Prediction of the Flow Field in Two-Phase Jets with Phase Changes Using Nested Physics-Informed Neural Network

This is the authors' abstract. We don't add key points for this paper.

Nozzle jets are widely used in the industrial field, but they are often accompanied by phase changes. The phase change process directly impacts changes in the flow field and the performance of the jet. Simulations of two-phase jets with phase changes are complex, involving multiple physical fields and multi-scales. To address this, we propose a nested physics-informed neural network (N-PINN) to reconstruct flow fields from sparse monitoring data. By decoupling phase change and flow dynamics into two sub-models, N-PINN achieves higher accuracy than neural network (ANN) and PINN. It reduces the relative error in pressure ratio along the centerline of nozzle by up to 86.57% and 37.33%, and in the condensation shock region, local errors are reduced by up to 88.74% and 54.87%, respectively. N-PINN also demonstrates strong temporal extrapolation capability, accurately predicting transient flow evolution. In particular, it achieves relative errors of 3.46%, 3.54%, and 4.02% at three progressive time steps, and compared to ANN, reduces pressure ratio error beyond the training horizon by up to 9.22% globally and 38.41% in the condensation shock region. This study provides an efficient surrogate model for two-phase jets with explicit consideration of physical mechanisms, while offering valuable reference for experimental design.