An improved analysis procedure for the transitional separation bubble on the airfoil surface has been developed. Three different two-equation turbulence models, namely, the two-layer κ-ε model of Chen ＆ Patel, the low-Re κ-ε model of Lam ＆ Bremhorst, and the κ-ω model of Wilcox, have been compared for the analysis by incorporating them successfully in the Navier-Stokes procedure developed earlier. The calculation domain includes the regions of laminar boundary layer, separation and reattached turbulent boundary layer. The outer boundary is placed sufficiently far from the airfoil surface so that the potential-flow conditions can be applied as boundary conditions. The domain is still compact enough to achieve computational efficiency.
As a preliminary study, comparison of the turbulence models were made for the turbulent flow on the flat plate with increasingly adverse pressure gradient. The results show that two-layer κ-ε model of Chen and Patel and the κ-ω model of Wilcox perform better than the low-Reynolds-number κ-ε model of Lam and Bremhorst especially in the skin-friction distribution. The low-Reynolds-number κ-ε model overpredicts the skin friction in the region of adverse pressure gradient.
For the separation bubble on an airfoil, calculations for three different NACA airfoil sections at various angles of attack and Reynolds numbers are made and the results of two-equation turbulence models are compared with those of the algebraic eddy-viscosity model of Baldwin and Lomax adopted in Choi and Kang. All two-equation turbulence models appear to give improved results over the algebraic eddy-viscosity model especially in the reattachment region of leading-edge bubble. But the low-Reynolds-number κ-ε model needs the delicate iterative process to obtain the converged solution and the κ-ω model is very sensitive to the freestream value of ω, which is unknown priori.
The two-layer κ-ε model therefore is adopted to establish a new transition criterion for leading-edge bubbles. This new criterion is developed by using the results obtained by prescribed transition points that fit the data most closely. The proposed criterion correlates the transition Reynolds number with the Reynolds number at separation and the mean Thwaites parameter which is measure of the adverse pressure gradient. The results show that this correlation performs excellently for all the cases tested.