Transient growth in an airfoil separation bubble

In this work, transient growth in a laminar separation bubble in a low–to–moderate Reynolds number airfoil flow is investigated. Optimal two and three–dimensional initial perturbations are computed for the flow over a NACA 0012 airfoil at angle–of–attack α = 5◦ with chord based Re = 5 × 104. At this Reynolds number, the pressure surface boundary layer remains attached over the length of the airfoil while the suction surface boundary layer undergoes separation before becoming two–dimensionally unstable leading to periodic vortex shedding and reattachment. Transient growth analysis shows that this flow supports large energy growth for both two and three– dimensional perturbations. Optimal growth values and flow topologies show that two–dimensional mechanisms are the primary energy growth mechanisms. Upstream of vortex shedding, the primary growth mechanism appears to be the Orr mechanism while a separate mechanism appears to drive further energy growth downstream in the base flow shed vorticity.