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基于基因表达式编程的数据驱动湍流建模

赵耀民 徐晓伟

赵耀民, 徐晓伟. 基于基因表达式编程的数据驱动湍流建模. 力学学报, 2021, 53(10): 1-16 doi: 10.6052/0459-1879-21-391
引用本文: 赵耀民, 徐晓伟. 基于基因表达式编程的数据驱动湍流建模. 力学学报, 2021, 53(10): 1-16 doi: 10.6052/0459-1879-21-391
Zhao Yaomin, Xu Xiaowei. Data-driven turbulence modelling based on gene-expression programming. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(10): 1-16 doi: 10.6052/0459-1879-21-391
Citation: Zhao Yaomin, Xu Xiaowei. Data-driven turbulence modelling based on gene-expression programming. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(10): 1-16 doi: 10.6052/0459-1879-21-391

基于基因表达式编程的数据驱动湍流建模

doi: 10.6052/0459-1879-21-391
详细信息
    作者简介:

    赵耀民, 研究员, 研究方向: 湍流与转捩、高精度数值模拟、数据驱动湍流建模. E-mail: yaomin.zhao@pku.edu.cn

    通讯作者:

    赵耀民, 研究员, 研究方向: 湍流与转捩、高精度数值模拟、数据驱动湍流建模. E-mail: yaomin.zhao@pku.edu.cn

DATA-DRIVEN TURBULENCE MODELLING BASED ON GENE-EXPRESSION PROGRAMMING

  • 摘要: 计算流体动力学是湍流研究的重要手段, 其中雷诺平均模拟在航空航天等实际工程中得到了广泛应用. 雷诺平均模拟的结果很大程度上依赖于湍流模型的预测精度, 而实际工程应用中常用的模型往往精度有限. 近年来, 数据驱动的湍流建模方法得到越来越多的关注. 本文介绍了基于基因表达式编程 (gene-expression programming, GEP) 方法的湍流建模相关进展. 本文首先讨论基因表达式编程应用于湍流建模的具体方法, 包括: 基本算法、显式代数应力模型和湍流传热两种建模框架、模型测试方法以及损失函数设置等. 在此基础上, 基因表达式编程方法被应用于涡轮叶栅尾流混合、竖直平板间自然对流、三维横向流中的射流等问题. 结果表明, GEP可以有效提升常用模型对于尾流混合损失、壁面热通量等关键参数的预测精度. 基因表达式编程方法可以显式给出模型方程, 因此模型具有可解释性强等特点. 基于双向耦合方法得到的模型还被证明具有较好的后验测试精度和鲁棒性. 基因表达式编程方法还被初步应用于大涡模拟亚格子应力和边界层转捩等问题的建模, 在不同湍流建模领域表现出很大的潜力.

     

  • 图  1  机器学习湍流建模示意图

    Figure  1.  Schematic for turbulence modelling with machine learning methods

    图  2  GEP方法的基因型及其表达过程

    Figure  2.  Genotype and expression process in GEP

    图  3  GEP方法流程图

    Figure  3.  Schematic for GEP method

    图  4  冻结训练流程示意图

    Figure  4.  Schematic for ‘frozen’ training method

    图  5  双向耦合方法训练流程示意图

    Figure  5.  Schematic for CFD-driven machine learning method

    图  6  航空发动机内流叶栅尾流混合算例示意图

    Figure  6.  Simulation setup for cases

    图  7  不同涡轮叶栅算例(见表1)中的尾流损失剖面

    Figure  7.  Kinetic wake loss profiles from test cases in Table 1

    图  8  来流尾流扰动下低压涡轮叶栅的锁相平均湍动能云图[48]

    Figure  8.  Phase-lock averaged TKE contours for LPT flow disturbed by incoming wakes[48]

    图  9  以竖直槽道流中的自然对流算例的计算域

    Figure  9.  Computational domain of natural convection case in a differentially heated vertical channel

    图  10  湍流普朗特数的先验预测

    Figure  10.  Prediction of turbulent Prandtl number

    图  11  平均温度剖面和垂直壁面方向的热通量的后验预测

    Figure  11.  Prediction of mean temperature profiles and wall-normal heat flux

    图  12  横流中的射流示意图

    Figure  12.  The schematic description of jet in crossflow case

    图  13  流向位置x/d=20的热通量预测

    Figure  13.  The prediction of heat flux vector at x/d=20

    图  14  壁面绝热效率的流向分布

    Figure  14.  Wall adiabatic effectiveness streamwise distribution

    表  1  涡轮叶栅尾流混合算例

    Table  1.   Parameters of turbine wake mixing cases.

    CasesReMaFlow features
    HPT A570,0000.9transition & shocks
    HPT B1,100,0000.9transition & shocks
    LPT C60,0000.4transition & open separation
    LPT D100,0000.4Transition & closed separation
    下载: 导出CSV
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  • 网络出版日期:  2021-08-30

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