On the use of explainable deep learning to assess the bubble-induced turbulence model for multi-phase flows

The widely used Euler–Euler two-fluid approach for numerical simulations of bubbly flows requires several closure models. Among them, Bubble Induced Turbulence (BIT) models are needed to model turbulence generation and dissipation due to liquid–gas interactions. Understanding how BIT models affect the average flow quantities is key for the improvement of such models. Explainable Deep Learning is rapidly growing over many research fields as a powerful tool to gain understanding of complex models. In the present work, the Sato BIT model is analyzed by means of SHapley Additive exPlanations values, identifying regions of importance among different flow quantities, such as gas distribution, liquid velocity, and turbulent kinetic energy. The results show that Sato effectively increases the stability of the system through an extra turbulent viscosity, leading to higher energy dissipation. Key regions were identified where important flow instabilities were dampened, exhibiting less sensitivity to temporal velocity fluctuations. This work presents a novel methodology to study BIT models, encouraging further studies comparing different modeling approaches.