Some issues related to the modeling of interfacial areas in gas-liquid flows I. The conceptual issues

Two-phase flow modeling has been under constant development for the past fo rty years. valid for two-phase flows where the phases are strongly coupled to the two-fluid model valid for two-phase flows where the phases are a pri ori weakly coupled. However the latter model has been used extensively in c omputer codes because of its potential in handling many different physical situations. The two-fluid model is based on the balance equations for mass, momentum an d energy, averaged in a certain sense and expressed for each phase and for the interface between the phases. The difficulty in using the two-fluid mod el stems from the closure relations needed to arrive at a complete set of p artial differential equations describing the flow. These closure relations should supply the information lost during the averaging of the balance equa tions and should specify in particular the interactions of mass, momentum a nd energy between the phases. Another requirement for the interaction terms is that they should satisfy the interfacial balance equations. Some of the se terms such as the added mass term or the lift force term do not depend o n the interfacial area but some others do, such as the mass transfer term, the drag term or the heat flux term. It is then necessary to model the inte rfacial area in order to evaluate the corresponding fluxes. Another benefit resulting from the modeling of the interfacial area would be to replace th e usual static flow pattern maps which specify the flow configuration by a dynamic follow-up of the flow pattern. All these reasons explain why so muc h effort has been put during the past twenty years on the modeling and meas urement of the interfacial area in two-phase flows. This article contains t wo parts. The first one deals with the conceptual issues and has the follow ing objectives: 1. to give precise definitions of the interfacial area concentrations; 2. to explain the origin of the interfacial area concentration transport eq uation suggested by M. Ishii in 1975; 3. to explain some paradoxical behaviors encountered when calculating the i nterfacial area concentration transport velocity. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.