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kεNet: discovering the turbulence model and applying for low Reynolds number turbulent channel flow

kεNet湍流模型研究及其在低雷诺数槽道流中的应用

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Abstract

We propose a physics informed deep learning neural network, termed kεNet, for discovering the closure model of Reynolds stress in Reynolds-averaged Navier-Stokes (RANS) equations. The kεNet consists of a traditional physics uninformed neural network and several physics informed equations, e.g., the formula of Reynolds stress, the transport equations of turbulence kinetic energy k and turbulence dissipation rate ε. A low Reynolds number k-ε correction for turbulent channel flow is considered as an example. Based on the kεNet, all model parameters of the RANS are calibrated simultaneously with the specified mathematical formula, through training the neural network with data from direct numerical simulation. The gained turbulence model is utilized in OpenFOAM, an open source computational fluid dynamics (CFD) code, and predicts reasonable good results for a turbulent channel flow with Reτ = 5200 and 2000.

摘要

我们提出了一种基于物理信息的深度学习网络(kεNet), 可用于RANS方程中发现封闭的湍流模型. kεNet由一个传统的典型神经网络结构和若干个基于物理信息的方程组成, 如雷诺应力方程、k方程和ε方程. 以低雷诺数下的槽道流动的湍流模型的修正为例,通过训练基于物理信息的神经网络, 模型参数得到了修正. 修正后的湍流模型参数应用于OpenFOAM软件进行计算, 能够非常好地预测Reτ = 5200 和2000下的槽道流动.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 91852117), the foundation of National Key Laboratory of Science and Technology on Aerodynamic Design and Research (Grant No. 614220121040106), and Shanghai Rising-Star Program (Grant No. 19QC1400200)

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Authors and Affiliations

  1. School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Longfeng Hou  (侯龙锋), Bing Zhu  (朱兵) & Ying Wang  (王莹)

  2. National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Xi’an, 710072, China

    Longfeng Hou  (侯龙锋)

Authors
  1. Longfeng Hou  (侯龙锋)
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  2. Bing Zhu  (朱兵)
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  3. Ying Wang  (王莹)
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Contributions

Bing Zhu designed the conceptualization of this research and do the funding acquisition of this research. Longfeng Hou did the technical investigation and the original draft writing of this work. Ying Wang offered the resources and did the editing of this article.

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Correspondence to Bing Zhu  (朱兵).

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Hou, L., Zhu, B. & Wang, Y. kεNet: discovering the turbulence model and applying for low Reynolds number turbulent channel flow. Acta Mech. Sin. 39, 322326 (2023). https://doi.org/10.1007/s10409-022-22326-x

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