基于伴随抛物化稳定性方程(APSE)来计算非平行边界层稳定性的方法,并以此确定考虑感受性的中性曲线下支位置。该方法从Mack模态的增长区开始进行计算,因此有效地解决了使用LPSE方法计算时所存在的问题。在不同工况下,与线性稳定性理论(LST)以及LPSE给出的预测结果进行了对比。从对比结果中可以看出该方法给出的预测结果与LPSE给定上游主导模态的预测结果一致,同时不必依赖于入口初值的选取且效率更高。该方法有进一步发展的潜力,可以有效地应用于高超声速边界层转捩的预测研究中。
In hypersonic boundary layers,the lower branch of the neutral curve for the second Mack mode needs to consider the non-parallel effect and the modal synchronization mechanism.The linear parabolized stability equations(LPSE)are firstly used to find the lower branch of the neutral curve in hypersonic boundary layers,but face two major challenges:First,it is difficult to give the discrete spectrum as the initial condition at the inlet because the discrete mode is stable there and an iterative method is hard to be adopted;Second,due to the synchronization of the fast mode and the slow mode,the evolution of these modes should be computed separately to determine the lower branch of the neutral curve,resulting in the calculation efficiency relatively low.To solve the above problems,a new method for calculating the stability of non-parallel boundary layers based on the adjoint parabolized stability equations(APSE)is proposed in the present study,and it can be used to determine the lower branch with the consideration of the receptivity.This method starts from the unstable region of the Mack mode,as a result,the initial condition of the calculation is easier to give compared to LPSE.We compare the results given by the present method to those by both the linear stability theory(LST)and LPSE for various conditions.The prediction for the dominant mode upstream given by our new method is consistent with that by LPSE,but our new method does not rely on the selection of the initial value at the inlet,thus the efficiency is higher.The present method has the potential to further predict transition in hypersonic boundary layers.
作者
谷晓培
刘建新
GU Xiaopei;LIU Jianxin(Department of Mechanics,Tianjin University,Tianjin 300072,China)
出处
《空气动力学学报》
CSCD
北大核心
2021年第2期62-72,共11页
Acta Aerodynamica Sinica
基金
国家重点研发计划(2016YFA0401200)
国家自然科学基金青年基金(114202167)。
关键词
伴随抛物化稳定性方程
第二模态
中性曲线
高超声速边界层
离散谱
adjoint parabolized stability equations
second mode
neutral curve
hypersonic boundary layer
discrete spectrum
