Extension of Wray-Agarwal Algebraic Transition Model to Include Compressibility for the Analysis of External Transonic Flows

The Wray-Agarwal Algebraic Transition (WA-AT) model has shown accuracy comparable to RANS transition models with three (k-kL-ω) to four transport (k, ω, γ, Reθt) equations. This paper presents a compressibility correction to the local correlation-based Wray-Agarwal algebraic transition model with validation test cases. The original WA-AT and the WA-AT model with compressibility correction (WA-ATC) are applied to the NLR-QE airfoil at zero-degree angle of attack for a range of Mach numbers. The pressure coefficient distributions on the airfoil agree with the experimental data. The WA-ATC model offers some improvement on the prediction of transition location but shows minimal difference in the prediction of drag coefficient. Both models predict the drag coefficient within the range observed in the experiments. This particular 2D test case does not fully exemplify the difference between the WA-AT and WA-ATC models; however this investigation demonstrates the accuracy of the WA-AT model for 2D transonic flows. The transition on the transonic 10° cone is also calculated as a validation test case and the results show some differences in the predictions from the WA-AT and WA-ATC models. Finally, both the models are applied to compute transition in subsonic flow past a 3D 6:1 prolate spheroid; the results show little difference between the transition location predictions from the WA-AT and WA-ATC models, and are close to the experimental data.