Nonlinear analysis of dynamic stability and the prediction of wing rock

Nonlinear analysis of dynamic stability for a delta wing in rolling motion at high angles of attack is presented based on a modeled differential equation for wing rolling motion. A method for determining the aerodynamic coefficients up to third-order approximation in the modeled equation, which are functions of the amplitude of wing rolling oscillation at a fixed high angle of attack, is proposed by use of the Fourier expansion approach. Using the modeled equations of motion combined with the aerodynamic coefficients determined by the conical Eulerian computations of supersonic flow past a forced rolling delta wing, we predicted the rock motion of a delta wing that was set into a free-to-roll motion. The results were compared with those obtained by direct coupling calculations based on solving the unsteady flow equations and the wing motion equations simultaneously, which proved to be in fairly good agreement with each other. A numerical investigation of active control technique of the wing rock was also performed by use of the present method.