ＯＴＥＣVol. 18 (2013)，69〜76

規則波中における浮体型振り子発電装置のエネルギー変換性能に関する研究

Equation Chapter 1 Section 1つ๎Ἴ୰࡟࠾ࡅࡿᾋయᆺ᣺ࡾᏊⓎ㟁⿦⨨ࡢ࢚ࢿࣝࢠ࣮ኚ᥮ᛶ⬟࡟㛵ࡍࡿ◊✲௒஭ ᗣ㈗*1, Ọ⏣ ಟ୍*1, ㇏⏣ ࿴㝯*2, ᮧୖ ኳඖ*1, ℩ᡞཱྀ ಇ᫂*1
Conversion Efficiency of Floating Pendulum Wave Energy Converter in Regular Waves
Yasutaka IMAI*1, Shuichi NAGATA*1, Kazutaka TOYOTA*2,Tengen MURAKAMI*1 and Toshiaki SETOGUCHI*1*1*2

Saga Univ. Inst. of Ocean Energy
Honjo1, Saga, 840-8502 Japan

Deceased (Saga Univ. Inst. of Ocean Energy)

A model test with a power take-off system composed of pulleys, belts and a generator is made and tank tests arecarried out in regular waves to evaluate performance of a floating pendulum wave energy converter (FPWEC) proposedby Watabe. A primary conversion efficiency, secondary conversion efficiency and generating efficiency of this device
are obtained from a free oscillation tests. Also, 2D numerical code using a boundary element method based on velocity
potential theory to estimate the primary conversion efficiency of this device is developed. The result of the code isvalidated by comparing with the experimental results.
Key Words : Wave Erengy Converter, Pendulum, Primary Conversion Efficiency

1. ⥴   ゝᅛᐃᆺ᣺ࡾᏊᘧἼຊⓎ㟁⿦⨨ࡣྍື≀యᆺⓎ㟁⿦⨨ࡢ୍✀࡛࠶ࡿ㸬Ώ㒊ࡽ 1) ࡣࡇࡢ⿦⨨ࡀ㧗࠸࢚ࢿࣝࢠ࣮ኚ᥮ຠ⋡ࢆᣢࡘࡇ࡜㸪ᘓ⠏㈝ࡢ⣙ 70%ࡣࢣ࣮ࢯࣥࡢᘓ㐀㈝࡛࠶ࡿࡇ࡜ࢆ♧ࡋࡓ㸬ࡉࡽ࡟ࡼࡾపᘓ㐀㈝࡛㸪࠿ࡘ࢚ࢿࣝࢠ࣮ࡢ኱ࡁ࠸኱Ἴ㧗࣭㛗࿘ᮇࡢἼ࡟ᑐᛂ࡛ࡁࡿᾋయᆺ᣺ࡾᏊᘧἼຊⓎ㟁⿦⨨㸦Floating Pendulum Wave EnergyConverter : FPWEC㸧ࢆᥦ᱌ࡋࡓ㸬Ώ㒊ࡽ 2) ࡣᮏ⿦⨨ࡢ Power Take Off 㸦PTO㸧ࢩࢫࢸ࣒࡟࣮ࣟࢱ࣮࣮࣏ࣜ࣋ࣥࣥ
ࣉࢆ᥇⏝ࡋࡓ㸬ࡲࡓつ๎Ἴ୰࡟࠾ࡅࡿᮏ⿦⨨ࡢ୍ḟኚ᥮ຠ⋡ࢆ஧ḟඖỈᵴᐇ㦂࡛ィ ࡋࡓ㸬Toyota ࡽ 3) ࡣྠᵝࡢᾋయᆺ᣺ࡾᏊᘧⓎ㟁⿦⨨ࡢつ๎Ἴ୰࡟࠾ࡅࡿⓎ㟁ຠ⋡ࢆ஧ḟඖỈᵴᐇ㦂࡟ࡼࡾィ ࡋࡓ㸬ࡇࡢᐇ㦂ᶍᆺ࡛ࡣ᣺ࡾᏊࡢᅇ㌿㐠ືࢆࣉ࣮࣮ࣜ࠾ࡼࡧ࣋ࣝࢺࢆ⏝࠸࡚ቑ㏿ࡋⓎ㟁ࡋࡓ㸬Park ࡽ 4) ࡣ᣺ࡾᏊᅇ㌿㒊࡟࣮ࣔࢱ࣮࠾ࡼࡧィࢭࣥࢧࢆ⏝࠸࡚ FPWEC ࡢ୍ḟኚ᥮ຠ⋡ࢆィ ࡋࡓ㸬Nam ࡽ 5),6) ࡣ㧗ḟቃ⏺せ⣲ἲࢆ⏝࠸࡚つ๎Ἴ࣭୙つ๎Ἴ୰࡟࠾ࡅࡿᮏ⿦⨨ࡢ 3D 㐠ືࢆィ⟬ࡋ㸪Ỉᵴᐇ㦂⤖ᯝ࡜ẚ㍑ࢆ⾜ࡗࡓ㸬ࡋ࠿ࡋ㸪ィ⟬࡟ࡼࡿ୍ḟኚ᥮ຠ⋡࡜ᐇ㦂⤖ᯝࡣẚ㍑ࡉࢀ࡚࠸࡞࠸㸬ᮏ◊✲࡛ࡣ㸪ࣉ࣮࣮ࣜ㸪࣋ࣝࢺ㸪Ⓨ㟁ᶵ࠿ࡽ࡞ࡿ PTO ࢩࢫࢸ࣒ࢆࡶࡘ FPWEC ᶍᆺࢆ⏝࠸࡚㸪つ๎Ἴ୰࡟࠾ࡅࡿᮏ⿦⨨ࡢⓎ㟁ຠ⋡ࢆィ ࡍࡿࡓࡵ࡟஧ḟඖỈᵴᐇ㦂ࢆᐇ᪋ࡋࡓ㸬ḟ࡟✵Ẽ୰࡟࠾࠸࡚᣺ࡾᏊࡢ⮬⏤᣺ືᐇ㦂࡟ࡼࡾ஧ḟኚ᥮ຠ⋡ࢆ⟬ฟࡋ㸪ᮏ⿦⨨ࡢ୍ḟኚ᥮ຠ⋡ࢆᚓࡓ㸬ࡉࡽ࡟㸪㏿ᗘ࣏ࢸࣥࢩࣕࣝㄽ࡟ᇶ࡙ࡁ஧ḟඖቃ⏺せ⣲ἲࣉࣟࢢ࣒ࣛࢆ㛤Ⓨࡋ㸪ᮏ⿦⨨ࡢ୍ḟኚ᥮ຠ⋡ࢆ⟬ฟࡋࡓ㸬ィ⟬࡟ࡼࡿ୍ḟኚ᥮ຠ⋡࡜Ỉᵴᐇ㦂⤖ᯝ࡜ẚ㍑ࡋ㸪ᮏィ⟬ࣉࣟࢢ࣒ࣛࡢ᭷ຠᛶࢆ♧ࡋࡓ㸬*ཎ✏ཷ௜ 2013 ᖺ 8 ᭶ 11 ᪥
బ㈡኱Ꮫᾏὒ࢚ࢿࣝࢠ࣮◊✲ࢭࣥࢱ࣮㸦ࠛ840-8502 బ㈡ᕷᮏᗉ 1㸧
*2
ᨾே㸦బ㈡኱Ꮫᾏὒ࢚ࢿࣝࢠ࣮◊✲ࢭࣥࢱ࣮㸧E-mail: imai@ioes.saga-u.ac.jp
*169

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今井康貴 , 永田修一 , 豊田和隆 , 村上天元 , 瀬戸口俊明

2. ᐇ㦂ᶍᆺ࡜ᐇ㦂᪉ἲ௒ᅇᐇ㦂࡟౑⏝ࡋࡓ 2 ✀㢮ࡢᶍᆺࢆ Fig.1㸪Fig.2 ࡟♧ࡍ㸬Fig.1 ࡣ๓ᖺᗘࡲ࡛౑⏝ࡋ࡚࠸ࡓᶍᆺ࡛࠶ࡾ㸪௨㝆㸪ᪧᆺᶍᆺ࡜グ㏙ࡍࡿ㸬Fig.2 ࡣ᪂ࡓ࡟〇సࡋࡓᶍᆺ࡛࠶ࡾ㸪᪂ᆺᶍᆺ࡜グ㏙ࡍࡿ㸬᪂ᆺᶍᆺ࡛ࡣᾋయࢆ✚ᴟⓗ࡟ືᦂࡉࡏ㸪ᾋయ࡜᣺ࡾᏊࡢ┦ᑐ㐠ືࢆᪧᆺࡼࡾ኱ࡁࡃࡋ࡚Ⓨ㟁ຠ⋡ࢆ㧗ࡵࡿࢥࣥࢭࣉࢺ࡛タィࡋࡓ㸬ࡇࢀࡽࡢᶍᆺ
ࢆ Fig.3 ࡢࡼ࠺࡟஧ḟඖỈᵴ࡟㓄⨨ࡋ㸪つ๎Ἴ୰Ⓨ㟁ᐇ㦂ࢆ⾜ࡗࡓ㸬Fig 1 Old ModelFig 2 New Model
Fig 3 Experimental arrangement

Fig 4 Power Take Off system
Fig.4 ࡟ᶍᆺ࡟ᦚ㍕ࡋࡓ PTO ࢩࢫࢸ࣒ࢆ♧ࡍ㸬6 ࡘࡢࣉ࣮࣮ࣜ࠾ࡼࡧ 3 ᮏࡢ࣋ࣝࢺ࡟ࡼࡗ࡚᣺ࡾᏊ㍈ࡢᅇ㌿㏿ᗘࢆ 28.8 ಸ࡟ቑ㏿ࡋ㸪SKY 㟁Ꮚ♫〇 HR125 Ⓨ㟁ᶵࢆ㥑ືࡍࡿ㸬஺ὶ୕┦ࡢⓎ㟁ᶵฟຊࢆᩚὶჾ㸦Shindengen
S10VTA60㸧࡟ࡼࡗ࡚┤ὶ࡟ኚ᥮ࡋ㸪᢬ᢠ R ࡢ୧➃㸦Fig㸬4 ࡢ A㸫B 㛫㸧ࡢ㟁ᅽ V ࢆィ ࡋࡓ㸬Ⓨ㟁ฟຊ Pout ࡣḟᘧࡼࡾồࡵࡓ㸬PoutV2 / R(1)᭱⤊ⓗ࡟Ⓨ㟁ฟຊࡣࢭ࣓ࣥࢺ᢬ᢠ࡛⇕࡜ࡋ࡚ᾘ㈝ࡋࡓ㸬
3. ᐇ㦂⤖ᯝࡲࡎ㸪ᾋయᆺ᣺ࡾᏊᘧἼຊⓎ㟁⿦⨨ࡢ୍ḟኚ᥮ຠ⋡ࢆィ⟬࡛ồࡵࡿ㝿࡟Ⓨ㟁ࣘࢽࢵࢺࡢῶ⾶ಀᩘࡀᚲせ࡟࡞ࡿ㸬ࡑࡇ࡛✵Ẽ୰࡟࠾࠸࡚つᐃࡢ㔜ࡾࢆᦚ㍕ࡋ࡚⮬⏤᣺ືࢆࡉࡏ㸪ῶ⾶ಀᩘࢆィ ࡋࡓ㸬Fig.5 ࡟ᐇ㦂ᶵჾ㓄⨨ࢆ♧ࡍ㸬እ㒊᢬ᢠ R ࡣ 15, 100, 500Ȑ࡜ࡋࡓ㸬ᐇ㦂࡟ࡼࡗ࡚ᚓࡽࢀࡓⓎ㟁ࣘࢽࢵࢺࡢῶ⾶ಀᩘࢆ Fig.6 ࡟♧ࡍ㸬ᅗࡢᶓ㍈ࡣỈᐊ㛗 L ࡟ᑐࡍࡿἼ㛗Ȣ㸪⦪㍈ࡣῶ⾶ಀᩘࢆ♧ࡍ㸬᣺ࡾᏊࡢ௙஦ࡣῶ⾶ಀᩘ c p ࠾ࡼࡧᅇ㌿ゅ\ ࢆ⏝࠸࡚ḟᘧ࡛⾲ࡉࢀࡿ㸬

³2S /V0c p\ (t ) dt
2

³2S /V0c p (iV<e ) (t ) dt
iV t2

S c pV< [J]2(2)規則波中における浮体型振り子発電装置のエネルギー変換性能に関する研究

Fig.5 Damping test

71

Fig.6 Damping Coefficientࡲࡓ㸪᣺ࡾᏊࡢฟຊ Wp ࡣḟᘧ࡛ồࡲࡿ㸬Wp

1TS c pV<2V2SS c pV<212c pV <22[W](3)Wp ࡢ᫬㛫ᖹᆒ࡜Ⓨ㟁ฟຊࡢẚ࠿ࡽ஧ḟኚ᥮ຠ⋡ K2 ࡀồࡲࡿ㸬᭱⤊ຠ⋡ K ࢆ K2 ࡛๭ࡿࡇ࡜࡟ࡼࡾ୍ḟኚ᥮ຠ⋡ K1ࢆồࡵࡓ㸬ᪧᆺᶍᆺ࡜᪂ᆺᶍᆺࡢᐇ㦂⤖ᯝࡢẚ㍑ࢆ Fig.7,8 ࡟♧ࡍ㸬ࢢࣛࣇࡢᶓ㍈ࡣἼ㛗ȢࢆỈᐊ㛗ࡉ L ࡛㝖ࡋࡓ↓ḟඖ್㸪⦪㍈ࡀୖ࠿ࡽ㡰࡟(a)Surge㸪(b)Heave㸪(c)Pitch㸪(d)୍ḟኚ᥮ຠ⋡㸪(e)࢚ࢿࣝࢠ࣮཰ᨭࢆ♧ࡍ㸬᪂ᆺᶍᆺࡢ᪉ࡀᪧᆺ
ᶍᆺ࡟ẚ࡭㸪ࡍ࡭࡚ࡢἼ㛗ᇦ࡛ Surge ᪉ྥࡢ᣺ᖜࡀ኱ࡁࡃ㸪Ἴ㛗ࡀ㛗ࡃ࡞ࡿ࡟ࡘࢀ࡚ Heave㸪Pitch ᪉ྥࡢ᣺ᖜࡢቑ኱ࡀᢚไࡉࢀ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿ㸬ࡇࢀࡣ᪂ᆺᶍᆺࡢ᪉ࡀప㔜ᚰ࡛࠶ࡾ㸪Ỉ㠃ኚື᫬ࡢἐỈయ✚ࡢኚ໬ࡀᑠࡉ
࠸ࡇ࡜࡜㸪Ỉᖹ᪉ྥࡢ㐠ືࢆపῶࡉࡏࡿ㖄┤ῶᦂᯈࡢ᭷↓ࡀᙳ㡪ࡋ࡚࠸ࡿ࡜⪃࠼ࡽࢀࡿ㸬୍ḟኚ᥮ຠ⋡ࡢ᭱኱್ࡣ᪂ᆺࡢ᪉ࡀᪧᆺࡼࡾ㧗࠸㸬ࡲࡓ P ࡀ኱࡟࡞ࡿ࡟ࡘࢀ୍ḟኚ᥮ຠ⋡ࡀ᭱኱࡟࡞ࡿȢ/L ࡶ኱࡟࡞ࡿ㸬














Fig.7 Motion amplitude and Primary conversion efficiency

Fig.8 Motion amplitude and Primary conversion efficiency

P=0.5m, R=15Ȑ

P=1.3m, R=15Ȑ

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今井康貴 , 永田修一 , 豊田和隆 , 村上天元 , 瀬戸口俊明

4. ᩘ್ゎᯒ4࣭1 ᇶᮏ௬ᐃ࣏ࢸࣥࢩࣕࣝ⌮ㄽ࠾ࡼࡧቃ⏺せ⣲ἲ 7)ࢆ࣮࣋ࢫ࡜ࡋࡓᩘ್ゎᯒࣉࣟࢢ࣒ࣛࡢ㛤Ⓨࢆ⾜ࡗࡓ㸬Fig.9 ࡟⿦⨨ཬࡧ⿦⨨࿘㎶ࡢὶయ㒊ࢆ♧ࡍ㸬ᾋయ࠿ࡽ༑ศ㞳ࢀࡓ୍ᐃỈ῝ᇦ࡟௬᝿ቃ⏺㠃ࢆタࡅ㸪ὶయᇦࢆෆᇦ Region 1 ࡜እᇦ: Region W ࠾ࡼࡧእᇦ / Region L ࡟ศ๭ࡋࡓ㸬ࡲࡓ㸪ᾋయෆ㒊ࡢ㡿ᇦࢆ Region 2㸪Region 3 ࡜ᐃ⩏ࡋࡓ㸬

Fig.9 Definition Sketchx ᪉ྥ࠾ࡼࡧ z ᪉ྥࡢ୪㐍㐠ືࢆ [ ࠾ࡼࡧ K ࡜ࡍࡿ㸬y ㍈ࡲࢃࡾࡢᅇ㌿㐠ື㸦ࣆࢵࢳ㸧ࢆȟ㸪᣺ࡾᏊࡢᅇ㌿ゅࢆ\࡜࠾ࡃ㸬㐠ືࡀ࿘ᮇ T 㸪෇࿘Ἴᩘ V ࡛࿘ᮇⓗ࡛࠶ࡿ࡜௬ᐃࡍࡿ࡜㸪㐠ືࡣḟᘧ࡛⾲⌧ࡉࢀࡿ㸬[x0  x0Re ª¬ X  eiV t º¼ , KRe ª¬ Z  eiV t º¼ , Tz0  z 0Re ª¬4  eiV t º¼ , \Re ª¬<  eiV t º¼

(4)

ࡇࡇ࡛ i ࡣ⹫ᩘ༢఩㸪 X  Z  4 ࡣࡑࢀࡒࢀ๓ᚋᦂ㸪ୖୗᦂ㸪⦪ᦂࡢ」⣲᣺ᖜ࡛࠶ࡿ㸬\ ࡣ᣺ࡾᏊᅇ㌿ࡢ」⣲᣺ᖜࢆ♧ࡍ㸬 Re > @ ࡣ」⣲ᩘࡢᐇ㒊ࢆ࡜ࡿࡇ࡜ࢆ♧ࡍ㸬ὶయࡣ㠀⢓ᛶ㸪㠀ᅽ⦰㸪㠀ᅇ㌿࡛࠶ࡿࡓࡵ㏿ᗘ࣏ࢸࣥࢩࣕࣝ ) x, z; t ࡀᏑᅾࡍࡿ㸬g] 0) x, z; tVRe ª¬I x, z eiV t º¼

(5)

I ࡣࣛࣉࣛࢫ᪉⛬ᘧࢆ‶㊊ࡍࡿ㸬 2I(6)0≀య࠿ࡽୖὶഃ࠾ࡼࡧୗὶഃࡢ༑ศ㞳ࢀࡓ࡜ࡇࢁ࡟௬᝿ቃ⏺ AB x l ࠾ࡼࡧ AcBc x lc ࢆタࡅࡿ㸬 CE ࠾ࡼࡧ
SS c ࡶྠᵝ࡟௬᝿ቃ⏺࡛࠶ࡿ㸬ὶయ㡿ᇦࢆ㡿ᇦ :㡿ᇦ /㡿ᇦ 㹼 ࡟ศ๭ࡍࡿ㸬㡿ᇦ : ࡛ࡣ㐲᪉࠿ࡽࡢධᑕἼ

࠾ࡼࡧ཯ᑕἼ㸪㡿ᇦ / ࡛ࡣ㏱㐣ἼࡢࡳࡀᏑᅾࡍࡿ㸬㡿ᇦ :㡿ᇦ / ࡟࠾ࡅࡿ㏿ᗘ࣏ࢸࣥࢩࣕࣝ I W ࠾ࡼࡧ I L ࡣࡑࢀࡒࢀḟᘧ࡛⾲ࡍࡇ࡜ࡀ࡛ࡁࡿ㸬

I W x, zª eikx  K eikx ºr¬«¼»

cosh k z  hcosh kh

cosh k z  hcosh khࡇࡇ࡛ K r ࡣ཯ᑕ⋡㸪 K t ࡣ㏱㐣⋡࡛࠶ࡿ㸬 k ࡣἼᩘ࡛࠶ࡾ㸪ḟࡢศᩓ㛵ಀᘧࢆ‶㊊ࡍࡿ㸬

I L x, z

K t eikx

V2gk tanh kh

(7)
(8)

(9)

㛗ࡉࢆỈ῝ h ࡛↓ḟඖ໬ࡍࡿ㸬xc

x / h, zcz/h(10)௨㝆ࡢᘧࡣỈ῝࡛↓ḟඖ໬ࡋࡓࡶࡢ࡜ࡍࡿ㸬ࡲࡓࢲࢵࢩࣗグྕࢆ┬␎ࡍࡿ㸬ྛቃ⏺࡟࠾ࡅࡿ᮲௳ࡣ௨ୗࡢࡼ࠺࡟࡞ࡿ㸬D ⮬⏤⾲㠃wIwn*I(11)

規則波中における浮体型振り子発電装置のエネルギー変換性能に関する研究73

E Ỉᗏ
wI
wn0(12)ª X dz Z dx 4h ­dxdz ½º
i* «®( x  x0 )  ( z  z0 ) ¾»
dsds ¿¼¬ 9 0 ds 9 0 ds 9 0 ¯(13)F ≀య⾲㠃wIwnG ቃ⏺ $%

I (l, z) ª¬eiOl  Kr eiOl º¼ A(O z)(14)wI(l , z) iO ª¬eiOl  Kr eiOl º¼ A(O z)
wn

(15)

I (l ', z ) Kt eiOl ' A(O z )(16)wI(lc, z) iO Kt eiOl c A(O z)
wn

(17)

H ቃ⏺ $’%’

ቃ⏺ &(66’࡟࠾࠸࡚ࡣቃ⏺࡟࠾࠸࡚ I ࠾ࡼࡧ wI wn ࡀ➼ࡋ࠸࡜ࡍࡿ㸬(11)㹼(17)࡟࠾࠸࡚

cos hO ( z  1)
, Ocosh OA(O z )kh, *=V 2h(18)g࡛࠶ࡿ㸬ࡲࡓ㸪 n ࡣἲ⥺᪉ྥࡢ༢఩࣋ࢡࢺࣝࢆ⾲ࡍ㸬 ቃ⏺✚ศ᪉⛬ᘧ4࣭2ቃ⏺ࢆ 1 ಶࡢᚤᑠ࡞⥺せ⣲࡟ศ๭ࡋ㸪せ⣲ j j 1,.., N ࡢ୰Ⅼࡢᗙᶆࢆ [ j , K j 㸪せ⣲㛗ࡉࢆ 's j ࡜ࡍࡿ㸬ࡲࡓ
I [ j ,K j ࠾ࡼࡧࡑࡢᚤศ I j
I [ j ,K j ࡣࢢ࣮ࣜࣥࡢἲ๎ࢆ‶㊊ࡍ
せ⣲ j ࡟࠾ࡅࡿ㏿ᗘ࣏ࢸࣥࢩࣕࣝࢆ I jࡿ㸬Nª Fij  I ( j )  Eij  I ( j ) º 0 ,¦¬¼
j 1

(i 1 ~ N )(19)

G ij  Eij , (for region-1, region-3)½°°
G ij  Eij , (for region-2)°°
11w
log Rij ds , Eijlog Rij ds ¾°
S 'SijS 'Sij wn°
1/2°ª([ j  [i )2  (K j  Ki ) 2 º°¿¬¼FijFij³EijRij(20)³ࡇࡇ࡛ G ij ࡣࢡࣟࢿࢵ࣮࢝ࡢࢹࣝࢱグྕ࡛࠶ࡿ㸬4࣭3 㐠ື᪉⛬ᘧࣁ࣑ࣝࢺࣥࡢཎ⌮ࢆ⏝࠸࡚᣺ࡾᏊᘧἼຊⓎ㟁⿦⨨ࡢ㐠ື᪉⛬ᘧࢆᑟฟࡍࡿ㸬㐠ື࢚ࢿࣝࢠ࣮ࢆ T 㸪࣏ࢸࣥࢩࣕ
࢚ࣝࢿࣝࢠ࣮ࢆ W ࡜࠾ࡃ࡜㸪㐠ື᪉⛬ᘧࡣḟᘧࡢࡼ࠺࡟⾲⌧࡛ࡁࡿ㸬
G ª ³ T  W dt º  ³tb«¬ t a»¼

tbta^F G[  F GK  T GT  P G[  P GK  T GT  T G\  c \G\  P GK  T GT `dt 0mxmzmTw
xw
zw

Tw

\pszsT(21)ࡇࡇ࡛ G ࡣኚศ㸪 PxW 㸪 PzW ࡣ≀య࡟స⏝ࡍࡿỈᖹ࠾ࡼࡧ㖄┤᪉ྥࡢὶయຊ㸪 TTW ࡣ≀య㔜ᚰ࿘ࡾࡢ࣮࣓ࣔࣥࢺࢆ♧ࡍ㸬 Pzs 㸪 TTs ࡣ㟼ᅽ࡟ࡼࡿ᚟ཎຊ࠾ࡼࡧ᚟ཎ࣮࣓ࣔࣥࢺࢆ♧ࡍ㸬 Fxm 㸪 Fzm ࡣỈᖹ࠾ࡼࡧ㖄┤᪉ྥࡢಀ␃ຊ㸪 TTmࡣ㔜ᚰࡲࢃࡾࡢಀ␃࣮࣓ࣔࣥࢺࢆ♧ࡍ㸬 T\m ࡣ᣺ࡾᏊ㔜ᚰࡲࢃࡾࡢ࣮࣓ࣔࣥࢺ㸪 c p ࡣῶ⾶ಀᩘࢆ♧ࡍ㸬᣺ࡾᏊࡢ㔜ᚰᗙᶆ x pG , , y pG ࡣḟᘧ࡛⾲ࡉࢀࡿ㸬

74

今井康貴 , 永田修一 , 豊田和隆 , 村上天元 , 瀬戸口俊明

xPG

lx p  [  ( z p  z0 )T  p sin\ , zPG2

lz p  K  ( x p  x0 )T  p cos\2(22)l p ࡣ᣺ࡾᏊࡢ㛗ࡉ࡛࠶ࡿ㸬㐠ື࢚ࢿࣝࢠ࣮ T ࠾ࡼࡧ࣏ࢸࣥࢩ࢚ࣕࣝࢿࣝࢠ࣮ W ࡣලయⓗ࡟ࡣḟᘧࡢࡼ࠺࡟グ㏙࡛ࡁࡿ㸬l p21111( M 1  M 2 )([ 2  K 2 )  I1T 2  I 2\ 2  M 2 ª¬^( x p  x0 ) 2  ( z p  z0 ) 2 `T 2  \ 2  2 ( x p  x0 )KT  ( z p  z0 )[T22224
l p ^( x p  x0 )sin\  ( z p  z0 )cos\ `T\ l p\ ([ cos\  K sin\ ) º¼^

TW

M 2 gl p (1  cos\ )

`(23)

(24)

M 1 ࡣⓎ㟁ᾋయࡢ㉁㔞㸦᣺ࡾᏊ㉁㔞ࢆ㝖ࡃ㸧
㸪I1 ࡣⓎ㟁ᾋయࡢ㔜ᚰࡲࢃࡾࡢ័ᛶ࣮࣓ࣔࣥࢺ㸪M 2 ࡣ᣺ࡾᏊࡢ㉁㔞㸪
I 2 ࡣ᣺ࡾᏊࡢ㔜ᚰ࿘ࡾࡢ័ᛶ࣮࣓ࣔࣥࢺࢆ♧ࡍ㸬

ᅗ 9 ࡟♧ࡍࡼ࠺࡟ᾋయࡣ n* ᮏࡢಀ␃⣴࡛ಀ␃ࡉࢀࡿ࡜ࡍࡿ㸬 k ␒┠ࡢಀ␃⥺ࡢ୧➃ᗙᶆࢆ Dk ak , bk ࠾ࡼࡧ
Ek ck , d k ࡜ࡍࡿ㸬ࡲࡓ k ␒┠ࡢಀ␃⣴ࡢࣂࢿᐃᩘࢆ K k 㸪㛗ࡉࢆ mk 㸪ึᮇᙇຊࢆ f k 㸪Ỉᖹ࠿ࡽࡢゅᗘࢆ H k ࡜࠾ࡃ㸬ಀ␃ຊࡣḟᘧ࡛⾲ࡉࢀࡿ㸬
n*

½n*°°

 K xx( k )[  K xz( k )K  K x(Tk )T °¦°k 1FxmFzm¦  K zx(k )[  K zz(k )K  K z(Tk )T ¾

TTm

(k )
KT( kx)[  KT( kz )K  KTTT¦
k 1

k 1n*(25)°°°°¿ࡇࡇ࡛㸪

K k  f k cos2 H k  f k½°°
K xz( k ) K zx( k ) K k  f k cos H k sin H k°°
K x(Tk ) KT( kx) K k  f k Sk cos2 H k  f k z0  bk°°
K zz( k ) K k  f k sin 2 H k  f k°
¾K z(Tk ) KT( kz ) K k Sk  f k z0  bk cos H k sin H k  f k x0  ak cos 2 H k °°(k )KTTSk K k Sk  f k z0  bk cos 2 H k  f k Sk x0  ak cos H k sin H k °°° f k x 0 ck z0  bk tan H k  x0  ak  f k Sk z0  bk°°
Sk bk  z0  (ak  x0 ) tan H k f k F0k / mk¿K xx( k )^^`^

`

(26)

`ືᅽ࡟ࡼࡿὶయຊࡣḟᘧ࡛⾲ࡉࢀࡿ㸬

Pxw
Pzw
w

TTT\w

½°°°
i U g9 0 ª« I dx  I dx º» eiV t°°
C2¬ C1¼¾i U g9 0 ª« ³C I ^( x  x0 )dx  z  z0 dz`  ³C I ^( x  x0 )dx  z  z0 dz`º» eiV t °°2
¬ 1¼°
i U g9 0 «ª ³C I ( x  x p )dx  z  z p dz  ³C I ( x  x p )dx  z  z p dz »º eiV t °2¬ 1¼¿°i U g9 0 ª« ³ I dz  ³ I dz º» eiV t¬ C1³C2¼³^

`

^

(27)

`C1 ࡣ㡿ᇦ 1 ࠾ࡼࡧ 3 ࡢ࿘ᅖቃ⏺㸪 C2 ࡣ㡿ᇦ 2 ࡢ࿘ᅖቃ⏺ࢆ♧ࡍ㸬᚟ཎຊ Pzs ࠾ࡼࡧ᚟ཎ࣮࣓ࣔࣥࢺ TTs ࡣḟᘧ࡛⾲ࡉࢀࡿ㸬PzsTTs
ࡇࡇ࡛ U g l1Z  I14 eiV t½°¾
 U g ª¬ I1Z  I11  I 2 4º¼ eiV t °¿(28)

規則波中における浮体型振り子発電装置のエネルギー変換性能に関する研究75½³C ( x  x0 )dx , l1 ³C dx°¾I11 ³ ( x  x0 )2 dx , I 2 ( zb  z0 ) SV °C¿

I1ss(29)s㧗ḟ㡯ࢆ↓どࡍࡿ࡜㸪(21)࠿ࡽ㐠ື᪉⛬ᘧࡀᚓࡽࢀࡿ㸬1M1  M 2 [  M 2 z p  z0 T  M 2l p\2

M1  M 2 K  M 2 x p  x0 T^`MªM 2  z p  z0 [  x p  x0 K  « I1  22¬(30)

Pxw  Fxm

Pzw  Pzs  Fzm(31)^ x  x  z  z `º»¼T  12 M l z  z \ T  T  T
220pw0p2 p

^p

T0

`

11§2·
¨ I 2  M 2l p ¸\  M 2l p [  z p  z0 T  c p\42©
¹sTm

TT\(32)(33)(25)㹼(29)ࢆ(30)㹼(33)࡟௦ධࡋ㐃❧ࡉࡏ࡚ゎࡁ㸪ᾋయ㐠ື㸪᣺ࡾᏊ㐠ື㸪ྛせ⣲ࡢ㏿ᗘ࣏ࢸࣥࢩࣕࣝ࠾ࡼࡧࡑࡢ
ᚤศ್ࡀồࡲࡿ㸬ୖᘧ࠿ࡽồࡵࡓ᣺ࡾᏊࡢ㐠ື᣺ᖜࢆ⏝࠸࡚᣺ࡾᏊࡢ㐠ື࢚ࢿࣝࢠ࣮ࡣḟᘧ࡛⾲ࡉࢀࡿ

1 Tc \ 2 (t )dt
T ³0 pEp

1c V 2< 22 p

(34)ධᑕἼ࢚ࢿࣝࢠ࣮ࡣḟᘧ࡛⾲ࡉࢀࡿ㸬

Ein

S2kT

22kh ·§§H·¸ U g ¨1 sinh 2kh ¸¹© 2¹©

B¨(35)

ࡇࢀ࠿ࡽ㸪୍ḟኚ᥮ຠ⋡ࡣḟᘧ࡛⾲ࡉࢀࡿ㸬K1

Ep(36)

Ein

4࣭4 ᐇ㦂⤖ᯝ࡜ࡢẚ㍑
ୖグ᪉ἲࡢጇᙜᛶࢆ♧ࡍࡓࡵ㸪)3:(& ᶍᆺࡢィ⟬ࢆ⾜࠸㸪ィ⟬⤖ᯝࢆỈᵴᐇ㦂⤖ᯝ࡜ẚ㍑ࡋࡓ㸬





Fig.10 Comparison of calculated results andexperimental results (New model)

Fig.11 Comparison of calculated results andexperimental results (New model)

P=0.65m, R=100Ȑ᮲௳᫬࡟࠾ࡅࡿ᪂ᆺᶍᆺࡢ๓ᚋᦂ㸪ୖୗᦂ㸪⦪ᦂࡢ㐠ື᣺ᖜ㸪୍ḟኚ᥮ຠ⋡ࢆ Fig.10 ࡟♧ࡍ㸬ᪧᆺᶍᆺ࡛ྠ᮲௳ࡢሙྜࢆ Fig.11 ࡟♧ࡍ㸬㐠ື࠾ࡼࡧ୍ḟኚ᥮ຠ⋡ࡢィ⟬⤖ᯝࡣᐇ㦂⤖ᯝ࡟ࡼࡃྜ⮴ࡍࡿ⤖ᯝࡀᚓࡽࢀࡓ㸬

76

今井康貴 , 永田修一 , 豊田和隆 , 村上天元 , 瀬戸口俊明

5. ⤖   ㄒᮏㄽᩥ࡛ࡣ㸪ࣉ࣮࣮ࣜ㸪࣋ࣝࢺ࠾ࡼࡧⓎ㟁ᶵ࠿ࡽᵓᡂࡉࢀࡿ PTO ࢩࢫࢸ࣒ࢆࡶࡘ FPWEC ࡢⓎ㟁ຠ⋡ࢆホ౯ࡍࡿࡓࡵ࡟㸪஧ḟඖỈᵴ࡟࠾ࡅࡿつ๎Ἴ୰Ⓨ㟁ᐇ㦂ࢆ⾜࡞ࡗࡓ㸬Ⓨ㟁ᐇ㦂࠾ࡼࡧ᣺ࡾᏊࡢ✵Ẽ୰⮬⏤᣺ືᐇ㦂࠿ࡽ㸪ἼຊⓎ㟁⿦⨨ࡢ୍ḟኚ᥮ຠ⋡㸪஧ḟኚ᥮ຠ⋡㸪Ⓨ㟁ຠ⋡ࢆᚓࡓ㸬ࡉࡽ࡟㸪ᮏ⿦⨨ࡢ୍ḟኚ᥮ຠ⋡࠾ࡼࡧ㐠ືࢆホ౯ࡍࡿࡓࡵ࡟ቃ⏺せ⣲ἲࢆ⏝࠸ࡓᩘ್ゎᯒࣉࣟࢢ࣒ࣛࢆ㛤Ⓨࡋࡓ㸬୍ḟኚ᥮ຠ⋡࠾ࡼࡧ㐠ືࡢィ⟬⤖ᯝ࡜ᐇ㦂⤖ᯝࢆẚ㍑ࡍࡿࡇ࡜࡟ࡼࡗ࡚㸪ࣉࣟࢢ࣒ࣛࡢጇᙜᛶࢆ♧ࡋࡓ㸬ㅰ   ㎡ᮏ◊✲ࢆ୰ᚰ࡟࡞ࡗ࡚㐍ࡵ࡚ࡁࡓඹⴭ⪅ࡢ㇏⏣࿴㝯෸ᩍᤵࡣ⑓Ẽࡢࡓࡵ 2012 ᖺ 9 ᭶࡟௚⏺ࡉࢀࡓ㸬⏕๓ࡢࡈຌ⦼ࢆംࡧ㸪ࡈෞ⚟ࢆ࠾♳ࡾ⏦ࡋୖࡆࡲࡍ㸬ᩥ   ⊩(1) Watabe, T, Kondo, H, Shirai, H, and Seino, K, (1994). “Remodelling of Muroran Wave Test Plant”, Proc 4th Int Offshore andPolar Eng Conf, Osaka, ISOPE, Vol I.
(2) Watabe, T. (2008) Utilization of the Ocean Wave Energy, FUJI Print Press(3) Toyota, K, Nagata, S, Imai, Y, Ono, K, and Setoguchi, T, (2011), “Energy Conversion Characteristics on Floating Type
Pendulum Wave Energy Converter in Regular Waves”, Proc 21st Int Offshore and Polar Eng Conf, Maui, ISOPE, pp675-679.
(4) Park, J.Y, Shin, S.H, Hong, K.Y, and Kim, S.H, (2012), “A Study on the Wave Response and Efficiency of a Pendulum Wave
Energy Converter”, Proc 22nd Int Offshore and Polar Eng Conf, Rhodes, ISOPE, pp 601-606.
(5) Nam, B.W, Hong, S.Y, Shin, S.H, Hong S.W, and Kim, K.B, (2012a), “Prediction of the Hydrodynamic Performance of the
Floating Pendulum Wave Energy Converter in Regular and Irregular Waves”, Proc 22nd Int Offshore and Polar Eng Conf,Rhodes, ISOPE, pp 607-612.
(6) Nam, B.W, Hong, S.Y, and Shin, S.H, (2012b), “A Study on Wave-induced Motion of Floating Pendulum Wave EnergyConverter”, Asian Wave and Tidal Conference Series, AWTEC, pp 124-128.
(7) Ijima, T, Yoshida, A, and Yamamoto, T (1977). “Two-Dimensional Motions of Moored Floating Bodies with Arbitrary
Cross-Section,” Memoirs of Faculty of Engineering, Kyushu University, Vol.37, No.3, pp 107-132.