Modeling of turbulent transport term of interfacial area concentration in gas–liquid two-phase flow

Abstract

A new and rigorous modeling of basic transport equation and constitutive equations of turbulent transport terms of interfacial area concentration was carried out.Based on these local instant formulation, basic transport equation of interfacial area concentration was rigorously formulated in term of spatial correlation functions of characteristic function (local instant volume fraction) and its directional derivative of each phase. In the basic transport equations, interfacial area concentration is transported by averaged interfacial velocityIn the previous models, interfacial velocity is roughly approximated by velocity of each phase.In the present model, interfacial velocity is rigorously formulated in term of spatial correlation functions of characteristic function and velocity of each phase and their directional derivatives. In this new formulation, the averaged interfacial velocity was shown to be correlation functions of fluctuation of velocity and local instant void fraction and their derivatives which reflect the transport of interfacial area concentration due to interaction between interfacial area and turbulence of each phase. Basic conservation equations of spatial correlation functions of characteristic function and velocity of each phase were also derived based on the conservation equations momentum and its fluctuation of each phase. For practical purpose, further modeling of this turbulent transport terms of interfacial area concentration was carried out. As a result, constitutive equations of turbulent diffusion and lateral migration of interfacial area concentration were obtained which can be applied to various flow regime of two-phase flow. I. IntroductionThe two-phase flow phenomenon is playing an important role about safety issues of a nuclear reactor. In order to analyze two-phase flow phenomena, various models such as homogeneous model, slip model, drift flux model and two-fluid model have been proposed. Among these models, the two-fluid model (Ishii (1975), Delhaye (1968) is considered the most accurate model because this model treats each phase separately considering the phase interactions at gas-liquid interfaces.More realistic evaluation is attainable especially by taking a multi-dimensional effect into consideration appropriately. That is, it is desirable that many nuclear reactor safety problems are solved by using the two-phase CFD tools, which simulate the complex two-phase flows with a finer space and time resolution than that used in the present two-fluid model codes such as RELAP, TRAC, CATHARE, and ATHLET. There are, however, the following two difficulties to be resolved.(1) The CPU time drastically increases as the grid becomes fine.(2) There is no reliable and accurate modeling of the interfacial area for a finer mesh. The JNES have started the plan shown in Table 1 to prepare the two-phase CFD tool.

Large eddy simulation of spray atomization with a probability density function method

“…Some simplifications can be introduced in very dilute flows,where droplet or bubble scales are typically much smaller than the volume size: usually the cell-size h V 1ß3 . Kocamustafaogullari and Ishii (1995); Morel (2007); Kataoka et al (2012) proposed several formulations in this context which are limited to high Weber numbers. Regardless the simplifications, the use of the spatial averaging operator¤ introduces models in the averaged surface density equation to account for droplet break-up/bubble coalescence.…”

Transport of Interfacial Area Concentration in Two-Phase Flow

“…As for the conservation equation of interfacial velocity, Kataoka et al (2010Kataoka et al ( ,2011a have derived rigorous formulation based on the local instant formulation of interfacial area concentration and interfacial velocity, which is shown below. Since interface has no mass, momentum equation of interface cannot be formulated.…”