Solution Method of Flow Field in the Narrow Rectangular Channel Based on Physics-informed Neural Network
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摘要: 为了探索物理约束神经网络（PINN）在热工水力计算领域的应用潜力，本研究选取了窄矩形通道内层流和湍流状态下的多个工况，使用计算流体动力学（CFD）方法获得标签数据，并将连续性方程和Navier-Stokes方程（N-S方程）嵌入到神经网络模型中进行预测。研究结果表明，对于窄矩形通道内的不可压缩流动，PINN模型能够准确还原层流工况下的流场特点；湍流工况下可通过调整模型的损失项权重，使预测解与CFD数值解达到较好的一致性。因此，PINN模型能够应用于窄矩形通道的流场计算，并可进一步为更多场景下的流场快速分析积累经验。
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关键词:
- 物理约束神经网络（PINN） /
- 窄矩形通道 /
- Navier-Stokes方程（N-S方程）
Abstract: To explore the application potential of Physics-informed Neural Network (PINN) in the field of thermal and hydraulic calculation, multiple working conditions for both laminar and turbulent flow in a narrow rectangular channel were calculated in this study. Computational Fluid Dynamics (CFD) was utilized to obtain label data, and the continuity equation and N-S equations were embedded into the neural network model for prediction. The results show that for the incompressible flow in the narrow rectangular channel, the PINN model can accurately restore the flow field characteristics for laminar flow conditions. For turbulent conditions, the weight of the loss term of the model can be adjusted to achieve good consistency between the predicted solution and the CFD numerical solution. Therefore, the PINN model can be applied to the flow field calculation of narrow rectangular channels, and can further accumulate experience for the rapid analysis of flow fields in more scenarios. -
图 5 PINN预测结果和参考值对比
Figure 5. Comparison between PINN Predicted Value and Reference Value
图 7 湍流工况中轴向速度U随y轴变化
Figure 7. Change of Velocity U along y-Axis in Turbulence Flow Condition
图 8 引入自适应权重方法后轴向速度U随y轴变化
Figure 8. Change of Velocity U along y-Axis with Self-adaptive Weight Method
表 1 PINN模型参数
Table 1. Parameters of PINN Model
模型参数 设置 网络层数 4~9 每层神经元数 60~100 激活函数 tanh 初始学习率 0.001 优化算法 Adam/L-BFGS 
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表 2 层流工况中各物理量误差平均值
Table 2. Average Value of Physical Variable Errors in Lamilar Flow Condition
物理量 U V P MAE 8.03×10−2 9×10−4 1.42×10−2 $ {\varepsilon } $/% 7.83 118.15 1.32
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