Simulations on the trajectory and attitude of supercavitating vehicles with a general three-dimensional algorithm

The motion of supercavitating vehicles is significantly influenced by the complexity of the gas–liquid multiphase flow, time delay of the independent expansion of the cavity, and nonlinearity of the interaction between the cavity and vehicle. In this study, a set of general algorithms for simulations on the trajectory and attitude of the supercavitating vehicle is proposed, in which the mathematical model of the supercavitating vehicle is improved to be compatible with multi-degree-of-freedom problems, the three-dimensional cavity topology model is optimized, and the adaptability of the planing force model is extended. Kinematic and dynamic equations are established under general conditions. The corresponding compensators are designed based on the sliding mode and proportion integration differentiation (PID) control theory, and closed-loop control simulations are conducted. The results show that the performance of the sliding mode compensator is better than that of the PID compensator when the compensators have an equivalent intervention effect on the system states errors. Moreover, open-loop simulations are performed to explore the law of the influence of practical factors, such as mass, ventilation, and fins, on the trajectory and attitude characteristics.