Implementation of a Surface Roughness-Based Transition Onset Correction in the $\gamma \text{-}\stackrel{~}{R_{{\theta }_{\mathrm{t}}}}$ Transition Model

This paper presents an extension of the $γ-Rθt~$ transition model of Menter et al. (2006) that aims to take into account the effect of a specific type of surface roughness on the transition location. This was done by implementing the roughness transition onset correction of Stripf et al. (2009) inside the $γ-Rθt~$ model. Stripf et al. have developed a correlation that takes into account the height and spacing of distributed roughness elements to correct the transition Reynolds number predicted over a smooth surface. As the transition Reynolds number takes multiple forms in the $γ-Rθt~$ model, different implementations of the Stripf et al. correction were tested and are discussed here. We find that it is best to correct the value of the critical Reynolds number R_θc. Computation results on a rough, low-pressure turbine vane are presented and compared to experimental results of the Karlsruhe Institute of Technology. We find that there is a good agreement on the transition location between the computations and experiments. In particular, the model displays accurate sensitivity to the roughness height, though the influence of the roughness spacing, which is of second order in these experiments, is not as well captured. We therefore conclude that the roughness transition onset correction of Stripf et al. is well suited for use in the $γ-Rθt~$ model.