A deep learning framework for solving the prediction and reconstruction problem of Bingham fluid flow field

As a typical non-Newtonian fluid, Bingham fluid is employed in a multitude of fields, including petroleum, construction, and the chemical industry. However, due to the intricate intrinsic properties of Bingham fluids and the necessity for precision and efficacy in specific engineering applications, the rapid and precise prediction and reconstruction of its flow field information has become a challenge and a focal point of contemporary research. In this paper, we introduce a novel deep-learning approach to address the two-dimensional laminar motion of Bingham fluids. The proposed Papanastasiou Regularization Physics-Informed Neural Network (PR-PINN) framework effectively predicts and reconstructs the flow field of Bingham fluids. Initially, the framework applies Papanastasiou regularization to the governing equations of Bingham fluids, enhancing the network's adaptability to solving the flow field problem by incorporating boundary conditions and an adaptive weight assignment strategy. We consider two scenarios: equal-diameter circular pipe flow and conical pipe flow. The PR-PINN network is utilized for flow field prediction and reconstruction. Our results show that PR-PINN achieves high accuracy in flow field prediction and can reconstruct velocity and pressure fields using limited measurement data. Based on these findings, we explore the impact of boundary constraints, the effect of large intrinsic parameters on prediction accuracy, and the influence of measurement points and boundary constraints on flow field reconstruction. In summary, the PR-PINN network exhibits satisfactory performance and significant potential for predicting and reconstructing Bingham fluid flow fields.