Advanced computational fluid dynamics CFD -based models

5 Advanced computational fluid dynamics (CFD)-based models 

While the lower order models described in Section 6.3 are useful for the quick prediction of the overall performance of a reactor, these models often rely on simplified flow approximations and often fail to account for change in the local fluid dynamics or transport processes during the presence of internal hardware or changes in flow regimes. Moreover, these models are also based on empirical knowledge (as discussed in Section 6.4) of several parameters such as interfacial area, dispersion coefficients, and mass transfer coefficients. Some of these limitations may be avoided by using CFD models for simulations of gas-liquid-solid flows in three-phase slurry and fluidized bed. 

A hierarchy of computational models is available to simulate dispersed gas-liquid-solid flows in three-phase slurry and fluidized bed reactors [84] continuum (Euler-Euler) method, discrete particle/bubble (Euler-Lagrange) method, or front tracking/capturing methods. While every method has its own 

In the continuum (Euler-Euler)-type formulation, the gas, liquid, and solid phases are assumed to be continuum and the volume-averaged mass and momentum equations (see Table 6.10) are solved for each phase separately to predict the pressure, phase holdup, and phase velocity distributions. As a result of time and volume averaging, additional terms appear in the momentum conservation equations. These additional terms need closure models and such unclosed terms are highlighted in Table 6.10. 

In order to close the additional Reynolds (turbulent) stresses, several different eddy viscosity-based turbulence models, in which the additional turbulent stresses are related to the mean velocity gradient as shown in Table 6.11, are used to account for the turbulence in three-phase systems. Generally, the standard k-e turbulence model is solved only for the continuous phase or for mixture phase or for each phase. In the literature reports. 

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