Multifluid model

Our discussion of multiphase CFD models has thus far focused on describing the mass and momentum balances for each phase. In applications to chemical reactors, we will frequently need to include chemical species and enthalpy balances. As mentioned previously, the multifluid models do not resolve the interfaces between phases and models based on correlations will be needed to close the interphase mass- and heat-transfer terms. To keep the notation simple, we will consider only a two-phase gas-solid system with ag + as = 1. If we denote the mass fractions of Nsp chemical species in each phase by Yga and Ysa, respectively, we can write the species balance equations as... 

From the discussion above, we should keep in mind that even if no SGS micromixing model is used to describe the multiphase flow, it may often be the case that chemical reactions (and indeed micromixing) will be limited by mass/ heat transfer between the phases. Because the multifluid model (see Eqs. 164 and... 

The development of the Lagrangian models has been limited mainly by the inherent need for large computing capacity to carry out statistical averaging and computation of the phase interactions. The Lagrangian models are particularly applicable to very dilute or discrete flow situations for which multifluid models are not appropriate, or to situations in which the historic tracking of particles is important (such as in pulverized coal combustion in a furnace or the tracking of radioactive particles in gas-solid flows). 

Two-fluid or multifluid models can be extended to simulate not only gas-liquid flows but also any combinations of different phases present in stirred reactors. To simulate gas-liquid-solid, slurry reactors, liquid and solid phases are often lumped together and treated as a slurry phase with effective properties. This approximation is reasonable as long as the solid volume fraction is low ( 1 %). For higher solid loading. 

Sha et al [130, 131] developed a similar multifluid model for the simulation of gas-liquid bubbly flow. To guarantee the conservation of mass the population balance part of the model was solved by the discrete solution method presented by Hagesaether et al [52]. The 3D transient simulations of a rectangular column with dimensions 150 x 30 x 2000 (mm) and the gas evenly distributed at the bottom were run using the commercial software CFX4.4. For the same bubble size distribution and feed rate at the inlet, the simulations were carried out as two, three, six and eleven phase flows. The number of population balance equations solved was 10 in all the simulations. It was stated that the higher the number of phases used, the more accurate are the results. 

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 Lagrangian steady drag force on a single particle is commonly expressed by (5.48). For Eulerian model formulations one normally employs (5.34), hence for the multifluid models the standard steady drag force parameterization 3delds ... 

Bove [16] proposed a different approach to solve the multi-fluid model equations in the in-house code FLOTRACS. To solve the unsteady multifluid model together with a population balance equation for the dispersed phases size distribution, a time splitting strategy was adopted for the population balance equation. The transport operator (convection) of the equation was solved separately from the source terms in the inner iteration loop. In this way the convection operator which coincides with the continuity equation can be employed constructing the pressure-correction equation. The population balance source terms were solved In a separate step as part of the outer iteration loop. The complete population balance equation solution provides the... 

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

Figure 12 Schematic drawing of the structure-dependent multifluid model for mass transfer and reactions (Liu et al, 2015).

Multifluid Models with Granular Flow Closures 359... 

The Eulerian-Eulerian multifluid models for dense flows where a relatively large number of particles are considered determining a continuous phase in the control volume formulating the governing microscopic model equations. Different... 

Chao Z, Wang Y, Jakobsen JP, Femandino M, Jakobsen HA (2012) Investigation of particle-particle drag in a dense binary fluidized bed. Powder Technol 224 311-322 Chao Z, Wang Y, Jakobsen JP, Femandino M, Jakobsen HA (2012) Multifluid modeling of density segregation in a dense binary fluidized bed. Particuology 10 62-71... 

Geurst JA Drift mass, multifluid modeling of two-phase bubbly flow and superfluid hydrodynamics, Phys A 152 1-28, 1988. http //dx.doi.org/10.1016/0378-4371(88)... 

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