Prediction of bubble size distribution in cloud cavitation flow based on physics-informed neural network

The characterization of bubble size distribution (BSD) in the cloud cavitation region, which is critical for assessing cavitation erosion and noise, is currently inadequately captured by prevailing measurement techniques and numerical simulations. The population balanced equation (PBE) offers an effective framework for describing BSD, however, at a high computational cost. This study establishes an efficient approach to solve temporally averaged PBE using a physics-informed neural network (PINN) to determine the BSD in the cloud cavitation around a hydrofoil. By decomposing the PBE into two sub-equations for the number density n and the probability density function f, the multiscale complexity inherent in the PBE is effectively reduced. Two corresponding individual PINN networks, PINN-n and PINN-f, are created accordingly and trained to seek the solutions to the two sub-equations. Numerical simulations using large eddy simulation furnish the background flow field for the PBE, and experimental data at pointwise positions offer the boundary conditions of BSD. The reconstruction of void fraction from the solutions of number density and probability density function demonstrates that the PINN method is capable of solving the PBE with reasonable accuracy. A continuous mapping of BSD without requiring a prescribed distribution function can be acquired at any spatial location. The proposed method provides an efficient framework for predicting the BSD throughout the domain from sparse pointwise BSD information.