**1. Introduction**

Whilst high-speed planing hulls have always been of interest to naval architects, substantially less time and resources have been invested into research surrounding the topic than larger, more commercially exploitable areas, such as shipping. In industry, a lot of the knowledge was developed from experience working in the field, and it was commonplace to employ a 'trial and error' based design process. Despite this, in recent years there has begun a steady progression in the available work researching high-speed hulls. Notably, in recent years, as is the case across the board with all topics relating to naval architecture, advancements in the power and availability of computational resources have led to an increase in numerical studies using Computational Fluid Dynamics (CFD) to model complex flow.

The use of CFD provides numerous advantages over conventional model testing. Perhaps the most notable of these is the enhanced post processing capabilities and the ability to extract data that is difficult to measure experimentally, such as pressure fields and flow patterns. Before CFD may be used as a design tool with a high level of confidence, it is first necessary to explore its applicability to a given problem, ensuring that it is capable of producing accurate results. While numerous studies have investigated CFD's capabilities in relation to high-speed vessels, few have looked to determine its ability in modelling the nearfield wake patterns. The nearfield wake region of a planning hull is of specific interest for a number of reasons. Primarily in the case of a planning hull, it may have implications over the choice of propulsion system. There may also be a number or operation specific requirements on the wake produced by a vessel that require analysis of this flow.

A variant of the traditional planning hull that is of particular interest to naval architects is the stepped hull, which aims to minimise the resistance of a vessel through a reduction in the wetted surface area. It has been shown that the inclusion of steps is capable of producing a reduction of 10–15% in the hydrodynamic resistance and typically gives an increase in speed of 6–10 knots [1]. A stepped hull has one or more transverse discontinuities, or steps, behind each of which the hull elevation raises slightly. When the vessel is travelling at high speeds, air is drawn in through inlets, causing the flow to separate at each step. The forces generated by both the forebody and afterbody must combine to provide vertical equilibrium for a stepped vessel, as well being used to determine the resistance and trim. In order to determine the forces on the afterbody the nearfield wake profile of the forebody must be determined in order to calculate the intersection with the afterbody.

The study reported in this paper sets out to determine the accuracy of CFD in modelling the nearfield longitudinal wake profile through a comparison with physical testing. This will allow designers to use CFD as a tool for the analysis of wake of a planning hull with confidence. In addition to performing this validation, the paper will report on the systematic study of the CFD set up. This will ensure that the most accurate set up is established, as well as highlighting the effects that different set ups have on the accuracy of the simulation. Finally, the work will be used to justify whether CFD is capable of modelling the flow of a stepped hull as it separates from the forebody and interacts with the afterbody of the hull. Modelling the wake profiles without the presence of the afterbody changes the physics of the problem and simplifies it massively; however, it has previously been proposed for the analysis of stepped hulls by Savitsky and Morabito [2] and provides a good validation case for CFD being able to accurately model flow patterns. This simplification is necessary as experimentally extracting the wake profiles behind a step with anything other than photographs to compare is extremely challenging, and is something that has not been achieved by researchers to date. As such, there is no available validation data for cases where the afterbody is included.

The paper begins by presenting an in-depth literature review of previous numerical studies on the subject of planing hulls. Following this, the aims and the methodology are detailed before the numerical set up is outlined. Finally, the results are presented and discussed, before the work is rounded off with the concluding remarks.

#### **2. Literature Review**

There are few examples in literature of authors investigating the near-field longitudinal wake profiles using experimental, analytical or numerical means. A number of studies in the first half of the 20th century attempted to extract the longitudinal wake profiles of planing surfaces [3–6]; however, the focus of these studies is upon seaplane floats, and as such, the parameters are vastly different from those typical of planing hulls.

In the past 20 years, some work has been conducted upon the mid and far-field wake of planning hulls. Notably Thornhill et al. [7] conducted a series of bare hull resistance tests of a planing hull for a range of conditions in order to provide validation data for CFD using an array of capacitance probes. Following this, the same experimental strategy was employed by [8,9]. Callander [8] went on to use the measured experimental data to evaluate the MacPhail 2D + t method for application with planing hulls. His work concluded that the analytical method was able to model the trends of the experimental data; modification was required to improve its accuracy to a suitable level. De Luca [9] went on to use the data generated to evaluate the effectiveness of interceptors. He provided the profiles he obtained to carry out validation procedures. The experimental procedure followed by these researchers was unable to provide any data for the nearfield wake region due to the placement of the capacitance probes.

Savitsky and Morabito [2] conducted the first experimental investigation into the nearfield wake of planing hulls, developing empirical equations that quantitatively defined the longitudinal surface wake profiles at both the centreline (CL) and quarterbeam (QB). The authors found that the developed empirical formulae displayed good agreement with the experimental results; however, there is a noticeable scatter and it is clear that while an empirical equation may be capable of providing a good representation of the wake profiles they will not be entirely accurate for all cases. The work undertaken by Stavisky was comprehensive and was published with the intention of aiding the designers of stepped hulls determine how the flow of the fore hull intersects with the aft hull.

The second example of an experimental investigation into the nearfield wake of a planing hull was conducted by Gray-Stephens et al. [10]. This paper set out to determine the accuracy of the empirical wake equations derived by [2] when they were employed out with their published range or applicability. The study also examined the accuracy of the Linear Wake Assumption, which is often employed by researchers when modelling stepped hulls in an attempt to evaluate its validity for this application. A further motivation behind this paper was to provide detailed experimental data to be used for the validation of CFD in modelling the flow in this region, as is being undertaken by the present study.

The number of available numerical studies investigating both planing and stepped hulls has been increasing rapidly in recent years. This has led to vast improvements in the level of accuracy that is reported by authors, with a mean prediction error of 10% being considered achievable by the International Towing Tank Conference (ITTC) [11]. This prediction error is for the calculation of forces and there is little information available to evaluate the accuracy CFD in modelling wake field.

Following a study of the available literature, the authors of this paper were unable to identify any examples of experimental data being used to validate or evaluate the performance of CFD in calculating the longitudinal wake profiles of a high-speed planing hull. A number of studies do however make use of Savitsky's Wake Equations in conjunction with numerical methods, primarily as one-off validation cases of the CFD. In 2014, Faison [12] used the Savitsky Wake Equations to compare the wake profiles of transverse steps with the CFD generated profiles of swept back and cambered steps. The study found there to be significant differences between the numerical and empirical profiles however the authors were unable to determine if the differences were solely accountable to the change in design, or due to the superior accuracy of one the methods employed. In 2015 Ghadimi et al. [13] used the Savitsky Wake Equations to validate a numerical computation modelling the CL wake profile. The authors went on to use the validated simulation to investigate how altering the transom stern may reduce the wakes rooster tail height. The paper shows the validation comparison to have reasonably good correlation, but, once again, the authors are not able to comment on the reasons behind this difference. Moreover, in 2015, Lotfi et al. [14] compared a numerically generated CL wake profile to the equivalent one calculated using the Savitsky Wake Equations. Similarly to [12] the two methods are not shown to have good correlation, featuring an average error of 20%. Most recently, in 2017 Bakhtiari and Ghassemi [15] were investigating the effect of a forward swept step angle on the performance of a planing hull through the use of CFD. They employed the results of the Savitsky Wake Equations as part of their validation procedure, showing that there is a reasonable level of agreement between the two methods, but that they do not exactly agree.

No examples of authors investigating the modelling of the nearfield wake profiles with CFD were found, aside from those using the Savitsky Wake Equations as a brief validation case. Those using the Savitsky Wake Equations to validate their CFD model often found discrepancies between the two methods, however, were not able to identify which of the methods was closer to the physical solution. The lack of investigation into this topic is in part due to the lack of experimental nearfield wake data available in the public domain, with only two sources of this being identified. Some studies have compared mid and far-field experimental wake cuts with CFD results for conventional displacement ships. Analysis of the work submitted to the Gothenburg 2010 Workshop revealed that wave cuts closest to the hull tend to be well predicted; however, as distance from the hull increases, the results varied considerably [16]. This workshop was for a KCS vessel, and it is well known that CFD is significantly more accurate when evaluating conventional displacement ships compared to planing hulls. An example of this comparison being made for planing hulls was undertaken by Mancini [17]. The study compared the numerical results for the wake field to the experimental mid and far field wave cuts of the Naples Systematic Series. It was found that CFD was able to model the trends in a

satisfactory manner; however, it was noted that there was differences in both the amplitudes and phase of the results.

### **3. Aims and Objectives**

The primary aim of this study is to perform an in-depth investigation into the ability of CFD in modelling the near-field longitudinal wake profiles of a planing hull. An evaluation of both the CL and QB profiles will be made through a comparison with experimental data. Additionally, comments will be made upon the accuracy of CFD in comparison to Savitsky's Wake Equations and the Linear Wake Assumption. The secondary aim of the work is to investigate how the set-up of a CFD simulation may affect its accuracy, with the most accurate set up being presented in detail. Following this, the findings relating to the influence of a number of factors on the simulation results will be outlined so that their impact may be quantitatively understood. Throughout this study, there is a specific focus on turbulence modelling. In order to achieve these aims a number of objectifies have been identified:


#### **4. Methodology**

The global methodology of the project was broken down into two stages. The experimental work as performed by [10] was to be used as validation data:

The first stage was to set up a CFD simulation capable of accurately modelling the longitudinal wake profiles. The simulations were tuned to ensure the best set up was achieved, with a number of factors being systematically varied to determine the effects on the predicted wake profile. Once an accurate simulation had been developed, an extensive Validation & Verification (V & V) study was undertaken. All numerical simulations were performed using the commercial software, Star CCM+ (12.04.011-R8), on the University of Strathclyde's Archie-WeST High Performance Computer.

The second stage was for all cases that were experimentally tested to be run using the CFD simulation, allowing a comparison to be made over a range of conditions. The results were then assessed both quantitatively and qualitatively to provide a detailed assessment of the accuracy of CFD. As the paper [10] from which the experimental data was obtained also investigated the accuracy of Savitsky's Wake Equations and the Linear Wake Assumption comments will also be made towards the accuracy of CFD in relation to other methods.

While it is possible to develop a robust and reliable numerical model based on either an overset grid or morphing mesh methodology that is capable of resolving the final attitude of a planing vessel these approaches were not utilised. Instead, the hull was fixed in both sinkage and trim. This methodology was chosen for two key reasons. Firstly, the experimental study had employed a hull that was fixed in sinkage and trim to give the researchers more control over the position for which the wake profile was being extracted, allowing a broad range of cases to be examined. Secondly, it is known that CFD is accurate in modelling the position of a planing vessel that is free to sink and trim, and it was not the place of this study to further evaluate this. In order to ensure an exact comparison between the experimental data and the numerical result and give a fair evaluation of CFDs capabilities it was important that the hull positioning was exactly the same in the experimental and numerical studies. Introducing the typical ~10% error in both sinkage and trim of the CFD simulation through a model that was not fixed would add uncertainty and taint the analysis of the wake profiles.
