Proceedings of the ASME nd International Conference on Ocean, Offshore and Arctic Engineering OMAE2013 June 9-14, 2013, Nantes, France

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1 Proceedings of the ASME 3 3nd International Conference on Ocean, Offshore and Arctic Engineering OMAE3 June 9-4, 3, Nantes, France OMAE3-5 INVESTIGATION TO AIR COMPRESSIBILITY OF OSCILLATING WATER COLUMN WAVE ENERGY CONVERTERS Wanan Sheng University College Cork Cork, Ireland Joseh Brooks University College Cork Cork, Ireland Florent Thiebaut University College Cork Cork, Ireland Anthony Lewis University College Cork Cork, Ireland Marie Babuchon University of Nantes France Raymond Alcorn University College Cork Cork Ireland ABSTRACT It has been suggested that for full scale oscillating water column (OWC) devices, the ressure in and the volume of the air chambers can be large to create air comressibility in the air chamber. Due to comressibility, its density and temerature are different from those in atmoshere. When in exhalation, the ressurized air is driven out of the air chamber and mixes into the atmoshere outside the air chamber; whilst in inhalation, the atmoshere is sucked through the ower take-off (PTO) system into the air chamber, and mixes with the de-ressurized air in the chamber. This aer resents a study on air comressibility in OWC air chambers by theoretical analyses and the relevant exerimental studies. The theoretical analysis is based on the first-order differential equation for the flowrate and the chamber ressure, which has been derived for the air flow under the assumtions of the isentroic rocess and the known ower take-off characteristics. In the study, an orifice tye of PTO and a orous membrane tye PTO, which are suosed to reresent a tyical nonlinear and linear PTO for small models, resectively, are both investigated. The investigation has shown the feasibility of the theoretical method on the air comressibility and the ossible ower loss due to the air comressibility. INTRODUCTION As one of most successful wave energy converters (WECs), oscillating water column (OWC) WECs have gone through a quite long eriod of research and develoment, and the technologies are relatively advanced when comared to other wave energy converters. Practically, bottom-fixed OWC wave ower lants have so far been built and generated electricity to the grid, for examle, LIMPET in Scotland [] and PICO in Portugal []. And floating OWCs have been roosed and develoed for deloying in oen and deeer waters, where more wave energy resources are normally available [3-6]. For examle, Ocean Energy Ltd (Ireland [7]) has adoted the BBDB rincile and develoed it into a ractical WEC, the OE Buoy, which has undergone substantial develoments, staged from a small model in wave tank (:5), a larger model test in a large wave tank (:5) and scale model sea trials (:4) [8, 9]. Generally, OWC WECs have their advantages over many other wave energy converters in terms of (i) a confirmed concet; several ractical OWC lants have been built and actually generated electricity to the grids (Falcao [], and Heath[]); (ii) a device with a relatively high wave-to-wire energy conversion efficiency, including a high rimary energy conversion efficiency (Evans [] and Imai et al [3]), and a relatively high mechanical ower converting efficiency ([4, 5]); Coyright 3 by ASME Downloaded From: htt://roceedings.asmedigitalcollection.asme.org/ on /6/4 Terms of Use: htt://asme.org/terms

2 (iii) more imortantly, a small force/torque and a high seed for a certain ower take-off, such that the reliability of the ower take-off system should be guaranteed; (iv) no moving comonent in sea water, for a higher reliability and an easy maintainability of the wave energy conversion; (v) an adatable wave energy device, which can be bottomfixed tyes on shoreline or shallow water regions, or floating-tyes in shallow or dee water regions (Heath []). Theoretical work on the hydrodynamic erformance of OWCs has been rogressed a lot in the ast decades. Evans [6] and Evans & Porter [] studied the OWC system theoretically by emloying otential theory, and the theory shows that the maximum wave energy conversion by OWC can be %. Josset et al.[7] studied some foundation-tye OWC lants in time-domain. They divided the flow field into two subroblems: an interior roblem and an external roblem. In the simulation, the external roblem is solved once and it coules the interior roblems via their common surface. In addition, the interior roblem is also couled with the thermodynamic roblem in the air chamber and with a linear ower take-off system. As ointed out by Falcao et al.[8], there may be significant differences between the air charging (inhalation) and discharging (exhalation) rocesses. In discharging, the ressurized air asses through the PTO system with a larger density than that of atmoshere, and a comlicated air mixing rocess haens at the outside of the air chamber. It can be envisaged that the rocess in air chamber remains uniform and smooth during the exhalation rocess. Unlike exhalation rocess, in inhalation, the air in the chamber is de-ressurised, and its density and temerature are lower than those in atmoshere. When the atmoshere is inhaled in, the air mixing rocess occurs in the chamber. It can be exected that the inhalation may cause some non-uniformity of the air in the air chamber, and the comlicated energy exchange and transfer may haen. However, for analysis, the air inhalation rocess is normally simlified as a smooth and uniform rocess due to the fact that the recirocating wave excitation is relative slow. Comared to the slow wave excitation cycle, the air mixing rocess can be assumed to haen instantaneously so that the air in the chamber is ket uniform in the whole recirocating rocess, and a uniform state of the air can be considered in the air chamber. In the studies of the thermodynamics of the air flow in an OWC device, the comressibility and the thermal exchanges should be included, esecially for large OWC devices. As suggested in revious research, the air is normally considered as an isentroic rocess in an oen system. The energy exchange haens only through the oen boundaries, i.e., the work done to the air in the chamber by the interior water surface, and work done to the ower take-off system by the ressurized/deressurised air in the air chamber. As an ideal gas in the air chamber, the changes of the chamber ressure (gauge ressure, relative to the atmosheric ressure) cause the changes of air density and temerature in the air chamber for the comressible air (Falcao et al.[8], Josset et al. [7] and Nagata et al. [9]). This aer resents a study on the thermodynamics of OWC wave energy converters by including the air comressibility in the chamber, based on the thermodynamic equation of the air (Sheng et al.[]). To validate the theoretical method, exeriments have been conducted on a test rig. In the exeriment setu, a cylinder is used to reresent an OWC water column, and a iston for the interior free surface in a wellcontrolled manner but much more owerful than that tested in wave tank. From the exerimental data, esecially in the cases of high flow daming levels, air comressibility can be seen obviously. By comarisons to the test data, it is shown that the theoretical method redicts the air comressibility very well. THERMODYNAMICS OF AIR FLOW The details of the thermodynamics of air flow in OWC WECs can be found in Sheng et al.[]. For a comletion, the relevant equations are given here. Mass conservation Assuming the air volume of the chamber is V and the air density is ρ c, then the air mass in the chamber can be m ρcv () where m is the air mass, V the air volume, ρ c the air density in the chamber. Corresondingly, the air flowrate Q w driven by the water surface is simly exressed as Q w dv () where the negative sign means the air flowrate is ositive when the chamber volume is reduced. Differentiating (), it can be dm dv dρc ρc V (3) It must be noted that a ositive value of the mass rate means some air is inhaled in through the PTO system (inhalation), and a negative value of the mass rate means some air is driven out of the air chamber (exhalation). Due to the air comressibility, the air density changes in the air chamber in exhalation and inhalation. For the ressurized chamber, the ressurized air with a higher density (than that of atmoshere) is driven out through the ower takeoff system, while for de-ressurized chamber, the atmoshere is inhaled in through the ower take-off system. Thus, the air flow through the PTO system must be considered for exhalation and inhalation searately, following Josset et al.[7]. The air flow through the PTO system, Q can be calculated as following. Coyright 3 by ASME Downloaded From: htt://roceedings.asmedigitalcollection.asme.org/ on /6/4 Terms of Use: htt://asme.org/terms

3 Exhalation: Inhalation: Q ρ c Q ρ dm dm (5) where ρ id the density of atmoshere. Due to the uniformity of the ressure, the ower generated by the water surface (wave), P w, is calculated by the chamber ressure multilying the flow rate driven by the water surface, as Pw Q w (6) Corresondingly, the ower through the ower take-off system is Pto Q (7) And the ower loss due to the comressibility can be calculated as P P Ideal air w (4) η loss % (8) P w To simlify the thermodynamic roblem, the air in the chamber is assumed as isentroic, for which a state equation for the oen system is, c γ = constant (9) ρc where γ is the secific heat ratio of the air (γ =.4). Normally in OWC devices, the chamber (gauge) ressure is much smaller than the atmosheric ressure, which leads a linearized exression for the air density in the chamber as, and to γ ρ c ρ () dρ c ρ d () γ Substitute Eqs. () and () into (3) yielding dm Hence for exhalation, For inhalation, dv ρv d ρ γ γ () Q dv V γ d (3) Q dv V d γ (4) γ A simlified form of the air flowrate through the PTO has been given by Sarmento et al. [] (also see [, 3]), and the flowrate through the PTO system is exressed as, Q dv V d (5) γ where V is the air volume of the OWC in calm water. The second term in the RHS of the equation (5) is a modification due to air comressibility. THEORETICAL STUDIES Linear PTO system A linear PTO system in an OWC WEC means the air turbine or the PTO modelling device has a linear relation between the chamber ressure and the air flowrate through the PTO. For examle, a Wells turbine is often regarded as a linear ower take-off device (see Curran et al.[4]). For scale model tests, daming material (i.e., orous membrane) can be used to model the linear PTO system (Lewis et al. [5] and Forestier et al. [6]). Generally, linear PTO system has a relation, k (6) Q where k is the air flow daming coefficient, which can be decided when the PTO system is calibrated. Substitute (6) into (3), the equation for the exhalation rocess can be attained as, dv V γ d k (7) Substitute (6) into (4), the equation for the inhalation rocess is, dv V d γ γ k 8) The equations (7) and (8) are the thermodynamic equations for the chamber volume and ressure by including the air comressibility. Solving the first-order differential equations (7 and 8), the air volume or the chamber ressure can be obtained if the chamber ressure or the air volume is known. Orifice PTO system It is well known that an imulse turbine is a nonlinear PTO for OWC devices [7]. For an imulse turbine, the ressure dro across the turbine (the chamber ressure) can be aroximated as roortional to the flowrate squared. For small scale models, orifices are often used to model the nonlinear PTO system ([3, 8]) due to its simlicity and its well reresentative relation between ressure dro and flowrate. 3 Coyright 3 by ASME Downloaded From: htt://roceedings.asmedigitalcollection.asme.org/ on /6/4 Terms of Use: htt://asme.org/terms

4 Exhalation kq (9) or the flowrate (a ositive value) is calculated based on the chamber ressure Q () k Inhalation kq () or the flowrate (a negative value) is calculated based on the chamber ressure Q () k Substitute () into (3), we have an equation for the exhalation rocess, dv V γ d k (3) Substitute () into (4), we have an equation for the inhalation rocess, dv V d γ γ k (4) The equations (3) and (4) are the thermodynamic equations for the chamber volume and ressure by including the air comressibility. Solving the first-order differential equations (3 and 4), the air volume or the chamber ressure can be obtained if the chamber ressure or the air volume is known. Nonlinear PTO system (generic nonlinear PTO) A fully linear PTO system or a ure orifice nonlinear PTO system may be only ideal in ractical alications. More general, a conventional air turbine PTO may be exressed as a nd order olynomial. To reresent such a PTO mathematically, the relation of the flowrate and chamber ressure can be exressed for exhalation when, kq kq (5) In exhalation, the flowrate must be ositive, so Q k k 4k (6) k Similarly, for inhalation (when <) kq kq (7) Corresonding to the rocess of inhalation, the flowrate must be negative, so Q k k 4k (8) k Substitute (6) into (3), a first-order thermodynamic equation for the exhalation is dv V γ d k k k 4k (9) and (8) into (4), the thermodynamic equation for the inhalation will be γ dv V γ d k EXPERIMENT STUDIES k k 4k (3) The thermodynamics of the air in the chamber has been studied on a linear test rig (see Figure ). The test device consists of a linear drive and a cylinder and a iston of a diameter.3m. The comuter controlled linear drive can drive the iston in the cylinder u and down in a well controlled manner. The highest frequency of the drive is Hz and a stroke.3m. The iston motion is used to model the internal water surface in the OWC devices. The linear rig could roduce u to 5W neumatic ower in the cylinder which is much more owerful than that of the same size OWC in wave tank tests. Ideally, it can be used to roduce air comressibility in the cylinder. To study thermodynamics of the OWC with a nonlinear PTO system, an orifice is simly mounted on the to of the cylinder (see Figure ). Pressure sensor and thermocoule are used to measure the chamber ressure and the chamber temerature. In the test, the air flow generated by the iston can be easily calculated because the iston osition is readily available. For different daming levels of the orifice PTO, different sizes of the orifices have to be used. For a linear PTO of an OWC device, orous membranes are normally suggested and used in a small model (see Figure 4). In the exeriment setu, on the to of the cylinder, the air assage has been contracted to a smaller diameter of the linear PTO (.m in this study). To get a uniform flow at the orous disks, two.3m long PVC ies are used which guide a uniform flow at the orous disks which are installed at the connection oint of the two PVC ie. To study different daming levels, two different orous membranes can be used (identified by their color, Brown and Blue ). In addition, the different daming levels can be easily achieved by changing the layers of the membranes. CALIBRATION OF THE PTO In this section, the calibration of the PTO is investigated for the orifice and the orous membrane PTOs. As it is shown in the test data, the linearity of the membrane PTO is only an 4 Coyright 3 by ASME Downloaded From: htt://roceedings.asmedigitalcollection.asme.org/ on /6/4 Terms of Use: htt://asme.org/terms

5 aroximation. For a better reresentation, a nd -order olynomial is emloyed for the case. Cylinder Linear drive iston Figure Linear test rig and cylinder Figure 4 Drawing of the orous membrane test Figure Orifice PTO and sensors Figure 3 Extension for orous membrane PTO testing Orifice PTO Figure 5 shows an obvious hysteresis loo for the chamber ressure and the air flowrate through an orifice (diameter ϕ=.9m) driven by the iston for the comressible air in the chamber for a test case of amlitude A=.4m and frequency of f =.Hz. For calibrating the PTO, the air flowrate through the PTO must be calculated first, and this can be done via the formulas 3 & 4 (identified as New in the lot) or the simlified formula 5 (identified as Old in the lot). The comarisons of these two methods are given in Figure 6. It can be seen that these two methods give very close results in this case. The PTO can be calibrated based on the measured chamber ressure and the air flowrate through the PTO, see the Figure 7. The calibrated daming coefficients are then used to reroduce the relation of the chamber ressure and the PTO flowrate. Table shows the calibration of the orifice PTO daming coefficients for different amlitude (A) and frequency (f) of the iston motions, and it can be seen that the daming coefficients are very consistent regardless of the amlitudes and frequencies of the iston motion. It also can be seen that the daming coefficients are different for the exhalation and inhalation. The reason for this may be the air flow conditions are different in the inhalation and exhalation. In the rig test, the orifice has a chamfer of 6 (see θ in the Figure 8). Obviously the different inhalation and exhalation conditions are due to the asymmetrical sides of the orifice in exhalation and inhalation. In addition, the conditions of the oen atmoshere and the chamber may also cause the difference, and this will be seen in the next examle. 5 Coyright 3 by ASME Downloaded From: htt://roceedings.asmedigitalcollection.asme.org/ on /6/4 Terms of Use: htt://asme.org/terms

6 Table Calibration for orifice ower take-off (ϕ=.9m) Test case Daming coefficient k A (m) f (Hz) exhalation inhalation average Porous membrane PTO Figure 5 Chamber ressure vs. air flowrate (A=.4m, f=.hz, ϕ=.9m) Figure 6 Flowrate driven by iston and flowrates through the orifice It has been suosed that the orous membrane can be used to model a linear relation between the ressure dro (Foretier et al. [6]). However, a fully linear relation can only be an aroximation because the test data have shown some nonlinearities (see Figure 9). In the figure, the measured data for chamber ressure and flowrate have shown obvious nonlinearities. Again, the flowrates through the PTO calculated via Eqs. 3 & 4 and Eq. 5 are very close. For such a PTO, a linear exression may not be good enough, because its daming coefficient can be very much deendent on the amlitudes and frequencies of the iston motions (see Table ). A better exression for the PTO is the generic nonlinear relation through the Eqs. 5 and 7, and the corresonding daming coefficients are also given in Table. Obviously, the generic nonlinear exression gives much more consistent results for which the coefficients k and k are constants regardless of the amlitude and frequency of the iston motion. Form Figure, it can be seen that the generic nonlinear exression gives the closest fit when comared to the linear and the orifice fittings. Figure 7 Calibration of the daming coefficients Figure 9 Chamber ressure vs. air flowrate (A=.4m, f=.hz, disc: brown=, blue=) Figure 8 Chamfered orifice for testing 6 Downloaded From: htt://roceedings.asmedigitalcollection.asme.org/ on /6/4 Terms of Use: htt://asme.org/terms Coyright 3 by ASME

7 frequency is used. The smaller maximum chamber ressure causes a smaller hysteresis loo in the ressure and flowrate. Figure Calibration of the daming coefficients RESULTS AND ANALYSIS Orifice PTO Solving the thermodynamic equations (3 and 4) of an OWC device with an orifice PTO, the chamber ressure can be obtained if the iston motion is known, or the volume of the air chamber and thus the flowrate can be resolved if the chamber ressure is measured. Figure gives an examle of the theoretical result for an orifice of.9m under a iston motion of amlitude.45m and frequency of.5hz. It can be seen that the theoretical result is very close to the measured data. Due to the limited amlitude and frequency of the iston motion, the created ressure in the chamber is relatively small where the maximum ressure is about 5 Pa, much smaller than the maximum ressure shown in Figure 5, where a higher Figure Comarison of the theoretical result and the measured data (A=.45m, f=.5hz, ϕ=.9m). Porous membrane PTO Solving the thermodynamic equations (9 and 3) of an OWC device with a orous membrane PTO, the chamber ressure can be obtained if the iston motion is known. Figure gives an examle of the theoretical result for the orous membrane PTO of one brown and one blue of a diameter.m in a iston motion of amlitude.75m and frequency.833hz. Again, it can be seen that the theoretical result is very close to the measured data. Though the maximum chamber ressure is about Pa, larger than the revious case and the maximum flow rate is much higher, the comressibility is less obvious (with a smaller hysteresis loo of the chamber ressure and the flowrate). =============================================================================== Table Polynomial fitting for the orous materials as the PTO (Brown= Blue=) Test case exhalation inhalation average linear A(m) f(hz) k k k k k k K E+4.54E+6.79E+4.57E+6.8E+4.56E+6 5.E E+4.54E+6.83E+4.54E+6.84E+4.54E E E+4.5E+6.89E+4.5E+6.89E+4.5E+6 6.4E E+4.57E+6.85E+4.5E+6.85E+4.54E+6 5.7E E+4.5E+6.94E+4.49E+6.93E+4.5E E E+4.49E+6.8E+4.7E+6.98E+4.6E E E+4.58E+6.89E+4.63E+6 3.E+4.6E E E+4.59E+6 3.3E+4.55E+6 3.E+4.57E E+4 =============================================================================== 7 Coyright 3 by ASME Downloaded From: htt://roceedings.asmedigitalcollection.asme.org/ on /6/4 Terms of Use: htt://asme.org/terms

8 largely due to the large air flowrate through the orous membrane PTO. Figure Comarison of the theoretical result and the measured data (A=.75m, f=.833hz), memebranes: brown+ blue. Figure 3 Power comarison for an orifice PTO (A=.45m, f=.5hz, ϕ=.9m) Power loss Power loss is a concern of the OWC wave energy converters due to air comressibility in the air chamber. In this section, the ower loss is studied based on the analytical method above. Figure 3 shows a comarison of the time series of the inut ower given by the iston and the PTO ower extracted by an orifice PTO. From the time series, it can be seen that there are some difference between the inut ower (rovided by the iston) and the PTO ower (which is available to the PTO system), esecially at the negative eak of the ressure. The maximum difference of the owers can be about % in this case. However, the difference between the average inut ower and PTO ower is much smaller than the aearance, which is only.5% (Table 3). The reason for this is that when the air in the chamber is ressurized or deressurised, art of the inut ower is stored in the comressible air. When the chamber ressure returns from its ositive or negative eaks, the stored ower may be released. This is actually consistent with the assumtion of isentroic rocess in the chamber. Generally the inut ower and the PTO ower are similar, and a small difference between the inut and the PTO owers can be seen, which can be regarded the ower loss through the oen boundary (the PTO system). It can be exlained as when the air is ressurized and driven out of the chamber, its temerature is higher (thus internal energy is higher) than the atmoshere which is sucked into the chamber in the inhalation rocess. The difference between the internal energy of the exhaled and inhaled air is the ower loss due to air comressibility in the air chamber. Obviously, the ower loss will very much deend on the maximum chamber ressure and the flowrate. Similar result can be seen for the orous membrane PTO, though the air comressibility is not as large as those of orifice PTO (Figure ). From Table 4, it can still be seen that there is %-% of the ower loss. The ower losses in these cases are Figure 4 ower comarison for the orous membrane PTO (A=.75m, f=.833, Brown=, Blue=, ϕ =.m) Table 3 Power loss due to air comressibility Test case max Qmax (m3/s) Power (Pa) Loss (%) A (m) f (Hz) Table 4 Power loss due to air comressibility Test case max Qmax (m3/s) Power (Pa) Loss (%) A (m) f (Hz) Downloaded From: htt://roceedings.asmedigitalcollection.asme.org/ on /6/4 Terms of Use: htt://asme.org/terms Coyright 3 by ASME

9 CONCLUSIONS The aer resents the thermodynamic studies of OWC wave energy converters. To simlify the thermodynamic analysis, the rocess is assumed to be an isentroic oen-system under which the thermodynamic equation has been derived by combining the known PTO characteristics. Solving the thermodynamic equation, the air comressibility and the ossible ower loss in the recirocating rocess of ressurising and de-ressurising the air can be investigated. From the study, the following conclusions can be drawn: The theoretical results have shown close results to the exerimental data. Hence the assumtion of the isentroic air is generally accetable, which much simlifies the theoretical analysis. The calibration of the orifice PTO has shown consistent daming coefficients for exhalation and inhalation, and the difference of the daming coefficients between the exhalation and inhalation may be caused the different flow condition, for examle, the chamfer of the orifice has made the orifice has different boundaries for the inhalation and exhalation. For the orous membrane PTO, its linearity can only be an aroximation. A better exression for such a PTO is the olynomial function, which is a generic exression for the nonlinear ower take-off system. The generic exression gives consistent daming coefficients. Power loss due to the comressibility haens in the mass exchanges through the PTO system when the ressurized air with high internal energy (than atmoshere) is driven out of the chamber in the exhalation and the atmoshere is sucked into the chamber. ACKNOWLEDGEMENTS This material is based uon works suorted by the Science Foundation Ireland (SFI) under the Charles Parsons Award. Statistics and data were correct at the time of writing the article; however the authors wish to disclaim any resonsibility for any inaccuracies that may arise. REFERENCES [] Voith Hydro, htt:// cited on: 8/9/. [] PICO OWC, htt:// cited on: 8/9/. [3] Alves, M., Costa, I. R., Sarmento, A. and Chozas, J. F.,, "Performance evaluation of an axisymmetric floating OWC," The Proceedings of the th () International Offshore and Polar Engineering Conference, Beijing, China, June -5,. [4] Ikoma, T., Masuda, K., Rheem, C. K. et al.,, "Primary conversion efficiency of OWC tye WECs installed on a large floating structure," Proceedings of the ASME 3st International Conference on Ocean, Offshore and Arctic Engineering, Rio de Janeiro, Brazil, July -6,. [5] Payne, G., Taylor, J. R. M., Bruce, T. and Parkin, P., 8, "Assessment of boundary-element method for modelling a freefloating sloed wave energy device. Part : numerical modelling," Ocean Engineering, Vol. 35, [6] Payne, G., Taylor, J. R. M., Bruce, T. and Parkin, P., 8, "Assessment of boundary-element method for modelling a freefloating sloed wave energy device. Part : exerimental validation," Ocean Engineering, Vol. 35, [7] Ocean Energy Ltd, htt:// cited on: 7/9/. [8] CORES (FP7), htt://hmrc.ucc.ie/cores/, cited on: 8/9/. [9] Sheng, W., Lewis, A. and Alcorn, R.,, "Numerical studies on floating OWC hydrodynamics," Proceedings of the 3th International Conference on Ocean, Offshore and Arctic Engineering (OMAE ), Rotterdam, the Netherlands, 9-4th June,. [] Falcao, A.,, "Wave energy utilization: a review of the technologies," Renewable and Sustainable Energy Reviews, Vol. 4, [] Heath, T.,, "A review of oscillating water columns," Philosohical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences, Vol. 37, [] Evans, D. V. and Porter, R., 995, "Hydrodynamic characteristics of an oscillating water column device," Alied Ocean Research, Vol. 7, [3] Imai, Y., Toyota, K., Nagata, S. et al.,, "An exerimental study on generating efficiency of a wave energy converter 'Backward Bent Duct Buoy'," Proceedings of the 9th Euroean Wave and Tidal Energy Conference, Southamton, UK, 5-9th Se,. [4] Setoguchi, T. and Takao, M., 6, "Current status of self rectifying air turbines for wave energy conversion," Energy Conversion and Management, Vol. 47, [5] Takao, M. and Setoguchi, T.,, "Air turbines for wave energy conversion," International Journal of Rotating Machinery, Vol.,. doi:.55// [6] Evans, D. V., 98, "Wave-ower absortion by systems of oscillating surface ressure distributions," Journal of Fluids Mechanics, Vol. 4, [7] Josset, C. and Clément, A. H., 7, "A time-domain numerical simulator for oscillating water column wave ower lants," Renewable Energy, Vol. 3, [8] Falcao, A. F. d. O. and Justino, P. A. P., 999, "OWC wave energy devices with air flow control," Ocean Engineering, Vol. 6, [9] Nagata, S., Toyota, K., Imai, Y. et al.,, "Frequency domain analysis on rimary conversion efficiency of a floating OWC-tye wave energy converter 'Backward bent Duct Buoy'," 9 Coyright 3 by ASME Downloaded From: htt://roceedings.asmedigitalcollection.asme.org/ on /6/4 Terms of Use: htt://asme.org/terms

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