Unsteady lift for the Wagner problem of starting flow at large angle of attack

A total vortex force line (TVFL) method has been proposed recently which is capable of studying and understanding the unsteady lift force behavior of inviscid starting flow of a flat plate at an angle of attack (AoA) up to 20 degree. The role of additional leading and trailing edge vortices on the Wagner lift curve has been correctly analyzed. In this paper we consider starting flow at much higher AoAs. By comparing with CFD simulations, we find that the TVFL method, derived originally for lift, predicts well the normal force for large angle of attack up to 40 degree. The oscillatory behavior of the normal force is related to leading and trailing edge vortices in a similar way as the lift oscillation for lower angle of attack. It is shown that apart from the initial singularity, the peak value of the normal force coefficient does not exceed a value around 3. Since the TVFL method can clearly identify the origins of lift increasing or decreasing mechanisms due to vortices, the correct prediction of the normal force for large AoAs means that this method can be used to study flapping flight problems.