Prediction of horizontal and vertical turning maneuvers of a generic submarine model by closed-form solutions and CFD

Turning maneuvering performance of a generic submarine in both the horizontal and vertical planes is investigated using closed-form (analytical) solutions and the Computational Fluid Dynamics (CFD) method. The aim is to provide a simple yet improvable method throughout the design phase of an underwater vehicle. Both the turning circle maneuver in the horizontal plane and the rising maneuver in the vertical plane are performed. Vehicle trajectories are obtained using closed-form solutions and a linearized maneuvering model with a limited set of hydrodynamic coefficients computed from the CFD model. The derivation of the closed-form solution is based on the basic mechanical principles of steady circular motion, while the hydrodynamic coefficients are determined via steady CFD simulations using a single grid topology. The steady turning diameter serves as the figure of merit in a turning circle maneuver. For the rising maneuver, trajectories predicted by both methods are directly compared. The methods are found to be in good agreement for both maneuvers. Maneuvering predictions made with the linear coefficient set are also open to development. As the design of the submarine evolve, nonlinear and coupled effects can be included in the mathematical model by incorporating related hydrodynamic coefficients to obtain more accurate results.