Both for Frozen rotor and
Rotating frame, the frame rotation tensor
is expressed through the vector of angular velocity
as
Among RANS-EVM implemented in COMSOL, Realizable k-
ε, k-
ω and Spalart–Allmaras have a functional dependence on the rotation rate tensor
Ω, which must be written in an “objective manner”, that is, as seen in the absolute frame. Namely, for
Rotating frame Ω is defined as
while for Frozen rotor it is correctly defined automatically (since velocity in the absolute frame is used).
According to an advanced analysis used for the derivation of nonlinear eddy-viscosity models, in Rotating frame the effective rotation rate which enters the definition of turbulence viscosity
μT should be written as
where cΩ is larger than
1. For example, it is equal to
3 for the Realizable
k-
ε model. In the current implementation this approach is skipped, but still can be added manually.
Writing Πij for
Rotating frame in an objective manner would lead to
cRRD = 2 (then
Equation 3-233 can be called a “Coriolis redistribution term”). Writing
Pij in an objective manner too would lead to
cRRD = 1, that is, only a frame rotation correction to the advective term of the Reynolds stress equation would be left, exactly as for
Frozen rotor. The current approach is chosen to localize the effect of the system rotation to the single tensor variable
. This is possible because the production is always linear in rotation, and only linear in rotation models of the pressure–strain correlation are considered here.
for Wilcox R-
for SSG-LRR, 
for Elliptic Blending R-