Nonlinear aeroelastic analysis of a multi-element airfoil with free play using continuation method

Abstract

In this study, the nonlinear aeroelastic response of a NACA0012 airfoil with leading-edge and trailing-edge control surfaces is studied numerically using a modified filtered impulse function method and continuation method. The source of nonlinearity comes from the free play behavior of both control surfaces which leads to the nonlinear properties of the structural stiffness matrix. The aerodynamic responses of these aeroelastic systems for varying oscillation frequencies are assumed to be linear for small deflections. These responses are developed using a reduced-order model by using the proposed modified filtered impulse function method on inviscid rotational flows computed using CFD methods for the Euler Equations. Key factors for maintaining accuracy using the proposed filtered impulse function are discussed with examples. The linearized aeroelastic equations are solved using the continuation method with the adaptive step size for three different situations that could arise in practice. The analysis process is conducted in the modes tracking and parameter variation separately. This study shows that compared to the airfoil with a single trailing-edge control surface in free play, the presence of the leading-edge flap motion could decrease the flutter speed and dominate the flutter mode in the absence of free play behavior. However, only slight differences could be observed from the limit cycle oscillations (LCO) analysis for which the structural nonlinearity is dominant owing to free play.