**9. Concluding Remarks**

This work has set out to evaluate the capabilities of CFD in modelling the nearfield longitudinal wake profile of a planing hull. It undertook a systematic study investigating what factors influenced a simulations accuracy in modelling the nearfield wake, with a particular emphasis on turbulence modelling approach and choice of turbulence model. Finally, it looked to verify whether CFD was able to model flow features of the nearfield wake region and the spray sheet. An extensive literature review revealed that there have been no previous studies looking to investigate the accuracy of CFD in modelling the nearfield longitudinal wake profile of a planing hull. A CFD simulation was set and a systematic study of a number of factors undertaken to ensure the presented set up was the most accurate. Following this, an in-depth validation and verification study was completed to ensure that the numerical results may be utilised with a high level of confidence. Following this experimental data was compared to the numerical results to make a judgment on the ability of CFD in modelling the nearfield longitudinal wake profile of a planing hull. A broad range of conditions was considered to ensure a thorough and robust validation case.

The study showed that CFD may be considered accurate and robust in this application. The numerical Centreline Profile results showed extremely good correlation with the experimental data, with a comparison error of between 0.03 mm and 4.72 mm. CFD was shown to be less capable at modelling the quarterbeam Profile, however there was still good correlation between the experimental and numerical results. Further analysis revealed that this is due to the inability of CFD to model the feature lines that are caused by different aspects of flow interacting with one another. The fact that the use of a symmetry plane on the centreline was found to have no impact on the resulting nearfield wake suggests that a RANS approach fails to model flow that is transient across the centreline. Higher fidelity methods such as LES of DES are suggested as an alternate approach to accurately model these features. A qualitative comparison of the entire nearfield wake pattern in the form of photos and free surface elevation plots confirmed CFD's ability to accurately model the wake pattern of a planing hull, excluding these feature lines.

The study also showed that the calculation of the wake profiles was far less sensitive to the set-up of the simulation than the calculation of forces. With this knowledge, it is safe to make the assumption that once a simulation is considered accurate at modelling the forces acting on a planning hull it may also be considered accurate in the modelling of the nearfield wake. The approach to modelling turbulence was shown to be the most influential in the accuracy of both the forces and the wake field.

This work increases the level of confidence with which CFD may be utilised when modelling stepped hulls, where calculating the nearfield wake region correctly is vital to determine the portion of the afterbody that will be wetted. Investigating the ability of CFD to model the longitudinal wake profile without the presence of the afterbody represents a large simplification of the problem; however, it does show CFD to be capable of accurately modelling the physics of a similar problem. This simplification was suggested by [2] and assumes the presence of the afterbody has no effect upon the flow pattern of the forebody. It is necessary as experimentally measuring this flow pattern with the presence of the afterbody is extremely challenging and is something that has not been achieved to date and, as such, no validation data exists. Having established that CFD provides an accurate and robust solution for the nearfield flow pattern of a planing hull the researchers plan to expand this research to extract and analyse the flow patterns associated with the steps of a stepped planing hull using a numerical methodology as part of their future research.

**Author Contributions:** Conceptualization, A.G.-S., T.T., and S.D.; Data curation, A.G.-S.; Formal analysis, A.G.-S.; Funding acquisition, S.D.; Investigation, A.G.-S.; Methodology, A.G.-S., T.T., and S.D.; Project administration, A.G.-S. and T.T.; Resources, T.T.; Supervision, T.T. and S.D.; Validation, A.G.-S.; Visualization, A.G.-S.; Writing—Original draft, A.G.-S.; Writing—Review & editing, T.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the EPSRC as part of the research project: "Shipping in Changing Climates" (EPSRC Grant no. EP/K039253/1).

**Acknowledgments:** Numerical Results were obtained using the ARCHIE-WeSt High Performance Computer (www.archie-west.ac.uk) based at the University of Strathclyde. The work presented in this paper is taken from the first authors Doctoral Thesis. The first author gratefully acknowledges the scholarship provided by the University of Strathclyde, which fully supports his PhD.

**Conflicts of Interest:** The authors declare no conflict of interest.

**Data Statement:** The underlying data in this paper is openly available from the University of Strathclyde's data repository at: https://doi.org/10.15129/35ef2762-5cd4-480a-90be-745b38ef1539.

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