Case 3.1 Geometric Model Of Wigley Hull

3. Geometry and Methods:

3.1 Geometric Model of Wigley Hull:

An STL-format model of a Wigley hull (Figure 1) is included in the Wigley hull example case provided with OpenFOAM. Its dimensions are L = 1 m, B = 0.1 m, H = 0.0625 m.

In initial simulations, difficulties arose due to the fact that wave elevation sometimes crossed the upper limit of the domain in some regions near the hull. Following this, the mesh was extended in its height from 0.0399 to 0.31 metres. The Wigley hull model, being an open surface, had to be closed, so that the meshing utilities would not create cells on its inside, and made higher, so that the waves would not move to the top of the hull.

Fig. 1. Wigley hull model

The simplest solution found was to place a rotated

The blockMesh utility allows for the generation of a mesh consisting of blocks, defined by up to eight vertices, that contain hexahedral mesh elements. It is only suited for geometries that can be easily achieved with a series of simple blocks.

Each block is assigned its own local coordinate system, and the user can define how many cells the block will be divided into along each coordinate. The implementation of mesh grading, which makes the size of cells in a certain direction become progressively smaller or larger along that direction, is also an option.

The snappyHexMesh utility is used for the definition of more complex geometries. It presupposes the previous existence of a mesh created with blockMesh (known as the background mesh), as well as files in the STL format containing the shape of the geometric features to be implemented. snappyHexMesh adapts the existing mesh to the new geometry and refines the region around it (i.e., generates smaller-sized cells in the region). It can also be used to refine other regions of the

2. Summary of the simulations performed on the Wigley hull

4. Results and discussion:

4.1 Drag Coefficients:

The steady state values for the drag forces were obtained by observing the dependence of the drag force in time, identifying the instants during which the forces are oscillating around a fixed value, and time-averaging the forces throughout that time range. Examples of the convergence and averaging on Wigley hull cases are shown in Figure 8 and Figure 9. Fig. 8. Evolution of drag force throughout the simulation and indication of the mean force for the Wigley hull with Fr = 0.250 Fig. 9. Evolution of drag force throughout the simulation and indication of the mean force for the Wigley hull with Fr = 0.400

The total drag coefficients obtained for the unrefined mesh and for the cases with full mesh refinement are presented in Figure 10. Fig. 10. Total drag coefficients on the Wigley hull for different full mesh refinements

The comparison between results for the different cell refinement levels near the hull surface is shown in Figure 11. The cell level of 3 corresponds to the initial unrefined mesh. Fig. 11. Total drag coefficients on the Wigley hull for different refinement levels around the