Vortex Shedding From a Bilge Keel in a Transient Turbulent Flow

Abstract

The hydrodynamic damping of a bilge keel during the roll motion of a ship is fairly well understood and its basic principle can be summarized as follows: The larger the bilge keel attached to the hull, the stronger is its roll damping effect. The geometric limitations regarding the size of the bilge keel are set by class regulations mainly dependent on the ship’s length, breadth and draft. Most bilge keel shapes are simple flat bars attached to the center of the bilge radius. While the added resistance of the bilge keel has to be kept as low as possible, the effective area for the cross flow generated by the roll motion should be maximized. Therefore the bilge keel’s cross section has to be kept small and its camber line parallel to the streamlines. In more sophisticated designs L-shaped bilge keels are applied in order to increase the damping effect on the roll motion. The aspects above need to be considered when defining the geometric limits of a bilge keel, however to further optimize the design of bilge keels numerical simulations are needed. Even with today’s computing power, the costs of simulating a full ship hull with a sufficiently high mesh resolution to capture viscous vortex shedding effects would be prohibitive. To address and overcome this restriction a numerical test setup was developed that simulates the flow only in the near vicinity of the bilge keel. By further neglecting the influence of the free surface, it was possible to use a standard single-phase, incompressible, turbulent, transient solver. The open source FVM code OpenFOAM was used for all three stages of the simulation: mesh generation, solution process and post-processing. With this simplified simulation model a systematic investigation of the turbulence model, the temporal and spacial discretization, as well as the principles of vortex shedding was carried out. The damping efficiency of the bilge keels was evaluated on basis of the mechanical work — by moving the hull through a viscous fluid — and the kinetic energy transported within the vortices. The findings from these flow simulations provide insights into the principles of bilge keel vortex shedding and their interaction with the hull and enable the development of bilge keel design guidelines.