Multifluid Modeling Framework

The average multifluid model equations are outlined in the following together with the conventional interfacial closures that are frequently adopted in gas-liquid bubbly flow analyzes. The average multi-fluid continuity equation for phase k reads  

The phasic volume fractions must also satisfy the compatibility condition  

In a consistent manner the momentum balance for phase k yields  

The limiting steps in the model development are the formulation of closure relations or closure laws determining turbulence effects, interfacial transfer fluxes and the bubble coalescence and breakage processes. When sufliciently dilute dispersions are considered, only particle - fluid interactions are significant and the two-fluid closures can be employed. In these particular cases, only the interaction between each of the dispersed gas phases (d) and the continuous liquid phase (c) is considered parameterizing the last term on the RHS of (8.12)  

The steady drag-, added mass-, lift-, turbulent diffusion- and wall forces, respectively, are presented in sect 5.2. Moreover, the force terms for dilute dispersions are multiplied by the liquid fraction due to the reduced liquid volume available for considerable gas loadings [59]. 

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Figure 8 Framework of the EMMS-based multifluid model (EFM) (Hong et al, 2012).

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