*8.6. Quarter Beam Wake Profiles*

This section presents the numerical and experimental results, in the same manner as for the previous section whereby the results for all cases are not presented, instead being detailed in Appendix A. Similarly, the results of Savitsky's Wake Equations and the Linear Wake Assumption as calculated

by [10] are not presented in this section, however they are included in the appendixes to allow for an easy comparison between methods.

The ability of CFD to model the QB profiles is seen to be strongly related to the speed of the hull. Whilst the trim effects the shape of the wake, it does not appear to influence CFDs capabilities in calculating the profile, with the same trends being seen for both the 3◦ & 4◦ trim conditions. As the speed is shown to be influential, plots of QB profiles for all speeds in the 4◦ condition are displayed in Figure 12 and will be discussed in this section.

**Figure 12.** Quarterbeam Profiles [τ = 4◦].

Once again, CFD is shown to be relatively accurate for almost all cases. The case that features the best fit between CFD and the experimental data is 2 ms−<sup>1</sup> where is a maximum difference of 6.54 mm, however for the most part the difference this is smaller than 3.34 mm.

As the speed increases the accuracy of the QB profiles decreases. As is discussed in the following wake pattern section, it appears that CFD set up as used in this work is incapable of modelling the feature lines that appear between the interacting aspects of flow. These feature lines are why the experimental QB wake profiles have disturbances, whilst the inability to model these feature lines is why the CFD wake profiles are smooth. Cases that have the largest disturbances (3 and 4.5 ms<sup>−</sup>1) are seen to be the ones that CFD is least capable of modelling. This results in a maximum discrepancy of 12.9 mm in the 3 ms−<sup>1</sup> case, where the CFD performs poorly for distances over 0.4 m from the hull. Despite this, for distances less than 0.4 m from the hull, the CFD result is still considered accurate.

Despite the fact that the CFD is unable to model the feature lines visible in the wake patterns at higher speeds, the quarter beam profiles are still shown to have relatively good correlation with the experimental data. CFD performs well in the region closer to the hull before the feature lines impact the profile; however, is still able to model the trends of the profiles where feature lines impact the results. When the results of Savitsky's Wake Equations and The Linear Wake Assumption are considered it is seen that neither of these methods are capable of modelling the feature lines either, and that the results generated through CFD are considerably more accurate.

### *8.7. Wake Pattern*

One of the notable advantages in using CFD is that the post processing capabilities are significantly improved, and that analysis of the simulation offers far more possibilities. Experimental tests at 4.5 ms−<sup>1</sup> provided only six seconds of run time. Measurements of certain parameters is made more difficult by this time restriction. In addition to this increased challenge, it is not always possible to acquire certain data from experimental testing, such as free surface elevation plots.

In addition to allowing a comparison of quantitative data in the form of wake profile plots, a qualitative comparison of photos taken during the tank testing is made with free surface contour plots from the CFD simulations. The wake profile plots give a far better measure of the accuracy of the CFD; however, comparing the wake patterns from both methods offers further insight. One of the key issues when comparing the photos and the elevation plots is that it is impossible to ensure that the views are at the same scale and perspective to allow a valid comparison. It is possible to ensure that the scale and angles are similar; however, engineering judgment must be employed when making visual comparisons.

Figures 13 and 14 show these comparisons for the trim angles 4◦, 2◦, and 4.5 ms−1. As can be seen both cases show similar wake patterns, further validating the ability of CFD in calculating the longitudinal wake profiles and wave pattern of a planing hull. One of the notable differences is that the experimental photos show far more distinct feature lines, created by the interaction of different aspects of flow. Some of these are visible in the contour plots; however, they are far less clearly defined. It is thought to be the inability to accurately model these feature lines from the intersecting parts of flow that leads to the loss of accuracy in some of the quarter beam wake profiles, as mentioned previously. In general, aside from these pronounced feature lines the CFD is very capable of modelling the wake elevation.

Finally, it is possible to compare the spray patterns of the two methods. Once again, there is issues in ensuring that the comparison is made from the same angle and scale, and, as such, engineering judgment must once again be used. Figure 15 shows the sheet spray for 4 ◦ trim at 4.5 m/s. In order to visualise the spray the isosurface value must be changed from 0.5 to 0.99 as the spray is not considered to be a free surface, and instead is a mixture of air and water. As can be determined from the visual comparison the spray pattern appears to be well captured.

*J. Mar. Sci. Eng.* **2020**, *8*, 516

**Figure 13.** Wake Pattern Comparison [τ = 4◦ and *speed* = 2 ms<sup>−</sup>1].

**Figure 14.** Wake Pattern Comparison [τ = 4◦ and *speed* = 4.5 ms<sup>−</sup>1].

**Figure 15.** Spray Sheet [τ = 4◦ and *speed* = 4.5 ms<sup>−</sup>1].
