Formulation of steady-state void fraction through the principle of minimum entropy production

Abstract

The complexity of the actual operation of thermal engineering systems comprises multiphase interfacial phenomena evolving out of equilibrium. Therefore, their generalised formulation can contribute towards better understanding and control of these phenomena, eventually pushing the existing related technologies beyond the state-of-the-art. In this respect, variational principles are significant for a more comprehensive physical representation and for closing the problem, while obtaining relatively simpler mathematical formulations. In this study, a general variational formulation of dissipative two-phase flows based on the minimum entropy production is developed. In particular, this study provides a general expression of the entropy generation rate, which introduces interfacial contributions due to surface tension between different phases, and is used to estimate two-phase flow fraction based on Prigogine's theorem of minimum entropy generation. Subsequently, this formulation is investigated in terms of different assumptions and pressure drop models, and employed to clarify the implementation of Prigogine's theorem to obtain the widely-accepted Zivi's expression of void fraction and the effect of different assumptions on the deviation from his expression. A new expression is finally obtained to cover laminar flow conditions, which are implicitly excluded from the applicability of Zivi’s expression.