Rankine Source Method for Ship–Ship Interaction Problems

Abstract

A Rankine source method is extended and applied to ship-ship interaction problems. The method covers the nonlinear steady flow and linear seakeeping in the frequency domain. The nonlinear steady flow solution accounts fo r the nonlinear free-surface conditions, ship wave, and dynamic trim and sinkage. Periodic flow due to waves is linearized with respect to the wave amplitude, taking into account interactions with the nonlinear steady flow following Hachmann approach, which considers the steady perturbation potential as constant in the body-fixed reference frame. This is advantageous fo r the prediction o f ship motions at moderate to high Froude numbers. In this context, a new formulation o f the boundary condition fo r the multibody case is derived. Two examples are considered, overtaking in calm water and replenishment at sea. For a feeder vessel overtaken by a container ship, horizontal forces and yaw moment are computed and compared with ref erence data. As an example o f replenishment operation, interaction between a frigate and a supply vessel is studied. Ship motions are computed fo r two relative positions and three forward speeds and compared with model test data fo r the largest forward speed. The Rankine source method proves as more accurate compared with a zero-speed freesurface Green function method.

Ships speed limitations for reliable maintenance of the quay walls of navigation channels in ports

“…Kadri and Weihs [14] modelled hydrodynamic interactions between two slender bodies of revolution moving in close proximity, in an unbounded, inviscid, and incompressible fluid. Von Graefe et al [35] introduced the nonlinear steady flow method that accounts for the nonlinear free-surface conditions, ship wave, and dynamic trim and sinkage. Hydrodynamic interactions between two ships advancing in waves were also considered by Chen and Fang [5].…”

Seakeeping criteria of a moored and articulated multibody floating platform in head seas

“…Beck (1996); Scorpio et al (1996) and Subramani (1998), representing the hulls and free-surface boundaries via desingularized Rankine sources, computed nonlinear ship motions in an ideal fluid using the Euler-Lagrange method. Such a method was then extended and applied to ship-ship interaction problems (von Graefe et al, 2015). Nevertheless, to capture the nonlinearities of viscous and/or complex free-surface flows, high-fidelity viscous-flow solvers are the preferred choice (Jiang, 2021).Computational fluid dynamics (CFD) has been commonly applied in wave-structure interaction (WSI) problems based on generally two approaches: Eulerian (meshbased) and Lagrangian (mesh-free) methods.…”

Achieving Drag Reduction with Hullform Improvement in Different Optimizing Methods

“…The Rankine source method and Reynolds Averaged Navier Stokes (RANS) based viscous flow methods are potential flow panel methods that were developed in several studies with quite advanced techniques. The Rankine source method is considered fast, efficient, and highly precise in potential flow theory, e.g., Rankine source method with the optimization algorithm Nonlinear Programming Method (NLP) in monohull (Zhang and Zhang, 2015) and multihull optimization (Von Graefe et al, 2013;Von Graefe et al, 2015). The Michell integral method or thin ship theory is considered a more straightforward and faster CFD method (Tuck and Lazauskas, 1998).…”