Theoretical and experimental study of dynamics of supercavitating vehicles with cone cavitators

A mathematical model of a supercavitating underwater vehicle dynamics based on the complete set of equations of the 6-DOF motion of an elongated solid body is considered. Originating from the G. V. Logvinovich's principle of independence of the cavity section expansion, the approximation mathematical model of a `slender' cavity is used to calculate the supercavitation flow. The hydrodynamic forces acting on various structural elements of the underwater vehicle were estimated using the approximation dependencies obtained both from the experiments, and the theoretical solutions. The developed mathematical model of the supercavitating vehicle dynamics has been verified by comparing the calculated parameters with those obtained during towing tests of the model of a supercavitating underwater vehicle in the high-speed experimental tank at the Institute of Hydromechanics of the National Academy of Sciences of Ukraine. The main attention was paid to the dynamics of supercaviting models with the cone cavitators. Basing on the experimental results, the new approximation formula for the lift on the inclined cone cavitators was proposed. The simulated and the experimental shapes of the stationary and non-stationary cavities behind the inclined cone cavitators were compared. Verification of the mathematical model `as a whole' was carried out by comparing the calculated kinematic parameters with those obtained during the towing tests of the movable supercavitating model with one degree of freedom in pitch. Various modes of the motion of the supercavitating model were organized in the tests: planing along the lower cavity's wall; planing along the upper cavity's wall; motion with the fins without touching the cavity walls by the model body; oscillatory motion between the upper and lower cavity walls. The experimental and calculated kinematic characteristics of the supercavitating model are compared. Their sufficiently good qualitative and quantitative agreement shows that the developed mathematical model adequately predicts the dynamic behavior of the underwater supercavitating vehicle.