Verification and Validation of the Spalart Allmaras Model with Rotation and Curvature Correction for Incompressible and Compressbile Flows

Abstract

The Spalart-Allmaras turbulence model is the model which gets the highest technological readiness level in the NASA turbulence  model resource home page. The model is widely used to predict external incompressible and compressbile flows. Different corrections to this model incorporating additional physical effects are presented on the same home page. Unfortunately none of these corrections are available in the official OpenFOAM version. Furthermore, no publicly available repository which contains the full set of corrections  suggested by  Shur et al. [1] to account for curvature and rotation effects was found.  In this technical note, the rotation and streamline curvature correction is incorporated into the Spalart-Allmaras model in order to overcome this limitation. The same equations as suggested in Shur et al. [1] are implemented and verified by means of the incompressible flow in a rotating channel, a 2D bump flow in a channel and a channel flow exhibiting a U-turn. Regarding the rotating channel flow and the flow in a U-turn some quantitative differences remain with respect to the results of Shur et al. [1]. For the rotating channel flow, a careful consistency check with respect to the analytical relations leading to the computation of the factor multiplied with the production term was made. No inconsistencies in the implementation where found. Unfortunately the exact reason for the differences between the present results compared to the computations of Shur et al. [1], was not found.  The interested readers are encouraged to help to clarify these issues. In the fourth test case it is shown that the model predicts a more correct turbulent viscosity distribution in the transonic flow around a delta wing. Applying the streamline and curvature corrections to the Spalart-Allmaras model predicts an earlier vortex breakdown compared to the standard Spalart-Allmaras model for a high angle of attack configuration. The agreement with the reference experiments is much better when using the corrections proposed by Shur et al. [1] to the Spalart-Allmaras compared to the standard Splart-Allmaras model.