Nonlinear aeroelastic behavior of an airfoil with free-play in transonic flow

An investigation has been made into the nonlinear aeroelastic behavior of an airfoil system with free-play nonlinear stiffness in transonic flow. Computational Fluid Dynamics (CFD) and Reduced Order Model (ROM) based on Euler and Navier-Stokes equations are implemented to calculate unsteady aerodynamic forces. Results show that the nonlinear aeroelastic system experiences various bifurcations with increasing Mach number. Regular subcritical bifurcations are observed in low Mach number region. Subsequently, complex Limit Cycle Oscillations (LCOs) and even non-periodic motions appear at specific airspeed regions. When the Mach number is increased above the freeze Mach number, regular subcritical bifurcations occur again. Comparisons with inviscid solutions are used to identify and elaborate the effect of viscosity with the help of aeroelastic analysis techniques, including root locus, Single Degree of Freedom (SDOF) flutter and aerodynamic influence coefficient (AIC). For low Mach numbers in the transonic regime, the viscosity has little effect on the linear flutter characteristic because of limited influence on AIC, but a remarkable impact on the nonlinear dynamic behavior due to the sensitivity of the nonlinear structure. As the Mach number increases, the viscosity becomes significantly important due to the existence of shock-boundary layer interaction. It affects the unstable mechanism of linear flutter, impacts the aerodynamic center and hence the snap-through phenomenon, influences the AIC and consequently the nonlinear aeroelastic response. When the Mach number is increased further, the shock wave dominates the air flow and the viscosity is of minor importance.