Journal of Jilin University(Engineering and Technology Edition) ›› 2024, Vol. 54 ›› Issue (4): 874-882.doi: 10.13229/j.cnki.jdxbgxb.20220611

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Reduced-order modelling of a bluff body turbulent wake flow field using hierarchical convolutional neural network autoencoder

Chao XIA1,2(),Meng-jia WANG1,2,Jian-yue Zhu3(),Zhi-gang YANG1,2,4   

  1. 1.School of Automotive Studies，Tongji University，Shanghai 201804，China
    2.Shanghai Automotive Wind Tunnel Center，Tongji University，Shanghai 201804，China
    3.Institute of Rail Transit，Tongji University，Shanghai 201804，China
    4.Beijing Aeronautical Science & Technology Research Institute，Beijing 102211，China
  • Received:2022-05-19 Online:2024-04-01 Published:2024-05-17
  • Contact: Jian-yue Zhu E-mail:chao.xia@tongji.edu.cn;zhujianyue@tongji.edu.cn

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Abstract:

In this study， a nonlinear hierarchical convolutional autoencoder （H-CNN-AE） is employed to sort the energy content of the latent vectors of AE， which is analogous to the method of proper orthogonal decomposition （POD）， and at the same time result in better performance in terms of reduced-order modelling within limits. This method is applied to a turbulent wake behind a three-dimensional circular cylinder bluff body at Re=20 000. We assess the ability of H-CNN-AE with L2 error and compares it with the results of POD. Furthermore， the concept of grouping AE-modes is extended. We observe the change of mean square error between the reconstructed and the original flow when adding the number of latent vectors of each group. It is demonstrated that when the number of subnetworks and low-dimensional vectors in latent space of each subnetwork is small， H-CNN-AE has better capability to restore the flow field than POD. However， it is also found that the strength of H-CNN-AE will weaken with the increase of the number of subnetworks and latent AE modes and will even be inferior to POD under certain conditions.

Key words: hierarchical autoencoder, convolutional neural network, bluff body turbulent wake, reduced order model

CLC Number: 

  • U462

Fig.1

Conventional convolutional neural network based autoencoder"

Fig.2

Hierarchical Autoencoder"

Fig.3

Computational case of a flow around 3D circular cylinder"

Table 1

Structure of CNN based hierarchical autoencoder"

网络层No.输出图形
Input1（192，384，2）
Input21（1）
Conv（f=16）1（192，384，16）
MaxPooling（192，384，16）
Conv（f=8）3（24，48，8）
MaxPooling（12，24，8）
Conv（f=4）1（12，24，4）
MaxPooling（6，12，4）
Conv（f=2）1（6，12，2）
Reshape1（144）
Dense4（64）
（32）
（16）
（1）
Concatenate1（2）
Dense4（16）
（32）
（64）
（144）
Reshape1（6，12，2）
Conv（f=2）1（6，12，2）
Upsampling1（12，24，2）
Conv（f=4）（12，24，4）
Upsampling3（96，192，8）
Conv（f=8）（96，192，8）
Upsampling1（192，384，8）
Conv（f=16）（192，384，16）
Conv（f=2）1（192，384，2）

Fig.4

Training error of network"

Table2

Time-averaged L2 error of different activation functions"

激活函数L2误差
softsign1.045
tanh1.094
Relu2.209

Fig.5

Comparison of reconstruction results between H-CNN-AE and POD"

Fig.6

Comparison of mode of streamwise velocity u between H-CNN-AE and POD"

Fig.7

POD processing of AE modes"

Fig.8

Reconstructed flow field L2 error at different n and ne"

Fig.9

Reconstructed flow field L2 error with four subnetworks"

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