Transonic time responses of the MBB A-3 supercritical airfoil including active controls

Abstract

Aeroelastic time-response analyses are performed for the MBB A-3 supercritical airfoil in small-disturbance transonic flow based on the use of transonic code LTRAN2-NLR. Three degrees of freedom are considered: plunge, pitch, and aileron pitch. The main objective was to investigate the applicability and accuracy of statespace aeroelastic modeling for two-dimensional airfoils with active controls in transonic flow. A state-space aeroelastic model was formulated using a Fade aerodynamic approximation. The resulting equations are explicitly solved in the time domain yielding the aeroelastic displacement responses. Parallel time-marching response histories were determined numerically through a coupled integration of the structural equations of motion with the unsteady aerodynamic forces of LTRAN2-NLR. The Fade and time-integration responses are in good agreement. The Fade eigenvalues compare well with the time-marching damping and frequency estimates. A simple feedback control loop was included in the aeroelastic system to study the effects of active control on the aeroelastic response. A variety of control laws utilizing displacement, velocity, and acceleration sensing were considered. Transonic time-response behavior of the MBB A-3 airfoil is discussed and comparisons are made. b,c ce CQ ^ Cp,C*p [C] { G } h KA,KD,KV [K] m M [M] p {p }