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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): 2640-2655 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): 2640-2655 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): 2640-2655 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): 2640-2655 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

  • 中图分类号: O35

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
  • [1] Pope SB. Turbulent Flows. Cambridge University Press, 2000
    [2] Slotnick J, Khodadoust A, Alonso J, et al. CFD vision 2030 study: A path to revolutionary computational aero-sciences. NASA Technical Report, NASA/CR-2014-218178, 2014
    [3] Launder BE, Reece EJ, Rodi W. Progress in the development of a Reynolds-stress turbulence closure. Journal of Fluid Mechanics, 1975, 68(3): 537-566 doi: 10.1017/S0022112075001814
    [4] Spalart P, Allmaras S. A one-equation turbulence model for aerodynamic flows//30th Aerospace Sciences Meeting and Exhibit, 1992: 439
    [5] Launder BE, Spalding DB. The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering, 1974, 3(2): 269-289 doi: 10.1016/0045-7825(74)90029-2
    [6] Wilcox DC. Reassessment of the scale-determining equation for advanced turbulence models. AIAA Journal, 1988, 26(11): 1299-1310 doi: 10.2514/3.10041
    [7] Menter FR. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal, 1994, 32(8): 1598-1605 doi: 10.2514/3.12149
    [8] Hunt JCR, Savill AM. Guidelines and criteria for the use of turbulence models in complex flows//Prediction of Turbulent Flows, Cambridge University Press, 2005: 291-343
    [9] Yoder DA, DeBonis JR, Georgiadis NJ. Modeling of turbulent shear flows. NASA Technical Report, NASA/TM-2013-218072, 2013
    [10] Brunton SL, Noack BR, Koumoutsakos P. Machine learning for fluid mechanics. Annual Review of Fluid Mechanics, 2020, 52: 477-508 doi: 10.1146/annurev-fluid-010719-060214
    [11] Duraisamy K, Iaccarino G, Xiao H. Turbulence modeling in the age of data. Annual Review of Fluid Mechanics, 2019, 51: 357-377 doi: 10.1146/annurev-fluid-010518-040547
    [12] 张伟伟, 朱林阳, 刘溢浪等. 机器学习在湍流模型构建中的应用进展. 空气动力学学报, 2019, 37(3): 444-454 (Zhang Weiwei, Zhu Linyang, Liu Yilang, et al. Progresses in the application of machine learning in turbulence modeling. Acta Aerodynamica Sinica, 2019, 37(3): 444-454 (in Chinese) doi: 10.7638/kqdlxxb-2019.0036
    [13] Edeling WN, Cinnella P, Dwight RP. Predictive RANS simulations via Bayesian model-scenario averaging. Journal of Computational Physics, 2014, 275: 65-91 doi: 10.1016/j.jcp.2014.06.052
    [14] Parish EJ, Duraisamy K. A paradigm for data-driven predictive modeling using field inversion and machine learning. Journal of Computational Physics, 2016, 305: 758-774 doi: 10.1016/j.jcp.2015.11.012
    [15] Ferrero A, Iollo A, Larocca F. Field inversion for data-augmented RANS modelling in turbomachinery flows. Computer & Fluids, 2020, 201: 104474
    [16] Zhang ZJ, Duraisamy K. Machine learning methods for data-driven turbulence modeling//AIAA Computational Fluid Dynamics Conference, 2015: 2015-2460
    [17] Yang M, Xiao Z. Improving the kωγ–Ar transition model by the field inversion and machine learning framework. Physics of Fluids, 2020, 32: 064101 doi: 10.1063/5.0008493
    [18] Holland JR, Baeder JD, Duraisamy K. Field inversion and machine learning with embedded neural networks: physics-consistent neural network training//AIAA Aviation 2019 Forum, 2019
    [19] Duraisamy K. Perspectives on machine learning-augmented Reynolds-averaged and large eddy simulation models of turbulence. Physical Review Fluids, 2021, 6(5): 05054
    [20] Wang JX, Wu JL, Xiao H. Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data. Physical Review Fluids, 2017, 2(3): 034603 doi: 10.1103/PhysRevFluids.2.034603
    [21] Ling J, Kurzawski A, Templeton J. Reynolds averaged turbulence modelling using deep neural networks with embedded invariance. Journal of Fluid Mechanics, 2016, 807: 155-166 doi: 10.1017/jfm.2016.615
    [22] Pope SB. A more general effective-viscosity hypothesis. Journal of Fluid Mechanics, 1975, 72(2): 331-340 doi: 10.1017/S0022112075003382
    [23] Yin Y, Yang P, Zhang Y, et al. Feature selection and processing of turbulence modeling based on an artificial neural network. Physics of Fluids, 2020, 32: 105117 doi: 10.1063/5.0022561
    [24] Zhu L, Zhang W, Kou J, et al. Machine learning methods for turbulence modeling in subsonic flows around airfoils. Physics of Fluids, 2019, 31(1): 015105
    [25] Zhu L, Zhang W, Sun X, et al. Turbulence closure for high Reynolds number airfoil flows by deep neural networks. Aerospace Science and Technology, 2021, 110: 106452
    [26] Zhu L, Zhang W, Kou J, et al. Machine learning methods for turbulence modeling in subsonic flows around airfoils. Physics of Fluids, 2019, 31: 015105 doi: 10.1063/1.5061693
    [27] Xie C, Wang J, Li H, et al. Artificial neural network mixed model for large eddy simulation of compressible isotropic turbulence. Physics of Fluids, 2019, 31: 085112 doi: 10.1063/1.5110788
    [28] Xie C, Yuan Z, Wang J. Artificial neural network-based nonlinear algebraic models for large eddy simulation of turbulence. Physics of Fluids, 2020, 32: 115101 doi: 10.1063/5.0025138
    [29] 谢晨月, 袁泽龙, 王建春等. 基于人工神经网络的湍流大涡模拟方法. 力学学报, 2021, 53(1): 1-16 (Xie Chenyue, Yuan Zelong, Wang Jianchun, et al. Artificialneural network-based subgrid-scale models for large-eddy simulation of turbulence. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(1): 1-16 (in Chinese)
    [30] Weatheritt J, Sandberg RD. A novel evolutionary algorithm applied to algebraic modifications of the RANS stress−strain relationship. Journal of Computational Physics, 2016, 325: 22-37 doi: 10.1016/j.jcp.2016.08.015
    [31] Ferreira C. Algorithm for solving gene expression programming: a new adaptive problems. Complex System, 2001, 13(2): 87-129
    [32] Lav C, Sandberg RD, Philip J. A framework to develop data-driven turbulence models for flows with organised unsteadiness. Journal of Computational Physics, 2019, 383: 148-165 doi: 10.1016/j.jcp.2019.01.022
    [33] Weatheritt J, Zhao Y, Sandberg RD, et al. Data-driven scalar-flux model development with application to jet in cross flow. International Journal of Heat and Mass Transfer, 2020, 147: 118931 doi: 10.1016/j.ijheatmasstransfer.2019.118931
    [34] Reissmann M, Hasslberger J, Sandberg RD, et al. Application of gene expression programming to a-posteriori LES modeling of a Taylor Green vortex. Journal of Computational Physics, 2021, 424: 109859 doi: 10.1016/j.jcp.2020.109859
    [35] Schoepplein M, Weatheritt J, Sandberg RD, et al. Application of an evolutionary algorithm to LES modelling of turbulent transport in premixed flames. Journal of Computational Physics, 2018, 374: 1166-1179 doi: 10.1016/j.jcp.2018.08.016
    [36] Weatheritt J, Sandberg RD. The development of algebraic stress models using a novel evolutionary algorithm. International Journal of Heat and Fluid Flow, 2017, 68: 298-318 doi: 10.1016/j.ijheatfluidflow.2017.09.017
    [37] Akolekar HD, Weatheritt J, Hutchins N, et al. Development and use of machine-learnt algebraic Reynolds stress models for enhanced prediction of wake mixing in LPTs. Journal of Turbomachinery, 2019, 141(4): 041010 doi: 10.1115/1.4041753
    [38] Batcherlor GK. Diffusion in a field of homogeneous turbulence. Austral. J. Sci. Res., 1949, 2: 437-450
    [39] Daly BJ, Harlow FH. Transport equations in turbulence. Physics of Fluids, 1970, 13(11): 2634-2649 doi: 10.1063/1.1692845
    [40] Younis BA, Speziale CG, Clark TT. A rational model for the turbulent scalar fluxes. Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences, 2005, 461(2054): 575-594
    [41] Wu JL, Xiao H, Sun R, et al. RANS equations with explicit data-driven Reynolds stress closure can be ill-conditioned. Journal of Fluid Mechanics, 2019, 869: 553-586 doi: 10.1017/jfm.2019.205
    [42] Thompson RL, Sampaio LEB, de Bragança Alves FAV, et al. A methodology to evaluate statistical errors in DNS data of plane channel flows. Computer & Fluids, 2016, 130: 1-7
    [43] Poroseva SV, Colmenares JD, Murman SM. On the accuracy of RANS simulations with DNS data. Physics of Fluids, 2016, 28(11): 115102 doi: 10.1063/1.4966639
    [44] Zhao Y, Akolekar HD, Weatheritt J, et al. RANS turbulence model development using CFD-driven machine learning. Journal of Computational Physics, 2020, 411: 109413 doi: 10.1016/j.jcp.2020.109413
    [45] Pichler R, Sandberg RD, Michelassi V, et al. Investigation of the accuracy of RANS models to predict the flow through a low-pressure turbine. Journal of Turbomachinery, 2016, 138: 121009 doi: 10.1115/1.4033507
    [46] Akolekar HD, Zhao Y, Sandberg RD, et al. Integration of machine-learning and computational fluid dynamics to develop turbulence models for improved turbine-wake mixing prediction. ASME Turbo Expo, GT2020-14732, 2020
    [47] Weatheritt J, Pichler R, Sandberg RD, et al. Machine learning for turbulence model development using a high-fidelity HPT cascade simulation. ASME Turbo Expo, GT2017-63497, 2017
    [48] Akolekar HD, Sandberg RD, Hutchins N, et al. Machine-learnt turbulence closures for low-pressure turbines with unsteady inflow conditions. Journal of Turbomachinery, 2019, 141(10): 101009 doi: 10.1115/1.4043907
    [49] Ng CS, Ooi A, Lohse D, et al. Vertical natural convection: application of the unifying theory of thermal convection. Journal of Fluid Mechanics, 2015, 764: 349-361 doi: 10.1017/jfm.2014.712
    [50] Xu X, Ooi A, Sandberg RD. Data-driven algebraic models of the turbulent Prandtl number for buoyancy-affected flow near a vertical surface. International Journal of Heat and Mass Transfer, 2021, 179: 121737 doi: 10.1016/j.ijheatmasstransfer.2021.121737
    [51] Bodart J, Coletti F, Bermejo-Moreno I, et al. High-fidelity simulation of a turbulent inclined jet in a crossflow. Center for Turbulence Research Annual Research Briefs, 2013, 19: 263-275
    [52] Sakai E, Takahashi T, Watanabe H. Large-eddy simulation of an inclined round jet issuing into a crossflow. International Journal of Heat and Mass Transfer, 2014, 69: 300-311 doi: 10.1016/j.ijheatmasstransfer.2013.10.027
    [53] Akolekar HD, Waschkowski F, Zhao Y, et al. Transition modeling for low pressure turbines using computational fluid dynamics driven machine learning. Energies, 2021, 14: 4608 doi: 10.3390/en14154608
    [54] Pacciani R, Marconcini M. Calculation of high-lift cascades in low pressure turbine conditions using a three-equation model. Journal of Turbomachinery, 2011, 133: 1-9
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出版历程
  • 收稿日期:  2021-08-13
  • 录用日期:  2021-08-30
  • 网络出版日期:  2021-08-31
  • 刊出日期:  2021-10-26

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