Scaling Laws for an Airfoil with MFC-Actuated Trailing Edge Plate

This study describes the steady effects on the lift coefficient of an airfoil with a plate mounted on the trailing edge and actuated with MFC piezoelectric devices. The problem is analysed numerically with a low fidelity model which has been validated experimentally. A linear structural model is developed taking into account large beam rotations. Finite differences have been used to solve the structure equations, while XFoil is employed to solve the aerodynamic problem by virtue of its speed, accuracy, and widespread use. The performance of the system is evaluated by the derivative of the lift coefficient with respect to the actuation force. The behaviour of this scalar value as a function of both structural and aerodynamic parameters is modelled with approximate, closed form scaling laws when possible. A rather simple but accurate scaling law can be envisaged for the inviscid, uncoupled results. The viscous ones can be described as functions of the boundary layer properties over the actuation system. The coupled formulation suggests that aeroelastic effects decrease the actuation efficacy and can be modelled as a power law of both flight velocity and actuator length. The new insight provided in the present paper can be useful in preliminary design to rapidly evaluate the performance advantage that can be obtained from this morphing technology.