In a project supported by CSBC Corporation, Chung Yuan Christian University in Taiwan and the National Taiwan University recently studied the influence of triangular fins installed near the stern of a merchant ship on resistance performance, using Gridgen^® as their preprocessing tool. CYCU's numerical simulations based on computational fluid dynamics techniques were used as a validation base to give flow details around the fin and ship hull and to understand the flow interaction near the stern, to supplement the experimental measurements conducted by NTU.

The studied ship hull, similar to most modern merchant ships, is generally described as a sophisticated curved surface, especially at the bow and stern. Because of the turbulent flow nature arising in the ship flow problem, the flow characteristics inside the boundary layer needed to be adequately resolved. The grid clustering near the ship hull to capture the velocity gradient can yield cells with high aspect ratio, potentially resulting in highly skewed grids.

An additional difficulty is the length scale of the triangular fin, which in practice is less than 1 per cent of the ship length. The fin, as an appendage of the ship, generally creates only a small percentage additional drag, but that small amount of drag can be difficult to compute if the grid is not accurate and appropriate.

Figure 2 shows the induced vortex by the triangular fin near the stern.

Because Gridgen provides great flexibility in generating high quality grids, the CYCU team was able to create clean multi-block structured grids for the grid blocks around the fin, where the embedded elliptic smoothing solver and spacing control were employed to ensure the required grid orthogonality and first near-wall distance. Figure 1 depicts a typical hull grid created for flow computation. The resistance prediction of the ship hull without the fin first was calculated to provide a baseline for the influence of triangular fins on resistance. The grids for the ship hull with triangular fins were then obtained simply by replacing several grid blocks in the original grid with new grid blocks describing the correct fin geometry, where only a small amount of effort was required. This strategy facilitated the grid generation for ship hulls with different geometrical characteristics of fins and also ensured the same discretization error level among different ship hulls, further improving the prediction accuracy of induced resistance due to the fin.

An induced vortex is produced by the triangular fin at certain angles of attack because the installed fin is not aligned with the local flow direction. Figure 2 depicts the visualization of the induced vortex near ship stern. Figures 3a and 3b illustrate the pressure contour in the vicinity of the triangular fin, indicating there is a stagnation region on the pressure side and a low pressure region on the suction side, where the flow accelerates over the triangular fin. This results in a local tip vortex behind the triangular fin, Figure 4, which apparently is unfavorable to ship resistance characteristics.

Figures 3a and 3b show from two angles the pressure distribution on the fin.

Even without optimizing the triangular fin for reduction of the induced resistance, an adequate fin design method is expected to be developed based on the predictions obtained in these numerical and experimental results.

Figure 4 shows the axial velocity contours of the modified fin.

Prof. Dr.-Ing. Shiu-Wu Chau
Department of Mechanical Engineering
National Taiwan University of Science and Technology
www-e.ntust.edu.tw
May 2009