Application of an Elliptic Blending Reynolds Stress Model in Attached and Separated flows (Invited)

Abstract

A novel Reynolds stress model is presented that can be integrated up to the wall through the use of an elliptic blending of a near wall model for the pressure redistribution term and a homogeneous model farther away from the wall. The main novelty of the proposed model consists in using the homogeneous dissipation rate of turbulent kinetic energy ε h instead of ε to model the anisotropic dissipation rate tensor. The model parameters are calibrated by using DNS results for a plane channel flow with a friction Reynolds number of Reτ = 2000. The accuracy of the model is further demonstrated for the channel flow at Reτ = 1000, 4200, and 52000 through comparison with DNS data. To test the model performance in separated flows the periodic hill flow at several Reynolds numbers (Re b = 2800, 5600, 10600, 37000) is considered. For the hill flow, the model performs reasonable well showing slightly better results when compared to results obtained with the Menter's SST k −ω model although both models fail to reproduce the high turbulence levels in the initial separated shear layer. Two external aerodynamics problems are studied in addition to the internal flows: the NACA 0012 at varying angles of attack and the NACA 4412 with a trailing edge separation (Aoa = 12 o ). The flow over the NACA 0012 airfoil is considered for Rec = 10 6 at angles of attack AoA = 0,5,10,15,16,17,18,19. For the lower angles of attack AoA < 17 o the new Reynolds stress model predictions for lift and drag are in close agreement with the experimental values and also agree with the SST model predictions. For the highest angle of attack AoA = 19 o the Reynolds stress model predicts flow separation and thus the lift and drag results are closer to the experimental values when compared to the SST model results. A similar result is found for the 2D NACA 4412 airfoil with trailing edge separation case (AoA = 12 o ). For the cases considered in this study the new Reynolds stress model was very robust but provided only small improvements over the two-equation model results in the flows with separation. Further calibration of the model parameters in a flow with separation could improve the results and will be considered as a next step.

Verification and Validation of OpenFOAM for High-Lift Aircraft Flows

“…Table 1 shows the lift and drag coefficients for 0,10 and 15 degrees AoA for a range of CFD codes obtained from the NASA TMR site. It can be seen that OpenFOAM and STAR-CCM+ fall within the range of the other codes which was also shown in Stoellinger et al [17]. However it should be noted that some of these use different versions of the SA model (i.e no-ft2 or SA-neg) and thus likely contribute to the differences observed between these range of codes.…”

“…widely for flows subject to corner separation [31]. The use of a Reynolds stress model [17] or the SA-QCR [29] model was predicted to help this, however none of the 3rd HLPW participants using the SA-QCR or Reynolds stress models captured the inboard separation [26]. In addition participants who used some form of a transition model also did not capture the inboard separation.…”