跨声速流动替代湍流模型的一种神经网络方法

朱林阳; 孙旭翔; 刘溢浪; 张伟伟

doi:10.1007/s10409-021-09057-z

One neural network approach for the surrogate turbulence model in transonic flows

doi: 10.1007/s10409-021-09057-z

Zhu Linyang^{1, 2},
Sun Xuxiang¹,
Liu Yilang³,
Zhang Weiwei^{1,*
, ,}

1.
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China
2.
State Key Laboratory of Aerodynamics, China Aerodynamics R&D Center, Mianyang 621000, China
3.
Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China

Funds:

the National Numerical Wind Tunnel Project Grant

and the National Natural Science Foundation of China Grant

More Information

Corresponding author: Zhang Weiwei, E-mail address: aeroelastic@nwpu.edu.cn (Weiwei Zhang)

摘要

摘要: 随着深度神经网络等人工智能技术的发展, 数据驱动的机器学习方法也开始广泛应用于湍流模型的改进和构建中. 针对航空工程中的高雷诺数湍流, 我们之前的工作已经建立了适用于不同来流条件下二维亚声速翼型绕流的数据驱动模型. 本工作中, 采用全连接神经网络构建了三维跨声速机翼绕流中涡黏封闭的代理模型, 这在现有的工作中研究较少. 所构建模型仅基于ONERA-M6机翼两个状态的数据集, 并与Navier-Stokes方程求解器耦合. 采用四个不同机翼的亚、跨声速标模来测试模型性能. 迭代过程稳定并获得了收敛解, 实现了对原RANS模型的替代. 通过与SA模型计算的源数据对比, 结果表明, 所提出的模型能够很好地泛化到测试算例中. 在所有算例中, 截面上摩擦阻力系数的平均误差小于4%. 本工作表明将数据驱动方法应用于湍流模型化是可行的, 本文的建模模式是有效的.
Abstract: With the rapid development of artificial intelligence techniques such as neural networks, data-driven machine learning methods are popular in improving and constructing turbulence models. For high Reynolds number turbulence in aerodynamics, our previous work built a data-driven model applicable to subsonic airfoil flows with different free stream conditions. The results calculated by the proposed model are encouraging. In this work, we aim to model the turbulence of transonic wing flows with fully connected deep neural networks, where there is less research at present. The proposed model is driven by two flow cases of the ONERA (Office National d’Etudes et de Recherches Aérospatiales) wing and coupled with the Navier-Stokes equation solver. Four subcritical and transonic benchmark cases of different wings are used to evaluate the model performance. The iteration process is stable, and final convergence is achieved. The proposed model can be used to surrogate the traditional Reynolds averaged Navier-Stokes turbulence model. Compared with the data calculated by the Spallart-Allmaras model, the results show that the proposed model can be well generalized to the test cases. The mean relative error of the drag coefficient at different sections is below 4% for each case. This work demonstrates that modeling turbulence by data-driven methods is feasible and that our modeling pattern is effective.
- Deep neural network /
- Turbulence modeling /
- Transonic /
- High Reynolds number

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1. Schematic of the adopted mixing length.

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2. Schematic diagrams of a fully connected deep neural network and b single neuron.

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3. Schematic of some activation functions.

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4. Coupling of the proposed model with CFD solver.

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5. The error evolution of the training and validation sets (refer to the left y-axis) and the evolution of stability loss (refer to the right y-axis).

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6. View of meshes over the ONERA-M6 wing.

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7. Comparison of C_p distributions at several sections obtained with the SA model and the ML model as well as the experimental results for case P1.

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8. Comparison of C_f distributions at several sections obtained with the SA model and ML model for case P1.

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9. Comparison of C_f distributions at several sections obtained with the SA model and the ML model for case P2.

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10. Comparison of C_f contours at the upper surface of the ONERA-M6 wing for cases P1 and P2.

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11. Comparison of C_f distributions at several sections obtained with the SA model and the ML model for case P3.

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12. Comparison of C_f distributions at several sections obtained with the SA model and ML model for case P4.

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13. Comparison of C_f contours at the upper surface of the DPW-W1/W2 wing for cases P3 and P4.

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14. Comparison of friction drag coefficient C_d,f at several sections for test cases.

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15. Coupling of the data-driven turbulence model with the CFD solver.

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16. Residual history of density for test cases.

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Table 1. The flow features used as the regression input, where ${‖ \cdot ‖}_{\infty}$ denotes the infinity norm

Feature	Description	Sign
Q1	Density	ρ
Q2	Nonorthogonality between velocity and its gradient	$\| u_{i} u_{j} \frac{\partial u_{i}}{\partial x_{j}} \| / {‖ \nabla U ‖}_{\infty}$
Q3	Pressure gradient along a streamline	$u_{i} \frac{\partial P}{\partial x_{i}}$
Q4	Entropy	S′
Q5	Local velocity scaled by the friction velocity	$\sqrt{u^{2} + v^{2}} / u_{τ}$
Q6	Local velocity	$\sqrt{u^{2} + v^{2}}$
Q7	Strain rate	${‖ S^{+} ‖}_{\infty}$
Q8	Rotation rate	${‖ R^{+} ‖}_{\infty}$

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Table 2. The training parameters

Parameters	Value
Batch normalization [48]	Adopted
Activation function	Tanh
Optimizer	Adamax
Learning rates	ReduceLROnPlateau
λ₁	1×10⁻⁷
λ₂	2×10⁻⁶
λ₃	1

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Table 3. Spanwise locations of different wings

Section	y/b
Section	M6	DPW-W1/DPW-W2
1234567	0.200.440.650.800.900.950.99	0.0260.1570.2980.4200.5110.6820.945

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Table 4. The training, validation and test cases

	Case	Ma	α (°)	Re (×10⁶)	Wing
Training	T1	0.76	1.25	11.72	ONERA-M6
Training	T2	0.79	3.70	11.72	ONERA-M6
Validation	−	0.83	3.02	11.72	ONERA-M6
Test	P1	0.84	3.06	11.72	ONERA-M6
	P2	0.699	3.06	11.72	ONERA-M6
	P3	0.76	0.5	5	DPW-W1
	P4	0.76	0.5	5	DPW-W2

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One neural network approach for the surrogate turbulence model in transonic flows

doi: 10.1007/s10409-021-09057-z

Corresponding author: Zhang Weiwei, E-mail address: aeroelastic@nwpu.edu.cn (Weiwei Zhang)

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One neural network approach for the surrogate turbulence model in transonic flows

doi: 10.1007/s10409-021-09057-z

Corresponding author: Zhang Weiwei, E-mail address: aeroelastic@nwpu.edu.cn (Weiwei Zhang)

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