Experimental study of a floating wave energy system oscillating

water column type with four degrees of freedom

Andre Teodoro Varandaandrevaranda@tecnico.ulisboa.pt

Instituto Superior Tecnico, Lisboa, Portugal

October 2015

Abstract

Demanding need for new forms of renewable energy, specifically Wave Energy, accounts for thecurrently huge range of existing Wave Energy Converters (WECs), in an attempt to make economicalthe energy extraction. This work presents one of the early stages of development of the FLOWCwhich is a non-axisymmetric floating oscillating water column (OWC) wave energy converter designedto maximize the wave energy absorption through the excitation of the pitch oscillation mode and itscoupling with other two main oscillation modes surge and heave.

This papers describes the manufacturing and experimental testing of a 1:100 scaled FLOWC ’smodel in two-dimensional regular and irregular waves. An idealized keel with ballast is attached to themodel in order to obtain the desired floating stability. Aiming the oscillating water column’s poweranalysis, an energy simulator extracting system is designed and calibrated. Moorings are chosen tominimize their influence on the model’s oscillation modes. The analysis is purely experimental and isbased on the Linear Wave Theory. Model’s performance is evaluated by calculating the capture widthand 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’sattachment points on the model.Keywords: Wave Energy Converter (WEC), Oscillating Water Column (OWC), FLOWC, Non-axisymmetric system, Experimental testing.

1. Introduction

The arguments presented here are based, especially,on the Heat (2012), Gomes (2013), Falcao (2014)and Rocha (2014) works. Our planet’s surface iscovered mostly by oceans. The phenomena re-sponsible for all their momentum - solar radiation,planet’s rotation and gravity forces interactions, of-fer us unlimited energy sources of enormous poten-tial - wind, waves, tidal currents, changes in salin-ity and thermal gradients. Now and in the future,with the appearance of new and specific technolo-gies, their extraction is and will be possible, cur-rently standing out Offshore Wind and Tidal En-ergy. Studies indicate that, among all these sources,wave energy leads in terms of theoretical availableenergy, despite its early stage of development, esti-mated between 8,000 and 80,000 TWh / year. Theuse of this form of energy led to the creation ofover a thousand patents, until 1980 (McCormick,1981), inspiring some of the modern technologies,and their number has increased significantly sincethen. The first patent, dating back to 1799, refersto a machine developed by Girard and his son with

the main purpose of driving hydraulic pumps andmills (Ross, 1995; Luoma, 2008).

The waves energy potential does not present auniform global distribution. Cornett (2008) at-tributed the greatest potential to southern andnorthern temperate zones. Minor seasonal varia-tions in sea conditions are typical of the southernhemisphere, making it the most attractive place toWave Energy exploitation (Barstow et al., 2008).The power associated with waves is measured interms 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 expo-nentially decreasing with depth. Unlike the energyflow associated with wind, energy flow from wavesis mainly concentrated near the ocean surface, jus-tifying the growing investment in Wave Energy. Forgreater energy capacity areas and with good condi-tions for this resource exploitation, Barstow et al.(2008) admits annual average potential between 20and 70 kW/m, with the highest values recordedin the Southern Hemisphere. Panicker (1976) es-timates a available power in the ocean surface be-

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tween 10 and 100 TW for depths greater or equalto 100 m. Other studies have quantified the powerthat reaches the world coastline on 2.11±0.05 TW(Gunn and Stock-Williams, 2012).

1.1. Oscillating water column review

The first record of the Oscillating Water Column(OWC) concept dates back to the nineteenth cen-tury, with the development and installation of 34whistling navigation buoys. Another record datesback to 1910, in Royan, when the french Praceique-Bochaux developed a device in his home to produceelectricity (Falcao, 2012). Only 37 years later, in1947, Yoshio Masuda develop another device basedon the same operating mode, a navigation buoyequipped with an air turbine (Masuda, 1985).

OWC converters, usually called first generationdevices, consist of fixed or floating submerged struc-tures with an inner chamber open below and abovethe water surface. The existing water columnwithin the chamber behaves like a piston, excitedby the waves or by the wave-structure dynamicinteraction, if the system is floating, producing abi-directional air flow through the upper opening.This, in turn, is equipped with an air turbine and anelectrical generator. Due to the air flow characteris-tics, excited by the water column free surface oscil-lating motion, valves or a self-rectifying air turbineshould be used. Self-rectifying air turbines are morereliable and low-cost solutions. The Oscillating Wa-ter Column’s definition translates the interactionbetween three bodies, excited by the oscillatory en-ergy from waves: structure (fixed or floating); watercolumn; motive air column/volume (air-chamber).

Simplicity of the technique inherent with OWCconcept, as a means of extracting clean energy, iscause for the great investment in this type of con-verters. Besides the main movable part, the watercolumn, can be seen as a natural structure, otheradvantages can also be enumerated: the existenceof few moving parts; location adaptability (shore-line, nearshore and offshore); the use of an air tur-bine, which obviates the need for gear boxes (reduc-ing efficiency); its reliability and serviceability; theability to use efficiently the operating space. Highenergy costs can be justified due to the ratio be-tween the size of existing projects and their costs,as well as the existence of weak electrical networksin profitable coastal areas.

The main OWC prototypes, models and plat-forms, contructed in large and medium scales are:the Uraga navigation buoy (0.07-0.5 kW), installedin 1947 result of Yoshio Masuda efforts; the Kaimei(8×125 kW), also projected by Yoshio Masuda, in1976, consisting in a test platform for air turbines;the NEL (with several OWCs), between 1975-82,developed by the British wave energy program; the

Sakata (60 kW), in 1990; the Islay I (75 kW), in1991, Queen’s University Belfast responsibility; theOsprey 1 (2000 kW), a very large and powerful de-vice that sank few weeks after its positioning, in1995; the Mighty Whale (110 kW), developed bythe Japan Marine Science and Technology Center,in 1998; the Pico Power Plant (400 kW), projectedby IST (Instituto Superior Tecnico) and installed in1999 at Azores; the LIMPET (500 kW), developedalso by Queen’s University Belfast in 2000, usingVoith Hydro Wavegen PTO (Power Take Off) tech-nology, an evolution from the Islay I project; theOceanlinx Mk1 (500 kW), in 2005, and the Ocean-linx Mk3 (≈50 kW), in 2010, Oceanlinx’s projects;the OE Buoy, criated from Yoshio Masuda’s BBDB(Backward Bent Duct Buoy) concept, in 2006; theMutriku (16×18.5 kW), in operation since 20010 byEnte Vasco Energia, using Voith Hydro Wavegenturbines; the Spar Buoy, tested in 2012, InstitutoSuperior Tecnico responsibility.

1.2. The FLOWC model

The paper presents a new wave energy converter,the FLOWC (Fig.1), that was designed and builtat 1:100 scale, and finally tested in a wave flume.This is a floating offshore system, Oscillating WaterColumn (OWC) type. His geometry in the neutralposition consists of a tubular profile, formed by cir-cular profiles in planes perpendicular to the vertical,following a specific angle and presenting a deflec-tion below the level of the water free surface. TheOWC lower mouth ends in the plane perpendicu-lar to the wave direction and is directed oppositelyto it. In turn, the top of the model ends in theplane perpendicular to the vertical direction. Forits buoyancy, the model has an air chamber alongalmost its entire body (excluding the volume forplacement of the energy extraction system simula-tor). A keel with ballast has been implemented inorder to ensure stability. The model’s main physicalcharacteristics are present in Tab.1.

Figure 1: FLOWC model at 1:100 scale (startingpoint and end result) and used referential.

The non-axisymmetric geometry of the FLOWC

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is intended to maximize the wave energy absorptionthrough the excitation of the pitch oscillation mode(rotation around the axis parallel to the incidentwave crest) and its coupling with the other two mainoscillation modes surge (in the wave direction) andheave (in the vertical direction).

Table 1: Model main physical characteristics at1:100 scale, in the neutral position (Fig.1(b)).

Characteristic Value Unit

Model width 180 [mm]Waterplane area 25447 [mm2]OWC diameter 120 [mm]OWC area 11310 [mm2]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 ya 2,42541×108 [g mm2]Mass centera ≈-180 [mm]Floatinga center ≈-143 [mm]Metacentrea ≈47,1 [mm]

This paper focuses on the first sub-phase of thefirst wave energy converter development stage, thevalidation model (Holmes, 2009), where a small-scale model (1:25-100) is subjected to tests intwo-dimensional regular waves. Due to the non-axisymmetric geometry, a performance comparisonis performed between the design (FLOWC-A) andthe reversed position (with respect to the wave di-rection, FLOWC-B) is performed. Whenever possi-ble, a qualitative comparison is carried out betweenthe results from model FLOWC and from modelSpar Buoy at 1:120 scale (Gomes, 2013). It alsoperforms a slight initial approach to the second sub-phase of this validation stage, with the conductionof several tests in two-dimensional irregular waves.These tests aim a first assessment of the perfor-mance of the model in two-dimensional conditions.

The charcateristics natural periods of the modelwere found experimentally. Model displacements insix degrees of freedom, water and oscillating watercolumn free surfaces elevation and pressure insidethe model air-chamber are continually analyzed, ei-ther in time domain or in the frequency domain.The power available to the turbine simulator iscalculated for various model configurations. Oth-ers interest parameters like waves reflection, from

aLast step modelling values in SolidWorks c©; for this step,almost all the instrumentation belonging to the model wasmodeled together with the same.

the used absorbing beach, and phase differences aremeasured in regular waves.

2. Formulation and important calibrations

This section presents the adopted formulation andcalibrations for the experimental data treatmentand obtaining results. Besides Gomes (2013),Falnes (2002) constitutes an important contributionto the adopted formulation.

2.1. Scale factors

Either in the model design and construction or inthe experimental data post processing it is neces-sary to consider scaling factors, between values re-lated to prototype (numerical values and final re-sults), at full-scale, and results of tests at modelscale. The aim is to faithfully reproduce the proto-type, geometrically, kinematically and dynamically.

Table 2: Main scale factors considered for this work.

Quantity Scale factorb

Distance [m] s

Period [s] s1/2 s1/2ρ s

−1/2γ

Frequency [s-1] s−1/2 s−1/2ρ s

1/2γ

Mass flow rate [kg s-1] s5/2 s1/2ρ s

1/2γ

Pressure [Pa ou kg m-1 s-2] s sγ

Power [W ou kg m2 s-3] s7/2 s−1/2ρ s

3/2γ

A good kinematic and dynamic reproduction isachieved if the reasons between displacements, ve-locities, accelerations and forces existing betweenthe model and the prototype are constant.

Froude criterion was used, considering only thegravity and inertial forces. Used scale factors arediscriminated in Tab.2. Viscous scale factors areneglected, since these forces tend to be much higherthan the expected ones at model scale.

2.2. Linear wave theory

The waves propagation dynamics is complex andhighly nonlinear. The study of floating bodies sub-jects to two-dimensional waves requires the appli-cation of simplified motion equations and specificboundary conditions. Linear Wave Theory is gen-erally used in the Wave Energy Converters study.This theory application requires that some condi-tions are assumed: inviscid (potential), incompress-ible and irrotational flow; constant depth, h, andhard and impermeable bottom surface (z = −h);wave amplitudes, Aw, are small compared to itslength, λw, and depth, h. By expressing thoseboundary conditions, in the bed bottom and on the

bs% and sγ respectively represent the ratios between fluidsdensities (ρ) and ratios between fluids specific weigth (γ =ρg). They have values very close to the unit, so can beneglected.

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water free surface, and using the velocity potential,the Bernoulli equation and the definition of wavenumber, κ, given by

κ =w

vf=

2π

λw, (1)

it is possible to obtain the dispersion relation

w2 = gκ tanh(κh) , (2)

where w, vf are, respectively, the wave angularfrequency and phase (propagation) velocity, and grepresents the gravity acceleration. In the WECsstudy, the ratio between the power available at theturbine simulator (or turbine) and the wave energyflux is an important assessment factor,

Lc =P

Pw, (3)

where P is the power available to the power ex-traction system (in this case, by OWC). Lc is thecapture width, which defines the WEC efficiency.Wave average energy flux is given by Pw and definesthe wave power per plane wave crest unit, throughthe plane perpendicular to the propagation direc-tion, between the bottom and the free surface. Inshallow waters, it can be expressed by,

Pw =ρwgwA

2w

4κ

(1 +

2κh

sinh(2κh)

), h < λ/2 , (4)

wherein ρw is the water density. In deep water, theEq.(4) can be simplified by applying the dispersionrelation (Eq.(2)),

Pw =ρwg

2A2w

4w, h > λ/2 . (5)

For irregular waves, with the Eq.(4) generalizationand discretization and considering its approach byN regular waves, the wave average energy flux canbe obtained,

Pw =ρwg

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N∑i=1

wiA2w,i

κi

(1 +

2κih

sinh(2κih)

). (6)

For this equations, Aw and w are obtained fromtrials without the model in the wave flume (or tank)and represent reference values that do not accountfor the model’s surface reflections and radiations.

2.3. Regular wavesEven for regular waves, phase differences, ψu, canbe calculated. Their analysis allows the evaluationof the different interest parameters response to thewater free surface elevation. They can be calculatedby

ψu = 2πtu − tηwpηw

, (7)

where tηw and tu represents, respectively, the zero-downcrossing time of water free surface elevationand the following u parameter zero-downcrossingtime, in a given constant wave period, pηw . Forthe highly nonlinear FLOWC model this analysisis valid only for some tested wave periods, pw, ofequal value that periods from different interest pa-rameters, pu. Another interest parameter in regularwaves is the waves reflection coefficient,

Kr =Aw,RAw,I

, 0 ≤ Aw,R ≤ Aw,I , (8)

which allows evaluate the validity of testin with agiven absorption beach. Aw,R and Aw,I are, respec-tively, the reflected and incident wave amplitude,obtained from trials without the model in the waveflume (or tank).

Offshore devices are not subject to wave reflec-tions. Then, Holmes (2009) defined a maximumreflection of 20% for acceptable model testing.

2.4. Irregular wavesThe water free surface elevation variance, σ2, de-fined by the variance (or power) density spectrumintegration, represents another interesting param-eter in the analysis of irregular waves, because itis proportional to the waves energy. The variance(or power) density spectrum, Sw, can be obtainedusing the (Discret) Fourier Transformed ((D)FT),and, for the null average free surface elevation value,is defined by

Sw(wi) =A2w,i

2∆w, ∆w = constante , (9)

where i = 1, ..., N represents each regular harmonic,in which ∆w is defined by the interval between theseveral regular harmonics angular frequencies. Itcan be implemented for other interest parametersas well. For the results analysis, variances are eas-ily calculated using the irregular series time-domainanalysis,

σ2ηw =

1

Nt

Nt∑j=1

(ηw,j − ηw)2 , (10)

wherein σ refers to the standard deviation, thewater free surface elevation is given by ηw, andj = 1, ..., Nt are the acquired samples, in time-domain.

2.5. Filters calibrationsThis work’s major focus is the assessment of theenergy extraction system’s available power, P . Insmall scale models, it becomes necessary to simu-late this extraction by imposing a controlled pres-sure drop between the model air chamber and theatmosphere and by varying this pressure drop cre-ated damping. This can be achieved by having holes

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or filter between the model air chamber and the at-mosphere, in order to create respectively a linear(typical of Wells turbines) (Gato and Falcao, 1988)or a quadratic (typical of impulse turbines) (Falcaoet al., 2011) relationship between the created pres-sure difference and the air flow rate. The used tur-bine simulator (Fig.2) intends to impose a linearrelationship, k, with the use of filters.

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 determinethe relationship between air mass (or volume) flowrate, ma, 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 cal-ibration involves three stages: filter area calcula-tion, Af , using the relationships from the numericalmodel and Gomes (2013), for various filters num-bers, Nf ; filter(s) calibrations using a similar ma-terial (AL650 synthetic carpet) that the one usedby Gomes (2013), directly in the turbine simulatormounted on the fixed model and with the help of afastening system; filter(s) calibrations using a fixedvertical pipe (Lopes et al., 2007). The obtainedvalues are discriminated in Tab.3. The filter area,limited by the model’s geometry, has been set forthe maximum use of 3 filters.

For this calibrations, pressure inside the airchamber, p, and OWC position, ηowc, measure-ments must be performed. To prevent systematicerrors, careful calibrations to the probe within themodel and to the pressure sensor are required. Rel-atively large acquisition time periods are performed(120 s in this study), in order to obtain a large num-ber of points. Applying a well defined low-pass fil-ter to the acquired data is of utmost importance inorder to eliminate signals’s high frequencies, thatare responsible for random errors, and to allow theOWC’s velocity correct calculation (to obtain thevolume flow rate). Temperature, pressure and rela-tive humidity of air are measured by sensors for theair density, ρa, and consequently the air mass flowrate calculations.

Table 3: Interest model scale parameters in the tur-bine simulator’s linear coefficients calculation.

Method Af [mm2]Af [mm2]Af [mm2] NfNfNf k(m)m x 106 [m s]ck(m)m x 106 [m s]ck(m)m x 106 [m s]c

Fixed11298

1 121.4180

model2 62.296603 36.33343

Vertical2124

1 148.78775

pipe2 70.036733 45.21351

For the air mass flow rate and therefore the avail-able power calculations, fixed model’s calibrationcoefficients are considered. The difference betweenthese values and those for the vertical pipe can beexplained by the small leaks existence in the verti-cal tube system (higher flow rates for equal pressurevalues) or by the OWC’s nonlinear oscillation phe-nomena, due to its large diameter (higher pressurevalues for identical flow rate values). Thus, thesereflect a good reliability in the turbine simulatoruse and in the cover sealing.

3. Modelling, manufacturing and experi-mental testing

The FLOWC model was modeled using theSolidWorks c©program. In this step some impor-tant considerations were taken into account: themesh from the numerical model and with it theinternal and external diameters, the floating posi-tion and the tubular profile; the desired mass centreand floating centre positions; the buoy and all in-strumentation materials (density, strength and flex-ibility); geometric scale factors and OWC maxi-mum amplitude. Some static charges simulationsin the keel were carried out using the same pro-gram. The buoy material, acrylonitrile butadienestyrene (ABS), was subjected to tensile tests andits impermeability was also analyzed.

The model’s manufacture supported severalphases: computational model cutting in severalparts, so that it can be manufactured by the rapidprototyping machine, and the consequent bond-ing technique idealization (punctual male-femaletype); parts manufacturing; body assembling (us-ing epoxy) and surfaces waterproofing (using lac-quer and acrylic paint); capacitive probe introduc-tion and fixing for OWC elevation measuring (madeof 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 repeatedin order to obtain the correct neutral buoyancy po-sition. For the turbine simulator manufacture other

cSubscript m refers to a model scale value and superscriptm refers to the linear relationship, k, between air mass flowrate and pressure

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low density materials were used: ABS for the coverand tightening cap; stainless steel for the threadsand their nuts; high-density polyethylene (HDPE)for the pressure taps and their nuts.

Figure 3: Modeling ((1)-(4)) and assembly ((a)-(i))of FLOWC.

Experimental tests were carried out at the Labo-ratorio de Hidraulica do Instituto Superior Tecnico(LHIST) wave flume (Fig.4(a)), aiming the modelperformance evaluation under different sea condi-tions.

Capacitive probes are used (similar to that in-stalled in the model) for the water free surface el-evation measurement, which consist of two parallelrods made of a conductive material. Four probes arepositioned between the model and the wave-maker,for measuring the reflection and the energy flow,and one is at model position for phase differenceand energy flow measurements (the latter withoutthe model in the channel). A system consisting oftwo pressure taps, air hoses and low pressure sensors(GE Druck and Honeywell), is used for measuringthe pressure within the air-chamber of the model.In turn, for the model motion measurement in its sixdegrees of freedom, a video tracking system (Qual-isys) is used in which a rigid body is defined (in themodel) by infrared reflective spheres.

Due to the geometry of the model, it was decidedto use the 3 slack-mooring configurations (a, b andc) shown in Fig.4(b)-(c), in order to prevent drift.The main parameters of these configurations are de-tailed in Tab.4. Lead weights, bottom weights, ny-lon wires and small buoys were used.

dUnreferenced values are equal for all configurations.eConfiguration a values.fConfiguration b values.gConfiguration c values.

Table 4: Slack-mooring configurations parameters.

Parameter Valued Unit

l1 218e / 249f / 186g [mm]l2 160 [mm]l3 618 [mm]za -189e [mm]zb -154f [mm]zc -234g [mm]∆xa 870 [mm]αac 16e; g [◦]αb 13f [◦]mla 14,5 [g]ρla 11340 [kg/m3]mba 1,3 [g]ρba 340 [kg/m3]

Figure 4: Wave flume configuration and slack-mooring configurations: a - green; b - yellow; c -magenta.

4. Results and discussionThe model performance results are analyzed for var-ious configurations, each as a function of wave pe-riod, pw (peak period, Tp, in the case of irregularwaves), varying: wave amplitude, Aw, (significantwave height, Hs, in the case of irregular waves);number of filters applied in the turbine simulator(1, 2 or 3); mooring’s attachment position at themodel (a, b or c configurations).

4.1. FLOWC ’s natural periodsThe model’s natural period, for each oscillationmode, is defined as the time it takes to reach thesame position in the same movement direction, instanding water.

Natural periods for the surge, p(1)n , heave, p

(3)n ,

and pitch, p(5)n oscillation modes (Tab.5) were ob-

tained. By observing the physical model behavior itwas possible to make a correction to the heave’s nat-ural period, which should be approximately 22.22 s.

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Table 5: FLOWC’s natural periods for the mainoscillating modes.

Natural periods [s]h

Mooringsisurge heave pitch

p(1)np(1)np(1)n p

(3)np(3)np(3)n p

(5)np(5)np(5)n

a configuration 74.07 21.28 19.05b configuration 96.15 20.88 19.42c configuration 57.14 20.20 18.69

Looking at the Tab.5, the proximity of the heaveand pitch natural periods can be checked. Whereasthe main oscillation excitation modes are associ-ated with large system oscillations and thus withthe extracted energy maximization by a WEC, theapparent coupling of these oscillation modes trans-lates the existence of a power peak in wave periodsof about 20 s (full scale).

4.2. Regular waves

Analyzing the oscillation modes behavior, by in-creasing the wave amplitude, it can be seen an in-stability emergence and intensification in the yawmode (rotation around z) to 12.5-13.5 s of waveperiod. The large energy dissipation by this oscil-lation mode may be a reason for the low capturewidth registered for these wave period values. Thesame is true for the roll mode (rotation around x)to 7.7 s of wave period. In addition, a slight exci-tation of this oscillation mode, to 15-16 s of waveperiod, suggest its natural period’s existence in thisinterval. Contrary to Spar Buoy model, larger surgevalues appears to 25 s of wave period. The largestheave and pitch oscillation amplitudes occur for thewave period related with the pitch’s natural periodand to 10-11.76 s of wave period, where the high-est power peak can be found. However, the waveamplitude increase is responsible for the decreaseof the maximum values recorded for these two os-cillatory modes, as well as the capture width. Thewave amplitude increase is related to the fluid ve-locity increase and consequently with the surfaceviscous forces increase in the fluid-body interaction.This increase is even more significant in small scales,dissipating much of the energy available. There isa pressure and OWC amplitude increase, with themain oscillation modes’s amplitude rise. Low cap-ture width values, to 19.23 and 25 s of wave period,can be justified due to the high energy flux valuesfor those periods (typical of shallow water), not ap-propriate to offshore device testing.

Compared to data provided by the Spar Buoy

hPresented natural periods are the mean values obtainedfor the model: without moorings and filters; with mooringsand without filters; with moorings and one filter.

iSee Fig.4

model, the parameters related to energy extraction(water column and pressure oscillations and cap-ture width) have generally lower values in ampli-tude (1.3, 3 and 1.5 times, respectively). A higherpressure amplification to a smaller OWC amplifica-tion in the Spar Buoy model, and considering alsothe water column’s small surface area, in relation tothe FLOWC model (6 times lowest), indicates thatnon-linear effects existing in the water column’s freesurface of the last are responsible for the high dis-sipation of available power. Both models have thehighest power peak at approximately 10 s of waveperiod. In the model Spar Buoy is still possible toobserve the presence of two power peaks at approxi-mately 12.5 s. For the model FLOWC, the existenceof a second power peak at 19.23 s, despite its lowvalue, can be verified. This phenomenon, togetherwith the existence of higher amplitude values for thewater column and pressure oscillations, to 19.23 and25 s of wave periods in the FLOWC model, repre-sents the major difference observed, related to theenergy utilization, between the last and the SparBuoy model.

In turn, the 2 filters increase, applied to the tur-bine simulator, implies the observed roll mode in-stability’s increase (7.7 s). Moreover, the three fil-ters use is responsible for canceling this same in-stability. There is, however, an increase in the rollmode’s excitement for the wave period related to itsexpected natural period.

Compared to Spar Buoy model, the verified pres-sure loss influence on the FLOWC model’s dynam-ics presents a different behavior in the main oscil-lation modes’s excitation. In general, the instabil-ity reduction with the increase of pressure loss, ob-served for certain oscillation modes, is visible toboth models. On other hand, an increase of themajor instabilities is verified: yaw mode in theFLOWC model; roll mode in the Spar Buoy model.

A heave mode’s significant increase is noted withthe increased number of filters for the wave pe-riod relative to the pitch’s natural. The greaterOWC damping explains the increased pressure inthe model’s air chamber. On the other hand, highmain oscillation modes’s amplitudes entail a morepronounced increase in pressure for a decrease ofthe water column’s amplitude, due to the higherOWC’s speeds and to its consequent viscous forcesincrease.

An power peaks increase between 2 to 2.5 timesis verified for the capture width using three filters.This increase is 20% lower in the Spar Buoy modelfor wave periods related to its higher power peak. Inturn, the Spar Buoy model’s water column has a re-duction approximately 17% lower in its oscillationsand its pressure oscillations presents an amplifica-tion approximately 28% lower than those recorded

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Figure 5: Nondimensional capture width, by themodel width (diameter, dm), for all tested config-urations in regular waves (full scale): wave heightvariation for 1a configuration (circles); number offilters variation for a configuration and Aw = 1 m(red); slack-mooring configurations variation for 3filters and Aw = 1 m (triangles).

for the FLOWC model. This can be explainedby the nonlinear effects decrease, present in theOWC’s free surface, with the increased damping forFLOWC model. These facts show a significant de-pendence with the high existing ratios between thewater columns’s diameters and between the mainoscillation modes’s excitation, of both systems forthe considered wave periods.

Varying the slack-mooring configuration aims thedifferent modes of oscillation’s response change.For b mooring configuration is, in general, verifiedthe main registered instabilities reduction or annul-ment, as well as roll mode’s amplitude reducing forthe wave period supposedly relating to its naturalperiod. Also for this configuration, there is a slightheave and pitch’s amplitude increase, for the waveperiod relative to the pitch’s natural period, anda surge’s amplitude decrease to 25 s of wave pe-riod. These results suggest that the b configura-tion’s attachment point in the model is closer tothe centre of rotation than the one in a configu-ration. The c mooring configuration is related tothe larger restitution forces’s existence. Therefore,greater surge and pitch restrictions are observed.This might explain the slight decrease in yaw in-stability (12.5-13.5 s) comparing to the a configu-ration. The very low attachment point can, on theother hand, account for the checked roll instability’slarge increase(7.7 s). The largest restitution forcesare also responsible for the pronounced decrease inheave and pitch’s amplitudes to the wave period re-lated with the pitch’s natural period. Also for thismooring configuration, a worse pitch’s performance

for an identical heave’s performance, to 11.76 s waveperiod, reinforces the fact that the heave’s naturalperiod approach 22.22 s (about twice that heaves’sexcitation value). Greater OWC dependence withthe pitch mode is found for this wave period. LowerOWC’s amplitude values and higher pressure valuescan be justified by the nonlinear effects reductionon the OWC’s surface, as well as by the viscousforces, leading to the capture width increase. Thepitch mode’s importance for energy extraction is ob-served in the pressure decrease with the reductionof this oscillation mode, and the consequent cap-ture width reduction to wave periods related withits natural period (c configuration) and to 25 s (bconfiguration).

Changes in the model’s dynamics as well as inthe water column oscillations, are attenuated by amore or less stable OWC’s behavior.

Comparing the inverted model according to xaxis, FLOWC-B, with the numerically simulatedmodel, FLOWC-A, there are some important notedchanges. A pronounced heave’s amplitude decreasebetween 12.5 and 17.8 s, for an identical pitch modebehavior, suggests the importance of the directionof the device’s upper arm inclination in the heave’sexcitation for FLOWC-A mode. For FLOWC-Bmode, smaller but more stable values are obtainedfor the yaw instability (wider wave periods rangesubject to this instability). On the other hand, alarge increase in the roll instability (7.7 s) is de-tected, as well as for both instabilities to 11.76 sof wave period. The latter ones implies the mainoscillation modes’s amplitudes decrease for the saidwave period. There is a weak pitch influence on theOWC’s dynamics for FLOWC-B mode. This can bejustified by the decrease in the OWC’s amplitude,when this oscillation mode’s amplitude increases, to17.86 s and 18.52 s of wave period, together withthe low heave and surge values for these periods.

Still using the FLOWC-B mode, reduced surgeand heave’s amplitudes to 25 s, as well as reducedOWC and pressure’s amplitudes, suggest the im-portance of the lower mouthpiece’s direction forthe energy extraction, in the FLOWC-A model. Amore stable OWC and pressure behavior is checkedfor FLOWC-B mode, with the annulment of smallpower peaks recordedgreat among 12.5-16.13 s ofwave period. Minor OWC and pressure’s ampli-tudes values for the wave period related with thepitch’s natural period also justify the large capturewidth decrease, to 19.23 s, due, most likely, to annon-linear effects increase on the OWC’s surface.However, the FLOWC-B mode displays a slightcapture width increase for the higher power peakchecked. Checking the water column and oscilla-tion modes’s behavior, for that wave periods range(10-11,76 s), this shall be justified by the non-linear

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Figure 6: Nondimensional capture width’s compar-ative analysis, between the model in the correct po-sition (FLOWC-A - lower mouthpiece facing to thebatter) and the inverted model (FLOWC-B - lowermouthpiece facing to the breakwater), for 3a con-figuration and Aw = 1 m (full-scale).

effects decrease on the OWC’s surface and by thegreater main oscillation modes’s coupling efficiecy.

It was possible to verify high reflection coeffi-cient values for all tested wave periods (greater than20%). Reflection coefficients between 18 and 65%are obtained. For the higher recorded power peak,referring to 10-11.11 s of wave period, there are re-flection coefficient values between 20 and 30%. Themodel testing conditions are not appropriate, as re-ferred by Holmes (2009), differing enough of the realconditions for offshore devices.

4.3. Irregular waves

Compared to the Spar Buoy model results shown byGomes (2013), there is generally a similar behav-ior between both models’s main oscillating modesfor small significant wave heights. Among the testHs = 1.20 m for the model Spar Buoy and thetest Hs = 1.25 m for the model FLOWC, the firstshows, however, a higher surge (2 to 2.27 times)and pitch (55-57 times) energy performance. Amore effectively heave’s performance is verified forthe model FLOWC (1.4 to 2 times). Spar Buoymodel presents performances even 336%, 353%476% higher than the model under study, for theOWC, the pressure and the capture width respec-tively.

Analyzing the figure 7, the FLOWC model’s bestperformances are checked for: smaller significantwave heights, reflecting a high ratio between vis-cous and geometric scale effects; larger water col-umn’s damping (OWC’s lower speed entails a morestable behavior of the air flow); slack-mooring’s at-tachment points near the centers of mass and rota-tion of the model, in order to amplify the main os-

Figure 7: Nondimensional capture width, by themodel width (diameter, dm), for all tested config-urations in irregular waves (full scale): significantwave height variation for 1a configuration (circles);number of filters variation for a configuration andHs = 2.5 m (blue); slack-mooring configurationsvariation for 3 filters and Hs = 2.5 m (triangles).

cillation modes’s amplitudes, and consequently theOWC’s excitation. On the other hand, a worse per-formance is associated with OWC’s larger oscilla-tion amplitudes due, most likely, to the existenceof high nonlinear effects, amplified by the free sur-face’s higher oscillation speed. An amplification ofthe main oscillation modes becomes more relevantfor fixing the mooring above the center of mass andnear the center of buoyancy. The higher observedpressures, related to the use of this mooring config-uration, suggest the OWC’s more efficient excita-tion due to the more effective coupling of the mainoscillation modes. In general, these results are con-sistent with the performance observed for regularwaves.

5. Conclusions and future work

The model’s natural periods were obtained and theheave and pitch oscillation modes’s coupling wasconferred. Both in the model performance in reg-ular waves as in irregular waves, two-dimensional,a second oscillation mode’s excitation can be veri-fied, by multiple frequencies of the natural periodof pitch, for the main oscillation modes, and, forthe OWC and the pressure. It is therefore possi-ble to confirm a greater dependency of the model’sdynamics in this oscillation mode, for the testedrange of wave periods. The yaw ’s dynamic insta-bility and the roll ’s excitation, are responsible fordissipating much of the energy for a wide range ofwave periods. These instabilities may justify the ab-sence of a power peak, predicted by the numericalmodel. The presence of high viscous forces due toscale effects is observed for larger wave amplitudes

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and whenever high speeds are verified in the body-fluid interaction. A smaller or larger excitementof such instabilities appear to be possible by vary-ing the imposed OWC damping and/or the slack-mooring’s attachment point. Both imply changes inthe model’s dynamics, especially for the wave peri-ods that excites the pitch oscillation mode and forthe larger amplitudes of the main oscillation modes.The moorings influence in the capture width ap-pears to be only relevant when there is a restric-tion imposed to these modes for these wave periods.In the comparative analysis, between the model inthe correct position and in the inverted position,there is a better performance of the first for ma-jor wave periods. For the inverted model a morestable behaviour is observed, not likely to providea power peak for longer wave periods. However, itchecks slightly better performance for the periodsrelated to the power peak. The results obtainedfor irregular waves are in general in agreement withthose obtained for regular waving, although a bet-ter OWC performance is verified owing to more effi-cient main oscillation modes’s coupling (responsiblefor the major OWC excitation), associated with theexcitation of a wider band of frequencies.

Compared to the Spar Buoy model, the FLOWCmodel shows very low capture width’s values. Theonly advantage of this model, relative to the modelstudied by Gomes (2013), appears to be the greaterinfluence of the OWC’s damping in varying themodel’s dynamics.

In the future, taking into account the great dif-ference between the numerical and the experimen-tal results, the numerical model should be revisedand 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 tominimize the high viscous forces. A more efficientnumerical model validation, which uses the panelmethod, implies the need to test the model in a lin-ear array. Finally, the need to perform tests using adissipative beach, in order to minimize the reflectedenergy, is of utmost importance.

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