Game-theoretical explorations of the mesoscale flow structure and regime transitions in bubble columns

Understanding the mesoscale structure and regime transition in bubble columns is of great significance for reactor design and scaleup.Based on the energy-minimization multiscale(EMMS)model,a noncooperative game model with constraints is proposed to investigate the structural properties of gas-liquid systems in which small and large bubbles are chosen as players and the energy consumption form the objective function.The conservation equations of the system can be regarded as the constraints of the game.For the formulated noncooperative game model,the concept of the generalized Nash equilibrium(GNE)is used to characterize the solution.An algorithm is developed to numerically compute the GNE and some important structural parameters in the system.The numerical results show the existence of the GNE for all values of the superficial gas velocity Ug.As Ug varies,the trends in the state variables can be observed and the critical point of Ug identified.The overall trend of the flow regime transition agrees with the original EMMS model and experimental results,although the GNE calculation also reveals different single-bubble dominant mechanisms with increasing Ug.