Dynamic destabilization analysis of the reentry vehicles using bifurcation theory and unsteady numerical simulation

To study the problem about dynamic destabilization of the reentry vehicles, the bifurcation theory of nonlinear autonomous dynamic system is used together with the unsteady Navier-Stokes equations simulating the pitching process. The investigations shown that, the astronautic vehicles reentering into the atmosphere would generally occur a dynamic destabilization of pitching motion as their flight Mach number decreased, and the phenomenon of dynamic destabilization befallens at the point of the Hopf bifurcation, furthermore, there are two types of Hopf bifurcation named subcritical Hopf bifurcation and supercritical Hopf bifurcation. To validate the theory of the Hopf bifurcation, two reentry configurations are numerically studied. One is the Japanese capsule OREX, composed of a spherical cap facing forward and a reversed cone facing backward. With Mach number decreases in the reentry process for the capsule, the pitching motion would evolve from a point attractor to a periodic attractor, and the critical Mach number is about 2.2 when the subcritical Hopf bifurcation occurs, the theory analysis and simulation result is in good agreement with the experiment and flight test results. The other configuration is a flat-nose winged double-cone body, with the decrease of Mach number, its pitching motion would evolve from a periodic attractor to a point attractor, and the critical Mach number at which the supercritical Hopf bifurcation occurs is about 6.8.