Integrating physics-informed neural networks with partitioned coupling strategy for modeling conjugate heat transfer

doi:10.11949/0438-1157.20221174

Abstract

Abstract:

Physics-informed neural network (PINN) realizes deep learning with embedded physical knowledge by mathematically encoding partial differential equations, and has been successfully applied in the fields of fluid mechanics and heat transfer. However, due to the strong coupling of heat transfer in fluids and heat conduction in solids, regular PINN methods are difficult to effectively solve the conjugate heat transfer problems that commonly exist in the aforesaid fields. As a widely-used partitioned coupling strategy, the heat transfer coefficient forward temperature backward (hFTB) can feasibly deal with complex coupling relation in the interface by solving the fluid and solid domains separately. In this work, based on real physical property systems, a modeling strategy that combines partitioned coupling and PINN is proposed by using hFTB approach. Taking 2-D and 3-D conjugate heat transfer models as examples, the results of multi-physics fields obtained by the proposed strategy are compared with those by using conventional CFD simulation. The resulting maximum absolute errors of the solid temperature of the 2-D and 3-D models are only 0.19 K and 2.12 K, respectively, which reflects the effectiveness of the proposed strategy in modeling conjugate heat transfer under the real physical property systems.

Key words: physics-informed neural networks, partial differential equations, partitioned coupling, conjugate heat transfer, heat transfer coefficient forward temperature backward

摘要：

物理信息神经网络（PINN）通过对偏微分方程组进行数学编码，实现了内嵌物理知识的深度学习，已成功地应用于流体力学和传热领域。但是，由于固体导热和流体传热间强耦合关联，通用的PINN难以有效求解上述领域内普遍存在的共轭传热问题。作为应用较为广泛的分区耦合策略，传热系数正向温度反向法可通过分别独立求解流体域和固体域来灵活处理界面处的复杂耦合关系。本工作基于真实物性体系，利用传热系数正向温度反向法构建分区耦合PINN建模策略。以共轭传热二维和三维模型为例，将分区耦合PINN预测的多物理场结果与常规的CFD软件模拟结果进行对比，结果显示二维模型和三维模型的固体温度最大绝对误差分别为0.19 K和2.12 K，表明了分区耦合PINN策略处理真实物性下共轭传热建模问题的有效性。

关键词: 物理信息神经网络, 偏微分方程, 分区耦合, 共轭传热, 传热系数正向温度反向法

CLC Number:

TQ 021.3

Zhibin LU, Yimeng LI, Chang HE, Bingjian ZHANG, Qinglin CHEN, Ming PAN. Integrating physics-informed neural networks with partitioned coupling strategy for modeling conjugate heat transfer[J]. CIESC Journal, 2022, 73(12): 5483-5493.

陆至彬, 李依梦, 何畅, 张冰剑, 陈清林, 潘明. 集成分区耦合策略的物理信息神经网络模拟共轭传热过程研究[J]. 化工学报, 2022, 73(12): 5483-5493.

Figures/Tables 11

Fig.1 Flow chart of the hFTB method

Fig.2 Schematic of a typical PINN framework

Fig.3 The conjugate heat transfer model

Table 1 Geometric dimension of the 3-D conjugate heat transfer model

几何体	尺寸/cm
通道（L_c×D_c×H_c）	5.0 × 1.0 × 1.0
底座（L_b×D_b×H_b）	1.0 × 0.6 × 0.2
翅片（L×D×H）	1.0 × 0.6 × 0.4
热源（L_s×D_s）	0.4 × 0.2

Table 2 Fluid and solid properties used in the simulation

物性	单位	空气	铜
密度ρ	kg/m³	1.177	8978
热导率κ	W/(m·K)	0.0267	387.6
比热容C_p	J/(kg·K)	1007	381
黏度μ	kg/(m·s)	1.8832×10^-5	—

Fig.4 The partitioned coupling PINN strategy methodological framework and optimization procedure

Table 3 Non-dimensional scaling parameters

模型	L_scale/m	t_scale/s	M_scale/kg	T_scale/K	Const/K
二维模型	0.1	0.1	1×10^-3	20	273.15
三维模型	0.01	0.01	1×10^-6	20	293.15

Fig.5 Temperature convergence records at the fluid-solid interface of the 2-D model

Fig.6 Comparison of the results of the 2-D model

Fig.7 Temperature convergence records at the fluid-solid interface of the 3-D model

Fig.8 Comparison of the results of the 3-D model

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