Quasi-Single-Fluid Momentum Balance Models

1 Quasi-Single-Fluid (Momentum Balance) Models 

In the quasi-single-fluid models, the rising gas-liquid mixture is treated like a homogenous fluid of reduced density, and one set of continuity and momentum equations is solved for the two-phase mixture. The quasi-single-phase modeling technique has been relatively more popular and has been used extensively by Szekely and co-workers [34,42,43] and Guthrie and co-workers [1,2,15,25,44 7]. The k—s model is often used to represent turbulence. In most applications, the void fraction distribution is assumed a priori rather than being solved for, and this limits the predictive capability of these models. 

Although the models based on momentum balance are conceptually sound, the predictions are not always satisfactory and fail to account for many observed phenomena. This is attributed to the various assumptions made in simplifying the model and the characterization of a large number of empirical parameters contained in the model equations. It may be noted further that these models are valid only in the turbulent region and fail close to the walls of the vessel. 

The formulation of models based on this approach basically involves setting up the equations of motion in continuity, together with appropriate boundary conditions. The general forms of these equations used by various investigators [44,48] are given below using cylindrical polar coordinates, and assuming axisymmetric conditions. 

u and v represent velocity components in the axial (z) and radial (r) directions, respectively. The gas volume fraction uq appears in the axial direction momentum balance equation. For example, pg ao is the buoyancy force per unit volume through which the free convection effect is incorporated. The effective viscosity /Lteff appears in both the axial and radial direction momentum conservation equations and accommodates the effect of momentum transfer caused by the turbulence phenomena. 

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