A Two Dimensional Experimental Investigation of Slamming of an Oscillating Wave Surge Converter

Transcription

1 A Two Dimensional Experimental Investigation of Slamming of an Oscillating Wave Surge Converter Alan Henry 1, Olivier Kimmoun 2, Jonathan Nicholson 1, Guillaume Dupont 2, Yanji Wei 3, Frederic Dias 3 1 Engineering Research, Aquamarine Power Ltd., Edinburgh, Scotland 2 Structure Atmosphere Ocean department, Ecole Centrale Marseille, Marseille, France 3 School of Mathematical Sciences, University College Dublin, Dublin, Republic of Ireland. ABSTRACT This paper describes a series of experiments undertaken to investigate the slamming of an Oscillating Wave Surge Converter in extreme sea states. These two-dimensional experiments were undertaken in the Wave Flume at Ecole Centrale Marseille. Images from a high speed camera are used to identify the physics of the slamming process. A single pressure sensor is used to record the characteristic of the pressure. Finally numerical results are compared to the output from the experiments. KEY WORDS: Slamming; Impact; Pressure; Oyster; Wave Energy; Oscillating Wave Surge Converter; Two-dimensional Experiment. INTRODUCTION The energy dissipated on our shores by ocean waves represents a significant and as yet unexploited source of renewable energy. There are a multitude of diverse concepts for Wave Energy Conversion (WEC) with no one scheme yet gaining wide acceptance as the three bladed, horizontal-axis wind turbine has in the wind industry. One such device is being developed by Aquamarine Power Ltd and is called Oyster. Oyster is classed as an Oscillating Wave Surge Converter (OWSC) as it extracts energy from the horizontal or surging motion of water particles within ocean waves (Whittaker & Folley 2012). The device consists of a buoyant flap, which is hinged near the seabed and pierces the water surface. Wave action drives the flap back and forth, and this mechanical energy is used to pump fresh water to shore using two hydraulic cylinders. The high pressure water is fed into a conventional hydroelectric plant to generate electricity. Oyster is located in the shallow water depths (10 to 15m) of the nearshore region where shoaling amplifies the horizontal component of the water particle motion in the waves, thus increasing the power capture of the device (Folley et al 2007). The nearshore location has another positive effect on the wave resource in that it filters the extreme wave heights through the process of depth induced wave breaking. These large and infrequent extreme wave heights represent a portion of the wave resource which cannot be exploited economically but which the WEC must be designed to survive. So while depth induced wave breaking and shoaling effects reduce the gross wave power in the nearshore compared to that offshore, the exploitable portion of the wave resource is only marginally reduced, as it is the largest wave heights that are affected most (Folley & Whittaker 2009). The nearshore region therefore has an exploitable resource comparable with offshore locations but with limited, and potentially damaging, extremes. Furthermore, for a directionally sensitive device such as Oyster the nearshore region offers a wave resource with significantly less directional spread in wave angles due to wave refraction. However, even with the benefits of the nearshore region considered, designing a machine to survive in this aggressive environment for 25 years still represents a significant challenge. Consequently it is vitally important that an accurate description of the load cases is defined to ensure that a robust yet cost effective design is achieved. During scale model tests of Oyster in extreme sea states a slamming event was identified. This event was investigated further, both numerically and experimentally, by Henry et al (2013). The goal of the present work is to further develop our understanding of the slamming of Oyster, to determine what drives it and to help quantify the resultant loads on the structure. In this case a two dimensional (2D) experiment is carried out, in which a 40 th scale model of a generic Oyster shape spans the width of the wave flume at Ecole Centrale Marseille. This scenario offers a simplification of the problem in which the progression of the slam event on a vertical slice of Oyster can be viewed in side elevation, providing a superior view for the high speed camera which is difficult to achieve in three-dimensional (3D) experiments. The 2D experiments also provide a benchmark for the development of numerical model which is less computationally demanding than a 3D experiment. This is not the first time that an OWSC has been tested in 2D and previous work, which led to the development of the Oyster concept (Whittaker et al 2005), showed that there were significant differences in the behavior of the OWSC in 2D and 3D tests. This is primarily due to an alteration of the hydrodynamics which results in a change in phase between the wave and the flap. Of course there are also other differences between and OWSC in 2D and 3D, the most notable of which being the lack of edge effects such as vortex shedding and the blockage effects present in the 2D scenario. With this in mind, the work presented in this paper represents an initial set of experiments which had the primary focus of confirming whether the impact event observed in previous 3D experiments at Queen s University Belfast could be recreated in a 2D experiment.

2 EXPERIMENTAL SETUP Wave Flume The two-dimensional experiments were undertaken in the wave flume at Ecole Centrale Marseille (ECM), Marseille, France. The flume measures m x 0.65 m x 1.5 m and has a flap type, hydraulically driven wave-maker at one end and an adjustable sloping porous (8% porosity) mesh beach suspended into the tank at the other. The Oyster scale model was placed on the flat bottom floor of the flume at a distance 12.2 m from the wave-maker. The longitudinal walls and floor of the flume are glass, supported by a metal frame allowing the complete visualisation of wave propagation down the length of the tank; the Oyster body/wave interaction and the absorption of the waves at the porous mesh beach. Wavemaker Model The model is constructed of a CNC machined, closed-cell foam, buoyant flap, which is free to pivot in pitch about an aluminium tubular axle, on two deep groove single row stainless steel bearings. It is mounted onto two six-axis load cells with a hinge height of 100 mm. The gap beneath the flap and between the load cells is filled with a closed-cell foam which attaches to the flume floor with no interference with the model. Due to the scale and functional requirements of the model, the sensors have been carefully selected so as not to alter the model s inertial characteristics. The flap has been designed to house and compliment the functionality of the sensors so that data can be acquired with minimal contamination and then synchronised to the wave data and high speed camera images. In addition due to the environmental conditions to which it is tested in, the sensors have been modified to assure waterproof protection. The mass of the Oyster flap model is 4.27 kg, the centre of mass -0.24, -9.94, mm [X, Y, Z] and the rotational inertia about the hinge in Pitch is kgm 2. The model and transducer positions can be seen in Figure 3. Fig. 1: Side elevation diagram of the wave flume at ECM. Wave profiles were measured by a set of resistance wire wave gauges. Seven wave gauges referred to as R1-R7 were installed along the tank near to the wave-maker, mid flume, directly in front of and behind of the Oyster model, as shown in Figure 1. The positions in terms of distance from the wave maker of the wave gauges were R1=1.222 m, R2=5.178 m, R3 =5.358 m, R4=5.718 m, R5=6.075 m, R6= m, and R7= m. The acquisition of the wave gauge signals is triggered by the start of the wave-maker and synchronized to the data and images in post processing. In an attempt to reproduce the impacts seen in the 3D experiments, a series of tests with various wave conditions and water depth were carried out in the 2D flume. Two water depths were tested 355 mm and 305 mm, Mean water Level (MWL) and MWL -2 m at full scale respectively. Oyster Scale Model and Transducers A 40 th scale model of Oyster was used with simplified geometry, that is a generic box shape, measuring 646 x 310 x 87.5 mm (width x height x thickness). Fig. 2: Dimetric CAD Render of the Oyster Model Fig. 3: Oyster 40 th scale model 2D drawing with cutaways showing dimensions and transducer positions Rotation The flap angle is measured via a Kistler Triaxial K-Beam 8395 accelerometer. This is mounted with one of its sensing elements coaxially coincident to the pivoting hinge axis. The rotational signal, after a calibration procedure, can then be inferred from the coaxial sensing element s sensitivity to gravity. The accelerometer is mounted into bespoke machined aluminum housing and potted. It is then mounted onto the hinge axis internally via two M4 screws and accessed via a removable foam insert. The flap angle can also be derived from images from the high speed camera which will be discussed later. Loads Load data is taken via two submersible AMTI load cells. Two load cells are used to give the model the required structural stiffness to prevent interference between the flume wall and the flap throughout the tests. The load cells are much like a spool with nominal dimensions of 63.5 mm in height and a diameter of 60 mm. Each unit has eight threaded holes on the top and bottom faces for mounting. The measuring element of the unit consists of a short, thin-walled tube to which strain gauges are arranged in a Wheatstone bridge configuration so as to measure the loads in six degrees of freedom, three moments, Pitch, Roll and Yaw and three forces, Surge, Sway and Heave. The output from the load cells are then amplified, using a Fylde FE-366-TA Micro Analog 2 Signal Conditioning Module, before being converted to a digital signal. The loads cells are mounted below the hinge line at a spacing of 340 mm. After a bespoke calibration procedure the loads are transformed to the centre of the hinge line of the model.

3 Dropping the water level had the desired effect as the intensity of the slamming event was greatly increased with the water level dropping on the front face of the flap and the jet being ejected far in front of the model, as will be discussed in detail in the following section. For the lowest water depth, h=305 mm, 7 wave periods for regular wave were performed, from T=1.26 s (λ=1.9 m) up to T=2.00 s (λ=3.3 m). For each period, the maximum wave steepness corresponding to the mechanical limit of the flap wavemaker was performed. Table 1 gives the parameters of generated waves. The heights presented correspond to the measured values before the reflected wave from the Oyster model reach the wave gauge R2. Fig. 4: Photo of the experiments showing the Camera Pressure Pressure data is taken via a single Kistler 211B B6 pressure sensor, flush mounted into the rigid and smooth PVC flap face at a distance of 210 mm (Fig. 3) from the hinge, at a water depth of 25 mm below the initial mean Water Level (MWL). The sensor is piezo electric and has a sensitive diaphragm of 5.5 mm diameter. The output from the sensor is then amplified, using a piezo-tron coupler, before being converted to a digital signal. Camera The advantage of the 2D experiments in the flume is the ability to view the fluid / body interaction from the immediate side of the model. The clearance between each side of the model and the flume walls being just 2mm. A high speed camera (Vision Research Phantom V641) is installed close to the glass wall of the tank in order to capture the impact or fluid-body interaction area. Images were captured from two angles. The camera enables a resolution of 2560 x 1600 pixels at a frequency up to 1400 fps (2000 fps reducing the resolution). The high speed camera was used for visualization of the interaction between the free surface and the Oyster model. After several sensitivity studies the high speed video recording was in the range of 195 to 2000 fps, depending on the time period of the tests. Data Acquisition System Two different acquisition systems were used during the experiments; one for the acquisition of the wave gauges, a National Instruments PCI- 6031E board, and a second one for the acquisition of the loads, the pressure and the rotation, a National Instruments USB-6363X system. EXPERIMENTS The initial experimental runs were promising in terms of the phase between the wave and the flap but only produced very mild slamming events. The most noticeable difference between these events and those seen in the 3D experiments was that the water level on the front face of the flap did not drop to significant level prior to the impact. A number of different wave periods and wave heights were tried, as well as focused wave packets to increase the wave height at the model, but none were successful. It was known from previous work that the slamming was more intense in tests which simulated extreme wave conditions at low tidal levels. Therefore, in order to encourage slamming to take place, the water level in the wave tank was dropped by 50 mm, which equates to a low tidal level of -2 m at full scale. This represents a significant low tidal level for a typical wave energy site in Western Europe. T(s) H (m) kh Table 1: Wave parameters for h=305 mm. Heights are measured values. Among these different periods, the case for T=1.9 s seemed the most interesting in terms of flap oscillation and pressure response. This case corresponds to shallow water and the corresponding Ursell number is U r =(A/h)/(kh) 2 =0.86. In Figure 5, the time evolution of the free surface at wave gauge R2 is displayed for 2 tests with the same parameters, T=1.9 s, and H=0.1 m. It is interesting to show that the repeatability is very good for these experiments, and also that the wave shape is typical of Cnoidal waves. In order to understand the nonlinearity of the wave, the free surface is reconstructed using a Fourier decomposition on moving windows: N η(x, t) = X n (t) cos(n(ωt kx) + φ n (t)) n=1 With X n (t) and ϕ n (t) the amplitude and the phase of the Fourier modes of the nth order wave component and ω and k, the frequency and the wave number. The moving windows of width twice the period allow us to obtain the time evolution of the Fourier coefficients. In Figure 5, the free surface reconstruction for n=1 to 4 is displayed. We can see clearly that the 4 th component is necessary to well describe the wave. Furthermore the first order description results in an amplitude of 66mm and shows that a classical linear analysis is not adapted to these shallow water cases. More specifically, it is difficult to calculate the reflection and transmission coefficients by a separation method, such as Mansard & Funk (1980). η (cm) t (s) Fig. 5: Sample from wave gauge R2, (Left) Test 28, (Right) Test 54. RESULTS raw linear 2nd order 3rd order 4th order t (s) In the following section data and images from test 28, which had a nominal wave of T=1.9 s, H=0.1 m in a water depth of 305 mm, are analyzed. In general the slamming event observed in the original 3D experiments was recreated in the 2D flume. The slamming event follows the following sequence as illustrated with images from the high speed camera in Figure 6. In the figure the wave enters from the left, or the seaward side of the image raw linear 2nd order 3rd order 4th order

4 Frame A, t = 0 ms Frame E, t = 667 ms Frame B, t = 333 ms Frame F, t = 697 ms Frame C, t = 436 ms Frame G, t = 733 ms Frame D, t = 574 ms Frame H, t = 795 ms Fig. 6: A sequence of frames showing the process of the slam event. Time, in milliseconds, from the first image is given above each frame.

5 Starting with the flap in the vertical position, the landward motion of the water under the crest of the wave forces the flap towards the land and the top of the flap submerges. The flap is then held at an angle towards the land as the pressure of the water on its front face is balanced by the restoring moment of its inherent buoyancy (Frame A). As the crest passes and the pressure on the front face reduces, the buoyancy of the flap accelerates it back up, breaking the water surface (Frame B) as it travels towards the vertical position. At this point down rushing water (Frame C) lowers the water level on the front face of the flap almost to the hinge line (Frame D). Note that, at this point the water surface is particularly disturbed. With water building up behind it and a void in front of it, the flap is accelerated seaward creating a water jet as it re-enters the water (Frame E), leaving air bubbles where it met the disturbed water surface. The water jet travels up the face of the flap (Frames F and G) and is ejected as the top of the flap enters the water (H). This sequence matches that in the 3D experiments which can be seen in the images presented in Figure 16 in the Appendix. The only notable exception being the shape of the water surface on the seaward face of the flap, which is straight across the flap in 2D but concave in 3D, see Figure 17 in the Appendix. The concave shape means that the water jet moves up the flap from the hinge and in from the two sides, intensifying the pressure at the centre of the flap. However, the blockage effects of the side walls in the 2D experiment may still result in higher overall magnitude of pressure. Overall the slamming on Oyster can be seen to be related to the water entry problem which has been studied extensively since the early works of Wagner (1932) and von Karman (1929) - see also Faltinsen (1993). The classical water entry problem involves the dropping of a wedge into water, which results in a similar process in terms of the generation of a water jet which runs up the face of the object and is ejected as a thin film. Prior work has shown that the pressure is greatest under the root of the water jet and its magnitude decreases as the jet root moves up the body Xu (2010). Of course Oyster s flap is not entering the water in the same manner as a free falling wedge, but other modes of entry including oblique entry have been also been studied, such as the work of Judge et al (2004). until the wave reflections from the wave paddle contaminate the incident waves. Fig. 7: Example time history of flap angle and angular velocity The time history of the pressure signal during one of the tests is shown in Figure 8. The raw pressure signal is high pass filtered to remove the drift on the piezo-electric sensor. The root of the jet forms approximately 200 mm from the top of the flap in Frame E, at t = 667 ms. The jet root reaches the top of the flap in Frame H, at t = 795 ms. Therefore, the jet root travelled up the seaward face of the flap at a velocity of approximately 1.56 m/s. It should be noted that aside from the slamming process outlined above there is also a portion of the event shown in Frames D to E in which air would appear to be entrapped between the flap and the disturbed water surface that the flap hits. The entrapped air might be related to the drop of the thin jet down the face of the flap, which causes a small cavity in water, whose closure gives the bubble formation. Due to the lack of a pressure sensor in this area it is difficult to investigate this further but it will be the subject of future studies. In terms of the dynamics of the flap, the angle and angular velocity are derived from the accelerometer and are shown for two wave cycles in Figure 7. The flap angle is zero when the flap is vertical and negative when the flap is pitched seaward, towards the wave maker. Likewise a negative angular velocity signifies that the flap is moving seaward. Figure 7 shows that the flap moves to maximum seaward angle of 60 degrees and reaches a peak angular velocity of 400 deg/sec. These values are broadly in-line with that observed in previous 3D experiments. The flap dynamics are reasonably repeatable for 6 to 10 wave cycles, once the build-up period of 3 or 4 waves has passed, and Fig. 8: Time history of pressure in Test 28 showing the variability of the peak pressure in each slam, approximately every 2 seconds. The time series of pressure in Figure 8 shows that there is a significant variation in the magnitude of the peak pressure in each wave cycle. This is to be expected as it is well known that wave impacts and slamming are a stochastic process, dependent and tiny perturbation of the water surface. One of the largest pressure peaks in the time series is plotted in Figure 9, which has a peak pressure of approximately 10 kpa with a rise time of 30 ms.

6 D E Fig. 9: Time history of a pressure peak recorded during the tests. The blue circles in Figure 9 refer to each subsequent frame of the sequence of images in Figure 10, in which the red dot marks the location of the pressure transducer, while the yellow line highlights the principle axis of the flap. It can be seen that the pressure builds as the root of the jet approaches, peaking in the last image when the jet root is directly over the pressure transducer. A F B Fig. 10: Sequence of images showing the evolution of the building jet. The red dot is the location of the pressure transducer and the yellow line denotes the principle axis of the flap. The images from the high speed camera highlight the similarity of this slamming event with that of a water entry problem. That is that the body s oblique or angled entry into the fluid generates a jet and the highest pressure is found at the root of this jet. Identification of this physical process allows comparison with theoretical work which will be discussed in the following section. C COMPARISON WITH OTHER METHODS Analytical Method The slamming observed in the experiments has some similarities with the water entry problem of a wedge but Wagner's classical theory (see, e.g. Faltinsen 1993) cannot be used directly to model the wave impact because of the angular velocity of the flap. However, while Xu et al. (2010) considered the problem of a body that enters water with horizontal, vertical and rotational velocities, there are very few studies that include the effect of rotation, which is obviously important in this case. It is still too early to tell if the results of Xu et al. (2010) can be extrapolated to the slamming of Oyster but the velocities and angular

7 velocities observed in these experiments are of the same order of magnitude, that is, 1 m/s for the velocity and several radians per second for the angular velocity. However, the observed jet seems to be thicker than the jets of Xu et al. (2010). There is also some analogy with the impacts observed during sloshing experiments. Lafeber et al. (2012) have identified three Elementary Loading Processes (ELPs) that occur in sloshing. The loading process due to the slamming of the flap is closely related to the ELP 2, which includes both slosh-type and flipthrough type impacts as described for example in Lugni et al. (2006) and Colagrossi et al. (2010). Both impacts are completely described by Froude scaling because the loading is purely hydrodynamic, without interference from either the compressibility of the gas or the liquid. Numerical Method The numerical simulation of wave slamming on the oscillating flap is performed using the commercial CFD package, ANSYS FLUENT. The fluid flow is assumed to be incompressible and the behavior of the fluid is modeled with unsteady Reynolds-Averaged Navier-Stokes equations, which are discretized using the Finite Volume Method (FVM) with the Volume of Fluid (VOF) approach for interface capturing. The dynamic mesh method is applied to model the motion of the wave maker and the oscillation of the flap. It is essential that the experiment is reproduced as completely as possible in our numerical model. The dimension of the computational domain is exactly the same as that in the experiment, while the wave is generated by the flap-type wave maker whose moving boundary is modeled by dynamic mesh method. The initial mesh of the wave maker, shown in Figure 11(a), is a sector region filled with the quadrilateral cells which is updated with the constant ratio dynamic layering method. The local mesh of the flap is shown in Figure 11(b), which is a rectangular region filled with triangular meshes, which would be updated as the flap rotates using a smoothing and re-meshing method. The boundary layer mesh, colored cyan in Figure 11(b), is generated adjacent to the surface of the flap, which will be moving passively with the flap, but without any deformation. This mesh scheme can enhance stability of the model and improve the accuracy. At the end of the flume, an artificial momentum term is imposed to simulate the damping beach, where the transmitted waves are absorbed effectively. The flap is considered as a one degree of freedom rigid body, the rotation of which can be calculated by numerically integrating the Newton-Euler equation of motion. The torque exerted on the flap includes wave torque and the mass torque. The wave torque is the pressure integrated over the flap surface at each time step which includes the hydrostatic pressure (the buoyancy) as well as the dynamic pressure. The torque due to the mass of the flap is updated at each time step depending on the orientation of the body. A fourth-order multipoint Adams-Moulton scheme is adopted for updating the angular velocity, in order to enhance the stability of the model. Further details of the numerical model can be found in Wei et al (2014). The wave profile is monitored at seven locations in the numerical model as in the experiment. Pressure histories are gathered at points on the flap distributed every 25 mm from the top to the bottom. Point04 is the exact position of the single pressure transducer in the experiment. Output from the simulation is presented in Figure 12. It shows the water elevation and the velocity contour during a slamming event. The wave propagates from left to right. The frames correspond to the frames captured in the experiment shown in Figure 6. Frame A shows the flap as it starts to rise up. The water level keeps on dropping since the reversing flow is blocked by the flap, and lowers the level of the water in front of the flap (Frames B and C). Most of the seaward face is exposed and a gap is formed between the flap and the water surface, but the water level drop is less significant than that in the experiment (Frame D). The air gap is rapidly extruded by the pitching flap as it enters the water from the bottom up. The velocity at the contact point increases quickly (Frame E). Water is ejected from top of the front face finally (Frame F). The water jet has a relatively slow velocity in the simulation compared to the experiment. The front end of the jet falls down quickly (Frames G and H), which is quite different from the experiment, in which the water jet reaches a considerable distance in front of the model. It indicates that the slamming pressure is underestimated in the simulation. Frame A, ω=0 deg/s Frame E, ω= deg/s Frame B, ω=-70.3 deg/s Frame F, ω= deg/s (a) Wavemaker (b) OWSC Fig. 11: Mesh of the numerical model. Frame C, ω= deg/s Frame G, ω=-87.6 deg/s Frame D, ω= deg/s Frame H, ω=-39.9 deg/s Fig. 12: Water elevation and velocity contour during a slamming event

8 The rotation and angular velocity of the flap are compared with the experiments in Figures 13 and 14. The time series of the flap rotation agrees qualitatively with experiment, but the amplitude is about 8 smaller than in the experiment. The non-linear variation of the angular velocity is consistent with the experiment. The positive peak is only slightly smaller than the experiment, but the negative peak is different. The discrepancy is associated with the drop in water level, which is less significant in the simulation, and therefore the wave force owing to the hydrostatic pressure difference on two sides of the flap is smaller. The numerical model can reproduce the global behavior of the wave interacting with the oscillating flap, and the flow behavior of wave slamming is captured in the simulation. The flap rotation and angular velocity are in good agreement with the experiment. However, slamming is indeed a very local phenomenon; the impact pressure is identified as a spike in the pressure time histories, but is largely underestimated compared to that measured in the experiment. The numerical simulation of the free surface should be improved in order to predict the impact pressure more accurately in the future. Furthermore, as the numerical benchmark introduced within the ISOPE Sloshing Symposium has indicated, numerical results are strongly affected by the quality of grid refinement and time resolution during the jet formation and evolution. A convergence analysis of the numerical results will be performed in the future. CONCLUSIONS Fig. 13 Comparison of flap rotation (H = 0.1 m, T = 1.9 s). Fig. 14 Comparison of flap angular velocity (H = 0.1 m, T = 1.9 s). Figure 15 presents the time history of pressure at Point04. Note that the initial hydrostatic pressure was subtracted from the pressure values. A pressure spike is captured in each wave period, which corresponds to the point at which the slam pressure arrives. The spike is not as sharp as that in the experiment, and the peak pressure in the experiment (5 to 10 kpa) is almost two orders of magnitude higher than in the simulation ( Pa). Hence, the impact loading is underestimated in the simulation. One reason for this is that the relative velocity and the contact angle between the flap and the water surface are two critical parameters for the slamming intensity, the angular velocity of the flap at the moment of impact is underestimated, and the contact angle is overestimated in the simulation. Fig. 15: Time history of pressure variation on Point04 The initial two dimensional experiments have given further insights into the slamming of an OWSC. The general behaviour of the 2D representation of Oyster was found to be reasonably comparable with that of the 3D model reported by Henry et al (2013). Concerns over incorrect phase of the wave and flap in the 2D experiment were not realised and it is thought that in these extreme wave conditions simple linear hydrodynamics are overshadowed by the largely nonlinear nature of the slamming event. However it should be noted that there are still significant differences between 2D and 3D experiments in terms of the fluid-body interaction. The over-damped nature of the 2D experiment meant that the water level had to be dropped considerably to enthuse the slamming event to occur. As the water surface profile travels up the front face of the 2D flap it maintains a horizontal profile while in the 3D experiment it is concave, with water travelling up and in from the sides of the flap. Therefore the slam pressure in 2D could be less than that in the 3D experiment where the pressure may be intensified in the centre of the flap model. Meanwhile it could also be argued that the pressures in the 2D experiment are amplified by the blockage effect, whereby the pressure cannot escape around the sides of the flap. Nevertheless the 2D experiment was found to be a useful tool to investigate the problem and uncover the underlining physical processes, whereas the data from 3D experiments and simulations will ultimately be used in the design of the WEC. The simplification of the 2D experiment provides a greater insight into the fluid-body interaction. This allows the identification of the physics of the impact which informs the selection of scaling laws to be applied to the measurements made at model scale. This work has shown that the slamming of Oyster is closely related to the classic water entry problem, or ELP2 as described by Lafeber (2012), in which a building jet of water is formed close to the body. The pressure is greatest at the root of this jet where the fluid is accelerated. As there is no air entrapment the pressures can be scaled by Froude. However, air entrapment was identified in another physical process prior to the jet formation, see Frames D and E in Figure 6. The air entrapment may require an alternative scaling method to be applied to the pressure measured in this region of the flap due to the compressibility effects. Further two dimensional experiments are planned, the main improvement being the inclusion of further pressure transducers to map the pressure as it moves up the face of the flap. The data will also be used to further refine and validate the numerical and analytical methods.

9 ACKNOWLEDGEMENTS This study was funded partly by Science Foundation Ireland (SFI) under the research project "High-end computational modelling for wave energy systems". The authors would also like to give thanks to Laurent Brosset of GTT for his insights and advice in the area of fluid impacts. REFERENCES Sciences Research Council. GR/S12326/01 Whittaker, TJT, Folley, M, (2012). Nearshore Oscillating Wave Surge Converters and the Development of Oyster. Phil. Trans. R. Soc. A 370, Xu, G.D., Duan, W.Y., Wu, G.X. (2010). "Simulation of water entry of a wedge through free fall in three degrees of freedom." Proc. R. Soc. A 466, Colagrossi, A., Colicchio, G., Lugni, C. & Brocchini, M. (2010) A study of violent sloshing wave impacts using an improved SPH method. J. Hydraul. Res. 48, Faltinsen, O, M, (1993) Sea Loads and Ocean Structures, Cambridge. Folley, M, Whittaker, TJT, Henry, A, (2007). The Effect of Water Depth on the Performance of a Small Surging Wave Energy Converter. Ocean Engineering 34, Folley, M, Whittaker, TJT, (2009). Analysis of the Nearshore Wave Energy Resource. Renewable Energy 34, Henry, A., Rafiee, A., Schmitt, P., Dias, F. and Whittaker, TJT (2013). The Characteristics of Wave Impacts on an Oscillating Wave Surge Converter. In Proceedings of the 23rd International Offshore and Polar Engineering Conference, Anchorage, ISOPE, pp (also to appear in Journal of Ocean and Wind Energy 1, 2014) Judge, C. and Troesch, A. and Perlin, M. (2004) Initial water impact of a wedge at vertical and oblique angles. J. Eng. Math. 48(3) von Karman, T. (1929). "The impact of sea planes floats during landing." NACA TN, 321 Lafeber, W., Brosset, L., Bogaert, H. (2012). Elementary Loading Processes (ELP) involved in breaking wave impacts: findings from the sloshel project. In Proceedings of the 22nd International Offshore and Polar Engineering Conference, Rhodes, ISOPE, pp Lugni, C., Brocchini, M., and Faltinsen, O, M., (2006) Wave impact loads: The role of the flip-through, Phys. Fluids, 18, Mansard, E.P.D., Funke, E.R., (1980). The measurement of incident and reflected spectra using a least squares method. Proc. 15th International Conference on Coastal Engineering ASCE, Sydney, Australian, Wagner, H. (1932). Uber stoß- und gleitvorgange an der oberflache von flussigkeiten (Phenomena associated with impacts and sliding on liquid surfaces). Zeitschrift fur Angewandte Mathematik und Mechanik 12, Wei, Y., Henry, A., Kimmoun, O., Dias, F. (2014). "Numerical study of wave slamming on an oscillating flap". In Proceedings of ASME 2014 International Conference on Ocean, Offshore and Arctic Engineering, OMAE 2014, June 8-13, 2014, San Francisco, California Whittaker, T. J. T., Folley, M, Causon D. M., Ingram D. M., Mingham C. G. (2005). An Experimental and Numerical Study of Oscillating Wave Surge Converters, Engineering and Physical

10 APPENDIX The following two sequences of images are reproduced from Henry et al (2013) showing the slamming event as recorded in 3D experiments conducted at the wave tank in Queen s University Belfast with a 25 th scale model of a generic OWSC shape. A E A E B F B F C G C G D H D H Figure 17: Sequence of images during the impact event. The viewpoint is from an underwater location directly seaward of the model, Henry et al (2013) Figure 16: Sequence of images of the model during a wave cycle which resulted in a slam event. The viewpoint is above the water surface and seaward of the model, Henry et al (2013)