Smooth transitional RANS model and applications with crossflow effects

Abstract Transitional Reynolds-averaged Navier–Stokes (RANS) models have become relevant in the computational fluid dynamics (CFD) community as a practical approach to predict the transition to turbulence over the surface of aerospace configurations. These models capture the transition caused by the amplification of Tollmien-Schlichting waves, the bypass transition, and the stationary crossflow vortices. A fundamental aspect of transitional RANS models that still deserve continued attention is their numerical behavior. The source terms that are part of their formulation are commonly based on highly nonlinear functions, rendering more challenges in their convergence when compared to the underlying fully turbulent RANS models. The present work investigates the effects of smoothing these highly nonlinear, discontinuous functions that are embedded in the source terms of the Langtry-Menter transition model and its companion turbulence closure. There is particular interests in identifying improvements in the lift and drag coefficient convergence behavior. We consider the flat plate, the NACA 0012 and NLF(1)-0416 airfoils, and the 6:1 prolate spheroid configuration as test cases for transition caused by the amplification of Tollmien-Schlichting (TS) waves. We also consider flow conditions for which transition over the inclined 6:1 prolate spheroid is triggered by the amplification of stationary crossflow vortices. Our results show that the smooth functions lead to a faster convergence of the aerodynamic coefficients, which represents a reduced computational cost when compared to the original model.