Experimental study on stepped spray deflectors for planning hull

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STOCKHOLM , SWEDEN 2019

Experimental Study on Stepped Spray Deflectors for Planning Hull

LUCA CASTALDI

KTH ROYAL INSTITUTE OF TECHNOLOGY

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Planning vessels can reach high operational speeds thanks to their hull design.

Some hull forms will develop large volumes of spray attached to the hull surface.

The whisker spray is a thin layer consisting in droplets of water which can account for a large proportion of the total resistance. A new concept to redirect the spray, called deflectors, has been developed by the Swedish company Petestep.

These deflectors indicate higher efficiency than the time-proven spray rails technology by removing a bigger portion of the spray area. The spray is reflected back- wards rather than to the sides, which allows kinetic energy contained in the spray sheet to be converted to additional forward thrust. However, there have only been a few studies conducted on the effects of deflectors and there is no precise method to analyze their efficiency over the full range of operating speeds. For the above- mentioned reason, experimental testing is needed to have a more complete under- standing of the phenomenon in calm water and waves. In this study, model scale tests of a modular planning hull are carried out at the Davidson Laboratory towing tank. The goal is to verify the benefits of the spray deflectors by direct comparison with the bare hull configuration at the same trim angle.

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This thesis was written in full by Castaldi. However, the theoretical and experimental work was done in collaboration with Fran Osmak, a graduate student from the Royal In- stitute of Technology. Even though the responsibilities varied slightly through different stages of the project, both authors were equally involved overall. Decisions related to the continuation of the project were made jointly.

The first part of the project consisted of the theory review of research done in HSC field and then the design of the strips and physical setup of the experiments. Each author wrote their own theory review, with Castaldi focusing on numerical, and Osmak on experimental research. The rest of the first part was achieved jointly.

The second part of the project involved the design of the speed matrix, compliance with International Towing Tank Conference (ITTC) rules and documentation of the test procedures. This was done by Osmak.

The final work of organizing, postprocessing and interpreting the results was done by Castaldi.

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1 Introduction

1.1 The goal of the project

In the early 1900s, Dixon Kemp and Charles Mosher observed that when a craft with relatively straight after-body buttocks was underway with increasing speed, it would rise and skim on the surface of water [1].

Later, designers were introducing longitudinal, flow-separating steps in the planning hull’s bottom to further reduce wetted surface which mitigates drag at high speed, called spray rails. [2]

They consist of longitudinal appendages installed on the hull in order to reduce the spray resistance. These stripes detach the spray from the hull surface and deflect it towards the sides. At high speeds, wetted surface is reduced along with frictional drag.

Figure 1.1: Comparison of the spray generated by the planing hull with and without spray rails

In 2015 a Swedish company named Petestep, patented a new concept of spray deflection

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technology. These steps are located slightly forward to the stagnation generated during the planing mode.

The picture below shows that although both the technologies divert the flow away from the hull, the deflectors have an higher efficiency in reducing the wetted area.

Figure 1.2: Comparison of different spray deflection technologies

Numerical first [3] and several experimental studies later [4], [5] and [6] have been performed to demonstrate the potential of the innovative Petestep deflectors.

The goal of this project is to improve the knowledge of the deflection technology with an experimental study in the towing tank of Stevens Institute of Technology.

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1.2 High Speed Craft

Marine craft with their weight being supported by the combination of buoyancy and hydrodynamic lift of planing have the following hull forms: Round Bilge, Double Chine and Hard chine.

Figure 1.3: Planing hull forms

Exist other classes of Hish Speed Craft that overcome the hull speed.

Figure 1.4: Overview of the all possible classes of Advance Marine Vehicles

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When monohulls are fitted with hydrofoil (underwater wings), marine craft can, with sufficient speed; be entirely above the surface with dynamic lift.

Figure 1.5: Swedish electric hydrofoil boat candela above the water

Air-cushion Vehicle (ACV) and Surface Effect Ship (SES) belong to another class of high- speed vessel called Hovercraft since they are supported above the surface of the water by low-pressure air cushion by mechanically powered equipment.

Figure 1.6: Air cushion vessel

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To sum up, the picture below shoes three fundamentals means of supporting the weight of marine craft, buoyancy, hydrodynamic lift and mechanically powered lift. This is know as the "Sustention Triangle".

Figure 1.7: Sustention triangle

1.3 The planning mode

There is not an exact definition for the threshold of planing based solely on speed since hull loading constitutes displaced volume as well as dynamic lift factors. Some accepted definitions are:

• Speed at which water separates from the hull bottom at the transom [7].

• Speed at which the maximum trim angle of the hull begins to reduce.

• Speed-length ratio of 3.5 based on static waterline length.

• Lenght Froude number Fnl=1.0 based on static waterline length.

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• Buoyant component of planing load is negligible [8].

As states [2]: "In order to have paning occur, a hull bottom must have a three-dimensional shape, which in reaction to trim attitude and the velocity of water over the wetted shape, develops net positive pressure of magnitude that results in the center of gravity rising to an elevation that the remaining below-water volume is less than 50 percent of its static volume".

Figure 1.8: Representation of lifting forces of planing craft

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Net positive pressure is an essential condition for planing as hydrodynamic pressures generated by water flow over a surface can locally develop distributed areas of both positive and negative forces, respectively lifting up or sucking down the hull’s surface.

Hence, the net lifting force of a surface is a function of the projected areaA_p and the distributed hydrodynamic pressure.

For a HSC, the hydrodynamic pressure distribution on the hull creates a lift that supports a significant portion of its weight. As the speed increases, a lift force is generated, which hydrodynamically supports the hull and moves it out of water. As the wetted surface area decreases, the hydrodynamic lift rises further. Until the hydrodynamic lift balances the weight of the hull and, the buoyancy force decreases with the increase of hydrodynamic forces. Once the equilibrium is reached the craft is at planing condition.

The physics of the phenomena is described by Savitski in [9].

Figure 1.9: Rapresentation of hydrodynamic and hydrostatic of high speed craft

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For vertical equilibrium of forces

∆ = Ncosτ + Tsin(τ + ϵ) − Rfsinτ (1.1)

For horizontal equilibrium of forces

Tcos(τ + ϵ) = Rfcosτ + Nsinτ (1.2)

For equilibrium of pitching moments

Ne + Rf f f − T f = 0 (1.3)

Where:

• T = propeller thrust;

• ∆ = mд: weight of boat;

• τ = trim angle of keel;

• R_f = viscous component of drag;

• ϵ = inclination of thrust line relative to keel;

• N = resultant of pressure forces acting normal to bottom;

• LCG = longitudinal distance of center of gravity from transom;

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• CG = center of gravity;

• e = distance between N and CG;

• f = distance between T and CG;

• f f = distance between R_f and CG.

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2 Literature Review

Over the last decades, researchers in naval architecture have developed new method- ologies for the reduction of drag in ships. In 1452 Leonardo da Vinci carried out tests on different models of ships for resistance prediction, it was not until 1955 Froude proposed a law whose idea was dividing the resistance into two components: frictional resistance and wave resistance [10]. A fast method for predicting the resistance of the ship is fundamental for exploring different designs of hull form in order to reduce the drag.

2.1 Experimental Analysis

The traditional experimental method for hydrodynamic performance prediction is towing tank testing in calm waters or in two-dimensional rocker flap made waves. There are a limited number of theoretical techniques for analysis of planing hulls. Savitsky’s method is among the most popular techniques [11].

In 1964, [9] performed experimental tests and provided empirical correlations for calculation of lift, drag, and center of pressure for wedge-shaped high-speed planing hulls.

His results were reported for a variety of speeds, deadrise angles, and loading.

Later [12], based on [13,14] revisited and modied their original method to include the effects of waves on acceleration and wave drag. The main advantage of this method is that it is simple and provides relatively accurate results for a number of hulls with a regular shape. [15] also performed model tests to determine hydrodynamic drag and lift coefficients for wedge-shaped high-speed planing hulls at different speeds. In addition, [16] found a model for prediction of turbulent water surface at the bow of the planing hull. [17] measured the pressure distribution on planing hulls to obtain the lift force and performed a series of experiments on prismatic hulls with a variety of dead-

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rise angles. [18] has studied the wetted surface characteristics and spray to determine the spray drag.

2.2 Numerical Analysis

Since the early 20th century a number of techniques have been developed for hydrodynamic analysis of HSC. Two main Computational Fluid Dinamics (CFD) methods exist for ship resistance: the potential flow theory and the finite volume methods that take viscosity into account [11].

Potential flow-based methods or Boundary element method (BEM) are applicable to steady state inviscid flows, in which the viscous effects are negligible. It has been ex- tensively developed for solving wave-making resistance and offers a wide range of engineering applications [11]. In this technique, the Navier–Stokes equations are reduced to the Euler equation and solved only on the boundary. This method reduces one dimen- sion of the fluid domain, leading to fewer unknowns. As a result, less memory and time are needed. Computational time for this method with an advanced computer is on the order of minutes and thus is relatively fast. However, simplification of governing equations limits their applicability. It is not recommended for simulation of viscous flows with complex free-surface profiles such as the ocean surface waves. When the free surface of the ocean is disturbed by the wind, waves are produced on the air-water boundary. In these flows, the viscous effects cannot be neglected and thus a comprehensive analysis of the flow is required [11] .

The usage of Finite Volume Method (FVM) gained momentum in later decades of the 20th century with the advances of computer technology. The FVM uses the integral form of the conservation equations as its starting point. The solution domain is sub- divided into a finite number of contiguous control volumes (CV), and the conservation

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equations are applied to each CV. At the centroid of each CV lies a computational node at which the variable values are to be calculated. "Finite volume" refers to the small volume surrounding each node point on a mesh. The FVM can accommodate any type of grid, so it is suitable for complex geometries [19].

FVM is a more appropriate and accurate technique for modeling turbulent and free- surface flows such as breaking waves than BEM. It can also be used to predict maneu- verability, seakeeping capability, and the dynamic running position of the hulls with complex geometries[11]..

2.3 Optimization of the hull

Ship design is an iterative process as many aspects of a ship are intertwined. Based on the vision of a customer, the ship designer has to develop the most cost efficient ship for a designated task, within the boundaries of international and national rules and regu- lations. Finding the best compromise within the given boundaries is the challenge for the ship designer. 2D and 3D design, modeling, simulation and calculation software is playing an important part in making the design process more efficient and successful [20]. As the desire/need to minimize the use of resources (e.g., fuel, building cost, time for design, etc.) became increasingly important, the use of optimization approaches gained momentum. Such optimization methods are typically applied during the phase of preliminary design, where the designers have the freedom to manipulate the design variables to identify an optimum design. [21].

2.3.1 Hard chine

Literature exists on the design optimization of low deadrise, hard chine, stepless planing hulls [22], and on planing craft with controlled trim angle [23]. The minimization of calm water resistance of hard chine planing craft has long been of interest [24]. Fur-

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ther [25] has shown multiobjective optimization problem formulation that involves total resistance in seaway, including the evaluation of maneuvering properties, and vertical impact acceleration [26] of the U.S. Coast Guard 110 ft WPB [27]. [28] presented a dual- objective optimization of a double-chine, planing hull form in calm and rough water using National University of Athens Series planing hull forms [29]. He demonstrated that the Evolutionary Algorithms constitutes a powerful and efficient tool for the accom- plishment of multi-objective optimization, resulting in hull forms with superior characteristics both in calm and rough waters.

[30] performed an optimization of a hard-chine semi-planing hull, based on the reduction of the total resistance at two different speeds through the integration of software optimisation with Reynolds-Averaged Navier–Stokes simulations with low number of cells. The aim of this paper was the searching for a method that could be reasonably fast and reliable to optimise the hull shape, in order to minimize the total resistance. Their work demonstrates that it is possible to perform multi-objective optimizations using the support of viscous CFD solvers without heavily increasing computing time and costs.

2.3.2 Catamaran

[31] used a numerical method to optimize the design of the catamaran planing vessel.

The predictions of catamaran planing vessels by hydrodynamic performance are mainly carried out by model tank tests and empirical formulas [32]. In their research, the influence of the key design parameters on the catamaran planing vessel performance is studied using the dynamic grid technology. In this method is used a small domain surrounding the hull, making the domain moving together with the hull in the calm flow field.

While displacement type Deep-V mono hulls have superior seakeeping behaviour at

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high speed, catamarans typically have modest behaviour in rough seas. It is therefore a logical progression to combine the superior seakeeping performance of a displacement type Deep-V mono-hull with the high-speed benefits of a catamaran to take the advantages of both hull forms. This hybridisation of two hullforms has been proposed for the first time at Newcastle University by [33]. This application has developed through successive projects ([34]; [35]) and a recent PhD research, all of which resulted in the first systematic Deep-V catamaran (UNEW-DVC) series including limited model tests supporting the series development by [36]. Newcastle University designed and built a Deep-V catamaran as a school research vessel and the research vessel has large deck area, excellent stability and good speed potential with low wave wash ([37]). [38] is a further validation of the hull resistance by using advanced numerical analysis methods in conjunction with the model tests. An assessment of the numerical predictions of the hull resistance is also made and compared against physical model test results and showing good agreement.

2.3.3 Vessel with lifting surfaces

[39] performed an optimization of an 80 foot, canoe stern boat with integrated lifting surfaces. This paper shows that benevolent wave cancellation can be produced at multiple speeds through simultaneous changes in hull shape and lifting surface size and placement, using automatic geometry morphing. The optimization used a medium- fidelity, potential flow tool called AEGIR, coupled with an automated geometry morphing and optimization tool called NavADE (Navatek Automated Design Environment).

2.3.4 Trim tab and Interceptors

[40] optimized planing boats with a trim tab and an interceptor by using Savitsky’s equations with the genetic algorithm, a method for solving optimization problems based on natural selection, the process that drives biological evolution. The trim tab and the

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interceptor have been used to optimize the running trim and motion control of semi- planing and planing boats at various speeds and sea conditions for many years. Their results show a decrease in the total resistance of the boat with an interceptor and a trim tab at a specific trim angle.

In [37] it was identified that the Deep-V catamaran has substantial amount of dynamic trim that limited the visibility of the captain and also increased the wave-making resistance thereby preventing the vessel from attaining its maximum speed in certain sea states. [41] therefore applied devices such as Trim Tabs, Interceptors, Transom Wedges and Integrated Transom Wedges-Tabs to control the dynamic trim and improvement of fuel efficiency of the vessel. All of these energy saving devices were fitted into a model for tests in Newcastle University’s Towing Tank. Model test verification confirmed that the optimum appendage was the interceptors, they produced a 5% power saving and 1.2

°trim reduction at 15 knots.

[42] demonstrated that the effect of the interceptor decreases from keel to chine for the same blade deployment heights. The experimental results [43] showed a remarkable drag reduction of up to 15% for mono-hull model and up to 12% for catamaran model with interceptors. [44] showed that a controllable interceptor system decreases the pitch motion by 41.3% in the regular wave and 32.4% in the irregular wave.

[45] analyzed the hydrodynamic performance of a new transom-interceptor configuration that can be used to control the motion behaviour of a fast ship in waves. They showed improvement in motion behaviour of a fast planing vessel with a ride control system sailing in head waves. The new transom-interceptor configuration was designed to generate lift in both the positive and negative direction as an extension of the control force in the opposite or negative direction contributes to a better control of the ship motions. This especially holds for fast ships that do not naturally have large running

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trim angles at high forward speeds. They showed that this new transom interceptor configuration leads to a lower level of the vertical peak accelerations and it results in a more favourable sea keeping behaviour of the ship in comparison with the conventional interceptor design. Later [46] developed a computational tool for the design and optimization of these ride control systems for high speed planing monohulls. Showing that active trim devices can effectively be used to establish a momentarily change in the running trim. This resulted in lower levels of vertical accelerations, which improves the operability of the vessel.

[47] provide a simple and suitable method for designing interceptor dimensions in a given planing boat. This paper studies the effects of height and span (width) and boundary layer thickness at the interceptor location simultaneously. Although it has been proved that the interceptors are very useful in trim control and resistance reduction [40], choosing the wrong size interceptors could not only limit their effectiveness, but also endanger the planing boat due to the creation of a strong moment leading to negative trim [48]. The results showed that the boundary layer thickness at the stern, where the interceptor is installed, should be taken into account in estimating the interceptor height and span. The interceptor height, moreover, should not be higher than 60 % of boundary layer thickness at transom. For optimum efficiency, the interceptor span length should be seven times as much as the interceptor height.

2.3.5 Stepped hull

[49] addressed an experimental and numerical study of a stepped planing hull and the related fluid dynamics phenomena typically occurring in the unwetted aft body area behind the step. The same ow conditions are analyzed via Reynolds Averaged Navier- Stokes (RANS) and Large Eddy Simulations (LES), with different moving mesh techniques. The flow patterns obtained numerically through LES on a rened grid appear

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similar to the ones observed in towing tank investigations through photographic ac- quisitions. These flow patterns are dominated by a rather complex 3D arrangement of vortices originating from air spillage at both sides of the step.

In [50] more insight was gained regarding the advantages and disadvantages of operating stepped hulls by testing both an unstepped and an adjustable stepped version of a generic, 5-foot, prismatic planing boat model at the U.S. Naval Academy Hydromechan- ics Laboratory. [51] used standard turbulent model with Volume Of Fluid (VOF) model to simulate free surface flow around a high speed stepped planing hull. The numerical method investigated the influence of a step on the pressure distribution, hydrodynamics characteristics, and wake profile of a modern high-speed chine planing hull. The results obtained showed good agreement with the experimental results. [52] presented the three dimensional VOF approach for examining the characteristics of a planing hull with one transverse step. Resistance, lift, running draft, dynamic trim angle, and wetted area are compared with available experimental data and those of a semi-empirical method at volumetric Froude number in the range of 2.41–7.12. Wetted area at the fore- body chines-dry mode is qualitatively compared with a typical underwater photograph of a stepped hull. The quantitative and qualitative results are found in acceptable cor- relation with experimental data, hence they can be reliably used in the stepped hull hydrodynamic investigation. [53] presented a CFD-based design of a multiple step solution starting from a non-stepped hull configuration. An optimization of the unwetted aft body area behind the steps was performed in order to enhance the performance of a non-stepped hull geometry and to avoid the dynamic instabilities phenomena, such as the porpoising phenomenon at the highest speeds. The results of the analytical method has been validated against Savitsky method and CFD full scale analysis for the non- stepped hull geometry.

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2.3.6 Air cavity designs

[54] improved the knowledge of air-cavity phenomena with a systematic study on different cavity shapes, obtained by modifying the same type of planing hull. The approach is oriented to find the better design solution for the application of air cavity on a yacht of 18 m. The design has been obtained with the idea using the natural low pressure under the bottom of high-speed crafts, in order to stabilize an air-layer instead of the traditional air-cushion. Four different scale models have been tested to different velocities and air flow. More than 200 different tests have been conducted in the towing tank of the University of Naples, using the ITTC ‘57 methodology. Results show that also planing hull can reach important resistance reduction, compared to conventional hull. The presence of air layer, although involves a good drag reduction, does not influence the lift of this kind of boats. In addition, the differences between mother hull and Air Cavity Ship models, in terms of trim and sinkage, are negligible.

2.3.7 Spray rails

[55] demonstrates that spray strips extending aft from the bow about 70 percent of the hull length decreased the resistance somewhat at high speed but increased the resistance at low speed. An experiment was also made with bottom spray strips extending only forward of the high-speed stagnation line. This arrangement gave a 6% reduction in resistance at high speed with no increase in resistance at low speed.

[56] provides an experimental verification of the reduction of planing boat drag which can be achieved by using longitudinal strips forward of the stagnation line to deflect the whisker spray from the hull surface. It also verifies that full effectiveness of the strips at a particular design speed can be obtained with strips of very short length. Two models were fitted with spray deflectors located forward of the stagnation line and were tested

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in considerably higher speeds than the model reported on in [55]. At Fv = 6.0, the resistance with the long spray rails was 15% below the bare. Both the long and short spray rails were designed for a speed corresponding to Fv = 5.0, and in each case a resistance reduction of about 7 % was obtained.

In [57] the resistance and seakeeping performance of a high-speed monohull vessel were investigated through a series of model tests in a towing tank. The hull had a slen- der wave-piercing bow, round bilge, and small deadrise angle at the stern. Tests on the bare hull in calm water were first conducted and tests on spray rails followed. The spray rails were designed to control the flow direction and induce a hydrodynamic lift force on the hull bottom to reduce trim angle and increase rise of the hull. Attaching the rails on the optimum location effectively reduced the pitch and heave motion responses. The vertical acceleration at the fore perpendicular reduced by 11.3%. It was further revealed that the spray rails did not have any negative effects on the resistance performance of the hull, while they effectively stabilized the vessel in calm water and waves. The maximum trim of the bare hull was 4.65 °at the designed speed, but the spray rails at optimum location reduced trim by 0.97 °

2.4 Discussion

The increase in use of high speed planing crafts demands more research and the experimental works and its resistance is one of the most important factors that affects the performance of the craft. The most reliable method to predict the resistance of ship is the towing tank test, but it is time-consuming and very expensive [58].

Towing tank tests are necessary for new ship designs and prototypes to understand the phenomena behind new prototypes and to gain the knowledge necessary for the numerical techniques.

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The disadvantages such as scale effects of the artificial environment are obvious. The waves are unidirectional, artificially generated and pseudo-random. Furthermore, the motion signals of the model are usually measured by seaworthiness instruments, which may restrict the model’s freedom motions in some sense [59].

The inherent limitations of empirical and experimental techniques have motivated researchers to use full scale CFD methods in recent years [60]. With the advancement in the computer hardware and software, numerical techniques have become effective tools for complex hydrodynamic analysis and CFD is used throughout the design process [11]. The most important advantage of numerical methods is that they do not suffer limitations that are normally encountered in model testing such as the size of the hull, environmental conditions and analysis of the results for prototype hulls[11]. They also eliminate the cost of physical models. Numerical techniques allow for hydrodynamic modeling of real size hulls, investigation of physical components in early design phases, and obtaining detailed information (trim, draught, heave, pitch, vertical acceleration), which are otherwise cumbersome to obtain with experiments.

It is clear, nowadays, that CFD is becoming a fundamental support for hydrodynamic investigations in order to perform detailed analysis and to reduce the number of more expensive towing tank tests. Experimental Fluid Dynamics tests however, are always necessary alongside validation of numerical results [49].

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3 Methodology

3.1 Previous Studies

The present research is intended to give continuity to the experimental work performed by Molchanov and Lundmark in [5] and [6] respectively. They performed experimental tests with a modular hull with 3 bottom configurations to benchmark two spray deflection technologies.

They measured a significant reduction in total resistance for the deflector configuration but they were not able to conduct a direct comparison between the two technologies because they obtained different running trim at the same velocities.

The picture below displays the hull modular feature which was a critical factor in their research. On the left, the bare hull configuration obtained by inserting additional flat plates on the hull bottom. At the center, some strips attached longitudinally along the keel resemble the usual spray rails technology. On the right, triangular flat plate joined at the keel of the model, simulate the innovative Petestep hull shape.

Figure 3.1: Modular model in three different configurations

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3.2 Model

The model adopted for this study was inherited directly from the previous research. The model was manufactured in-house from marine grade Divinycell foam. It was designed with a transversal step located in the front part of the model to enable the modular capabilities.

In this study, the transversal step has not influenced the calm water resistance tests because it was situated in the dry frontal area of the planing mode.

Below are reported its main dimensions.

Figure 3.2: Back view of the model

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Figure 3.3: Bottom view of the model

Figure 3.4: Side view of the model

The following table lists its main hydrostatic characteristics.

Table 3.1: Hydrostatics

Displacement 22.83 kg Volume displaced 0.022m³

Draft 0.082 m WL Length 1.69 m

Length-Beam ratio 4.686 Length-Volume ratio 6.007 Block coeff. 0.446 Prismatic coeff. 0.745

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3.3 Stagnation Line

As the model enter in the planing mode, it stabilizes at a certain equilibrium position, which is defined by a fixed trim angle. The intersection between the hull bottom and the water surface is called stagnation line. This area is where the pressure reaches the highest values and it is where the whisker spray is generated. The whisker spray is a thin spray consisting in droplets of water. The main spray on the other side, is a con- tinuous blister of water in the form of a cone originated at the intersection between the stagnation line and the chine.

The schematic image below displays the subdivision of a planing hull bottom in three main areas: the frontal dry area, the spray area and the submerged area.

Figure 3.5: The three areas characteristic of the planing regime

In the next underwater photo it is possible to visualize the main variables that determi- nate the stagnation line: the length at the keelKL, the length at the chine CL and the angle at the chineα. Moreover, the picture highlights the main path of a drop of water before and after it is redirected. The sketch shows also the bow wave which is another free surface disturbance originated at the chine intersection with the water.

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Figure 3.6: Whisker Spray generated by the stagnation line at 2.6 Fn

3.4 Strips Location

The strips are designed for a specific speed with a specific stagnation line. At the design speed they are parallel to the stagnation line and they are placed a bit in front of it to enable the deflection of the whisker spray from the hull.

The sketch simulates the installation of the deflectors and it provides an example of both the longitudinal and the normal distance from the stagnation line.

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Figure 3.7: Simulation of the strips placement at the design speed of 4.0F_nV

3.5 Initial Strips Design

The first attempt of deflectors was not successful. These strips were designed for being parallel to the stagnation line at 3.4F_nv. They were characterized by one transversal angle of tapering, which was not enough to ensure the strips to be out of the water at the keel.

Figure 3.8: Three dimensional model of the first version of the strips.

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The underwater picture shows the wrong design of the deflectors. No clear stagnation line is present and the main spray is generated from the joining point of the strips at the keel.

Figure 3.9: Underwater photo of the first concept of the deflectors

3.6 Final Strips Design

In order to overcome the issue of the deflectors touching the water surface at the keel, it was added a second longitudinal angle of tapering. This allowed to have strips with minimum thickness at the keel and maximum thickness of 1inch at the chine.

Three sets of deflectors were manufactured from an expanded PVC foam to investigate the benefits of the deflection technology for a wide range of planing speeds, from 2.6 to 5.2F_nV. Therefore, 3 design speed were selected at equal distance one from the other:

3.2F_nV, 4.0F_nV and 4.8F_nV.

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Figure 3.10: Length comparison between strips for different design speeds

Figure 3.11: Rendering of the second iteration of the strips.

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Below a representation of the second iteration of the deflector tested in the towing tank of Davidson laboratory. The presence of the stagnation line is evident and it is located a bit after the appendages.

Figure 3.12: Underwater photo of the final strips design at the speed of 3.4F_nV

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4 Results

4.1 Bare Hull

As an initial step to determine the right placement for the strips, the trim of the bare hull was established by running an important amount of calm water tests. The graph below shows all the results acquired from this extensive study. The trim values reported for each velocity is the average of three independent tests.

Figure 4.1: Variation of the stagnation line in relation to the speed

The inclination of the stagnation line at each tested speed was calculated by analysing the underwater pictures of the bare hull and by determining both the length at the keel LK and the length at the chine LC. The angle α between the stagnation line and the keel was obtained with simple trigonometric calculations.

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The graph below shows the figures obtained from this analysis. As expected,alpha is inversely proportional to the running speed and it presents the same trend of trim angle. As the speed increases, the consequent increment of the lift forces pushes a greater part of the model out of the water. Thus, to gain a new equilibrium position the the trim decreases accordingly.

Figure 4.2: Variation of the angleα in relation to the speed

Finally, a graphical representation of the the stagnation line along the bottom of the model was obtained for all the tested speeds. The following figure has proven to be an useful tool during the design process of the strips and their placement.

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Figure 4.3: Representation of the stagnation line for the range of speeds

4.2 Low Strips

To establish the efficiency of the strips regarding spray deflection, a direct comparison between the bare hull resistance and the model equipped with the deflectors was performed at the same running conditions.

The investigation of the lower part of the speed range was conducted by design a set of strips which were parallel to the stagnation line of the bare hull at the speed of 3.2F_nV. The strips were placed at distance from the stagnation line of 2inches along the chine which resulted to a minimum normal distance of 0.85inches.

The efficiency values reported for each velocity are the average of three separate tests.

The plot shows a reduction of the total resistance of about 2% overall, with a peak of performance of 5% at 2.8F_nV.

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Figure 4.4: Calm water performances of the deflectors designed for 3.2FnV

4.3 Middle Strips

The study of the middle area of the speed range was carried out with a dedicated pair of deflectors designed to be parallel to the stagnation line of the bare hull at the velocity 4.0F_nV .

At first, the strips were placed at the sameLC distance of2 inches from the stagnation line, as for the previous set of strips. This led to a lower normal distance of 0.69inches, since it depends on the inclination of the stagnation line, which is represented by the anglealpha.

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The following graph shows worse performances in general than the previous set of strips, reaching approximately 1% at the design speed and figures slightly below zero at higher speeds.

Figure 4.5: First calm water performances of the deflectors designed for 4.0F_nV

In order to gain more insights about the negative effects of the strips, a second attempt was executed placing them at aLC distance of 2.5 inches from the stagnation line. The normal distance increased to 0.87inches but the results obtained followed the same ten- dency found at the initial position. The plot below reports the values obtained from the calm water test. It is clear that this position worsened the performance on the whole with a negative peak of −1% at the velocity of 4.4F_nV

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Figure 4.6: Second calm water performances of the deflectors designed for 4.0FnV

At this stage, in order to understand the reasons of the issue related to the strips placement, it was developed a 3 dimensional model in Rhino which enabled to simulate the running condition at the design speed. From this study it was evident that the strips were slightly touching the water and so, increasing the drag considerably. Based on the three dimensional model, a new location was established which corresponded to aLC of 4 from the stagnation lineinches and 1.39 inches of normal minimum distance.

The plots displays the values obtained with the new location. A greater distance of the deflectors from the stagnation line enhanced the performances at every running condition with a peak of drag reduction of about 4.5% at 3.2F_nV. The results reported at each tested speed are the average of three separate tests.

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Figure 4.7: Third calm water performances of the deflectors designed for 4.0FnV

4.4 High Strips

The higher region of the speed test range was analysed with a separate pair of deflectors designed to be parallel to the stagnation line of the bare hull at the speed of 4.8F_nV. Initially the first placement was adopted to be the same as for the other sets of strips, LC of 2 inches from the stagnation line. Since alpha diminishes as the velocity of the model increases, it resulted an even lower normal distance from the stagnation line of 0.61inches. As mentioned before, the strips were too close to the stagnation line and thus, in contact with the water surface which led to an increment in the total resistance.

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The wrong placement of the strips is highlighted by the plot below. At the design speed the deflectors increases the resistance by 0.6% and it can be observed a negative peak of

−1.5% at the velocity of 5.2F_nV.

Figure 4.8: Initial calm water performances of the deflectors designed for 4.8F_nV

As for the previous experimental studies, a new location was determined to avoid the strips touching the water surface. TheLC distance was set to be 3 inches from the stagnation line, which resulted in a minimum normal distance of 0.91 inches.

The graph below presents the results achieved with the deflectors installed at the new placement. Similar deflection capabilities are showed in proximity of the design region of about 1.5%. At lower speed after an initial loss of performance at 4.4F_nV, there is a dramatic improvement of efficiency up to 4.5% at 4.0F_nV.

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Figure 4.9: Final calm water performances of the deflectors designed for 4.8FnV

4.5 Discussion - Underwater Investigation

To explain the experimental results obtained in the towing tank, it was performed a deep analysis of the underwater pictures. Each photo was build to represent a comparison between the spray generated by the bare hull and the spray redirected by the strips at the same running speed. The positive and negative values of the performance were showed beside each photo in order to detect beneficial or unfavourable phenomena. 4 different conditions have been observed.

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The image below shows how the underwater photos of all the running velocity were gathered one beside to the other in order to find similar pattern between different set of strips.

Figure 4.10: Overview of the underwater analysis

4.5.1 Strips at the design speed

The strips were design to be parallel to the stagnation line to one specific velocity. The image below shows how the strips follow the stagnation line along its path from the keel to the chine.

Figure 4.11: Model at 4.0FnV equipped with strips for middle range of speeds.

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Overall the set of strips performed well, showing 2% in total drag reduction at their design speed, with slight loss of efficiency at higher and lower speeds.

The image below shows a schematic representation of the model in this condition. The blue light area is the spray that the strips are not able and the green triangle is the de- tached spray.

Figure 4.12: In this condition the strips and stagnation line are parallel.

The general performance of the strips depends on the ratio between the two triangles:

Green Trianдle

Liдht − blue Trianдle (4.1)

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4.5.2 Strips at higher speed speed

When the model were tested at speed higher than the design speed of the strips it has been observed a gradual deterioration of the efficiency in redirecting the spray.

The stagnation line, as the velocity increases tends to move away from the strips. The image below shows how the angleα between the keel and the stagnation line diminishes.

Figure 4.13: Model at 3.8F_nV equipped with strips for low range of speeds.

The following image is a schematic representation of the hull bottom when the running speed is higher of the design strips velocity. As the angleα diminishes the distance at the cineLC increases significantly.

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As a consequence the ratio between the redirected spray triangle and the wetted spray triangle decreases, and so the efficiency.

Figure 4.14: In this condition the strips and stagnation line are divergent.

4.5.3 Strips at lower speed speed

The picture below shows how in this condition the stagnation line has a higher angle at keel than the strips.

The schematic representation explains the reasons behind the increment in performances of the strips in relation to the design speed. When the running speed of the model is lower than the design speed of the strips, the angleα increases and the distance at the chineCL diminishes accordingly. Hence, the ratio between the redirected spray triangle and the wetted spray triangle increases and so the strips performance.

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In this condition thethree different sets of strips showed opposing behaviours. On the one hand the strips design for the ranges of low and high speeds showed a slight loss of the efficiency of about 0.5% from the design condition. On the other hand the strips designed for the range of middle speeds gradually improved the performance.

Figure 4.15: Model at 3.4F_nV equipped with strips for middle range of speeds.

The reason lies in the fact that the former have similar normal distance between the stagnation line and the strips 0.85 and 0.91 inches respectively. The latter were placed at 1.39 inches.

The minimum distance from the stagnation line is a key factor to have better performance in this condition. The strips position along the keel has to be determined care- fully because, as the angleα increases, the stagnation line gets closer to the strips and the chances that the strips touch the water surface, increase accordingly.

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Figure 4.16: In this condition the strips and stagnation line are touching at the chine.

4.5.4 Ventilation

The picture below shows the stagnation line crossing the strips at the middle. In the submerged part of the hull is possible to detect the presence of air bubbles originated at the intersection point.

Figure 4.17: Model at 4.0F_nV equipped with strips for high range of speeds.

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By studying the sets of strips at lower speeds than the design speeds it was observed a relevant jump in strips performances up to 5%. In this condition the best strips performance were obtained.

The schematic picture represent this particular condition. As the velocity decreasesα increases until some part of the strips is partially submerged in proximity to the chine.

Figure 4.18: In this condition the stagnation line is crossing the strips at the middle.

Thus, at the intersection point, the air is trapped between the strips and the water surface decreasing the submerged wetted area, the blue triangle. Moreover, due to the stagnation line inclination, the ratio between the green triangle and the blue light triangle increases drastically.

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5 Conclusions

The major goal of this thesis was to evaluate the efficiency of the innovative spray deflectors ideated by Petestep.

The effects of the spray deflection and the resulting reduction of wetted area were studied on a wide range of planing speeds, from 2.6F_nV to 5.2F_nV. More than 300 tests were performed in the towing tank of Davidson Laboratory in order to assess the total resistance of the model with and without spray deflectors. The two configuration were studied separately and then they were compared at the same running velocities.

The experimental results were validated by using the semi-empirical Savitsky’s equations [12] which showed good agreement with the bare hull total resistance figures.

Overall, the deflectors reduces the total resistance of the bare hull model as expected.

The spray deflection technologies, such as the spray rails or the studied deflectors, detach from the hull the whisker spray generated during the planing mode, leading to reduced wetted area, lower frictional resistance, and therefore less drag forces. In this study the application of the deflectors has resulted in a benefit of approximately 2% for the most tested velocities, with peaks of 5% at certain running conditions.

The best performance were obtained when the test was conducted under the design velocities of the deflectors. Underwater photos showed an air ventilation phenomena originated from the point of intersection between the stagnation line and the deflectors.

The presence of air cavities reduced the frictional resistance by decreasing the wetted surface area [61] and the deflectors efficiency improved further.

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6 Future work

More efforts and investigations are required to further improve the general knowledge of the spray deflection technologies and to assess the real potential of the deflectors. In order to extend the work carried out by the present research, interesting fields of study are suggested below.

6.1 Strips Placement

In this work it has been showed that the distance of the strips from the stagnation line is a key factor for the spray deflection. A smaller distance will reduce more wetted area and lower the frictional drag. On the other side that will endanger the strips of touching the water surface. Still, additional tests in calm water condition are required to determine the most efficient location for the strips.

It has been proven that the highest benefits from the deflector implementation occurs when the stagnation line intersects the strip approximately in the middle. Additional investigations are needed to understand the magnitude of the ventilation phenoma and more work has to be performed to establish the most efficient cross point on the strips.

6.2 Strips Geometry

The first iteration of the strips was not successful. They were touching the water at the keel because of the wrong design. The second iteration of the design significantly improved the strips performance allowing the spray deflection at acceptable distance from the stagnation line without touching the water surface.

To obtain greater efficiencies the strips should be placed even closer to the stagnation line without being in contact with the water surface. Since the most significant amount

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of the spray is generated from the rear part of the stagnation line, an interesting design solution would be to remove ¹₄ of the strip length at the keel. This would enable to avoid the critical area in proximity of the stagnation point and to reduce even more wetted area.

6.3 Final deflectors

The feature of spray deflection is a direct result of the Petestep hull shape, which is provided with several vee steps on its bottom. The strips manufactured for the research were ideated with the aim to emulate the Petestep technology in calm water condition.

On the one hand the appendages design enabled to shift easily along the keel to find a more efficient position. On the other hand they were not suitable to determine the vertical acceleration in waves. The reason lies in the facts that the strips, would modify the bottom surface and they would drastically interact with the waves. Hence, it is necessary to design a plate deflector, which ensures a smooth surface before the characteristic vee step.

Moreover the model used in this study was inherited from a previous research, where modular features of the hull were necessary. Thus, the hull bottom is characterised by a transversal step in the frontal part which allows the attachment of several add-on.

This step is fixed and it would affect the experimental results in waves so to perform an investigation in waves it will be required to choose a different model.

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Experimental study on stepped spray deflectors for planning hull