MS Thesis R. Hager - Hawaii National Marine Renewable Energy ...
MS Thesis R. Hager - Hawaii National Marine Renewable Energy ... MS Thesis R. Hager - Hawaii National Marine Renewable Energy ...
concavity from concave down to concave up at Body 21. The maximum power absorptionefficiency decreases more rapidly with the convex bodies than the concave. However, notefrom Table 4.3 and Figure 4.29 that the maximum power absorption efficiency isconsistently higher for convex bodies compared to concave. At a period of 0.6 sec themaximum power absorption efficiency fall from 86.30% to 70.77% from the most convexbody to the most concave body. Comparatively, at a period of 1.0 sec the maximum powerabsorption efficiency falls from 53.04% to 49.70% from the most convex body to the mostconcave body.The wave no longer detects the shape of the body at a period of 1.0 sec (1 Hz) because thewavelengths are much greater than the body length, as seen in Figure 4.30. As previouslystated for the wave to detect the body’s shape the body length must span a significantportion of the wavelength. Note at a period of 1.0 sec the body spans 11% of thewavelength.Figures 4.31 and 4.32 present the normalized heave forces versus the normalized frequenciesfor Bodies 1, 21, and 39 as the body is impinged at 0° and 180°, respectively. Recall the forceis normalized byX igWB (H /2), and the frequency is normalized by 2B2g. Note fromFigures 4.30 and 4.31 that the concave bodies consistently experience greater force than theconvex bodies. Additionally, the curved faces of the bodies (0°) experience greater forcesthan the flat face of the bodies (180°). The percentage difference between the normalizedforce as the wave impinges body 1 at 0° and 180° at T = 0.6 sec is 85.91%. Comparatively ,76
the percentage difference between the normalized force as the wave impinges body 1 at 0°and 180° at T = 1 sec is 6.13%. Where percentage difference is:( x y)Percent _ Difference ( x y) 2 Note these conclusions are restricted to the assumptions made that the waterline crosssectionalarea and the draft remain constant rather than the submerged volume remainingconstant. A smaller draft corresponds to larger excitation forces and greater powerabsorption (Backer, 2009). A smaller waterline cross-sectional area corresponds to a smallerhydrostatic resorting coefficient, and thus results in resonance occurring at a lower naturalfrequency, affecting the power absorption efficiency (Backer, 2009). The submerged volumewill also have an effect on the hydrostatic restoring coefficient, and thus on the frequency atwhich resonance occurs. Thus, there is a trade-off in whether to keep the waterline crosssectionalarea or the submerged volume constant. Future research should be done to furtherexplore this issue.77
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concavity from concave down to concave up at Body 21. The maximum power absorptionefficiency decreases more rapidly with the convex bodies than the concave. However, notefrom Table 4.3 and Figure 4.29 that the maximum power absorption efficiency isconsistently higher for convex bodies compared to concave. At a period of 0.6 sec themaximum power absorption efficiency fall from 86.30% to 70.77% from the most convexbody to the most concave body. Comparatively, at a period of 1.0 sec the maximum powerabsorption efficiency falls from 53.04% to 49.70% from the most convex body to the mostconcave body.The wave no longer detects the shape of the body at a period of 1.0 sec (1 Hz) because thewavelengths are much greater than the body length, as seen in Figure 4.30. As previouslystated for the wave to detect the body’s shape the body length must span a significantportion of the wavelength. Note at a period of 1.0 sec the body spans 11% of thewavelength.Figures 4.31 and 4.32 present the normalized heave forces versus the normalized frequenciesfor Bodies 1, 21, and 39 as the body is impinged at 0° and 180°, respectively. Recall the forceis normalized byX igWB (H /2), and the frequency is normalized by 2B2g. Note fromFigures 4.30 and 4.31 that the concave bodies consistently experience greater force than theconvex bodies. Additionally, the curved faces of the bodies (0°) experience greater forcesthan the flat face of the bodies (180°). The percentage difference between the normalizedforce as the wave impinges body 1 at 0° and 180° at T = 0.6 sec is 85.91%. Comparatively ,76
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