A numerical study of the unsteady leading edge separation bubble on an oscillating airfoil

A preliminary study of unsteady leading edge separation bubbles on a NACA 0012 airfoil is undertaken using a finite difference procedure. In this preliminary study the interaction between the viscous and inviscid flow field is neglected. Prior to applying the procedure to the study of the leading edge bubble several calculations are performed, to assess the accuracy of the numerical procedure. These test cases include stagnation point flow, flow about a circular cylinder, and flow over an oscillating flat plate. Calculations are then carried out for flow over the leading edge of a NACA 0012 airfoil oscillating in pitch between 9° and 21° incidence at chord Reynolds numbers of 1.0 × 10⁶ and 2.5 × 10⁶. The results show that for the flow conditions considered, a small leading edge separation bubble is present throughout the entire motion cycle. The bubbles are predicted to move forward and decrease in size as the incidence increases. The results also indicate that the viscous flow in the leading edge region is quasi-steady and that the bubble height is inversely proportional to the Reynolds number. Even with the neglect of interaction, the predicted leading edge bubble behavior is in qualitative agreement with experimental data, indicating that the approach taken should be a feasible method of studying leading edge bubble dynamics and dynamic stall provided that the procedure is extended to include interaction effects.