基于数据驱动管道流体湍流模型的系数修正及流动特性分析

doi:10.19596/j.cnki.1001-246x.8517

摘要/Abstract

摘要：

为提高RANS湍流模型数值模拟的精度，基于人工神经网络对RANS中标准k-ε湍流模型系数进行预测与修正，并对受壁面射流扰动的管道流场进行分析。首先建立管道流的有限元模型，同时考虑壁面射流对管内流体流动状态的影响，对管道流的流动进行有限元仿真，得到管道流受扰动后的速度场分布。其次，搭建预测标准k-ε湍流模型系数的神经网络模型，预测描述管道内速度场变化趋势的标准k-ε湍流模型系数。最后, 将新的系数带入有限元模型计算，并与实验数据对比，发现修正后的湍流模型对管道各部分速度场的模拟精度均有较大提升，对标准k-ε湍流模型系数的预测与修正可以提高模型对管道内速度场变化趋势的模拟精度。

关键词: 人工神经网络, 数据驱动, k-ε湍流模型, 管道流, 壁面射流

Abstract:

To improve accuracy of the Reynolds-averaged Navier-Stokes (RANS) turbulence model simulation, relevant parameters in the standard k-ε model control equation are predicted and modified based on artificial neural networks (ANN). An investigation is analyzed for how the fluid field is affected by the wall injection as part of accuracy improvement processes. After initializing the finite element (FE) model of the fluid field, a standard k-ε turbulence model is used to perform relevant turbulent calculations. Meanwhile, circumstances of how wall injection affected the fluid field in the pipe are also added in the FE model. Transformations of the fluid are analyzed by the FE method. Thus, velocity field distribution after the wall injection is interpreted. Moreover, a neural network(NN) intelligent algorithm is established to predict standard k-ε model parameters. The NN model′s input is considered as a ratio of the velocity component in the streamwise direction and the average velocity of the fluid in the pipe. Parameters in the turbulence model control equation are network′s outputs. Thus, the network predicts standard k-ε model control equation parameters to describe the velocity field trend. The final step is retrieving the outcome parameters into the FEM calculation. Comparing with experiment data, simulation accuracy of the velocity field is significantly improved with the modified turbulence model. It shows that predicting and adjusting the standard k-ε model control equation parameters improves simulation accuracy of the velocity field trends.

Key words: artificial neural networks, data-driven, k-ε turbulence model, pipe flow, wall injection

梁炜光, 桑建兵, 田红艳, 段文杰, 陶雅萍, 李烽韬. 基于数据驱动管道流体湍流模型的系数修正及流动特性分析[J]. 计算物理, 2023, 40(1): 57-66.

Weiguang LIANG, Jianbing SANG, Hongyan TIAN, Wenjie DUAN, Yaping TAO, Fengtao LI. Flow Characteristic Analysis of Pipe Flow and Turbulence Model Coefficient Correction Based on Data-driven[J]. Chinese Journal of Computational Physics, 2023, 40(1): 57-66.

图/表 12

图1 管道内部流场的几何模型

Fig.1 Geometric model of the pipe flow field

图2 法向注射下的有限元模型网格划分

Fig.2 Meshing details of the pipe flow field under normal injection

表1 参数及值域

Table 1 Parameters and their domains in parameter space

参数	值域	固定增量
C_μ	[0.04, 0.16]	0.001
C_1ε	[1.2, 1.68]	0.004
C_2ε	[1.68, 2.16]	0.004
σ_k	[0.76, 1.24]	0.004
σ_ε	[1.06, 1.54]	0.004

图3 神经网络流程图

Fig.3 Flow chart of neural network

图4 神经网络结构

Fig.4 Structure of neural network

图5 对实验中管轴中心线上顺流向方向速度分量与管道内流体平均速度的比值进行FFT处理

Fig.5 FFT curve for the experiment data

图6 损失函数曲线

Fig.6 The curve of loss function

表2 神经网络预测湍流模型参数的统计指标

Table 2 Statistical indicators of turbulence model parameters

参数	MSE	RMSE	MAE	R²
C_μ	0.000 723	0.026 888	0.022 188	0.973 971
C_1ε	0.001 208	0.034 756	0.027 804	0.969 357
C_2ε	0.001 493	0.038 639	0.032 515	0.965 159
σ_k	0.001 084	0.032 924	0.024 412	0.971 609
σ_ε	0.001 218	0.034 899	0.028 719	0.967 306

表3 神经网络预测的湍流模型控制方程参数

Table 3 Prediction of k-ε turbulent model parameters with NN

C_μ	C_1ε	C_2ε	σ_k	σ_ε
0.083 209 09	1.385 580 1	1.910 502 9	0.971 979 1	1.264 098 8

图7 基于神经网络修正前后的标准k-ε湍流模型预测的velocity u/velocity曲线与实验数据

Fig.7 Velocity u/velocity curve based on the initial standard k-ε turbulence model, the modified standard k-ε turbulence model and experimental data

图8 基于修正后标准k-ε湍流模型预测的壁面注射流体扰动管内湍流情况下的管道各部分速度场

Fig.8 Velocity field of the pipe predicted with the modified standard k-ε turbulence model with wall injection

图9 基于神经网络修正前后的标准k-ε湍流模型预测的管道下游横截面平均速度

Fig.9 Mean velocity of downstream cross-section of the pipe based on the initial and modified standard k-ε turbulence model

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