Close Proximity of Terminator-Type Wave Energy Converters is Detrimental to Performance

Transcription

1 Close Proximity of Terminator-Type Wave Energy Converters is Detrimental to Performance MAURA SATERIALE Department of Engineering University of Hawaii, Manoa CAMERON KARTASCHEW Department of Engineering Swinburne University of Technology John St, Hawthorn VIC 3122, Australia ISAAC H-H CHAN Department of Engineering Swinburne University of Technology John St, Hawthorn VIC 3122, Australia GURWINDER SINGH Department of Engineering Swinburne University of Technology John St, Hawthorn VIC 3122, Australia DR. RICHARD MANASSEH Faculty of Engineering Swinburne University of Technology John St, Hawthorn VIC 3122, Australia

2 M. Sateriale, C. Kartaschew, I. Chan, G. Singh, & R. Manasseh Experiments were performed on the effect of placing multiple wave-energy converters in arrays. In particular, closely-spaced terminator configurations were investigated. A number of developments worldwide are occurring in which resonating wave energy converters are placed immediately next to each other, such as in a breakwater or sea-wall configuration. Laboratory models of three Helmholtz Resonators in both tandem and staggered arrangements showed that the q-factor is always less than unity, indicating that the output of the three devices when closely-spaced is less than that of the three independent devices. It is suggested that developments where wave-energy converters serve as a breakwater should not have active devices immediately next to each other, in order to maximize the return from capital investment. 1. Introduction Keywords: Helmholtz resonance, breakwater, wave energy converter, oscillating water column Ocean Wave Energy Converters (WECs) that can generate MW of electricity have a high capital cost [Barstow and Pontes, 2010]. To maximize harvestable energy, research must determine the optimal arrangements of WECs in an array or farm. While the majority of WEC designs are intended primarily for electricity generation, there are circumstances where the primary need is for coastal protection, for example, a breakwater to protect a harbor from waves [Arena, et. al., 2013], or to address erosion issues. Electricity generation is a welcome, but secondary, benefit of wave energy absorption by an array of such devices. From the electricity-generation perspective, a breakwater-type installation has the enormous advantage that much of the capital cost of construction is already covered by the harbor-protection imperative [Falcao, 2010]. Some of these designs, called terminators, completely eliminate wave action in their shadow, while partial terminators greatly reduce wave action. Of the several classes of WEC designs, the preferred class for breakwater-type terminators belong to the Oscillating Water Column (OWC) family of concepts [Falcao, 2010, Barbarit, et. al., 2012]. In an OWC there are no moving parts in the water, minimizing the risk of interference with harbor operations. The power is extracted from the movement of air above a chamber geometrically tuned to resonate at incoming wave frequencies. Beginning with Budal [1977], many authors, such as Wolgomat, et. al., [2012] and Sadaat, et. al., [2014] have explored interactions of WECs as a function of inter-device spacing. Budal s analytic work determined that the optimal distance for maximum power absorption, d a, for one row of devices parallel to incoming waves and encountering a single-mode wave to be d a between 0.5 and 1 wavelength (λ) apart. Evans [1980] noted that for WECs utilizing resonating chambers in a multichamber arrangement, the waves in the middle chamber achieve the highest amplitude. Work from the University of Hawaii has shown that chambers with a geometry that invokes Helmholtz resonance provides the greatest energy output, but did not study the interactive effects of chamber arrays [Saadat, et. al., 2014, Sateriale, et.al., 2014]. It is easy to show that the Helmholtz Resonator concept may be considered a type of OWC with a greater number of geometric parameters available for tuning. In the same way that the optimally-tuned length of an OWC can easily be derived from linearized and frictionless versions of the laws of mass and momentum conservation, the conditions for Helmholtz resonance of a WEC follows a similar form to that originally derived by Helmholtz [1885], as shown in equation 1. 1

3 Close Proximity of Terminator-Type Wave Energy Converters is Detrimental to Performance σ H 2 = ghb AL, (1) where σ H is the radian frequency of ocean waves, B is the inlet width, g is gravitational acceleration (9.81m/s 2 ), H is the ocean water depth, L is the length of the narrow channel connecting the chamber to the open ocean, and A is the horizontal cross sectional area of the chamber (fig. 1). Figure 1: Diagram of wave chamber that invokes Helmholtz resonance This present study simulated wave energy capture devices at 30 m depths, with a 6 second wave period. Initial experiments determined the amplitude of device response relative to the input wave amplitude for a range of input wave frequencies to verify the existence of Helmholtz resonance. This established a baseline case for a single device. Further experiments measured the amplitudes of device response for arrays of two and three devices operating together in various configurations. The metric for determination of the effectiveness of an interacting array of WECs is the q-factor [5], which for three devices is given by q = (A 1 F )2 +( A 2 F )2 +( A 3 F )2 3( A 0 F )2, (2) where A 0 is the greatest amplitude achieved within a single device (i.e. the amplitude achieved when it is tuned to resonance), A n is the greatest amplitude in chamber n of each of the three chambers, and F is the amplitude of the waves before entering the chamber. A q factor greater than 1 indicates that constructing the chambers close enough that they do interact is superior to three chambers positioned sufficiently far apart that they do not interact. Conversely, q of less than unity indicates that the devices interfere detrimentally, and thus the return on the investment in constructing the devices would be poorer than expected. In a study [Magagna, et.al., 2011] in which three closely-spaced OWCs were used as pumps, which may be analogous to the present work, q values were generally less than 0.4. The aim of the present study is simply to determine if q is significantly greater than or less than unity for devices placed in close proximity, as they would be in a breakwater. 2

4 M. Sateriale, C. Kartaschew, I. Chan, G. Singh, & R. Manasseh 2. Experimental Method Experiments were performed in a 10 m long, 30 cm wide wave tank filled to a depth of 35 cm and driven by an oblong-shaped wave maker. The test device was placed 4 m from the pivot point of the wave maker. Downwave of the device was a ramp-shaped, plastic-covered beach to minimize wave reflections; It was 1.5 m long, and sat on the floor of the wave tank, making a 5.7 angle with the floor. The model length scale was 100:1. The amplitudes F of the waves prior to entering each chamber and the amplitude A n of the displacement within each chamber was tracked using a red bead on a fishing line that was free to rise with the water surface. The beads were visualized either by a video camera outside the wave tank and at right angles to the wave propagation direction, or by a submersible video camera (GoPro Hero 4) pointed toward the wavemaker. The videos were then analyzed using Kinovea tracking software from the Kinovea corporation, which exported the time/position of the bead as an Excel Spreadsheet, recording the time and x and y coordinates, normalized by a known 1 cm marker on the video taken prior to the experiment. It is well established (e.g. [2]) that for any natural oscillator designed to harvest power from an oscillating source, the maximum power is obtained when the damping due to the Power Take Off (PTO) is set equal to the damping due to all parasitic losses, e.g. friction due to viscous boundary layers in the fluid, etc. Therefore, from the narrow perspective of calculating the q-factor, it is sufficient to have a system in which devices are not fitted with a PTO, instead relying on parasitic losses to provide the damping. The useful power extractable by any PTO would be proportional to the square of the amplitudes A n measured at resonance, and since a similar constant of proportionality would be in both the numerator and denominator of eq. (2), details of PTO design are not likely to significantly alter the present results. Of course, this presumes linear dynamics governs both the device and PTO behavior, but since the present study only seeks to determine if q is significantly more or less than unity, the approximation is thought appropriate. To scale the experiment, the Froude number was used (eq. 3) [10] Fr = U M 2 = U 2 F gl M gl F, (3) where L is a characteristic length of the model and full scale, and U is the characteristic velocity of the water in the model and the full scale value. The waves were tested at several motor speeds of from 30% to 75% of the total motor speed, according to Table 1 to determine the base values for the amplification of the water height in the chambers (A o). Table 1: Characteristics of various motor speeds % Motor speed Frequency (Hz) Amplitude (m) Wavelength (m)

5 Close Proximity of Terminator-Type Wave Energy Converters is Detrimental to Performance In each run, the chamber (or chambers) was re-installed in the tank, the tank was re-filled and the camera and lighting re-set, thus permitting the full range of random errors due to variations in setup to occur. Recordings were typically made over 60 seconds, thus covering waves, to ensure amplitudes statistically representative of each run were estimated. The data from four runs were then averaged and standard errors representing 95% confidence intervals were calculated. When calculating ratios of variables each with statistical error, standard error propagation formula was used for q. 3. Results 3.1. Base Case: Single Chamber A single chamber centered on the centerline of the tank width was tested at a variety of frequencies to get values for A O and F (Fig. 2). Helmholtz resonance is achieved at 55% of the maximum motor speed, with a wave frequency of Hz (Table 2), as predicted by eq. (1). Figure 2: Tracking particle within a single chamber arrangement Table 2: A o, and F values for various frequencies. ω (Hz) Ao (cm) F (cm) Case 1: Three Parallel chambers Three parallel chambers immediately adjoining (terminators in a tandem arrangement) were tested at various wave frequencies. The amplitude is slightly higher in the middle chamber than the side chambers at every wave frequency (fig. 3) as predicted by Evans [1980], but this difference is not statistically significant at 95% confidence, when considering the error bars representing confidence intervals for the four rounds of experiments. 4

6 A/F M. Sateriale, C. Kartaschew, I. Chan, G. Singh, & R. Manasseh 1.8 A/F Values, Parallel Chambers left mid right left mid right left mid right left mid right left mid right left mid right Chambers at Various Frequencies (Hz) Figure 3: A/F values in arrays of parallel chambers for several frequencies. Error bars represent 95% statistical confidence intervals using the standard error propagation formula for q. Since the average amplitudes within the chamber are lower than they were for the single chamber cases, the q-values of the parallel chamber configurations are less than 1 (fig. 4), so there is no advantage to having three chambers immediately beside one another. Rather, the tandem arrangement is detrimental. The best value is at ω/ω 0=1.127, The difference in q-values at various frequency values is not statistically significant, but the q-value for all frequencies is still less than 1. This implies a significant economic inefficiency in the tandem arrangement, which is the most obvious choice for a breakwater. 5

7 Q Close Proximity of Terminator-Type Wave Energy Converters is Detrimental to Performance Average q, Tandem Chambers ω/ω o Figure 4: q values for three chambers in parallel (tandem arrangement), for ω/ω o values of to A value of q=1 means that placing devices in proximity is neither beneficial nor detrimental; here, the arrangement is detrimental for all frequencies, delivering at best half of the power expected for the same number of devices spaced very far apart. Error bars represent 95% statistical confidence intervals using the standard error propagation formula for q Case 2: Staggered configurations When the chambers are staggered with two parallel chambers at the side walls, in a configuration that is not a terminator, as shown in fig. 5, the resulting values of q-factor versus ω/ω o are shown in figure 6. 6

8 Q M. Sateriale, C. Kartaschew, I. Chan, G. Singh, & R. Manasseh Figure 5: Chambers staggered with two chambers one wavelength upstream of a third chamber 2.5 Average q, Staggered Chambers ω/ω o Figure 6: q-factors for staggered chambers for ω/ω o values of to A value of q=1 means that placing devices in proximity is neither beneficial nor detrimental; here, the arrangement is detrimental for all frequencies with the possible exception of the highest. Error bars represent 95% statistical confidence intervals using the standard error propagation formula for q. 7

9 Q Close Proximity of Terminator-Type Wave Energy Converters is Detrimental to Performance 3.4. Case 3: Two Parallel Chambers Spaced One Chamber-width Apart To determine whether slightly separated devices have lower interactions, two chambers arranged in tandem, but separated by width B were tested (fig 7). This is a partial terminator configuration. This required two input (A/F) values rather than three input values for the q-factor equation. Figure 8 shows results consistent with Case 1 (three tandem) and Case 2 (three staggered): the q-factors is less than unity, implying a detrimental economic performance. At ω/ω o = 1,q is Figure 7- Two separated tandem chambers [7] Average q, Separated Chambers ω/ω o Figure 8 - Average q-factor for two separated parallel arrays. A value of q=1 means that placing devices in proximity is neither beneficial nor detrimental; here, the arrangement is detrimental for all frequencies with the possible exception of the highest. Error bars represent 95% statistical confidence intervals using the standard error propagation formula for q. 4. Conclusions It has been determined that the cases of parallel chambers immediately beside each other, staggered chambers where two separated chambers are upwave of the third middle chamber, and two 8

10 M. Sateriale, C. Kartaschew, I. Chan, G. Singh, & R. Manasseh separated tandem chambers, detract from one another s effectiveness. Destructive interference between devices that are placed in such close proximity results in output that is always less than the same number of devices in isolation. While there is no exact array-interaction theory for the Helmholtz Resonator geometry explored in the present study, general comparisons may be drawn with the theories of Budal 1977] and Evans [1980], which both predict a q-factor of less than unity for devices placed as close as in the present study. Even in the third case, the separated tandem chambers, the separation was only 0.2 to 0.43 wavelengths, not the wavelengths for which Budal [1977] predicted a q-factor of greater than unity. If WECs are utilized for breakwaters or other coastal-protection structures, the present study suggests that it is inappropriate to have devices in immediate proximity, even though maximizing the number of generators along the breakwater may appear to be the most obvious choice. The added capital cost of constructing more devices with resonating chambers, turbines, power generators, etc., would not be represented by a greater benefit from more electricity generated. Instead, there could be at best a half and possibly less than a quarter of the power available if the same number of devices were widely spaced, representing a significant waste of capital. Thus, if it is desired to use a breakwater as an ancillary renewable energy generator, it would be better to have fewer WEC devices widely spaced along the structure. Acknowledgements Sateriale would like to acknowledge and thank the Australian Academy of Science (AAS) for its support through the East Asia Pacific Scholars Institute (EAPSI), as well as support from Dr. Richard Manasseh and Dr. Reza Ghorbani. This material is based upon work supported by the U.S. National Science Foundation under Grant No References Arena, F., Romolo, A., Malara, G., (2013). On design and building of a U-OWC wave energy converter in the Mediterranean Sea: a case study Babarit, A., Hals, J., Muliawan, M.J, Kurniawan, A., Moan, T., Krokstad, J. (2012), Numerical benchmarking study of a selection of wave energy converters Renewable Energy 41, Budal, K., (1977), Theory for absorption of wave power by a system of interacting bodies, Journal of Ship Research, vol. 21 (4), pp , Evans, D., (1980). Some analytic results for two- and three-dimensional wave energy absorbers. B. Count: Academic Press: Falcao, A. (2010), Wave energy utilization: A review of the technologies, Renewable and Sustainable Energy Reviews 14, Helmholtz, H. (1885) On The Sensations Of Tone As A Physiological Basis For The Theory Of Music. Second English Edition, p

11 Close Proximity of Terminator-Type Wave Energy Converters is Detrimental to Performance Magagna, D., Carr, D., Stagonas, D., McNabola, A., Gill, L., & Muller, G. (2011). Experimental evaluation of the performance of an array of multiple oscillating water columns. Paper presented at the 9 th European Wave and Tidal Energy Conference, University of South Hampton, UK, 5-9 September 2011 Mørk, G., Barstow, S., Kabuth, A., Pontes, M. (2010) Assessing The Global Wave Energy Potential. Proceedings of OMAE th International Conference on Ocean, Offshore Mechanics and Arctic Engineering Saadat, Y., Fernandez, N., Samimi, A., Alam, M., Shakeri, M., Ghorbani, R. (2014) Investigating of Helmholtz Wave Energy Converter. Renewable Energy 87 67e76 Sateriale, M., Ghorbani, R., Francis, O. (2014) Computational Fluid Dynamics (CFD) Simulation of Wave Absorbers at Helmholtz Resonance. Paper presented at Oceans 14: Taipei, Taipei, Taiwan. Wolgamot, H., Taylor, P., Taylor, R., (2012), The Interaction Factor and Directionality in Wave Energy Arrays 10