Flow Characteristic Analysis of Pipe Flow and Turbulence Model Coefficient Correction Based on Data-driven

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

Abstract

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

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.

Figures/Tables 12

Fig.1 Geometric model of the pipe flow field

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

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

Fig.3 Flow chart of neural network

Fig.4 Structure of neural network

Fig.5 FFT curve for the experiment data

Fig.6 The curve of loss function

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

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

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

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

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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