深度学习在边界层流动稳定性分析中的应用  

Application of deep learning in boundary layer flow instability analysis

作　　者：樊佳坤 姚方舟 黄江涛 徐家宽[1] 乔磊[4] 白俊强[1,4] FAN Jiakun;YAO Fangzhou;HUANG Jiangtao;XU Jiakuan;QIAO Lei;BAI Junqiang(School of Aeronautics,Northwestern Polytechnical University,Xi'an710072,China;Xi'an Aerospace Solid Propulsion Technology Institute,Xi'an710025,China;Aerospace Technology Institute,China Aerodynamics Research and Development Center,Mianyang621000,China;Unmanned System Research Institute,Northwestern Polytechnical University,Xi'an710072,China)

机构地区：[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

出　　处：《空气动力学学报》2024年第3期30-46,共17页Acta Aerodynamica Sinica

基　　金：国家自然科学基金(12102361);中央高校基本科研业务费(G2021KY05101)。

摘　　要：基于线性稳定性理论(linear stability theory,LST)的e^(N)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、N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。The e^(N) 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,N factor and transition location are predicted 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：线性稳定性理论 e^(N)方法 卷积神经网络 内嵌物理信息神经网络 流向不稳定性 横流不稳定性 

分 类 号：V211[航空宇航科学与技术—航空宇航推进理论与工程] V411[自动化与计算机技术—控制理论与控制工程] TP183[自动化与计算机技术—控制科学与工程]