Dynamic Stall modelling at low Reynolds Numbers

Dynamic stall is described by Mac Croskey et al. as a phenomenon that occurs on airfoils subjected to unsteady motion with high amplitude or frequency. The phenomenon occurs at higher angles of attack and lift values than steady stall. Dynamic stall can also be associated with the shedding of a vortex from the leading edge. This vortex usually affects the flow around the airfoil such that it increases further the instantaneous lift acting on the wing and produces a nose-down pitching moment when the vortex is swept toward the trailing edge. The modeling of dynamic stall is challenging even in 2D because it involves separated and turbulent flow. Typical 2D approaches range from semi-empirical, such as the Leishman-Beddoes (LB) or the ONERA models, to Computational Fluid Dynamic (CFD) methods.
This thesis makes two major contributions towards the development of a dynamic stall model for 3D wings at low Reynolds number based on the 2D Leishman-Beddoes model. The LB model has not been conceived with very low Reynolds number in mind. The first contribution of this thesis is the development of a modified Leishman-Beddoes model able to handle dynamic stall at low Reynolds number ranges. It uses Wagner theory for the incompressible attached flow and adapts the stall onset criterion by Sheng et al to low Reynolds numbers. In order to calibrate and validate the model, an extensive set of dynamic stall experiments were carried out in a low-speed wind tunnel for three airfoils: a flat plate, a NACA0012 wing, and a NACA0018 wing. This modified Leishman-Beddoes model results in better aerodynamic load predictions than the original model for low and medium reduced pitch rates. For the highest reduced pitch rates, neither model yields fully satisfactory predictions.
The second contribution is the development of a closed-form unsteady attached flow model for 3D wings. It combines the 2D Wagner unsteady aerodynamic loads calculation with Prandtl’s lifting line, by means of the unsteady Kutta-Joukowsky theorem. This new model was validated by means of comparison to the predictions of an unsteady vortex lattice model for impulsive and oscillatory motions of wings of different planforms and aspect ratios. An additional validation involved the calculation of the flutter speed and frequency of finite rectangular wings with pitch and plunge degrees of freedom and comparison to the predictions of an aeroelastic vortex lattice formulation.