Investigation of nonlinear aeroelastic behavior of airfoils with flow separation based on cubic static stall modeling

In this paper¡ by defining a new paradigm for nonlinear aerodynamic equations of flow separation and static stall¡ a new form of nonlinear aeroelastic equations for two degrees of freedom airfoils (torsional and bending) are presented. Structural equations are based on the nonlinear mass-spring model; include the nonlinear quadratic and cubic terms. Aerodynamic equations are obtained by combining the unsteady Wagner model and the nonlinear lift coefficient-angle of attack for simulating stall using a cubic approximation. Hamilton’s principle and Lagrange equations were used to derive the aeroelastic equations. The obtained integro-differential nonlinear aeroelastic equations are solved using a new time-history integration method. The aeroelastic behavior of the airfoil is compared in both unsteady and quasi-steady flow. Using the time-history method compared to the phase space method leads to fewer equations. The results show that the aeroelastic behavior of airfoil with a linear structure¡ using a nonlinear aerodynamic theory for the stall¡ causes oscillations with a limit cycle in unsteady and quasi-steady flow compared to other linear aerodynamic theories. Also¡ the use of the cubic curve instead of the piecewise linear curves which is commonly used in other references¡ although¡ causes an apparent complication of the equations¡ reduces the computational time due to faster convergence in solution and makes the reduction in errors. The results show that the use of nonlinear aerodynamic static stall not only reduces the instability velocity¡ but also reduces the amplitude of limit cycle oscillations in both unsteady and quasi-steady regimes.