A novel game theoretical model and generalized Nash equilibrium for meso-Scale flow structure in bubble columns

This paper studies the meso-scale structure in the gas-liquid systems in bubble columns which are widely used in industrial engineering from a novel view of noncooperative games. Based on the dual-bubble-size (DBS) model in the literature [Yang et al, 2007] which extended the idea of "compromise-in-competition between dominant mechanisms" in the energyminimization-multi-scale (EMMS) model to the hydrodynamics in the bubble columns, this paper formulates the problem as a noncooperative game between the different dominant mechanisms which are regarded to optimize the respective objective functions, i.e., different energy consumptions. The conservation equations of system state variables are considered as constraints on the strategies in the game. Then we give the option of strategy variables in the game and prove their resonability as well as equivalence. Generalized Nash equilibrium (GNE) for the game is then defined as well as the algorithm is proposed.