Transfer learning through physics-informed neural networks for bubble growth in superheated liquid domains

In this paper, a physics-informed neural network (PINN) technique is developed to study the heat and mass transfer for the process of vapour bubble growth in a superheated liquid domain and tested using three working fluids including water, R-134a and FC-72. The work represents a novel step in the development of PINNs for phase change scenarios where surface tension effects dominate, and acts as a necessary validation stage before PINN techniques can be applied to complex boiling analysis. Initially, a forward analysis was performed using water and R-134a as working fluids. For each of these investigations, the PINN algorithm was trained on 50 % of the available CFD data. The proposed algorithm was able to accurately infer velocity fields, particularly in the near-interfacial region. The resultant circulatory flow was found to maintain the desired circular shape of the growing bubbles. As a result, when predicting the evolution of a water vapour bubble, the developed PINN algorithm produced a reduction in peak error by 0.87 % compared to CFD reference data, and 3.42 % reduction in peak error for prediction of the evolution of the R-134a vapour bubble. To test and optimise the transfer learning capabilities of the developed methodology, the evolution of an FC-72 vapour bubble in superheated FC-72 was predicted without supplying supporting observational data. For this scenario, the PINN algorithm produced a peak error within 1.3 % of the unobserved CFD reference data. The proposed approach confirms the robustness of PINN methodologies as a method of solving phase-change problems where surface tension plays a pivotal, promising to expedite parametric studies in practice. This study represents a pioneering effort in the development of PINNs for phase change by applying the current algorithm to investigate bubble growth within superheated liquid domains, serving as a basis for the application of PINNs for boiling problems and as a benchmark for inverse training strategy.