Table 16, Fraction of data set where Error2D was within 10% of free stream speed
Upstream, no fin
Flow region Tetrahedral mesh 0.827
Down stream, no fin
Downstream, with fin
0.820 0.623
Hexahedral mesh 0.840
0.785 0.598
These tables show that there was very little effect of the mesh type on the accuracy of the predicted flow patterns, when compared to the observed flow patterns from the PIV experiments. The hexahedral mesh had a small advantage on the upstream side of the tug model, but on the downstream side, the tetrahedral mesh had a slight advantage. In general, the best predictions were for the upstream side of the tug and the worst predictions were for the downstream side of the tug, with the fin. This was to be expected since the downstream side of the flow was much more unsteady (Molyneux et al., 2007b).
For the flow on the upstream side of the hull (Figures 17 and 19), both meshes gave similar errors, with the worst predictions of flow vectors close to the hull and the accuracy of the predictions improving as the distance from the hull increased. PIV measurements close to the hull will likely be the most difficult to obtain accurately, because the hull, even when painted black, reflects the light and a bright band is seen in the pictures of the particles where the laser beam cuts the hull. Even though the analysis software includes a filter to reduce this effect, the experiment results obtained in this region may be subject to error.
On the downstream side of the hull without the fin, (Figures 21 and 23) the highest errors were seen on the underside of the hull, just before the corner of the bilge, and on the top of the
vortex caused by the flow
separation at the bilge. In the region under the hull, the CFD did not predict the observed speed of the flow, especially for the tetrahedral mesh. In this case the predicted flow was almost stationary, whereas the PIV measurements showed it was not. The hexahedral mesh gave slightly smaller error in this region.
The other area where the predicted flow did not match the observed flow was on the downstream side of the hull, between the bottom of the hull and the waterline. This was the region where the strongest flow velocities occurred. These high velocities were the result of the vortex caused by the flow separation off the corner of the bilge. Again the hexahedral gave smaller errors in this region but the difference was not significant relative to the tetrahedral mesh.
Table 18, Comparison of errors in velocity magnitude for in-plane vectors, Series 60 and escort tug, hexahedral mesh
Parameter Series 60, CB=0.6
Yaw angle 35
Errorv Errorw Error2D
degrees, Midship section 0.053 0.049 0.164
Escort tug, no fin
Yaw angle 45
degrees, Midship section 0.027 0.003 0.078
These differences may be due to the
Escort tug, with fin Yaw angle 45 degrees, Midship section
0.014 0.042 0.102
significant
differences in the hull shapes between the escort tug and the Series 60 hull. The escort tug was proportionally
Based on the numerical analysis, both meshes gave similar predictions of the flow patterns around the hull of an escort tug with a yaw angle of 45 degrees, and neither approach had a significant advantage in any of the conditions investigated.
The non-dimensional values for the errors between the PIV experiments and the CFD predictions for the escort tug at 45 degrees yaw are compared to the Series 60 model at 35 degrees yaw (Molyneux & Bose, 2007) in Table 17 for the tetrahedral mesh and Table 18 for the hexahedral mesh. These tables show that the accuracy of the CFD predictions for the escort tug was better than for the Series 60 model, and the CFD predictions showed less variation with the type of the mesh.
Table 17, Comparison of errors in velocity magnitude for in-plane vectors, Series 60 and escort tug, tetrahedral mesh
Parameter Series 60, CB=0.6
Yaw angle 35
Errorv Errorw Error2D
degrees, Midship section 0.091 0.013 0.241
Escort tug, no fin
Yaw angle 45
degrees, Midship section 0.024 0.010 0.070
Escort tug, with fin Yaw angle 45 degrees, Midship section
-0.01 0.040 0.098
When the fin was present (Figures 23 and 25) and the very large vortex was generated, the worst comparison between the experiment data and the CFD predictions occurred close to the hull on the downstream side between the bottom of the hull and the waterline, and under the hull. Both meshes showed relatively small errors in the flow around the vortex, but the hexahedral mesh gave relatively poor prediction of the flow patterns close to the waterline, compared with the tetrahedral mesh.
B-58
©2008: Royal Institution of Naval Architects
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