Assessment of RANS Transition Models

Many naval and aeronautical applications deal with flows which occur at Reynolds numbers that are typically larger than 10⁷. Under these conditions the laminar regime is confined to a very small region near the leading edge of the body and consequently the correct prediction of transition is not relevant. Therefore, the premature transition predicted by most turbulence models (Wilcox (1998)) is not an issue.
On the other hand, there are several applications that operate in the Reynolds number range of 10⁵ to 10⁶, such as underwater gliders, unmanned aerial vehicles (UAVs) and wind turbines. In these cases, the correct prediction of transition from laminar to turbulent flow becomes essential for the determination of the forces acting on the body and correct flow analysis. Therefore, standard turbulence models are not adequate for these low Reynolds number flows, which led to the development of transition models, such as the intermittency based γ-Re˜ θt (Langtry and Menter (2009)) and γ (Menter et al. (2015)) models, the k_T − k_L − ω model (Walters and Cokljat (2008)), built on the concept of laminar kinetic energy, and the amplification factor transport (AFT) transition model (Coder and Maughmer (2015)).
This paper presents a study of several features of the application of these transition models, namely: numerical robustness, i.e. the ability to reduce the iterative error to negligible levels; discretization errors and sensitivity to inlet conditions. To this end we have selected two test cases: the flow over a flat plate and the flow around the Eppler 387 airfoil. The availability of experimental data for both cases allows the determination of the modelling error of the skin friction coefficient for the flat plate and of the pressure coefficient on the surface of the airfoil. The different turbulence and transition models used here are described in section 2. Definition of the test cases including domain size and selected boundary conditions are presented in section 3, whereas section 4 describes the numerical settings and grid sets. The results obtained for each model are presented and discussed in section 5. Finally, section 6 presents the conclusions of this study.