ANSYS FLUENT 12.0 Theory Guide - 1.3.2 Multiphase Flow

1.3.2 Multiphase Flow

For multiphase flows , ANSYS FLUENT solves transport equations for two types of scalars: per phase and mixture. For an arbitrary scalar in phase-1, denoted by $\phi^k_l$ , ANSYS FLUENT solves the transport equation inside the volume occupied by phase-l

$\frac{\partial \alpha_{l} \rho_{l} \phi^k_l}{\partial t} + \... ...a_{l} \Gamma^k_l \nabla \phi^k_l) = S^k_l \; \; \; k = 1,...,N$

(1.3-5)

where $\alpha_{l}$ , $\rho_{l}$ , and $\vec {u}_l$ are the volume fraction, physical density, and velocity of phase-l, respectively. $\Gamma^{k}_{l}$ and are the diffusion coefficient and source term, respectively, which you will need to specify. In this case, scalar $\phi^k_l$ is associated only with one phase ( phase-l) and is considered an individual field variable of phase-l.

The mass flux for phase-l is defined as

$F_l = \int_{S} \alpha_l \rho_l \vec {u}_l \cdot d \vec{S}$

(1.3-6)

If the transport variable described by scalar $\phi^k_l$ represents the physical field that is shared between phases, or is considered the same for each phase, then you should consider this scalar as being associated with a mixture of phases, $\phi^k$ . In this case, the generic transport equation for the scalar is

$\frac{\partial \rho_{m} \phi^k}{\partial t} + \nabla \cdot (... ...i^k - \Gamma^k_m \nabla \phi^k) = S^{k_m} \; \; \; k = 1,...,N$

(1.3-7)

where mixture density $\rho_{m}$ , mixture velocity $\vec {u}_m$ , and mixture diffusivity for the scalar $\Gamma^k_m$ are calculated according to

$\rho_{m} = \sum_{l} \alpha_{l} \rho_{l}$

(1.3-8)

$\rho_{m} \vec {u}_m = \sum_{l} \alpha_{l} \rho_{l} \vec {u}_l$

(1.3-9)

$F_m = \int_{S} rho_m \vec {u}_m \cdot d \vec{S}$

(1.3-10)

$\Gamma^k_m = \sum_{l} \alpha_{l} \Gamma^k_l$

(1.3-11)

$S^k_m = \sum_{l} S^k_l$

(1.3-12)

To calculate mixture diffusivity , you will need to specify individual diffusivities for each material associated with individual phases.

Note that if the user-defined mass flux option is activated, then mass fluxes shown in Equation 1.3-6 and Equation 1.3-10 will need to be replaced in the corresponding scalar transport equations.

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