The interfacial modes and modal causality in a dispersed bubbly turbulent flow

While data-driven analysis has demonstrated significant success in single-phase flow systems, its application to multi-phase flows has been relatively limited with fewer examples. In this study, we present a modal analysis and modal causality analysis of dispersed bubbly turbulent flow, with the aim of providing new insights into the interfacial gas-liquid interaction. Our study employs an in-house coupled level-set volume-of-fluid solver, which is combined with a modified fast Fourier transforms algorithm to perform interface-resolved direct numerical simulations in a turbulent channel flow with 96 bubbles occupying 5.4% volume. In the downward flow orientation, we observe that bubbles are mainly clustered in the channel center, producing pseudo-turbulence with isotropic characteristics. We apply the proper orthogonal decomposition method to the phase-resolved, three-dimensional velocity field, radius of the bubble as well as the surface tension force in order to extract the dominant modes. Notably, our results reveal the presence of two energetic modes in both the gas and liquid phases, as well as the interface, namely, the vortex-ring mode and the quadrupolar mode. We further investigate the causal relationship across the gas-liquid interface using the modal information transfer entropy. Our findings demonstrate a strong causality between the gas phase and the surface tension, whereas the causality between the liquid phase and surface tension is comparatively weak due to the multi-scale characteristics of the turbulent fields. Overall, our novel approach to investigating the interfacial gas-liquid interaction in dispersed bubbly turbulent flow provides valuable insights that enhance physical understanding and could lead to improved flow control and efficiency in a range of industrial processes. The identification of previously unidentified energetic modes using the POD method has the potential to advance research in this field, with potential implications for future design of control strategies in complex systems.