Application of deep learning in boundary layer flow instability analysis

FAN Jiakun; YAO Fangzhou; HUANG Jiangtao; XU Jiakuan; QIAO Lei; BAI Junqiang

doi:10.7638/kqdlxxb-2023.0073

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Application of deep learning in boundary layer flow instability analysis

更新时间：2026-05-28

- Application of deep learning in boundary layer flow instability analysis
- Vol. 42, Issue 3, Pages: 30-46(2024)
- 作者机构：
  
  1. 西北工业大学航空学院,西安,710072
  2. 西安航天动力技术研究所,西安,710025
  3. 中国空气动力研究与发展中心空天技术研究所,绵阳,621000
  4. 西北工业大学无人系统技术研究院,西安,710072
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2023.0073
  CLC： V211;V411;TP183
- Published：2024
- 稿件说明：
移动端阅览
樊佳坤, 姚方舟, 黄江涛, 等. 深度学习在边界层流动稳定性分析中的应用[J]. 空气动力学学报, 2024, 42(3): 30−46.

FAN Jiakun, YAO Fangzhou, HUANG Jiangtao, et al. Application of deep learning in boundary layer flow instability analysis[J]. 2024, 42(3): 30-46.
樊佳坤, 姚方舟, 黄江涛, 等. 深度学习在边界层流动稳定性分析中的应用[J]. 空气动力学学报, 2024, 42(3): 30−46. DOI： 10.7638/kqdlxxb-2023.0073

FAN Jiakun, YAO Fangzhou, HUANG Jiangtao, et al. Application of deep learning in boundary layer flow instability analysis[J]. 2024, 42(3): 30-46. DOI： 10.7638/kqdlxxb-2023.0073.

摘要

基于线性稳定性理论（linear stability theory

LST）的e

方法是边界层转捩预测中比较可靠的方法之一。为了将传统LST特征值问题的求解过程大幅度简化和自动化，使用卷积神经网络（convolutional neural network

CNN）在边界层相似性解的LST分析样本集上进行训练，针对流向和横流不稳定性，分别在自然层流翼型和无限展长后掠翼上预测扰动的当地增长率、

因子和转捩位置，结果与标准LST一致性良好；验证了CNN可以将边界层剖面速度型导数信息编码为满足伽利略不变性的标量特征，在翼型边界层中起到了表征压力梯度的作用，在后掠翼边界层中起到了表征横流强度的作用；在CNN对LST特征值预测的基础上，以LST控制方程、边界条件和平凡解惩罚项构造总损失函数来训练内嵌物理信息神经网络（physics-informed neural network

PINN），实现了在不依赖样本的情况下对LST特征函数的准确预测，结果表明PINN可以为LST的特征函数问题提供有效的建模方法。

Abstract

The e

method based on linear stability theory (LST) is one of the more reliable methods in the prediction of boundary layer transition. In order to greatly simplify and automate the solution process of the traditional LST eigenvalue problem

the convolutional neural network (CNN) is trained on the LST analysis sample set of the boundary layer similarity solution. For the streamwise and crossflow instabilities

the local growth rate

factor and transition location are p

redicted by CNN on a naturally laminar airfoil and an infinite swept-back wing respectively

which are in good agreement with the results of standard LST. It is verified that CNN can encode the velocity derivative information of the boundary layer profile into a scalar feature that satisfies the Galilean invariance

and plays a role in characterizing the pressure gradient in the boundary layer of an airfoil or the crossflow intensity in the boundary layer of a swept-back wing. Based on the prediction of LST eigenvalues by CNN

the total loss function is constructed by the governing equations of LST

the boundary conditions and the trivial solution penalty term to train the physics-informed neural network (PINN)

which realizes an accurate prediction of LST eigenfunctions without relying on samples. The results show that the PINN model can provide an effective modeling method for the eigenfunction problem of LST.

关键词

Keywords

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