Experimental study of a floating wave energy system oscillating water column type with four degrees of freedom

Transcription

1 Experimental study of a floating wave energy system oscillating water column type with four degrees of freedom André Teodoro Varanda andrevaranda@tecnico.ulisboa.pt Instituto Superior Técnico, Lisboa, Portugal October 2015 Abstract Demanding need for new forms of renewable energy, specifically Wave Energy, accounts for the currently huge range of existing Wave Energy Converters (WECs), in an attempt to make economical the energy extraction. This work presents one of the early stages of development of the FLOWC which is a non-axisymmetric floating oscillating water column (OWC) wave energy converter designed to maximize the wave energy absorption through the excitation of the pitch oscillation mode and its coupling with other two main oscillation modes surge and heave. This papers describes the manufacturing and experimental testing of a 1:100 scaled FLOWC s model in two-dimensional regular and irregular waves. An idealized keel with ballast is attached to the model in order to obtain the desired floating stability. Aiming the oscillating water column s power analysis, an energy simulator extracting system is designed and calibrated. Moorings are chosen to minimize their influence on the model s oscillation modes. The analysis is purely experimental and is based on the Linear Wave Theory. Model s performance is evaluated by calculating the capture width and by making a comparison with the results obtained in the studied Spar Buoy model (Gomes, 2013). Various configurations are tested, by varying: the turbine simulator s pressure drop; the moorings s attachment points on the model. Keywords: Wave Energy Converter (WEC), Oscillating Water Column (OWC), FLOWC, Nonaxisymmetric system, Experimental testing. 1. Introduction The arguments presented here are based, especially, on the Heat (2012), Gomes (2013), Falcão (2014) and Rocha (2014) works. Our planet s surface is covered mostly by oceans. The phenomena responsible for all their momentum - solar radiation, planet s rotation and gravity forces interactions, offer us unlimited energy sources of enormous potential - wind, waves, tidal currents, changes in salinity and thermal gradients. Now and in the future, with the appearance of new and specific technologies, their extraction is and will be possible, currently standing out Offshore Wind and Tidal Energy. Studies indicate that, among all these sources, wave energy leads in terms of theoretical available energy, despite its early stage of development, estimated between 8,000 and 80,000 TWh / year. The use of this form of energy led to the creation of over a thousand patents, until 1980 (McCormick, 1981), inspiring some of the modern technologies, and their number has increased significantly since then. The first patent, dating back to 1799, refers to a machine developed by Girard and his son with the main purpose of driving hydraulic pumps and mills (Ross, 1995; Luoma, 2008). The waves energy potential does not present a uniform global distribution. Cornett (2008) attributed the greatest potential to southern and northern temperate zones. Minor seasonal variations in sea conditions are typical of the southern hemisphere, making it the most attractive place to Wave Energy exploitation (Barstow et al., 2008). The power associated with waves is measured in terms of power per wave crest unit length (kw/m), or, in some cases, per coast direction unit length, and is mainly focused on the ocean surface exponentially decreasing with depth. Unlike the energy flow associated with wind, energy flow from waves is mainly concentrated near the ocean surface, justifying the growing investment in Wave Energy. For greater energy capacity areas and with good conditions for this resource exploitation, Barstow et al. (2008) admits annual average potential between 20 and 70 kw/m, with the highest values recorded in the Southern Hemisphere. Panicker (1976) estimates a available power in the ocean surface be- 1

2 tween 10 and 100 TW for depths greater or equal to 100 m. Other studies have quantified the power that reaches the world coastline on 2.11±0.05 TW (Gunn and Stock-Williams, 2012) Oscillating water column review The first record of the Oscillating Water Column (OWC) concept dates back to the nineteenth century, with the development and installation of 34 whistling navigation buoys. Another record dates back to 1910, in Royan, when the french Praceique- Bochaux developed a device in his home to produce electricity (Falcão, 2012). Only 37 years later, in 1947, Yoshio Masuda develop another device based on the same operating mode, a navigation buoy equipped with an air turbine (Masuda, 1985). OWC converters, usually called first generation devices, consist of fixed or floating submerged structures with an inner chamber open below and above the water surface. The existing water column within the chamber behaves like a piston, excited by the waves or by the wave-structure dynamic interaction, if the system is floating, producing a bi-directional air flow through the upper opening. This, in turn, is equipped with an air turbine and an electrical generator. Due to the air flow characteristics, excited by the water column free surface oscillating motion, valves or a self-rectifying air turbine should be used. Self-rectifying air turbines are more reliable and low-cost solutions. The Oscillating Water Column s definition translates the interaction between three bodies, excited by the oscillatory energy from waves: structure (fixed or floating); water column; motive air column/volume (air-chamber). Simplicity of the technique inherent with OWC concept, as a means of extracting clean energy, is cause for the great investment in this type of converters. Besides the main movable part, the water column, can be seen as a natural structure, other advantages can also be enumerated: the existence of few moving parts; location adaptability (shoreline, nearshore and offshore); the use of an air turbine, which obviates the need for gear boxes (reducing efficiency); its reliability and serviceability; the ability to use efficiently the operating space. High energy costs can be justified due to the ratio between the size of existing projects and their costs, as well as the existence of weak electrical networks in profitable coastal areas. The main OWC prototypes, models and platforms, contructed in large and medium scales are: the Uraga navigation buoy ( kw), installed in 1947 result of Yoshio Masuda efforts; the Kaimei (8 125 kw), also projected by Yoshio Masuda, in 1976, consisting in a test platform for air turbines; the NEL (with several OWCs), between , developed by the British wave energy program; the Sakata (60 kw), in 1990; the Islay I (75 kw), in 1991, Queen s University Belfast responsibility; the Osprey 1 (2000 kw), a very large and powerful device that sank few weeks after its positioning, in 1995; the Mighty Whale (110 kw), developed by the Japan Marine Science and Technology Center, in 1998; the Pico Power Plant (400 kw), projected by IST (Instituto Superior Técnico) and installed in 1999 at Azores; the LIMPET (500 kw), developed also by Queen s University Belfast in 2000, using Voith Hydro Wavegen PTO (Power Take Off) technology, an evolution from the Islay I project; the Oceanlinx Mk1 (500 kw), in 2005, and the Oceanlinx Mk3 ( 50 kw), in 2010, Oceanlinx s projects; the OE Buoy, criated from Yoshio Masuda s BBDB (Backward Bent Duct Buoy) concept, in 2006; the Mutriku ( kw), in operation since by Ente Vasco Energia, using Voith Hydro Wavegen turbines; the Spar Buoy, tested in 2012, Instituto Superior Técnico responsibility The FLOWC model The paper presents a new wave energy converter, the FLOWC (Fig.1), that was designed and built at 1:100 scale, and finally tested in a wave flume. This is a floating offshore system, Oscillating Water Column (OWC) type. His geometry in the neutral position consists of a tubular profile, formed by circular profiles in planes perpendicular to the vertical, following a specific angle and presenting a deflection below the level of the water free surface. The OWC lower mouth ends in the plane perpendicular to the wave direction and is directed oppositely to it. In turn, the top of the model ends in the plane perpendicular to the vertical direction. For its buoyancy, the model has an air chamber along almost its entire body (excluding the volume for placement of the energy extraction system simulator). A keel with ballast has been implemented in order to ensure stability. The model s main physical characteristics are present in Tab.1. Figure 1: FLOWC model at 1:100 scale (starting point and end result) and used referential. The non-axisymmetric geometry of the FLOWC 2

3 is intended to maximize the wave energy absorption through the excitation of the pitch oscillation mode (rotation around the axis parallel to the incident wave crest) and its coupling with the other two main oscillation modes surge (in the wave direction) and heave (in the vertical direction). Table 1: Model main physical characteristics at 1:100 scale, in the neutral position (Fig.1(b)). Characteristic Value Unit Model width 180 [mm] Waterplane area [mm 2 ] OWC diameter 120 [mm] OWC area [mm 2 ] Draft (without keel) 250,2 [mm] Draft (with keel) 353,8 [mm] Arms angle 30 [ ] Deflection 60 [ ] Total height 475,4 [mm] Mass 4156 [g] Ballast mass (lead) 2196,5 [g] Inertia about y a 2, [g mm 2 ] Mass center a -180 [mm] Floating a center -143 [mm] Metacentre a 47,1 [mm] This paper focuses on the first sub-phase of the first wave energy converter development stage, the validation model (Holmes, 2009), where a smallscale model (1:25-100) is subjected to tests in two-dimensional regular waves. Due to the nonaxisymmetric geometry, a performance comparison is performed between the design (FLOWC-A) and the reversed position (with respect to the wave direction, FLOWC-B) is performed. Whenever possible, a qualitative comparison is carried out between the results from model FLOWC and from model Spar Buoy at 1:120 scale (Gomes, 2013). It also performs a slight initial approach to the second subphase of this validation stage, with the conduction of several tests in two-dimensional irregular waves. These tests aim a first assessment of the performance of the model in two-dimensional conditions. The charcateristics natural periods of the model were found experimentally. Model displacements in six degrees of freedom, water and oscillating water column free surfaces elevation and pressure inside the model air-chamber are continually analyzed, either in time domain or in the frequency domain. The power available to the turbine simulator is calculated for various model configurations. Others interest parameters like waves reflection, from a Last step modelling values in SolidWorks c ; for this step, almost all the instrumentation belonging to the model was modeled together with the same. the used absorbing beach, and phase differences are measured in regular waves. 2. Formulation and important calibrations This section presents the adopted formulation and calibrations for the experimental data treatment and obtaining results. Besides Gomes (2013), Falnes (2002) constitutes an important contribution to the adopted formulation Scale factors Either in the model design and construction or in the experimental data post processing it is necessary to consider scaling factors, between values related to prototype (numerical values and final results), at full-scale, and results of tests at model scale. The aim is to faithfully reproduce the prototype, geometrically, kinematically and dynamically. Table 2: Main scale factors considered for this work. Quantity Scale factor b Distance [m] s Period [s] s 1/2 s 1/2 ρ s 1/2 γ Frequency [s -1 ] s 1/2 s 1/2 ρ s 1/2 γ Mass flow rate [kg s -1 ] s 5/2 s 1/2 ρ s 1/2 γ Pressure [Pa ou kg m -1 s -2 ] s s γ Power [W ou kg m 2 s -3 ] s 7/2 s 1/2 ρ s 3/2 γ A good kinematic and dynamic reproduction is achieved if the reasons between displacements, velocities, accelerations and forces existing between the model and the prototype are constant. Froude criterion was used, considering only the gravity and inertial forces. Used scale factors are discriminated in Tab.2. Viscous scale factors are neglected, since these forces tend to be much higher than the expected ones at model scale Linear wave theory The waves propagation dynamics is complex and highly nonlinear. The study of floating bodies subjects to two-dimensional waves requires the application of simplified motion equations and specific boundary conditions. Linear Wave Theory is generally used in the Wave Energy Converters study. This theory application requires that some conditions are assumed: inviscid (potential), incompressible and irrotational flow; constant depth, h, and hard and impermeable bottom surface (z = h); wave amplitudes, A w, are small compared to its length, λ w, and depth, h. By expressing those boundary conditions, in the bed bottom and on the b s ϱ and s γ respectively represent the ratios between fluids densities (ρ) and ratios between fluids specific weigth (γ = ρg). They have values very close to the unit, so can be neglected. 3

4 water free surface, and using the velocity potential, the Bernoulli equation and the definition of wave number, κ, given by κ = w v f = 2π λ w, (1) it is possible to obtain the dispersion relation w 2 = gκ tanh(κh), (2) where w, v f are, respectively, the wave angular frequency and phase (propagation) velocity, and g represents the gravity acceleration. In the WECs study, the ratio between the power available at the turbine simulator (or turbine) and the wave energy flux is an important assessment factor, L c = P Pw, (3) where P is the power available to the power extraction system (in this case, by OWC). L c is the capture width, which defines the WEC efficiency. Wave average energy flux is given by P w and defines the wave power per plane wave crest unit, through the plane perpendicular to the propagation direction, between the bottom and the free surface. In shallow waters, it can be expressed by, P w = ρ wgwa 2 w 4κ ( 1 + 2κh sinh(2κh) ), h < λ/2, (4) wherein ρ w is the water density. In deep water, the Eq.(4) can be simplified by applying the dispersion relation (Eq.(2)), P w = ρ wg 2 A 2 w 4w, h > λ/2. (5) For irregular waves, with the Eq.(4) generalization and discretization and considering its approach by N regular waves, the wave average energy flux can be obtained, P w = ρ wg 4 N i=1 w i A 2 ( ) w,i 2κ i h 1 +. (6) κ i sinh(2κ i h) For this equations, A w and w are obtained from trials without the model in the wave flume (or tank) and represent reference values that do not account for the model s surface reflections and radiations Regular waves Even for regular waves, phase differences, ψ u, can be calculated. Their analysis allows the evaluation of the different interest parameters response to the water free surface elevation. They can be calculated by ψ u = 2π t u t ηw p ηw, (7) where t ηw and t u represents, respectively, the zerodowncrossing time of water free surface elevation and the following u parameter zero-downcrossing time, in a given constant wave period, p ηw. For the highly nonlinear FLOWC model this analysis is valid only for some tested wave periods, p w, of equal value that periods from different interest parameters, p u. Another interest parameter in regular waves is the waves reflection coefficient, K r = A w,r A w,i, 0 A w,r A w,i, (8) which allows evaluate the validity of testin with a given absorption beach. A w,r and A w,i are, respectively, the reflected and incident wave amplitude, obtained from trials without the model in the wave flume (or tank). Offshore devices are not subject to wave reflections. Then, Holmes (2009) defined a maximum reflection of 20% for acceptable model testing Irregular waves The water free surface elevation variance, σ 2, defined by the variance (or power) density spectrum integration, represents another interesting parameter in the analysis of irregular waves, because it is proportional to the waves energy. The variance (or power) density spectrum, S w, can be obtained using the (Discret) Fourier Transformed ((D)FT), and, for the null average free surface elevation value, is defined by S w (w i ) = A2 w,i 2 w, w = constante, (9) where i = 1,..., N represents each regular harmonic, in which w is defined by the interval between the several regular harmonics angular frequencies. It can be implemented for other interest parameters as well. For the results analysis, variances are easily calculated using the irregular series time-domain analysis, ση 2 w = 1 N t (η w,j η w ) 2, (10) N t j=1 wherein σ refers to the standard deviation, the water free surface elevation is given by η w, and j = 1,..., N t are the acquired samples, in timedomain Filters calibrations This work s major focus is the assessment of the energy extraction system s available power, P. In small scale models, it becomes necessary to simulate this extraction by imposing a controlled pressure drop between the model air chamber and the atmosphere and by varying this pressure drop created damping. This can be achieved by having holes 4

5 or filter between the model air chamber and the atmosphere, in order to create respectively a linear (typical of Wells turbines) (Gato and Falcão, 1988) or a quadratic (typical of impulse turbines) (Falcão et al., 2011) relationship between the created pressure difference and the air flow rate. The used turbine simulator (Fig.2) intends to impose a linear relationship, k, with the use of filters. Table 3: Interest model scale parameters in the turbine simulator s linear coefficients calculation. Method A f [mm 2 ] Fixed model Vertical pipe N f k m (m) x 10 6 [m s] c Figure 2: Turbine simulator: (a) exploded view; (b) cut in xz plane of the assembling without filters (extreme situation - 3 filters); (c) assembled. Filter calibrations were performed to determine the relationship between air mass (or volume) flow rate, ṁ a, and the pressure in the air chamber, p. Use of wind tunnels, in a controlled environment, is the ideial process. In this work the filters calibration involves three stages: filter area calculation, A f, using the relationships from the numerical model and Gomes (2013), for various filters numbers, N f ; filter(s) calibrations using a similar material (AL650 synthetic carpet) that the one used by Gomes (2013), directly in the turbine simulator mounted on the fixed model and with the help of a fastening system; filter(s) calibrations using a fixed vertical pipe (Lopes et al., 2007). The obtained values are discriminated in Tab.3. The filter area, limited by the model s geometry, has been set for the maximum use of 3 filters. For this calibrations, pressure inside the air chamber, p, and OWC position, η owc, measurements must be performed. To prevent systematic errors, careful calibrations to the probe within the model and to the pressure sensor are required. Relatively large acquisition time periods are performed (120 s in this study), in order to obtain a large number of points. Applying a well defined low-pass filter to the acquired data is of utmost importance in order to eliminate signals s high frequencies, that are responsible for random errors, and to allow the OWC s velocity correct calculation (to obtain the volume flow rate). Temperature, pressure and relative humidity of air are measured by sensors for the air density, ρ a, and consequently the air mass flow rate calculations. For the air mass flow rate and therefore the available power calculations, fixed model s calibration coefficients are considered. The difference between these values and those for the vertical pipe can be explained by the small leaks existence in the vertical tube system (higher flow rates for equal pressure values) or by the OWC s nonlinear oscillation phenomena, due to its large diameter (higher pressure values for identical flow rate values). Thus, these reflect a good reliability in the turbine simulator use and in the cover sealing. 3. Modelling, manufacturing and experimental testing The FLOWC model was modeled using the SolidWorks c program. In this step some important considerations were taken into account: the mesh from the numerical model and with it the internal and external diameters, the floating position and the tubular profile; the desired mass centre and floating centre positions; the buoy and all instrumentation materials (density, strength and flexibility); geometric scale factors and OWC maximum amplitude. Some static charges simulations in the keel were carried out using the same program. The buoy material, acrylonitrile butadiene styrene (ABS), was subjected to tensile tests and its impermeability was also analyzed. The model s manufacture supported several phases: computational model cutting in several parts, so that it can be manufactured by the rapid prototyping machine, and the consequent bonding technique idealization (punctual male-female type); parts manufacturing; body assembling (using epoxy) and surfaces waterproofing (using lacquer and acrylic paint); capacitive probe introduction and fixing for OWC elevation measuring (made of silver alloy); filling and fixing the ballast (lead) within the keel and assembling it in the model body (using acetate silicone). This last step was repeated in order to obtain the correct neutral buoyancy position. For the turbine simulator manufacture other c Subscript m refers to a model scale value and superscript m refers to the linear relationship, k, between air mass flow rate and pressure 5

6 low density materials were used: ABS for the cover and tightening cap; stainless steel for the threads and their nuts; high-density polyethylene (HDPE) for the pressure taps and their nuts. Table 4: Slack-mooring configurations parameters. Parameter Value d Unit l e / 249 f / 186 g [mm] l [mm] l [mm] z a -189 e [mm] z b -154 f [mm] z c -234 g [mm] x a 870 [mm] α ac 16 e; g [ ] α b 13 f [ ] m la 14,5 [g] ρ la [kg/m 3 ] m ba 1,3 [g] ρ ba 340 [kg/m 3 ] Figure 3: Modeling ((1)-(4)) and assembly ((a)-(i)) of FLOWC. Experimental tests were carried out at the Laboratório de Hidráulica do Instituto Superior Técnico (LHIST) wave flume (Fig.4(a)), aiming the model performance evaluation under different sea conditions. Capacitive probes are used (similar to that installed in the model) for the water free surface elevation measurement, which consist of two parallel rods made of a conductive material. Four probes are positioned between the model and the wave-maker, for measuring the reflection and the energy flow, and one is at model position for phase difference and energy flow measurements (the latter without the model in the channel). A system consisting of two pressure taps, air hoses and low pressure sensors (GE Druck and Honeywell), is used for measuring the pressure within the air-chamber of the model. In turn, for the model motion measurement in its six degrees of freedom, a video tracking system (Qualisys) is used in which a rigid body is defined (in the model) by infrared reflective spheres. Due to the geometry of the model, it was decided to use the 3 slack-mooring configurations (a, b and c) shown in Fig.4(b)-(c), in order to prevent drift. The main parameters of these configurations are detailed in Tab.4. Lead weights, bottom weights, nylon wires and small buoys were used. d Unreferenced values are equal for all configurations. e Configuration a values. f Configuration b values. g Configuration c values. Figure 4: Wave flume configuration and slackmooring configurations: a - green; b - yellow; c - magenta. 4. Results and discussion The model performance results are analyzed for various configurations, each as a function of wave period, p w (peak period, T p, in the case of irregular waves), varying: wave amplitude, A w, (significant wave height, H s, in the case of irregular waves); number of filters applied in the turbine simulator (1, 2 or 3); mooring s attachment position at the model (a, b or c configurations) FLOWC s natural periods The model s natural period, for each oscillation mode, is defined as the time it takes to reach the same position in the same movement direction, in standing water. Natural periods for the surge, p (1) n, heave, p (3) n, and pitch, p (5) n oscillation modes (Tab.5) were obtained. By observing the physical model behavior it was possible to make a correction to the heave s natural period, which should be approximately s. 6

7 Table 5: FLOWC s natural periods for the main oscillating modes. Natural periods [s] h Moorings i surge heave pitch p (1) n p (3) n p (5) n a configuration b configuration c configuration Looking at the Tab.5, the proximity of the heave and pitch natural periods can be checked. Whereas the main oscillation excitation modes are associated with large system oscillations and thus with the extracted energy maximization by a WEC, the apparent coupling of these oscillation modes translates the existence of a power peak in wave periods of about 20 s (full scale) Regular waves Analyzing the oscillation modes behavior, by increasing the wave amplitude, it can be seen an instability emergence and intensification in the yaw mode (rotation around z) to s of wave period. The large energy dissipation by this oscillation mode may be a reason for the low capture width registered for these wave period values. The same is true for the roll mode (rotation around x) to 7.7 s of wave period. In addition, a slight excitation of this oscillation mode, to s of wave period, suggest its natural period s existence in this interval. Contrary to Spar Buoy model, larger surge values appears to 25 s of wave period. The largest heave and pitch oscillation amplitudes occur for the wave period related with the pitch s natural period and to s of wave period, where the highest power peak can be found. However, the wave amplitude increase is responsible for the decrease of the maximum values recorded for these two oscillatory modes, as well as the capture width. The wave amplitude increase is related to the fluid velocity increase and consequently with the surface viscous forces increase in the fluid-body interaction. This increase is even more significant in small scales, dissipating much of the energy available. There is a pressure and OWC amplitude increase, with the main oscillation modes s amplitude rise. Low capture width values, to and 25 s of wave period, can be justified due to the high energy flux values for those periods (typical of shallow water), not appropriate to offshore device testing. Compared to data provided by the Spar Buoy h Presented natural periods are the mean values obtained for the model: without moorings and filters; with moorings and without filters; with moorings and one filter. i See Fig.4 model, the parameters related to energy extraction (water column and pressure oscillations and capture width) have generally lower values in amplitude (1.3, 3 and 1.5 times, respectively). A higher pressure amplification to a smaller OWC amplification in the Spar Buoy model, and considering also the water column s small surface area, in relation to the FLOWC model (6 times lowest), indicates that non-linear effects existing in the water column s free surface of the last are responsible for the high dissipation of available power. Both models have the highest power peak at approximately 10 s of wave period. In the model Spar Buoy is still possible to observe the presence of two power peaks at approximately 12.5 s. For the model FLOWC, the existence of a second power peak at s, despite its low value, can be verified. This phenomenon, together with the existence of higher amplitude values for the water column and pressure oscillations, to and 25 s of wave periods in the FLOWC model, represents the major difference observed, related to the energy utilization, between the last and the Spar Buoy model. In turn, the 2 filters increase, applied to the turbine simulator, implies the observed roll mode instability s increase (7.7 s). Moreover, the three filters use is responsible for canceling this same instability. There is, however, an increase in the roll mode s excitement for the wave period related to its expected natural period. Compared to Spar Buoy model, the verified pressure loss influence on the FLOWC model s dynamics presents a different behavior in the main oscillation modes s excitation. In general, the instability reduction with the increase of pressure loss, observed for certain oscillation modes, is visible to both models. On other hand, an increase of the major instabilities is verified: yaw mode in the FLOWC model; roll mode in the Spar Buoy model. A heave mode s significant increase is noted with the increased number of filters for the wave period relative to the pitch s natural. The greater OWC damping explains the increased pressure in the model s air chamber. On the other hand, high main oscillation modes s amplitudes entail a more pronounced increase in pressure for a decrease of the water column s amplitude, due to the higher OWC s speeds and to its consequent viscous forces increase. An power peaks increase between 2 to 2.5 times is verified for the capture width using three filters. This increase is 20% lower in the Spar Buoy model for wave periods related to its higher power peak. In turn, the Spar Buoy model s water column has a reduction approximately 17% lower in its oscillations and its pressure oscillations presents an amplification approximately 28% lower than those recorded 7

8 Figure 5: Nondimensional capture width, by the model width (diameter, d m ), for all tested configurations in regular waves (full scale): wave height variation for 1a configuration (circles); number of filters variation for a configuration and A w = 1 m (red); slack-mooring configurations variation for 3 filters and A w = 1 m (triangles). for the FLOWC model. This can be explained by the nonlinear effects decrease, present in the OWC s free surface, with the increased damping for FLOWC model. These facts show a significant dependence with the high existing ratios between the water columns s diameters and between the main oscillation modes s excitation, of both systems for the considered wave periods. Varying the slack-mooring configuration aims the different modes of oscillation s response change. For b mooring configuration is, in general, verified the main registered instabilities reduction or annulment, as well as roll mode s amplitude reducing for the wave period supposedly relating to its natural period. Also for this configuration, there is a slight heave and pitch s amplitude increase, for the wave period relative to the pitch s natural period, and a surge s amplitude decrease to 25 s of wave period. These results suggest that the b configuration s attachment point in the model is closer to the centre of rotation than the one in a configuration. The c mooring configuration is related to the larger restitution forces s existence. Therefore, greater surge and pitch restrictions are observed. This might explain the slight decrease in yaw instability ( s) comparing to the a configuration. The very low attachment point can, on the other hand, account for the checked roll instability s large increase(7.7 s). The largest restitution forces are also responsible for the pronounced decrease in heave and pitch s amplitudes to the wave period related with the pitch s natural period. Also for this mooring configuration, a worse pitch s performance for an identical heave s performance, to s wave period, reinforces the fact that the heave s natural period approach s (about twice that heaves s excitation value). Greater OWC dependence with the pitch mode is found for this wave period. Lower OWC s amplitude values and higher pressure values can be justified by the nonlinear effects reduction on the OWC s surface, as well as by the viscous forces, leading to the capture width increase. The pitch mode s importance for energy extraction is observed in the pressure decrease with the reduction of this oscillation mode, and the consequent capture width reduction to wave periods related with its natural period (c configuration) and to 25 s (b configuration). Changes in the model s dynamics as well as in the water column oscillations, are attenuated by a more or less stable OWC s behavior. Comparing the inverted model according to x axis, FLOWC-B, with the numerically simulated model, FLOWC-A, there are some important noted changes. A pronounced heave s amplitude decrease between 12.5 and 17.8 s, for an identical pitch mode behavior, suggests the importance of the direction of the device s upper arm inclination in the heave s excitation for FLOWC-A mode. For FLOWC-B mode, smaller but more stable values are obtained for the yaw instability (wider wave periods range subject to this instability). On the other hand, a large increase in the roll instability (7.7 s) is detected, as well as for both instabilities to s of wave period. The latter ones implies the main oscillation modes s amplitudes decrease for the said wave period. There is a weak pitch influence on the OWC s dynamics for FLOWC-B mode. This can be justified by the decrease in the OWC s amplitude, when this oscillation mode s amplitude increases, to s and s of wave period, together with the low heave and surge values for these periods. Still using the FLOWC-B mode, reduced surge and heave s amplitudes to 25 s, as well as reduced OWC and pressure s amplitudes, suggest the importance of the lower mouthpiece s direction for the energy extraction, in the FLOWC-A model. A more stable OWC and pressure behavior is checked for FLOWC-B mode, with the annulment of small power peaks recordedgreat among s of wave period. Minor OWC and pressure s amplitudes values for the wave period related with the pitch s natural period also justify the large capture width decrease, to s, due, most likely, to an non-linear effects increase on the OWC s surface. However, the FLOWC-B mode displays a slight capture width increase for the higher power peak checked. Checking the water column and oscillation modes s behavior, for that wave periods range (10-11,76 s), this shall be justified by the non-linear 8

9 Figure 6: Nondimensional capture width s comparative analysis, between the model in the correct position (FLOWC-A - lower mouthpiece facing to the batter) and the inverted model (FLOWC-B - lower mouthpiece facing to the breakwater), for 3a configuration and A w = 1 m (full-scale). effects decrease on the OWC s surface and by the greater main oscillation modes s coupling efficiecy. It was possible to verify high reflection coefficient values for all tested wave periods (greater than 20%). Reflection coefficients between 18 and 65% are obtained. For the higher recorded power peak, referring to s of wave period, there are reflection coefficient values between 20 and 30%. The model testing conditions are not appropriate, as referred by Holmes (2009), differing enough of the real conditions for offshore devices Irregular waves Compared to the Spar Buoy model results shown by Gomes (2013), there is generally a similar behavior between both models s main oscillating modes for small significant wave heights. Among the test H s = 1.20 m for the model Spar Buoy and the test H s = 1.25 m for the model FLOWC, the first shows, however, a higher surge (2 to 2.27 times) and pitch (55-57 times) energy performance. A more effectively heave s performance is verified for the model FLOWC (1.4 to 2 times). Spar Buoy model presents performances even 336%, 353% 476% higher than the model under study, for the OWC, the pressure and the capture width respectively. Analyzing the figure 7, the FLOWC model s best performances are checked for: smaller significant wave heights, reflecting a high ratio between viscous and geometric scale effects; larger water column s damping (OWC s lower speed entails a more stable behavior of the air flow); slack-mooring s attachment points near the centers of mass and rotation of the model, in order to amplify the main os- Figure 7: Nondimensional capture width, by the model width (diameter, d m ), for all tested configurations in irregular waves (full scale): significant wave height variation for 1a configuration (circles); number of filters variation for a configuration and H s = 2.5 m (blue); slack-mooring configurations variation for 3 filters and H s = 2.5 m (triangles). cillation modes s amplitudes, and consequently the OWC s excitation. On the other hand, a worse performance is associated with OWC s larger oscillation amplitudes due, most likely, to the existence of high nonlinear effects, amplified by the free surface s higher oscillation speed. An amplification of the main oscillation modes becomes more relevant for fixing the mooring above the center of mass and near the center of buoyancy. The higher observed pressures, related to the use of this mooring configuration, suggest the OWC s more efficient excitation due to the more effective coupling of the main oscillation modes. In general, these results are consistent with the performance observed for regular waves. 5. Conclusions and future work The model s natural periods were obtained and the heave and pitch oscillation modes s coupling was conferred. Both in the model performance in regular waves as in irregular waves, two-dimensional, a second oscillation mode s excitation can be verified, by multiple frequencies of the natural period of pitch, for the main oscillation modes, and, for the OWC and the pressure. It is therefore possible to confirm a greater dependency of the model s dynamics in this oscillation mode, for the tested range of wave periods. The yaw s dynamic instability and the roll s excitation, are responsible for dissipating much of the energy for a wide range of wave periods. These instabilities may justify the absence of a power peak, predicted by the numerical model. The presence of high viscous forces due to scale effects is observed for larger wave amplitudes 9

10 and whenever high speeds are verified in the bodyfluid interaction. A smaller or larger excitement of such instabilities appear to be possible by varying the imposed OWC damping and/or the slackmooring s attachment point. Both imply changes in the model s dynamics, especially for the wave periods that excites the pitch oscillation mode and for the larger amplitudes of the main oscillation modes. The moorings influence in the capture width appears to be only relevant when there is a restriction imposed to these modes for these wave periods. In the comparative analysis, between the model in the correct position and in the inverted position, there is a better performance of the first for major wave periods. For the inverted model a more stable behaviour is observed, not likely to provide a power peak for longer wave periods. However, it checks slightly better performance for the periods related to the power peak. The results obtained for irregular waves are in general in agreement with those obtained for regular waving, although a better OWC performance is verified owing to more efficient main oscillation modes s coupling (responsible for the major OWC excitation), associated with the excitation of a wider band of frequencies. Compared to the Spar Buoy model, the FLOWC model shows very low capture width s values. The only advantage of this model, relative to the model studied by Gomes (2013), appears to be the greater influence of the OWC s damping in varying the model s dynamics. In the future, taking into account the great difference between the numerical and the experimental results, the numerical model should be revised and the model s keel existence may be simulated. The nonlinearities s existence should be included, through an time domain analysis. Experimentally, larger scale tests should be performed in order to minimize the high viscous forces. A more efficient numerical model validation, which uses the panel method, implies the need to test the model in a linear array. Finally, the need to perform tests using a dissipative beach, in order to minimize the reflected energy, is of utmost importance. References Barstow, S., Mørk, G., Mollison, D., and Cruz, J. (2008). The wave energy resource. In Cruz, J., editor, Ocean Wave Energy - Current Status and Future Perspectives, pages Springer-Verlag. Cornett, A. M. (2008). A global wave energy resource assessment. In Proceeding of the Eighteenth (2008), Vancouver, BC, Canada. International Offshore and Polar Engineering Conference. Falcão, A. F. O. (2012). Ocean energy: Historical aspects of wave energy conversion. In Sayigh, A. A., editor, Comprehensive Renewable Energy, volume 8, chapter 2, pages 7 9. Elsevier. Falcão, A. F. O. (2014). 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