Shape optimization of elliptical disk-shaped cavitator based on physics-informed neural networks and multi-objective genetic algorithm

In order to avoid the problem of difficult control during high-speed motion of the supercavitating vehicle, this paper adopts an approach where the vehicle cruises at low speed and then transitions to high-speed straight-line navigation after the target is found. The non-body-of-revolution underwater vehicle exhibits good drag reduction in the low-speed state. Therefore, this paper employs an elliptical disk-shaped cavitator. The supercavity shape of the cavitator under high Fr condition is analyzed using computational fluid dynamics (CFD) simulations. Based on the Logvinovich model and the principle of independent expansion, a mathematical model of the supercavity shape for the elliptical disk-shaped cavitator is constructed as physical information, and a physics-informed neural networks (PINN) model was trained to predict the supercavity shape under specific cavitation number. The trained PINN model demonstrates high accuracy in predicting supercavity shapes under the specific cavitation number (σ = 0.054), as quantitatively validated against CFD results. To achieve an optimal balance between minimizing the cavitator size and maximizing the vehicle length, a Pareto frontier solution was obtained using the non-dominated sorting genetic algorithm II. The optimal results indicate that the long and short semi-axes of the cavitator are 0.0242 and 0.0163 m, respectively, and the length of the vehicle is 0.89 m. CFD results show that the cavity generated by the optimized cavitator can completely envelop the vehicle, meeting the design requirements.