Modeling and Simulation Studies on Aeroelasticity of an Airfoil with Simulink

Flutter problem needs to be solved using Computational Fluid Dynamic CFD for aerodynamics and Computational Structural Dynamics CSD for structural deflection in a coupled way. Three-dimensional numerical solutions are computationally expensive due to number of grid points and also unsteady grid motion simulations at various velocities to predict flutter speed. A simplified approach with lumped parameter modeling is quite useful to obtain results within a short duration. Hence, time domain simulation of flutter problem with lumped parameter model is considered in this study with the help of Simulink. The predicted flutter speed may be used as initial condition for 2-D or 3-D detailed numerical simulations. In the present study, the equation of motion for airfoil with two-degrees of freedom on heave and pitch motion is incorporated in Simulink environment. It has a capability to represent aerodynamic force and moment as third order polynomial in pitch angle. Simulation for NACA 0012 airfoil with linear aerodynamics is performed as verification study. The flutter feature is demonstrated as self sustained oscillation in heave and pitch motion, neither growing nor decaying on amplitude of oscillation with respect to time for a particular value of inflow velocity. The predicted results are consistent with results reported in the literature with CFD simulations for aerodynamics. In order to further verify the results, frequency domain approach for the system is considered. The velocity for which the damping ratio crosses zero value is considered as flutter speed, and this value is consistent with time domain prediction. By modeling the wind gust of 15 m/s as forcing term for a typical duration of about 1 s, the present aerofoil undergoes stall before flutter. The current time domain approach is simple and informative under Simulink platform. The simulation method may be extended for future flutter control under Simulink environment.