Two-equation turbulence model for unsteady separated flows around airfoils

Abstract

HE prediction of turbulent unsteady separated flows around airfoils is currently a priority in the domain of aeronautics. There are numerous studies in this domain, but the accurate prediction of the flow structure and aerodynamic parameters, especially near stall conditions, remain open questions, and considerable efforts have to be made to suggest an efficient way to resolve this problem. The majority of the studies devoted to the problem use different classes of turbulence models employing the steady Reynolds-averaged equations. A widely used turbulence model in the context of the eddy-viscosity concept is the two-equation model (Launder and Spalding1) and its various versions (Jones and Launder2 and Chien3 among others). However, this kind of model was originally conceived for free shear flows and then adapted for boundary-layer flows. It is not evident whether this model may be directly applicable in the elliptic flows around airfoils, as often discrepencies in the flow parameters appear when comparing with the physical experiments (see numerous papers reported in Ref. 4). One of the well-known reasons is that the various applications of the k-£ model provide generally too high a level of the eddy viscosity and of the turbulent kinetic energy production. In this study, we simulate the turbulent incompressible flow around an airfoil NACA 0012 at a Reynolds number range of 1$, by an unsteady approach, using the phase-averaging decomposition (Hussain and Reynolds5), in the form suggested by the experimental work of Cantwell and Coles.6 This decomposition provides the phase-averaged Navier-Stokes equations, as reported in the works of Ha Minh et al., 7 Chassaing,8 Braza and Nogues,9 and Franke and Rodi,10 among others. Furthermore, we introduce the unsteady vorticity into the production term of turbulent energy to improve the behavior of the two-equation model with respect to the physics of the flow.