BIFURCATION CATASTROPHE CHARACTERISTICS FOR UNSTEADY VENTILATIED SUPERCAVITY

Aiming at the instability of the unsteady ventilated supercavity, the bifurcation and catastrophe theory methodology is adopted to analyze the instability mechanism of the ventilated supercavity. Based on Logvinovich independence principle of the cavity section expansion and the ventilated mass balance equation, the integral equation that contacts the length of the unsteady ventilated supercavity and cavity number is obtained. According to calculus thought, the integral equation is divided into two first class Volterra equations to get the solution and the linear small disturbance system. Then the status catastrophe caused by static bifurcation is discussed and verified through numerical simulations. Theoretical analysis and numerical simulation results show that transcritical bifurcation at the equilibrium points of the unsteady ventilated supercavity leads to the generation of catastrophe at the bifurcation point. These phenomena reveal the instability mechanism of the stable ventilated supercavity as changing ventilatation parameters at the critical value, which are benefit to design stable control system for supercavitating vehicle.