Lower branch of second mode neutral curve determination base on APSE in hypersonic boundary layers

GU Xiaopei; LIU Jianxin

doi:10.7638/kqdlxxb-2019.0095

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Lower branch of second mode neutral curve determination base on APSE in hypersonic boundary layers

更新时间：2026-05-28

- Lower branch of second mode neutral curve determination base on APSE in hypersonic boundary layers
- Vol. 39, Issue 2, Pages: 62-72(2021)
- 作者机构：
  
  天津大学力学系,天津,300072
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2019.0095
  CLC： O317
- Published：2021
- 稿件说明：
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谷晓培, 刘建新. 基于APSE确定高超声速边界层第二模态中性曲线下支[J]. 空气动力学学报, 2021, 39(2): 62−72.

GU Xiaopei, LIU Jianxin. Lower branch of second mode neutral curve determination base on APSE in hypersonic boundary layers[J]. 2021, 39(2): 62-72.
谷晓培, 刘建新. 基于APSE确定高超声速边界层第二模态中性曲线下支[J]. 空气动力学学报, 2021, 39(2): 62−72. DOI： 10.7638/kqdlxxb-2019.0095

GU Xiaopei, LIU Jianxin. Lower branch of second mode neutral curve determination base on APSE in hypersonic boundary layers[J]. 2021, 39(2): 62-72. DOI： 10.7638/kqdlxxb-2019.0095.

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。

Abstract

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.

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references

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