An Approach for Computing Parameters for a Lagrangian Nonlinear Maneuvering and Seakeeping Model of Submerged Vessel Motion

Abstract

In this study, hydrodynamic forces on a submerged vessel maneuvering near a free surface are determined using a reformulated Lagrangian nonlinear maneuvering and seakeeping model derived using Lagrangian mechanics under ideal flow assumptions. A Lagrangian mechanics maneuvering model is first reformulated to simplify the computation of parameters; then, incident wave effects are incorporated into the reformulation; finally, the parameters are computed using a medium-fidelity time-domain potential-flow panel code. Predictions from the reformulated Lagrangian nonlinear maneuvering and seakeeping model, whose parameters are computed using the methods described here, are compared with direct numerical computations in two steps for a prolate spheroid maneuvering in the longitudinal plane near the free surface. First, the hydrodynamic force and moment predicted by the model are compared with solutions from the panel code for sinusoidal motion in surge, heave, and pitch in calm water. Second, the hydrodynamic force and moment are investigated for cases where the spheroid maneuvers to approach the surface in calm water and in plane progressive waves. To conclude, a physically intuitive formulation of the Lagrangian nonlinear maneuvering and seakeeping model is presented for control applications and simulations.

The Effect of a Linear Free Surface Boundary Condition on the Steady-State Wave-Making of Shallowly Submerged Underwater Vehicles

“…The boundary element method (BEM), Aegir [16], has been used in the past for the computation of parameters used in the LNMS model [7,8]. Aegir is a high-order timedomain Rankine-source BEM (using third-order B-splines for panel geometry and source distribution) that is able to include the effects of a free surface.…”

“…A framework for the LNMS model was developed from first-principle energy considerations by Battista et al using potential flow formulations [2,5,6]. The model was further reformulated to allow for parameter computation using a three-dimensional boundary element method (BEM) [7,8]. The reformulation process enabled the direct use of fluid potential functions generated by a boundary element method to populate the coefficient-based LNMS model.…”