Numerical study of saddle-node bifurcation for longitudinal flight with CFD/RBD technique

Abstract

The square cross section missile was found instability in the longitudinal direction at a certain Mach number in a range of angle of attack both in CFD and wind tunnel test results. To deeply understand the flight behavior and the aerodynamics of the missile, the coupled Computational Fluid Dynamic/Rigid Body Dynamics (CFD/RBD) approach was employed to simulate the free flight process, and the predict technique of dynamic stability derivatives was founded to analyze the types of equilibrium points. The study shows that the type of trim angle of attack is turned from stable node to an unstable saddle with the increase of Mach number, known as the saddle-node bifurcation. There are two extra stable nodes are produced and located on the left and right sides of the saddle point when the Mach number is bigger than the transition Mach number. Further simulation results of free pitching motions reveal the decrease of the attraction region of the two extra stable modes, which makes the pitching motion more complicated and sensitive. A slight change of the initial angle of attack may make the missile move from one trim point to another.