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In two phases, the turbulent dispersion force is modelled for a phase
pair as follows:
F12 = D12*grad(alpha1)
Where D12 is the turbulent dispersion coefficient between phases 1 and
2. This force is calculated equivalently whichever phase is chosen to be
phase 1 because the volume fractions are related by alpha1 = 1 - alpha2.
This means that F12 == - F21; i.e., the force in one phase equals the
reaction in the other.
In multiple phases, however, a force calculated in this way is no longer
consistent between phases, because the relationship between the volume
fractions no longer applies. The following form has been chosen instead.
F12 = D12*grad(alpha1/(alpha1 + alpha2))
I.e., rather than using the gradient of a phase directly, we use the
gradient of the phase within the two-phase sub-system associated with
the pair.
This reduces to the two-phase case above, and the models available in
the literature that are explicitly formulated for multiple phases can
also be expressed in this form.
Based on a patch contributed by Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden -
Rossendorf (HZDR) and VTT Technical Research Centre of Finland Ltd.
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