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23.7.1 Source Terms due to Mass Transfer

FLUENT adds contributions due to mass transfer only to the momentum, species, and energy equations. No source term is added for other scalars such as turbulence or user-defined scalars.

Let $m_{{p^i}{q^j}}$ be the mass transfer rate per unit volume from the $i^{\rm th}$ species of phase $p$ to the $j^{\rm th}$ species of phase $q$. In case a particular phase does not have a mixture material associated with it, the mass transfer will be with the bulk phase.

Mass Equation

The contribution to the mass source for phase $p$ in a cell is

 m_p = -m_{{p^i}{q^j}} (23.7-1)

and for phase $q$ is
 m_q = m_{{p^i}{q^j}} (23.7-2)

Momentum Equation

For VOF or mixture models, there is no momentum source.

For the Eulerian model, the momentum source in a cell for phase $p$ is

 {m_p{\vec u}_p} = -m_{{p^i}{q^j}}{\vec u}_p (23.7-3)

and for phase $q$ is
 {m_q{\vec u}_q} = m_{{p^i}{q^j}}{\vec u}_p (23.7-4)

Energy Equation

For all multiphase models, the following energy sources are added.

The energy source in a cell for phase $p$ is

 {H_p} = -m_{{p^i}{q^j}}(h^i_p) (23.7-5)

and for phase $q$ is
 {H_q} = m_{{p^i}{q^j}}(h^i_p + {h^f}^{i}_p - {h^f}^j_q) (23.7-6)

where ${h^f}^i_p$ and ${h^f}^j_q$ are the formation enthalpies of species $i$ of phase $p$ and species $j$ of phase $q$ respectively and $h^i_p$ is the enthalpy of species $i$ of phase $p$ (with reference to the formation enthalpy).

Species Equation

The species source in a cell for species $i$ of phase $p$ is

 m^i_p = -m_{{p^i}{q^j}} (23.7-7)

and for species $j$ of phase $q$ is
 m^j_q = m_{{p^i}{q^j}} (23.7-8)

Other Scalar Equations

No source/sink terms are added for turbulence quantities and other scalars. The transfer of these scalar quantities due to mass transfer could be modeled using user-defined source terms.

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© Fluent Inc. 2006-09-20