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

Highlights: ► Transport equation of interfacial area concentration is derived. ► Conservation equation of interfacial velocity is derived. ► Turbulent transport terms of interfacial area concentration were modeled. - Abstract: A modeling of basic transport equation and constitutive equations of turbulent transport terms of interfacial area concentration was carried out. Based on the local instant formulation, interfacial area concentration was 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 time averaged interfacial velocity. In the previous models, interfacial velocity is roughly approximated by velocity of each phase. In the present model, interfacial velocity is formulated in term of spatial correlation functions of characteristic function and velocity of each phase and their directional derivatives. In this formulation, the time 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.