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RANS turbulence model with curvature correction

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Old   July 24, 2022, 04:03
Default RANS turbulence model with curvature correction
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Hi, fomers
I am doing a propeller simulation by using a nonlinear k-epsilon model (ShihQuadraticKE in new version OpenFoam). Considering the blades rotation and tip vortex flows, maybe a curvature correction should be implemented.
In this paper, a curvature correction method was employed in SST k-omega model, and I want to use this correction in ShihQuadraticKE turbulence model, but I am confused with the following two questions:

1) In the reference, the production term of the Omega equation is multiplied by correction function Frc. Mimic this method, can the correction function Frc be multiplied by the production term of Epsilon equation?

2) In this paper, The Wij tensor which associates the effects of curvature corrections in the rotational rate tensor is defined by (Eq. (9), (10) and (11)). I am not familiar with the expression of tensors. The big question is that the above three equations are tensor form, how to translate it to vector form, so they can be easily implemented in Openfoam.
(p.s. Sorry I don't have permission to post pictures in the thread, please see the link the specific formula)

Any help is welcomed, Thanks!
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curvature correction, rans, turbulence model

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