The inhomogeneous hydrodynamic equations are as follows:
 | (5–21) |
describes momentum sources due to external body
forces, and user-defined momentum sources. For details, see Sources.
describes
the interfacial forces acting on phase 
due to the
presence of other phases. Additional information for the models available
for interfacial forces is available in Interphase Momentum Transfer Models.The term:
(5–22)
represents momentum transfer induced by interphase mass transfer. For details, see Interphase Mass Transfer.
The above momentum equations are valid for fluid phases only. For dispersed solid phases, additional terms are present representing additional stresses due to particle collisions.
Note: The viscous stress term contains the product of 
and 
.
Consequently, as the volume fraction approaches zero, so does the
dissipation. However for a dilute phase, the magnitude of the dissipation
is still significant because the mass of the dilute phase also goes
to zero as 
approaches
zero. This is true not only for momentum but also for any other transported
quantity that includes a diffusion term (such as energy). In particular,
if the volume fraction gradient is very large, the diffusion term
can cause severe convergence problems because the cell with the smaller
volume fraction will "see" a very large relative flux.
This problem can be significantly alleviated by using harmonic averaging
for the diffusion coefficients since the magnitude of the flux will
be more sensitive to the volume fraction of the cell with the smaller
mass. To change to harmonic averages, use the expert parameter settings diffusion coef averaging type = 3 for scalar equations and stress coef averaging type = 3 for momentum equations. For simulations
that are laminar, or that have regions of low turbulent viscosity
so that molecular diffusion is locally significant, a simple workaround
is to modify the viscosity and thermal conductivity using CEL so that,
below a volume fraction value of interest that is physically suitable,
viscosity and thermal conductivity approach zero as the volume fraction
approaches zero.
 | (5–23) |
describes
user specified mass sources. For details, see Sources.
is the mass flow rate per unit volume from
phase 
to phase 
. This term
only occurs if interphase mass transfer takes place. For details,
see Interphase Mass Transfer.
This is simply the constraint that the volume fractions sum to unity:
 | (5–24) |
This equation may also be combined with the phasic continuity equations to obtain a transported volume conservation equation. Take Equation 5–23, divide by phasic density, and sum over all phases. This yields:
 | (5–25) |
Interpreting this equation is simpler if you consider the special case of incompressible phases with no sources, in which it simplifies to:
 | (5–26) |
which requires the volume flows to have zero divergence. Equation 5–25 is the volume continuity equation solved by the CFX-Solver.
