On the Numerical Behavior of RANS-Based Transition Models

A comparison of several Reynolds-averaged Navier–Stokes (RANS) based transition models is presented. Four of the most widespread models are selected: the γ−Reθ, γ, amplification factor transport (AFT), and kT−kL−ω models, representative of different modeling approaches. The calculations are performed on several geometries: a flat plate, the Eppler 387 and NACA 0012 two-dimensional (2D) airfoils at two angles of attack, and the SD7003 wing. Distinct features such as the influence of the inlet boundary conditions, discretization error, and modeling error are discussed. It is found that all models present a strong sensitivity to the turbulence quantities inlet boundary conditions, and with the exception of the AFT model, are severely influenced by the decay of turbulence predicted by the underlying turbulence model. This makes the estimation of modeling errors troublesome because these quantities are rarely reported in experiments. Despite not having specific terms in their formulation to deal with separation-induced transition, both the AFT and kT−kL−ω models manage to predict it for the Eppler 387 foil, although presenting higher numerical uncertainty than the remaining models. However, both models show difficulties in the simulation of flows at Reynolds numbers under 105. The γ−Reθ and γ models are the most robust alternatives in terms of iterative and discretization error. The use of RANS compatible transition models allows for laminar flow and features such as laminar separation bubbles to be reproduced and can lead to greatly improved numerical solutions when compared to simulations performed with standard turbulence models.