A Correction Method for Unsteady Transonic Aerodynamics

This paper presents a new method for transonic pitching airfoils based on a RANS CFD study and the Theodorsen model of an oscillating pitching flat plate. This study quantifies the deviation of the lift coefficient predictions using CFD from that obtained using the Theodorsen model, which is based on the incompressible potential flow assumption. The present method corrects this theoretical model by modulating the Theodorsen functions by coefficient functions that depend on the reduced frequency and the Mach number. It is demonstrated that the modified theoretical model predicts lift coefficient in good agreement with the CFD results in the Mach number range from incompressible (M =0.2) to transonic (M =0.755) flow for a range of reduced frequencies typical of transonic flutter. The simulations are first validated by comparing pitching NACA0012 airfoil results with experimental results at transonic flight conditions, which establishes the requirements for a grid converged unsteady transonic solution. The hysteresis loop, Cl versus α, attains a grid independent solution that compares well with experiment. The present correction method will guide the development of a new state space model for the Variable Camber Continuous Trailing Edge Flap (VCCTEF) system and eventually a new transfer function that will be incorporated in a new aeroelastic framework leading to an appropriate transonic flutter model for use in the future aircraft systems in development under the NASA Advanced Air Transportation Technologies (AATT) project.