Parameterized physics-informed neural networks (P-PINNs) solution of uniform flow over an arbitrarily spinning spherical particle

Abstract

Neural network-based approaches have emerged as alternatives to conventional computational fluid dynamics (CFD) in solving multiphase flow problems. However, most of these approaches are based on data-driven machine learning methods that require training datasets prepared beforehand through CFD simulations or experiments and cannot be used independently. This study presents an unsupervised parameterized physics-informed neural networks (P-PINNs) approach for obtaining the full flow field information over a multi-dimensional parametric space. This approach is then applied to solve the three-dimensional flow around an arbitrarily rotating sphere subjected to a cross-flow. This solution is obtained for a continuous range of three parameters: the Reynolds number based on cross-flow (Re∈[1,400]), non-dimensional streamwise and spanwise angular velocity components (Ωx∗,Ωy∗∈[−3,3]). The predictions from the P-PINNs model are compared against particle-resolved direct numerical simulation (PR-DNS) results, demonstrating that the neural network model predicts all flow variables (velocity, pressure, and their spatial derivatives) accurately with R2≳0.9. The force and torque on the particle obtained from the P-PINNs model are also compared well against the corresponding PR-DNS results with R2>0.94. The key observation is that the computational cost of the unsupervised parameterized neural network model training and deployment is substantially lower than performing numerous conventional CFD simulations to systematically vary the parameters. Furthermore, once trained, the resultant neural network model is substantially more compact than the huge database of discretized numerical solutions. The P-PINNs model is then used to reveal several interesting flow features and phenomena about the rotating sphere, including flow symmetry, secondary drag and lift, critical Reynolds number, flow bifurcation, and flow separation. This study presents P-PINNs as an efficient alternative for solving parameterized flow problems, demonstrating its practical usage in flow physics discovery with the example of flow past an arbitrarily rotating sphere.