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7.2.Within-Phase Diffusion

The following within-phase diffusion term appears on the right-hand side (RHS) of all transport equations except volume fractions:

[d/dxi] * { Gphik * rk * [d/dxi] * phik }....(7.2.1)

where: the subscript k denotes the phase k; rk denotes the volume fraction of phase k; and Gphik denotes the diffusion coefficient of the dependent variable phi for phase k. The local volume-fraction multiplier in equation (7.2.1) allows for the dilution effect of the other phase. The diffusion coefficient for each phase is written as:

Gphik = RHOk*( ENUL/PRNDTL(phik) + ENUT/PRT(phik) ) .... (7.2.2)

where: ENUL is the molecular kinematic viscosity; and PRNDTL(phik) and PRT(phik) are the molecular and turbulent Prandtl numbers.

Note that there is only one laminar and one turbulent viscosity; these are often regarded as the phase-1 viscosities. If different viscosities are required for the second phase, the Prandtl numbers can be used to introduce the appropriate ratios.

If one of the phases, say phase 2, is a dispersed one consisting of droplets or particles, within-phase-diffusion effects can hardly occur (unless by coalescence). PRT(phi) may then be set to a large number, say 1.E10.