Some Notes on Boundary Conditions
An effect of dividing the momentum equations with and respectively is that for example ud obtains a value even if . In many cases ud will tend to uc in lack of a dispersed phase. So on inlets where , it is appropriate to set ud=uc.
A fixed value for should only be prescribed if there is no transport of toward the inlet. If, for example, a cloud of dispersed phase with higher than the prescribed value somehow reaches the inlet, will actually be “consumed”.
When specifying a dispersed phase flux, make sure to specify an appropriate velocity to go with the flux to avoid nonphysical concentrations of close to the boundary.
At walls, where it is possible to prescribe a wall leakage, the continuous phase normal velocity is set to
For a dispersed phase leakage:
That is, dispersed phase is injected with a low velocity and transported out with a velocity that is consistent with the specified flux. Wall leakage for one phase works best if combined with slip condition for the other phase so that the mixture is given maximum freedom to react to the leakage.