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In order to analyze accurately the thermohydrodynamic behavior of gas-liquid two-phase flows, it is important to obtain the appropriate basic equations of mass, momentum and energy conservation. The basic equations presently used are obtained based on the two-fluid model assuming that both phases are continuous fluid. However, when these equations are applied to a dispersed flow such as a bubbly or droplet flow, problems arise regarding matters such as the physical interpretation of each term and ill-posedness. In view of the above, simplified and physically reasonable basic equations for gas-liquid dispersed flows were developed based on the assumptions that phase change rate and/or chemical reaction rate are not so large at interface, that there is no heat generation in a dispersed phase and that a dispersed phase can be treated as isothermally rigid particles. Based on the local instant formulation of mass, momentum and energy conservation of the dispersed flow, time-averaged equations were obtained. It is shown that, in the derived averaged momentum equation, the terms of pressure gradient and viscous momentum diffusion do not appear and that, in the energy equation, the term of molecular thermal diffusion heat flux does not appear. These characteristics of the derived equations were shown to be very consistent concerning the physical interpretation of the gas-liquid dispersed flow. Furthermore, the basic equations obtained always maintained their well-posedness as regards the initial value problem.

Basic Equations and Their Mathematical Feature of Gas-Liquid Two-Phase Dispersed Flow Based on Two-Fluid Model