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

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Due to Kirchhoff decomposition, recall:niinAdditionally, recall the total potential must satisfy the body boundary condition: nIDnon SApplying Eq. (13) to Eq. (54) the complex amplitude of the excitation force results in:Xi ni I D dS (55)SXiiD I idS (56)nnSSubstituting Eq. (11) into Eq. (56), the complex amplitude of the excitation force per unitwave amplitude is:Xi iI IidS(57) nnSComplex amplitude of the excitation force for a two-dimensional single, heaving bodyThe spatial part of the complex incident and radiation potentials in two-dimensions are: I gAi cosh( k(z d ))e cosh( kd )ikx gicosh( k(z d))Re cosh( kd )ikxAs given in Appendix A, by use of the Haskind-Hanaoka relationship, the complexamplitude of the excitation force for a two-dimensional body is:48
XiAgCgi 2 (58)3.4 Equations of MotionThe equations of motion for a freely-floating, stable body are derived from equating Eq. (34)with Newton’s second law of physics,FT i m ijj . The mass matrix, m ij , for a twodimensionalbody is:m ijm000m00 0I 22where, m denotes the mass of the body and I 22 denotes the mass moment of inertia withrespect to the z-axis. Rewrite Eq. (34) as:FTi m k X eijjijjitj M B ijjijjwhere, k ij is the hydrostatic stiffness matrix. Thus, the time-dependent equations of motionper unit wave amplitude assuming harmonic oscillation is:X eiti ( m M ) B k (59) for j=1, 3, 5ijijjijjijj0The amplitude of the motion is written in terms of the complex amplitude of motion, :jj 0jite The equation of motion in the frequency domain per unit wave amplitude is:0Xi(60) for j=1, 3, 5j2 ( m M ) iB ( k ) ijijijij3.5 Wave <strong>Energy</strong>The total energy per unit area depth-averaged is:49
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 46 and 47: Mw k ieitS( D I) ijkrinjdS(46)3.3.3
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
Page 102 and 103:
Figure 5. 24 Filter Step Set-up, Co
Page 104 and 105:
5.6 Data ProcessingFigure 5. 26 Wav
Page 106 and 107:
5.8 Experimental DiscussionAs menti
Page 108 and 109:
5.8.3 Suggestions for Future Resear
Page 110 and 111:
110ikxxRekddzkgkn )cosh())(cosh(,
Page 112 and 113:
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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MS Thesis R. Hager - Hawaii National Marine Renewable Energy ...

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