DATA-DRIVEN TURBULENCE MODELLING BASED ON GENE-EXPRESSION PROGRAMMING
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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.Abstract: Computational fluid dynamics (CFD) is an important tool for turbulence research, and Reynolds-averaged Navier−Stokes (RANS) has been widely applied in many applications such as aerospace engineering. The predictive accuracy of RANS is usually significantly impacted by turbulence models, while models used in practical RANS simulations are sometimes not accurate enough. Recently, data driven turbulence modelling has gained its popularity, and different machine learning methods have been introduced to develop turbulence models with enhanced accuracy. In the present study, we review recent developments in data-driven turbulence modelling with the gene-expression-programming (GEP) method. We start with a brief introduction of the GEP method applied to turbulence modelling. The topics discussed in this paper include basic concepts of the GEP algorithm, training frameworks for explicit algebraic stress models and turbulent heat flux models, testing methods for data-driven models, and setup of cost functions. Thereafter, the applications of the GEP method in different areas, e.g. wake mixing for gas turbines, natural convection between two vertical plates, and jet in cross flow, have been discussed in details. Based on the given results, the trained GEP models are able to improve the predictive accuracy for different key parameters, including the kinetic wake loss and the turbulent heat flux in these cases. Furthermore, as the model equations are explicitly given by the GEP method, the trained models, either the explicit algebraic stress models or the turbulent heat flux models, can be further analyzed. Moreover, models trained with the CFD-driven methods have been applied in practical RANS calculations of different cases, and the results are shown to be accurate and robust in a posteriori tests. The GEP method has also been applied in sub-grid scale stress modelling in large-eddy simulations and also boundary layer transition, in which the method has demonstrated a great potential in different turbulence modelling areas.
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图 1 机器学习湍流建模示意图
Figure 1. Schematic for turbulence modelling with machine learning methods
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 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 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
表 1 涡轮叶栅尾流混合算例
Table 1. Parameters of turbine wake mixing cases
Cases Re Ma Flow features HPT A 570 000 0.9 transition & shocks HPT B 1 100 000 0.9 transition & shocks LPT C 60 000 0.4 transition & open separation LPT D 100 000 0.4 transition & closed separation 
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