Transonic Limit Cycle Oscillation Analysis Using Aerodynamic Describing Functions and Superposition Principle

Limit cycle oscillation for an airfoil in transonic air flow considering aerodynamic nonlinearity is studied. Transonic nonlinear aerodynamic forces are calculated by solving Euler equations or Navier-Stokes equations with respect to harmonic airfoil plunging/pitching motion, and then the aerodynamic describing functions and the super position principle are used to build an equivalent linearized aerodynamic model in the frequency domain; hence, the transonic limit cycle oscillation solutions can be obtained by the frequency domain flutter analysis method. The procedures for building the aerodynamic describing function and obtaining the limit cycle oscillation solution are described in detail. Four examples are adopted to verify the accuracy of the present method. The Isogai wing model with NACA 64A010 airfoil is used as the first example to verify the accuracy of the transonic linear flutter solution of the present method. Another NACA 64A010 airfoil model with different structural parameters is then adopted to study its transonic limit cycle oscillation characteristics considering only aerodynamic nonlinearity, and the NACA 0012 airfoil model with both aerodynamic and structural nonlinearities is investigated for its transonic limit cycle oscillation properties. The NLR 7301 airfoil is studied for its limit cycle oscillation characteristics in inviscid and viscous transonic flows, respectively. The results obtained by the present method are in good agreement with those obtained by the existing research with the harmonic balance method and time-marching method. The limitations of the present method are also discussed.