Two- and three-dimensional wake transitions of a NACA0012 airfoil

Flow transitions are an important fluid-dynamic phenomena for many reasons, including the direct effect on the aerodynamic forces acting on the body. In the present study, two-dimensional (2-D) and three-dimensional (3-D) wake transitions of a NACA0012 airfoil are studied for angles of attack in the range 0^ 20^ and Reynolds numbers 500 {Re} 5000. The study uses water-channel experiments and 2-D and 3-D numerical simulations based on the nodal spectral-element method, level-set function-based immersed-interface method and Floquet stability analysis. The different wake states are categorised based on the time-instantaneous wake structure, non-dimensional frequency and aerodynamic force coefficients. The wake states and transition boundaries are summarised in a wake regime map. The critical angle of attack and Reynolds number for the supercritical Hopf bifurcation (i. e. steady to periodic wake transition) varies as ₁ {Re}^-0. 65, while the critical angle of attack for the onset of three dimensionality varies as ₃₃ {Re}^-0. 5. Over the entire Reynolds number range, the transition to 3-D flow occurs through a mode C (subharmonic) transition. Beyond this initial transition, further instabilities of the 2-D periodic base flow arise and are investigated. For instance, at {Re}=2000 and ₃₃, ₂=11. 0^, mode C coexists together with modes related to modes A and QP seen in a stationary circular cylinder wake. In contrast, at {Re}=5000 and ₃₃, ₂=8. 0^, the dominant mode C coexists with mode QP. Three-dimensional simulations well beyond critical angles indicate that 2-D vortex-street transitions are approximately maintained in the fully saturated 3-D wakes in a spanwise-averaged sense.