Towards an Improved Description of Film-Cooling Heat Transfer Through Anisotropic RANS Modeling: A Combined LES/RANS Contribution

Abstract

This study focuses on the physics and the modeling of the heat transfer taking place within the Penn State 777 shaped hole flow configuration. To do so, a dedicated Large-Eddy Simulation conducted with the AVBP solver is carried out and shows good reproduction of the main flow characteristics observed in terms of features and adiabatic effectiveness. This simulation is then more deeply analyzed to conduct an a priori evaluation of the most current heat flux assumptions used in RANS modeling, being the Prandtl analogy and the Daly Harlow hypothesis. Results obtained for this shaped hole configuration confirm previous ones obtained for cylindrical holes, showing the deficiencies of classical RANS models. In particular, it is shown that the equivalent Turbulent Prandtl number usually fixed at 0.9 is here largely overestimated. The most representative value is indeed around 0.5 in most regions of interest. It is also showed that the diffusion process is not the same in all directions, namely the wall normal and transverse directions turbulent diffusion processes differ. A Reynolds-Stress model simulation using the Elliptic Blending Reynolds-Stress Model developed by Manceau is then conducted, combined with different advanced heat flux models. With this new and more advanced model, obtained results show major improvements compared to state of the art RANS simulation using the k-ω SST along with the Prandtl analogy. In particular, the centerline and the lateral effectiveness profiles are considerably enhanced, exhibiting a more representative lateral spreading. The respective contributions issued by the improved Reynolds-stress description and the heat flux models are eventually analyzed. A modified model for the heat flux formulation is hence suggested in an attempt to provide extra improvement compared to Daly-Harlow formulation. In conclusion, this work strongly advocates for the use of anisotropic models either for turbulent stress modeling or turbulent heat flux modeling for the description of film cooling phenomena at stake.