Phase dependent turbulence models can be used in conjunction with the inhomogeneous model (particle and mixture models) only.
The eddy viscosity hypothesis is assumed to hold for each turbulent
phase. Diffusion of momentum in phase 
is governed
by an effective viscosity:
 | (5–194) |
The following topics are discussed:
The default zero-equation model uses a formula based on geometric
length scale and the mean solution velocity. It is correlated for
single-phase turbulent pipe flow. The turbulence viscosity is modeled
as the product of a turbulent velocity scale, 
, and a turbulence length scale, 
, as proposed by Prandtl and Kolmogorov:
 | (5–195) |
where 
is a proportionality
constant. The velocity scale is calculated to be the maximum velocity
in phase 
. If you specify a value for the
velocity scale, it will be used for all phases. The length scale is
derived using the formula:
 | (5–196) |
where 
is the fluid domain
volume.
 | (5–197) |
The parameter 
is a turbulent Prandtl number
relating the dispersed phase kinematic eddy viscosity 
to the continuous phase kinematic eddy
viscosity 
.
In situations where the particle relaxation time is short compared
to turbulence dissipation time scales, you may safely use the default
value 
. If the particle relaxation time is long
compared to turbulence dissipation time scales, it may be better to
use a value of 
. This is highly model dependent. Several
models are available in the literature.
For the 
-
model, the
turbulent viscosity is modeled as:
 | (5–198) |
The transport equations for 
and 
in
a turbulent phase are assumed to take a similar form to the single-phase
transport equations:
 | (5–199) |
 | (5–200) |
Definitions of the terms are available. For details, see The k-epsilon Model in Ansys CFX.
The additional terms 
and 
represent interphase transfer for 
and 
respectively.
These are omitted in CFX, though they may be added as user sources.
Other two equation turbulence models are treated in a similar way.
The multiphase versions of Reynolds stress models are equivalent to the single phase version, with all flux and volumetric source terms multiplied by volume fractions. Single phase version information is available. For details, see Reynolds Stress Turbulence Models.
By default, no additional exchange terms are added, though they may be added as user sources.