### 2.3.3. Rotating Frame of Reference for Reynolds Stress Models

One of the advantages of Reynolds stress transport models, when compared to and models, is their ability to simulate the additional anisotropy of the Reynolds stresses due to the Coriolis forces appearing in the rotating frame of reference.

The necessary additional source terms to account for the Coriolis forces have been implemented into ANSYS CFX for use with any of the available Reynolds stress transport models. These terms are described in a book by Wilcox [30], and in more detail in a paper by Launder, Tselepidakis and Younis [31].

If the flow equations are written in the frame of the coordinate system, which rotates relative to the steady inertial frame with a rate then one new source term G ij has to be added directly to the right hand side of the transport equation for , Equation 2–110:

| (2–123)

where is a Levi-Chivita factor, equal to 1 if its indices {i,j,k} form an even permutation of {1,2,3}, equal to -1 for an odd permutation of {1,2,3}, and equal to 0 if any two indices are equal.

Besides the absolute velocity gradient tensor, participating in the production tensor Equation 2–120 and in the model equation for the pressure-strain correlation Equation 2–119, is written in the rotating frame as a sum of the strain rate tensor S ij:

| (2–124)

and the vorticity tensor , which has an additional term due to system rotation:

| (2–125)

This representation of the velocity gradient results in an apparent additional source term G ij Equation 2–123, coming from the production term (). That is why in reference [31] the Coriolis source term G ij differs from Equation 2–123 by an additional factor of 2.

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