Derivation of a macroscopic mixture model for two-phase turbulent flows

This article addresses the issue of reduced models to describe turbulent two-phase flows in industrial applications. A spatially-averaged mixture or drift-flux model is derived theoretically from the local instantaneous Navier-Stokes description. Reynolds-averaging and space-averaging are applied successively. Between these two steps, a model reduction is achieved to account for the non-equilibrium between phases via algebraic relations. Applications of this work are not limited to porous media but also include macroscopic descriptions to model high-shear regions developing near the walls for internal flows. Thermal effects, heat transfer at the wall and phase-change are also considered and briefly discussed. The final model describes the evolution of mixture variables, including effects of both sub-filter spatial variations, turbulence, and local non-equilibrium in velocity, pressure and enthalpy. This analysis provides bridges between different approaches to model two-phase flows (local instantaneous description, two fluid model, local drift-flux model and spatially-averaged drift-flux model). It clarifies the content of each model involved by defining them in terms of local instantaneous quantities. Turbulent fluctuations and phase intermittency are crucial mechanisms. Important effects to model also include void fraction dispersion and turbulent diffusion; then, it is necessary to model the relative velocity, including the drift velocity orthogonal to gravity induced by the complex interactions between turbulent velocity fluctuations and the interfacial momentum transfer. The final macroscopic (spatially-averaged) mixture formulation is open, in the sense that expressions to model the various terms representing the physics of the small scales are not provided; instead, the physical sense and the origin of these models are discussed. The paper is meant as a basis on which analyses on local imbalance assumptions or relative velocity closures can be assessed. CFD simulations can provide information to complement experiments in technically challenging physical conditions or on processes essential to the models yet difficult to access experimentally (such as interfacial transfers for instance). Different kinds of two-fluid models can be tested to analyse their consequences on the macroscopic spatially-averaged model. In addition, a new path to calibrate closure laws or propose new models is opened based on finer-scale descriptions. Guidelines to use fine simulations along with the open expressions to derive closure relations either for the local drift-flux or for the spatially-averaged models are presented. They concern the modelling of the local relative velocity, the spatial average of the diffusion of void fraction and of the pressure drop. (c) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This article addresses the issue of reduced models to describe turbulent two-phase flows in industrial applications and derives a spatially-averaged mixture or drift-flux model. The final model describes the evolution of mixture variables, including effects of turbulence, velocity, pressure, and enthalpy local non-equilibrium. The study also introduces a new path to calibrate closure laws or propose new models.