Modeling and simulations of supercavitating vehicle with planing force in the longitudinal plane

Pitching motion is one of the most important characteristics in the longitudinal plane for the maneuvering supercavitating vehicle. In this case, supercavity is unsteady to dramatically change hydrodynamic distribution of its vehicle because of some factors such as changes of ambient pressure and control surfaces, gravity, inertial force, and so on. More importantly, planing force is usually produced to provide restoring force and moment for motion stability. The maneuvering supercavity model is applied to model supercavitating vehicle with planing force in the longitudinal plane. The corresponding numerical algorithm is developed to simulate uncontrolled vehicle making a diving motion in the longitudinal plane and calculate planing force based on the model. The algorithm includes two intercoupling sub-algorithms: the self-developed cavitation number embedded coefficient correction algorithm for unsteady supercavity and Runge-Kutta algorithm for vehicle's trajectory. The model and numerical algorithm are validated to some extent by comparing numerical results with ones of the empirical supercavity model applied widely.