MS Thesis R. Hager - Hawaii National Marine Renewable Energy ...

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Mw k ieitS( D I) ijkrinjdS(46)3.3.3 Radiation ProblemThe radiation problem considers a body oscillating via an external force in calm water. Asthe body enters the water, a wave is radiated. The radiation force per unit amplitude in the i thcomponent due to the motion in the j th direction is:FRii t iejjnidS(47)S jRecall that the body boundary condition for the radiation potential may be written as:iin non SSurge, heave, and pitch, are denoted by i and j=1, 3 and 5. Thus, Eq. (47) may be rewrittenas:FRii t i iejjdS(48)nS jwhere, Eq. (48) may be rewritten in terms of the complex force in the i th direction due tomotion of unit amplitude in the j th direction (Newman, 1977):FRi i te jfij (49) jLet,fiji2 ( i) jdS Mij iB(50)ijnSUjit ije (51)46
Thus, Eq.(49) may be written as:FR ( MijUjBijUj) (52)i jwhere, B ij denotes the damping coefficient, which represents a reduction in harmonicoscillation via energy extraction. The variable M ij denotes the added-mass coefficient, whichdescribes the inertial and mass forces. Note B ij and M ij are symmetric tensors as given inAppendix A. M ij and B ij are functions of frequency of oscillation, the geometry, displacement,water depth, and distancing to surrounding bodies.Damping Coefficient for a two-dimensional single, heaving bodyRecall the boundary conditions are at the seabed, the body, and positive and negative infinityalong the x-axis. The derivation is given in Appendix A. The damping coefficient for a twodimensional,heaving body is:22gCg Bij(53)23.3.4 Haskind-Hanaoka RelationshipWhen the diffraction potential is unknown, the excitation force may still be calculated if theradiation and incident potentials are known using the Haskind-Hanaoka relationship(Newman, 1977). Recall the complex amplitude of the excitation force per unit waveamplitude is:X ( )n dS (54)iSD47Ii
Page 1 and 2: Geometric Effects on Maximum Power
Page 3 and 4: ABSTRACTNumerical simulations are c
Page 5 and 6: 3.7 Absorbed Wave Power ...........
Page 7 and 8: LIST OF FIGURESFigurePageFigure 1.1
Page 9 and 10: NOMENCLATUREA=incident wave amplitu
Page 11 and 12: 1.2 Advantages of Wave EnergyAdvant
Page 13 and 14: for various projects. Included in t
Page 15 and 16: pollution would occur from hydrauli
Page 17 and 18: Figure 1. 7 Average Annual Wave Pow
Page 19 and 20: Backer (2009) numerically and exper
Page 21 and 22: CHAPTER 2. WAVE ENERGY CONVERSION D
Page 23 and 24: 2.3 OrientationOrientation is defin
Page 25 and 26: Figure 2.4 Oscillating Water Column
Page 27 and 28: 2.5 Reference PointMeans of reactio
Page 29 and 30: Linear GeneratorTurbineRotary Gener
Page 31 and 32: Table 2. 1 WEC ClassificationsDevic
Page 33 and 34: 33P.T.O.MooringReferencePointOperat
Page 35 and 36: CHAPTER 3. THEORY AND GOVERNING EQU
Page 37 and 38: F(x,z,t) z 0DFDtFt u F 0 0 (4
Page 39 and 40: in ni(13)on S for i=1, 3in( r n)i3
Page 41 and 42: I iAg e ekz i( kx t)(30)cosh( k(z
Page 44 and 45: where ijkis the permutation symbol.
Page 48 and 49: Due to Kirchhoff decomposition, rec
Page 50 and 51: TE KE PE 20L Asin(kx) 1 2(61)dV d
Page 52 and 53: P I Iw dS (70)tnSIf the column
Page 54 and 55: 221 2P gA C(77)max g2 3.8 Maximum
Page 56 and 57: 4.2 AQWA Modeling ProcedureThe user
Page 58 and 59: : Local data has changed, and the c
Page 60 and 61: Figure 4. 5 Drawing in Design Modul
Page 62 and 63: 12. Delete all lines inside the cur
Page 64 and 65: 22. Edit the details of the slice u
Page 66 and 67: Figure 4. 15 Details of the Part7.
Page 68 and 69: Figure 4. 17 Details of the Mesh4.2
Page 70 and 71: Figure 4. 21 Detials of the Wave Di
Page 72 and 73: 5. Highlight Diffraction + Froude-K
Page 74 and 75: Table 4.1 Body Dimensions for Numer
Page 76 and 77: concavity from concave down to conc
Page 78 and 79: Figure 4. 29 Maximum Power Absorpti
Page 80 and 81: Table 4. 3 Numerical ResultsBodyNo.
Page 82 and 83: BodyNo.Bodyλ atT=2.1λ atT=1.0λ a
Page 84 and 85: WAVEFigure 5. 1 Body Faces Wave Mak
Page 86 and 87: The body connects to the aluminum p
Page 88 and 89: also allowed for flexibility in cre
Page 90 and 91: AB1 23 4 5 6 7CD8 9 10 11EFigure 5.
Page 92 and 93: and minimum voltage range of the DA
Page 94 and 95: Figure 5. 11 Deleting a Step from L
Page 96 and 97:
Figure 5. 14 Recording Options, Sig
Page 98 and 99:
Figure 5. 17 Right-mouse Click on t
Page 100 and 101:
Zero-OffsetThe Zero-Offset step rem
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Figure 5. 24 Filter Step Set-up, Co
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5.6 Data ProcessingFigure 5. 26 Wav
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5.8 Experimental DiscussionAs menti
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5.8.3 Suggestions for Future Resear
Page 110 and 111:
110ikxxRekddzkgkn )cosh())(cosh(,
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Proof M ij and B ij are Symmetric T
Page 114 and 115:
BIBILIOGRAPHYANSYS. (n.d.). ANSYS A
Page 116:
Trust, C. (2011). Capital, Operatin
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