ＯＴＥＣVol. 18 (2013)，77〜82

水素吸蔵合金の充填状態の計算（離散要素法による接触距離変更モデル）77Ỉ⣲྾ⶶྜ㔠ࡢ඘ሸ≧ែࡢィ⟬㸦㞳ᩓせ⣲ἲ࡟ࡼࡿ᥋ゐ㊥㞳ኚ᭦ࣔࢹࣝ㸧
ᯇୗᨻ⿱*1㸪㛛ฟᨻ๎*1㸪ගṊ㞝୍*2Analysis of Metal Hydride Packed-Bed
㸦Contact Diameter Change Model by Discrete Element Method㸧
Masahiro MATSUSHITA*1, Masanori MONDE and Yuichi MITSUTAKE*1

Institute of Ocean Energy, Saga University
Honjo-machi 1, Saga, 840-8502 JapanWe analyzed the metal hydride packed-bed by discrete element method (DEM). Some analyses carried out byRosin-Rammler distribution particles. In order to simulate the void fraction beyond 60% obtained by experiment, weare trying to develop van der Waals force model and contact diameter change model. Simulation results were close to
the experimental results by using intermediate contact diameter between the circumscribed circle diameter and the meanarea diameter.
Key Words : Atomization, Discrete element method, Energy storage, Hydrogen energy, Metal hydride, Packed bed,

1. ⥴   ゝỈ⣲྾ⶶྜ㔠ࢆ౑⏝ࡋࡓỈ⣲㈓ⶶ᪉ἲࡣ㸪Ᏻ඲ᛶࢆ㔜どࡋࡓ⏝㏵࡛᭷ᮃどࡉࢀ࡚࠸ࡿ㸬௒ᚋ㸪Ỉ⣲྾ⶶྜ㔠ࢆᐇ⏝ᬑཬࡋ࡚࠸ࡃࡓࡵ࡟ࡣ㸪タィィ⟬࡞࡝࡟౑⏝࡛ࡁࡿᇶᮏⓗ࡞≉ᛶࢆヲ⣽࡟ㄪ࡭ࡿࡇ࡜ࡀᚲせ࡛࠶ࡿ(1)㸬≉࡟㸪ఏ⇕≉ᛶࢆ⟬ฟࡍࡿୖ࡛㸪⢊యᒙࡢ඘ሸ≧ែࢆṇࡋࡃホ౯ࡍࡿࡇ࡜ࡀᚲせ࡛࠶ࡿ㸬ࡑࡇ࡛㸪ⴭ⪅ࡽࡣ㸪ࡇࢀࡲ࡛Ỉ⣲྾ⶶྜ㔠ࡀỈ⣲ࢆ྾ⶶᨺฟࡍࡿ㝿ࡢ඘ሸᒙࢆ┤᥋ྍど໬ࡍࡿᐇ㦂(2)~(4)ࢆ⾜࠸㸪✵㝽⋡ࡢኚ໬ࢆヲ⣽࡟ㄪ࡭ࡓ㸬ࡉࡽ࡟㸪ࡑࡢᐇ㦂⤖ᯝ࠿ࡽ✵㝽⋡ࡢᐇ㦂ᘧ(5)ࢆᵓ⠏ࡋ㸪Ỉ⣲྾ⶶྜ㔠ࡢ᭷ຠ⇕ఏᑟ⋡ࡢィ⟬(6)ࢆ⾜ࡗࡓ㸬ྍど໬ᐇ㦂ࡢ⤖ᯝ࡛ࡣ㸪Ỉ⣲྾ⶶྜ㔠ࡢ඘ሸᒙࡣ㸪Ỉ⣲྾ⶶᨺฟࢆ⧞ࡾ㏉ࡍࡇ࡜࡛㸪⢏Ꮚࡀᔂቯࡋ㸪㧗ᐦᗘ࡟ࡣ඘ሸ࡛ࡁ࡞࠸⢏Ꮚᒙ࡟࡞ࡿࡇ࡜ࡀศ࠿ࡗࡓ㸬ᚑࡗ࡚㸪ࡇࡢ඘ሸᒙࡢ⭾ᙇ㸪཰⦰㸪ᔂቯࢆྵࡵ࡚㸪඘ሸ≧ែࢆゎᯒ࡟ࡼࡗ࡚⟬ฟࡍࡿࡇ࡜ࡶᚲせ࡛࠶ࡿ㸬ࡑࡇ࡛㸪๓ሗ(7)࡛ࡣ㸪㞳ᩓせ⣲ἲ(8),(9)㸦Discrete element method, DEM㸧ࢆ౑⏝ࡋ㸪Ỉ⣲྾ⶶྜ㔠ࡢ඘ሸ≧ែࡢゎᯒ⤖ᯝ࡟ࡘ࠸࡚ሗ࿌ࡋࡓ㸬⤖ᯝࡣ㸪⢏Ꮚࢆ⌫ᙧ࡜ࡋ࡚ᢅࡗࡓሙྜ㸪ᐇ㦂࡟ᇶ࡙ࡃ⢏Ꮚᚄศᕸࡔࡅࢆ୚࠼࡚ィ⟬ࡋ࡚ࡶ㸪ᐇ㦂࡜ࡣ␗࡞ࡿ✵㝽⋡࡜࡞ࡗࡓ㸬ࡉࡽ࡟㸪⢏Ꮚ㛫ࡢࣇ࢓ࣥࢹ࣮ࣝ࣡ࣝࢫຊࢆ㔜ຊ࡜ࡢẚ࡜ࡋ࡚୚࠼ࡿࣔࢹࣝࢆᵓ⠏ࡋ㸪ᐇ㝿ࡼࡾ኱ࡁ࡞⢏Ꮚࡢゎᯒ࡟࠾࠸࡚ࡶ௜╔ຊࡢᙳ㡪ࢆ⪃៖࡛ࡁࡿࡼ࠺࡞ゎᯒࢆ⾜ࡗࡓ㸬ࡋ࠿ࡋ㸪௜╔ຊࡢࡳࡢᙳ㡪࡛ࡣᐇ㦂࡛ᚓࡽࢀࡓࡼ࠺࡞኱ࡁ࡞✵㝽⋡ࡢゎᯒ⤖ᯝࢆᚓࡿࡇ࡜ࡣ࡛ࡁ࡞࠿ࡗࡓ㸬ࡉࡽ࡟㸪እ᥋෇ᚄ࡜㠃✚┦ᙜᚄࢆ౑⏝ࡋ࡚㸪⢏Ꮚ㛫ࡢ᥋ゐ㊥㞳ࢆಶู࡟୚࠼ࡿࣔࢹࣝࢆᵓ⠏ࡋ㸪኱ࡁ࡞✵㝽⋡ࡢゎᯒ⤖ᯝ࡟࡞ࡿࡇ࡜ࢆ☜ㄆࡋࡓ㸬ᮏㄽᩥ࡛ࡣ㸪๓ሗ࡛♧ࡋࡓ⢏Ꮚ㛫ࡢ᥋ゐ㊥㞳ࢆኚ࠼ࡿࣔࢹࣝࢆᨵⰋࡋ㸪ྍど໬ᐇ㦂࡛ᚓࡽࢀࡓ 60㸣ࢆ㉸࠼ࡿࡼ࠺࡞኱ࡁ࡞✵㝽⋡ࡢ඘ሸ≧ែࢆィ⟬ࡍࡿࡓࡵࡢゎᯒ᪉ἲࡢ᳨ウࢆ⾜ࡗࡓࡢ࡛㸪ࡑࡢ⤖ᯝࢆሗ࿌ࡍࡿ㸬ゎᯒࡣ㸪㞳ᩓせ⣲ἲ㸦DEM㸧ࢆ౑⏝ࡋ㸪ᐇ㦂࠿ࡽᚓࡽࢀࡓ⢏Ꮚᚄศᕸࢆ౑⏝ࡋ࡚⾜ࡗࡓ㸬⢏Ꮚ㛫ࡢ᥋ゐ㊥㞳ࡣ㸪㸦1㸧ࡍ࡭࡚ࡢ⢏Ꮚ࡟୍ᐃ್ࢆ୚࠼ࡿ᪉ἲ㸪
㸦2㸧஘ᩘ࡟ࡼࡾྛ⢏Ꮚ࡟୍ᐃ್ࢆ୚࠼ࡿ᪉ἲ㸪㸦3㸧⢏Ꮚ㛫᥋ゐࡈ࡜࡟஘ᩘ࡟ࡼࡗ*ཎ✏ཷ௜ 2013 ᖺ 7 ᭶ 31 ᪥
బ㈡኱Ꮫ ᾏὒ࢚ࢿࣝࢠ࣮◊✲ࢭࣥࢱ࣮㸦ࠛ840-8502 బ㈡┴బ㈡ᕷᮏᗉ⏫㸯㸧
*2బ㈡኱Ꮫ኱Ꮫ㝔 ᕤᏛ⣔◊✲⛉ ᶵᲔࢩࢫࢸ࣒ᑓᨷ
E-mail: matusita@ioes.saga-u.ac.jp*1

78

松下政裕，門出政則，光武雄一

࡚ಶู࡟୚࠼ࡿ᪉ἲࡢ 3 ✀㢮ࡢ᪉ἲ࡛タᐃࡋ㸪Ỉ⣲྾ⶶྜ㔠ࡢ඘ሸ≧ែࡢゎᯒࢆ⾜ࡗࡓ㸬ゎᯒ⤖ᯝࡣ㸪ྍど໬ᐇ㦂࡛ᚓࡽࢀ඘ሸ≧ែ࡜ẚ㍑ࡋ࡚ሗ࿌ࢆ⾜࠺㸬

2. 㞳ᩓせ⣲ἲࢩ࣑࣮ࣗࣞࢩࣙࣥ
2࣭1 ᇶ♏ᘧ࠾ࡼࡧᗙᶆ⣔㞳ᩓせ⣲ἲ㸦DEM㸧࡛ࡣ㸪ಶࠎࡢ⢏Ꮚ㛫ࡢ᥋ゐຊࢆᅗ㸯࡟♧ࡍࡼ࠺࡞ࣇ࢛࣮ࢡࢺࣔࢹ࡛ࣝ⾲⌧ࡍࡿ㸬㞳ᩓせ⣲ἲ࡟࠾ࡅࡿຊ࡜࣮࣓ࣔࣥࢺࡢᇶ♏ᘧࢆ௨ୗ࡟♧ࡍ㸬==−==−−(1)+(2)−ȞnKnKsࡇࡇ࡛㸪㹫ࡣ⢏Ꮚࡢ㉁㔞㸪u ࡣ୪㐍ኚ఩㸪Ȟࡣࢲࢵࢩ࣏ࣗࢵࢺ

Slider⢓ᛶಀᩘ㸪K ࡣࣂࢿᙎᛶᐃᩘ㸪Fg ࡣ㔜ຊ㸪I ࡣ័ᛶ࣮࣓ࣔࣥࢺ㸪ȯࡣᅇ㌿ኚ఩㸪r ࡣ⢏Ꮚ༙ᚄ࡛࠶ࡿ㸬ゎᯒ᪉ἲࡢヲ⣽ࡣ๓ሗ(7)࡛ሗȞs࿌ࡋ࡚࠸ࡿࡢ࡛㸪ࡇࡇ࡛ࡣ┬␎ࡍࡿ㸬

Fig.1 Voigt
i model2࣭2 ィ⟬᮲௳ィ⟬ࡣỈ⣲྾ⶶྜ㔠㸦LaNi5㸧ࡢྍど໬ᐇ㦂⤖ᯝ(3)~(5)࡟ྜࢃࡏࡓ᮲௳࡛⾜ࡗࡓ㸬ᐜჾࡣෆᚄȭ27 mm ࡢ෇⟄ᆺࡢ࢞ࣛࢫ⎼࡛࠶ࡾ㸪Ỉ⣲྾ⶶྜ㔠ࡢ඘ሸ㔞ࡣ 50 g ࡛࠶ࡿ㸬ᐇ㝿ࡢ⢏Ꮚ࡛ࡣᩘ༑൨ಶࡢ⢏Ꮚ࡜࡞ࡾゎᯒࡣᅔ㞴࡛࠶ࡿࡓࡵ㸪⢏Ꮚಸ⋡ 200 ಸࡢ኱ࡁ࡞⢏Ꮚ࡜ࡋ࡚ゎᯒࢆ⾜ࡗࡓ㸬⾲ 1 ࡟ゎᯒࢆ⾜ࡗࡓ⢏Ꮚࡢタᐃ್ࢆ♧ࡍ㸬⢏Ꮚᚄศᕸࡣᐇ㦂⤖ᯝࢆࡶ࡜࡟ Rosin-Rammler ศᕸ࡛㏆ఝࡋࡓศᕸࢆ୚࠼࡚࠸ࡿ㸬Ỉ⣲྾ⶶᨺฟࢆ 5㸪10㸪50 ᅇ⧞ࡾ㏉ࡋࡓ᫬ࡢ⢏Ꮚᚄศᕸ࡟ᑐࡋゎᯒࢆ⾜ࡗࡓ㸬࡞࠾㸪ᐇ㦂⤖ᯝ࡛ࡣ⢏Ꮚᚄศᕸࡣ 15 ᅇࡢ⧞ࡾ㏉ࡋ௨㝆ࡣ࡯࡜ࢇ࡝ኚ໬ࡋ࡚
࠸࡞࠸ࡢ࡛㸪50 ᅇࡢ⤖ᯝ㸦RR-50㸧ࡀ 15 ᅇ௨㝆ࡢ⤖ᯝ࡛࠶ࡿ࡜⪃࠼࡚࠸ࡿ㸬Rosin-Rammler ศᕸࡣ௨ୗࡢᘧ࡛⾲ࡉࢀࡿ㸬= 1 − exp −(3)ࡲࡓ㸪ࣖࣥࢢ⋡㸪࣏࢔ࢯࣥẚ㸪ᦶ᧿ಀᩘࡀධຊ್࡜ࡋ࡚ᚲせ࡛࠶ࡿࡀ㸪Ỉ⣲྾ⶶྜ㔠 LaNi5 ࡢ≀ᛶ್ࡣධᡭ࡛
ࡁ࡞࠿ࡗࡓࡓࡵ㸪ࢽࢵࢣࣝࡢ್ཬࡧᦶ᧿࡟㛵ࡋ࡚ࡣࢽࢵࢣࣝ࡜࢞ࣛࢫࡢ್ࢆ౑⏝ࡋࡓ㸬
⾲ 2 ࡟౑⏝ࡋࡓ್ࢆ♧ࡍ㸬
2࣭3 ௜╔ຊࣔࢹࣝ๓ሗ࡜ྠᵝ࡟㸪⢏Ꮚ㛫௜╔ຊ࡜ࡋ࡚ࣇ࢓ࣥࢹ࣮ࣝ࣡ࣝ

Table 2 Setting valueࢫຊࢆ⪃៖ࡍࡿࣔࢹࣝࢆᑟධࡋࡓ㸬ࡇࡇ࡛ࡣ㸪኱ࡁ࡞⢏Ꮚᚄ࡜ࡋ࡚ィ⟬ࡋ࡚࠸ࡿࡓࡵ㸪㔜ຊ࡜ࡢẚ࡜ࡋ࡚ಀᩘࢆ
୚࠼ࡿࣔࢹࣝࢆ౑⏝ࡋࡓ㸬Young's modulus
Poisson's ratio
Friction coefficient
NickelNickel2.01011Pa
0.3

Glass
6.01010Pa
0.23

0.7

0.7

Table 1 Calculation particles
Name
RR-05
RR-10
RR-50

Cycle
number

De

51050

12.99
9.93
8.03

nTime

NumberMean number
diameter

Minimum
diameter

Maximum
diameter

Mean Wardell's
sphericity

1.25
1.25
1.25

200
200200310571
1,002

2.323 mm1.858 mm1.525 mm0.050 mm0.050 mm0.050 mm

7.350 mm
6.750 mm
6.150 mm

0.739
0.732
0.730水素吸蔵合金の充填状態の計算（離散要素法による接触距離変更モデル）

79=(4)

ࡇࡇ࡛㸪Fvw㸸ࣇ࢓ࣥࢹ࣮ࣝ࣡ࣝࢫຊ㸪Cvw㸸㔜ຊẚಀᩘ㸪Fg㸸㔜ຊ࡛࠶ࡿ㸬๓ሗࡢ⤖ᯝ࡜ࡋ࡚㸪௜╔ຊࣔࢹࣝࡢᑟධࡔࡅ࡛ࡣᐇ㦂⤖ᯝࡢࡼ࠺࡞኱ࡁ࡞✵㝽⋡ࡢ⤖ᯝࡣᚓࡽࢀ࡞࠿ࡗࡓ㸬ࡲ㸪௜╔ຊ࠶ࡾ
ࡓ㸪ಀᩘ Cvw ࢆ࠸ࡃࡘ࡟ࡍࡿࡇ࡜ࡀࡩࡉࢃࡋ࠸࠿ࡶࢃ࠿ࡗ࡚࠸࡞࠸㸬௒ᅇࡣ㸪௜╔ຊ࡞ࡋ㸦Cvw㸻0㸧㸦Cvw㸻10-5㸧ࡢ 2 ✀㢮ࡢタᐃ࡛ࡢゎᯒࢆ⾜ࡗࡓ㸬2࣭࣭4 ᥋ゐ㊥㞳ኚ᭦ࣔࢹࣝᐇ㦂⤖ᯝࡢࡼ࠺࡞኱ࡁ࡞✵㝽⋡࡜࡞ࡿࡼ࠺࡞ィ⟬⤖ᯝࢆᚓࡿࡓࡵ࡟ࡣ㸪」㞧࡞⢏Ꮚᙧ≧ࡢ⢏Ꮚ࡟ᑐࡍࡿィ⟬ࡀᚲせ࡛࠶ࡿ㸬ࡋ࠿ࡋ㸪ࡑࡢࡼ࠺࡞ィ⟬ࡣ㸪ィ⟬᫬㛫ࡀ⭾኱࡟࡞ࡾ⌧ᐇⓗ࡛ࡣ࡞࠸㸬ࡑࡇ࡛㸪ᇶᮏⓗ࡟ࡣ⢏Ꮚࢆ⌫ᙧ࡜ࡋ࡚ᢅ࠸㸪୺࡞ィ⟬ࡣ㠃✚┦ᙜᚄ RA ࢆ౑⏝ࡋ㸪⢏Ꮚ㛫ࡢ᥋ゐ࡟㛵ࡍࡿィ⟬࡛ࡣ㸪እ᥋෇ᚄ RC ࡜㠃✚┦ᙜᚄRA ࡢ୰㛫ⓗ࡞᥋ゐ㊥㞳 RB ࢆタᐃࡋ㸪ィ⟬ࢆ⾜࠺ࣔࢹࣝࢆ౑⏝ࡋࡓ㸬እ᥋෇ᚄࡣ㸪ᐇ㦂࠿ࡽᚓࡽࢀࡓ࣮࣡ࢹࣝࡢ⌫ᙧᗘȯw ࢆࡶ࡜࡟タᐃࡋࡓ㸬࣮࣡ࢹࣝࡢ⌫ᙧᗘࡣ௨ୗࡢᘧ࡛⾲ࡉࢀࡿ㸬
=(5)

๓㏙ࡢ⾲ 1 ࡟ࡣᐇ㦂࡛ᚓࡽࢀࡓ࣮࣡ࢹࣝ⌫ᙧᗘࡢᖹᆒ್ࡶ♧ࡋ࡚࠸ࡿ㸬㸦1㸧ࡍ࡭࡚ࡢ⢏Ꮚ࡟୍ᐃ್ࢆ୚࠼ࡿ᪉ἲ㸪
㸦2㸧஘ᩘ࡟ࡼࡾྛ⢏Ꮚ࡟୍ᐃ್ࢆ୚࠼ࡿ
᥋ゐ㊥㞳 RB ࡢタᐃ᪉ἲࡣ㸪᪉ἲ㸪㸦3㸧⢏Ꮚ㛫᥋ゐࡈ࡜࡟஘ᩘ࡟ࡼࡗ࡚ಶู࡟୚࠼ࡿ᪉ἲࡢ 3 ✀㢮ࢆ౑⏝ࡋࡓ㸬=+×(−)(6)

ࡇࡇ࡛㸪Cr ࡣ᥋ゐ㊥㞳ಀᩘ࡛࠶ࡾ㸪Cr=1.0 ࡢ࡜ࡁ㸪⢏Ꮚࡣእ᥋෇ᚄ࡛᥋ゐࡋ㸪Cr=0.0 ࡢ࡜ࡁ㸪⢏Ꮚࡣ㠃✚┦ᙜᚄ࡛᥋ゐࡍࡿࡇ࡜ࢆព࿡ࡍࡿ㸬ᅗ 2㸪3 ࡀ஘ᩘタᐃࡋࡓሙྜࡢ᥋ゐ㊥㞳ಀᩘ Cr ࡢ୍౛࡛࠶ࡿ㸬ᅗ 2 ࡣ㸪
㸦2㸧஘ᩘ࡟ࡼࡾྛ⢏Ꮚ࡟୍ᐃ್ࢆ୚࠼ࡿ᪉ἲ࡛㸪ྛ⢏Ꮚࡣ஘ᩘ࡛タᐃࡉࢀࡓ୍ᐃࡢ᥋ゐ㊥㞳࡛ᖖ࡟௚ࡢ⢏Ꮚ࡜᥋ゐࡋ࡚࠸ࡿ࡜ࡋࡓሙྜࡢ⢏Ꮚࡢ᥋ゐ㊥㞳ಀᩘࡢ౛ࢆ⾲ࡋ࡚࠾ࡾ㸪ࣉࣟࢵࢺࡢᩘࡣ⢏Ꮚᩘ࡛࠶ࡿ㸬ᅗ 3 ࡣ㸪
㸦3㸧⢏Ꮚ㛫᥋ゐࡈ࡜࡟஘ᩘ࡟ࡼࡗ࡚ಶู࡟୚࠼ࡿ᪉ἲ࡛㸪ಶࠎࡢ⢏Ꮚ㛫᥋ゐ࡛ࡑࢀࡒࢀ⢏Ꮚ㛫ࡢ᥋ゐ㊥㞳ࢆ஘ᩘ࡟ࡼࡗ࡚タᐃࡋ࡚࠸ࡿሙྜࡢ᥋ゐ㊥㞳ಀᩘࡢ౛ࢆ⾲ࡋ࡚࠾ࡾ㸪ࣉࣟࢵࢺࡢᩘࡣ᥋ゐᩘ࡛࠶ࡿ㸬ᙜึ㸪⢏Ꮚ㛫ࡢ᥋ゐࡀ⏕ࡌࡿࡈ࡜࡟㸪஘ᩘ࡟ࡼࡗ࡚᥋ゐ㊥㞳ࡢタᐃࢆ⾜ࡗ࡚࠸ࡓ㸬ࡋ࠿ࡋ㸪ࡑࡢሙྜ㸪ᑠࡉ࡞᥋ゐ㊥㞳ࡀタᐃࡉࢀࡿ࡜㸪⢏Ꮚࡀ᥋ゐࡋ࡞ࡃ࡞ࡿࡇ࡜ࡀከࡃ㸪⤖ᯝⓗ࡟㸪ḟ➨࡟኱ࡁ࡞᥋ゐ㊥㞳࡟೫ࡗ࡚࠸ࡃゎᯒ⤖ᯝ࡟࡞ࡗࡓ㸬ᚑࡗ࡚㸪⌧ᅾࡣࡍ࡭࡚ࡢ⢏Ꮚ㛫ࡢ᥋ゐ㊥㞳ࢆ᭱―ึ࡟஘ᩘ࡛Ỵᐃࡋ㸪ࡑࡢ್ࢆ౑⏝ࡋ࡚࠸ࡿ㸬஘ᩘࢆ౑⏝ࡋࡓሙྜࡢ᥋ゐ㊥㞳ಀᩘࡢᖹᆒ್ࡣ㸪ᅗ 2 ࡛ࡣCr=0.48㸪
―㻝㻚㻜㻜

㻝㻚㻜㻜

㻜㻚㻤㻜

㻜㻚㻤㻜

Contact radius ratio CrContact radius ratio Crᅗ 3 ࡛ࡣCr=0.51 ࡜࡞ࡗ࡚࠾ࡾ㸪⣙ 0.5 ࡛࡯ࡰᆒ୍࡟ศᕸࡍࡿࡼ࠺࡟タᐃ࡛ࡁ࡚࠸ࡿ㸬㻜㻚㻢㻜㻜㻚㻠㻜㻜㻚㻞㻜㻜㻚㻢㻜㻜㻚㻠㻜㻜㻚㻞㻜㻜㻚㻜㻜㻜㻚㻜㻜㻜㻜㻚㻜㻜㻝㻜㻚㻜㻜㻞㻜㻚㻜㻜㻟Particle radiusFig.2 Contact radius ratio by random number 㸦2㸧

㻜㻚㻜㻜㻠

㻜

㻜㻚㻜㻜㻝
㻜㻚㻜㻜㻞
㻜㻚㻜㻜㻟
Particle radius
Fig.3 Contact radius ratio by random number 㸦3㸧㻜㻚㻜㻜㻠

80

松下政裕，門出政則，光武雄一

3. ィ ⟬ ⤖ ᯝ3࣭1 ᥋ゐ㊥㞳୍ᐃ࡛ࡢィ⟬⤖ᯝࡲࡎ㸪᥋ゐ㊥㞳 RB ࢆ୍ᐃ್࡜ࡋࡓሙྜࡢゎᯒ⤖ᯝࢆ♧ࡍ㸬ᅗ 4 ࡣ࣮࣡ࢹࣝ⌫ᙧᗘࢆኚ࠼࡚㸪ᖖ࡟እ᥋෇ᚄ࡛᥋ゐࡍࡿ࡜ࡋࡓሙྜ㸦Cr=1.0㸧ࡢ⢏Ꮚࡢ඘ሸ≧ែࢆ⾲ࡋ࡚࠸ࡿ㸬ᅗ࡛ࡣ㸪᫂☜࡟⢏Ꮚᚄศᕸࡀࢃ࠿ࡿࡼ࠺࡟⢏Ꮚᚄࡢ㐪࠸࡛⢏ᏊࢆⰍศࡅࡋ࡚࠸ࡿ㸬⤖ᯝࡣ㸪࡝ࡢ⢏Ꮚᚄศᕸ࡟࠾࠸࡚ࡶ࣮࣡ࢹࣝ⌫ᙧᗘࡢኚ໬࡟ᑐࡋ㸪࡯ࡰ⥺ᙧ࡟య✚ࡀኚ໬ࡋ࡚࠸ࡿ㸬ࡘࡲࡾ㸪᥋ゐ㊥㞳ࢆኚ࠼ࡿࡇ࡜࡟ࡼࡗ࡚㸪┤᥋ⓗ࡟ゎᯒ⤖ᯝࡢ✵㝽⋡ࢆኚ࠼ࡿࡇ࡜ࡀ࡛ࡁࡿ㸬ᚑࡗ࡚㸪」㞧࡞⢏Ꮚᙧ≧ࢆ㐺ษ࡟ձȯZ 0.80
ղȯZ 0.90(a) RR-05, Cr = 1.0, Cvw = 1.0×105ճȯZ 1.00

ձȯZ 0.80
ղȯZ 0.90(b) RR-10, Cr = 1.0, Cvw = 1.0×105ճȯZ 1.00

⾲⌧࡛ࡁࡿࡼ࠺࡞᥋ゐ㊥㞳ࢆ୚࠼ࢀࡤ㸪ᐇ㦂⤖ᯝ࡜ྠࡌ✵㝽⋡ࡢゎᯒ⤖ᯝࡀᚓࡽࢀࡿ࡜ࡳࡽࢀࡿ㸬ᅗ 5 ࡣ㸪50 ࢧ࢖ࢡࣝࡢゎᯒ⤖ᯝ࡛㸪᥋ゐ㊥㞳ಀᩘ࡜✵㝽⋡ࡢ㛵ಀࢆ♧ࡋ࡚࠸ࡿ㸬ᶓ㍈ࡣ࣮࣡ࢹࣝ⌫ᙧᗘࢆᐇ㦂⤖ᯝࡢ 0.73 ࡜ࡋࡓሙྜࡢ Cr ࡢ್ࢆ⾲ࡋ࡚࠸ࡿ㸬ᅗ࡟ࡣ㸪ᐇ㦂⤖ᯝ࡜ࡋ࡚㸪ึᮇ✵㝽⋡Ȝ0㸪᭱኱྾ⶶ᫬✵㝽⋡Ȝ1㸪Ỉ⣲ᨺฟᚋ✵㝽⋡Ȝ2 ࡶ♧ࡋ࡚࠸ࡿ㸬እ᥋෇ᚄ࡜㠃✚┦ᙜᚄࡢ୰㛫್㸦Cr㸻0.5㸧࡜ࡋࡓሙྜ࡟㸪ᐇ㦂࡛ᚓࡽࢀࡓ✵㝽⋡࡜➼ࡋࡃ࡞ࡿ࡜ᮇᚅࡋࡓࡀ㸪ゎᯒ⤖ᯝࡢ✵㝽⋡ࡣ 70.4㸣࡛㸪ᐇ㦂⤖ᯝࡼࡾࡶᑡࡋ኱ࡁ࡞✵㝽⋡࡜࡞ࡗࡓ㸬ᅗ 6 ࡣ㸪ࢧ࢖ࢡࣝᩘ࡟ᑐࡍࡿ✵㝽⋡ኚ໬ࢆ♧ࡋ࡚࠾ࡾ㸪ᐇ㦂⤖ᯝ࡜ࡢẚ㍑ࢆ⾲ࡋ࡚࠸ࡿ㸬ᐇ㦂⤖ᯝࡣࢱࢵࣉ඘ሸ࡟ࡼࡿ඘ሸ㝈⏺ࡶ♧ࡋ࡚࠸ࡿ㸬ゎᯒ⤖ᯝࡣ㸪୸ࡀ Cr㸻0.5㸪ᅄゅࡀ Cr=0.0 ࡢ⤖ᯝ࡛㸪ⓑᢤࡁࡀ௜╔ຊ࡞ࡋ㸪ሬࡾࡘࡪࡋࡀ௜╔ຊ࠶ࡾࡢ⤖ᯝࢆ⾲ࡋ࡚࠸ࡿ㸬࣮࣡ࢹࣝ⌫ᙧᗘࡣ㸪ࡑࢀࡒࢀࡢࢧ࢖ࢡ࡛ࣝࡢᐇ㦂್ࢆ౑⏝ࡋࡓ㸬⤖ᯝࡣ㸪᥋ゐ㊥㞳ࢆ㸪㠃✚┦ᙜᚄ࡜ࡋࡓሙ

㻜㻚㻣㻡
Cr=0.5 Ȝ2㻜㻚㻣㻜ձȯZ 0.80
ղȯZ 0.90
ճȯZ 1.00(c) RR-50, Cr = 1.0, Cvw = 1.0×105
Fig.4 Calculation results of contact radius change model forvarious Wardell's sphericity

Ȝ0㻜㻚㻢㻜

Limit of packing

Ȝ1㻜㻚㻡㻡㻜㻚㻤
Void fraction ȜVoid fraction Ȝ㻜㻚㻢㻡㻜㻚㻡㻜
Cr=0.0㻜㻚㻠㻡㻜㻚㻠㻜

Limit of packing㻜㻚㻟㻡㻜㻝㻜㻞㻜㻟㻜㻠㻜
Cycle number.
Fig.6 Transition of void fraction.

㻡㻜㻢㻜㻜㻚㻣

Ȝ2Ȝ0㻜㻚㻢

Ȝ1㻜㻚㻡㻜

㻜㻚㻡
Contact radius ratio CrFig.5 Transition of void fraction. ( RR-50 )㻝水素吸蔵合金の充填状態の計算（離散要素法による接触距離変更モデル）81ྜ㸦Cr=0.0㸧࡟ẚ࡭㸪እ᥋෇ᚄ࡜㠃✚┦ᙜᚄࡢ୰㛫್㸦Cr=0.5㸧࡜ࡍࡿࡇ࡜࡛㸪ᐇ㦂⤖ᯝࡢࡼ࠺࡞኱ࡁ࡞✵㝽⋡ࡢゎᯒࡀ⾜࠼ࡿࡼ࠺࡟࡞ࡗ࡚࠸ࡿ㸬≉࡟㸪50 ࢧ࢖ࢡࣝࡢ⢏Ꮚᚄศᕸࡢゎᯒ⤖ᯝࡣᐇ㦂⤖ᯝ࡟㏆࠸ゎᯒ⤖ᯝࡀᚓࡽࢀ࡚࠸ࡿ㸬ࡋ࠿ࡋ㸪ࡉࡽ࡟ᐇ㦂⤖ᯝ࡜ྜ࠺ࡼ࠺࡞ゎᯒࢆ⾜࠺ࡓࡵ࡟ࡣ㸪௜╔ຊࡸ⢏Ꮚᚄศᕸ࡟ࡼࡿᙳ㡪ࡸタᐃ್࡟ࡘ࠸࡚ࡉࡽ࡟᳨ウࡍࡿᚲせࡀ࠶ࡿ㸬ࡲࡓ㸪௒ᅇࡢゎᯒ࡛ࡣ㸪⢏Ꮚࡢಸ⋡タᐃࡀ 200 ಸ࡜኱ࡁࡃ㸪ẚ㍑ⓗ⢏Ꮚᩘࡀᑡ࡞࠸ゎᯒ࡟࡞ࡗ࡚࠸ࡿࡇ࡜ࡶ⤖ᯝ࡟ᙳ㡪ࡋ࡚࠸ࡿ࡜⪃࠼ࡽࢀࡿ㸬ᚑࡗ࡚㸪⢏Ꮚಸ⋡ࢆୗࡆ㸪⢏Ꮚᩘࡀከ࠸ሙ
ྜࡢゎᯒࢆ⾜࠺ᚲせࡶ࠶ࡿ㸬3࣭࣭2 ᥋ゐ㊥㞳ࡢタᐃ᪉ἲ࡟ࡼࡿ㐪࠸
ᅗ 7 ࡟ 3 ✀㢮ࡢ᥋ゐ㊥㞳ࡢタᐃ᪉ἲ࡟ࡼࡿゎᯒ⤖ᯝࡢẚ㍑ࢆ♧ࡍ㸬ᅗ 7 ࡣ㸪5 ࢧ࢖ࢡࣝࡢ⢏Ꮚᚄศᕸ㸦RR-05㸧
࡟ᑐࡍࡿ⤖ᯝ࡛㸪࡝ࡢィ⟬ࡶ࣮࣡ࢹࣝ⌫ᙧᗘࡣᐇ㦂⤖ᯝࡢ 0.739 ࢆ౑⏝ࡋ࡚࠸ࡿ㸬ᅗ 7㸦1a㸧ࡣ㸪୍ᐃ್ Cr=0.5࡜ࡋ࡚௜╔ຊ࠶ࡾ㸪ᅗ 7㸦1㹠㸧ࡣ୍ᐃ್ Cr㸻0.5 ࡜ࡋ࡚௜╔ຊ࡞ࡋࡢ⤖ᯝࢆ♧ࡋ࡚࠸ࡿ㸬ᅗ 7㸦2㸧ࡣ㸪஘ᩘ࡟ࡼࡾྛ⢏Ꮚ࡟୍ᐃ್ࢆ୚࠼ࡿ᪉ἲ㸪ᅗ 7㸦3㸧ࡣ㸪⢏Ꮚ㛫᥋ゐࡈ࡜࡟஘ᩘ࡟ࡼࡗ࡚ಶู࡟୚࠼ࡿ᪉ἲࡢゎᯒ⤖ᯝࢆ♧ࡋ࡚࠸ࡿ㸬஘ᩘ౑⏝ࡢ᪉ἲ࡛ࡣ࡝ࡕࡽࡶ௜╔ຊ࠶ࡾࡢࡳࡢゎᯒ⤖ᯝ࡛࠶ࡿ㸬඘ሸ≧ែࢆぢࡿ㝈ࡾ㸪௜╔ຊࡢ᭷↓࡟ࡼࡿᙳ㡪ࡣࡳࡽࢀࡿࡀ㸪᥋ゐ㊥㞳ࡢタᐃ᪉ἲࡢ㐪࠸࡟ࡼࡿゎᯒ⤖ᯝ࡬ࡢᙳ㡪ࡣ᫂☜࡟ࡣࡳࡽࢀ࡚࠸࡞࠸㸬ᅗ 8 ࡟㸪ࡑࢀࡒࢀࡢゎᯒࡢ✵㝽⋡ࡢẚ㍑ࢆ♧ࡍ㸬ࡲࡔ㸪ィ⟬ࡣ 1 ᅇࡎࡘ࡛࠶ࡿࡓࡵ㸪஘ᩘࡢ౑⏝࡟ࡼࡾ⤖ᯝࡀ࡝ࡢ⛬ᗘࡢ⠊ᅖ࡟ࡦࢁࡀࡿ࠿࡞࡝ࡣ୙࡛᫂࠶ࡿ㸬ィ⟬᫬㛫ࡣ㸪஘ᩘࢆ౑⏝ࡋࡓሙྜࡢ᪉ࡀᑡࡋ㛗ࡃ࡞ࡿ㸬⤖ᯝࡣ࡝ࡢゎᯒ⤖ᯝࡶᐇ㦂ࡼࡾᑡࡋ኱ࡁ࡞✵㝽⋡࡟࡞ࡗ࡚࠸ࡿ㸬᥋ゐ㊥㞳ࡢタᐃ᪉ᘧࡣ㐪ࡗ࡚ࡶ㸪᥋ゐ㊥㞳ಀᩘࡢᖹᆒ
ࡀྠࡌ࡛࠶ࢀࡤ㸪ゎᯒ⤖ᯝࡣྠࡌࡼ࠺࡞✵㝽⋡࡜࡞ࡗࡓ㸬㻜㻚㻣㻡Void fraction Ȝ4. ࡲ ࡜ ࡵᮏሗ࿌ࡣ㸪㞳ᩓせ⣲ἲ㸦Distinct element method, DEM㸧ࢆ౑⏝ࡋ㸪Ỉ⣲྾ⶶྜ㔠ࡢ඘ሸ≧ែࡢゎᯒࢆ⾜ࡗࡓ㸬᥋ゐ㊥㞳ࢆኚ᭦࡛ࡁࡿࣔࢹࣝࢆᵓ⠏ࡋ㸪ゎᯒ⤖ᯝ࡜ᐇ㦂⤖ᯝ࡜ࡢẚ㍑ࢆ⾜ࡗࡓ㸬᥋ゐ㊥㞳ࡣ㸪㸦1㸧ࡍ࡭࡚ࡢ⢏Ꮚ࡟㻜㻚㻣㻜
㻜㻚㻢㻡

ab

Ȝ2Ȝ0㻜㻚㻢㻜୍ᐃ್ࢆ୚࠼ࡿ᪉ἲ㸪
㸦2㸧஘ᩘ࡟ࡼࡾྛ⢏Ꮚ࡟୍ᐃ್ࢆ୚࠼ࡿ᪉ἲ㸪㸦3㸧⢏Ꮚ㛫᥋ゐࡈ࡜࡟஘ᩘ࡟ࡼࡗ࡚ಶู࡟㻜㻚㻡㻡୚࠼ࡿ᪉ἲࡢ 3 ✀㢮ࡢ᪉ἲ࡛タᐃࡋ㸪ゎᯒࢆ⾜ࡗࡓ㸬⤖(1b) Cr=0.5, Cvw= 0.0

(1)

(2)

(3)

Fig.8 Comparison of void fraction ( RR-05 )ᯝࡣ㸪᥋ゐ㊥㞳ಀᩘ 0.5 ࡢ୍ᐃ್࡜ࡋ࡚ࡶ㸪஘ᩘ࡟ࡼࡗ

(1a) Cr=0.5, Cvw= 1.0×105

Ȝ1―(2) Cr=0.48, Cvw= 1.0×105

Fig.7 Calculation results of contact radius change model ( RR-05 )―(3) Cr=0.51, Cvw= 1.0×105

82松下政裕，門出政則，光武雄一

࡚᥋ゐ㊥㞳ಀᩘࡢᖹᆒ್ࡀ 0.5 ࡜࡞ࡿࡼ࠺࡟ࡋ࡚ࡶ㸪ྠࡌࡼ࠺࡞✵㝽⋡࡜࡞ࡗࡓ㸬᥋ゐ㊥㞳ࡢタᐃ᪉ἲࡀ␗࡞ࡗ࡚ࡶ㸪࣮࣡ࢹࣝࡢ⌫ᙧᗘ࡟ࡼࡿእ᥋෇ᚄ࡜㠃✚┦ᙜᚄࡢ୰㛫್ࢆ᥋ゐ㊥㞳࡜ࡍࡿࡇ࡜࡛㸪ᐇ㦂࡛ᚓࡽࢀࡓ඘ሸ≧ែ࡟㏆࠸✵㝽⋡ࡢィ⟬⤖ᯝࡀᚓࡽࢀࡿ㸬ࡓࡔࡋ㸪ࡉࡽ࡟ᐇ㦂⤖ᯝ࡜ྜ࠺ࡼ࠺࡞ィ⟬⤖ᯝࢆᚓࡿࡓࡵ࡟ࡣ㸪௜╔ຊࡸ⢏Ꮚᚄศᕸ࡟ࡼࡿᙳ㡪㸪஘ᩘ࡟ࡼࡿᙳ㡪ࡸタᐃ್࡟ࡘ࠸࡚ࡉࡽ࡟᳨ウࡍࡿᚲせࡀ࠶ࡿ㸬ࡲࡓ㸪௒ᅇࡢゎᯒࡣẚ㍑ⓗ⢏Ꮚᩘࡀᑡ࡞࠸᮲௳࡛⾜ࡗࡓࡓࡵ㸪⢏Ꮚᩘࢆቑࡸࡋࡓሙྜ࡟⤖ᯝࡀᙳ㡪ࢆཷࡅࡿྍ⬟ᛶࡶ࠶ࡿ㸬௒ᚋࡣ㸪ᐇ㝿ࡢ⢏Ꮚᒙ࡟㏆࡙ࡅࡿࡓࡵ㸪࡛ࡁࡿࡔࡅከࡃࡢ⢏Ꮚ࡛ࡢィ⟬ࢆ⾜࠺ணᐃ࡛࠶ࡿ㸬ࡲࡓ㸪ࢱࢵࣉ඘ሸࢆ⾜ࡗࡓ᫬ࡢゎᯒࡶᐇ⾜࡛ࡁࡿࡼ࠺࡟ᨵⰋࡍࡿணᐃ࡛࠶ࡿ㸬ྠ᫬࡟㸪ィ⟬᫬㛫▷⦰ࡢࡓࡵ㸪ࣉࣟࢢ࣒ࣛࢆᨵၿࡍࡿ㸬ࡑࡢୖ࡛㸪ࣇ࢓ࣥࢹ࣮ࣝ࣡ࣝࢫຊࣔࢹࣝ࡜⢏Ꮚ㛫᥋ゐ㊥㞳ኚ᭦ࣔࢹࣝࢆᨵⰋࡋ㸪ᵝࠎ࡞᮲௳࡛ࡢゎᯒࢆ⾜ࡗ࡚㸪ᐇ㦂⤖ᯝ࡟㏆࠸඘ሸ≧ែࢆィ⟬࡛ࡁࡿࡼ࠺࡞ゎᯒ᪉ἲࡢ◊✲ࢆ㐍ࡵ࡚࠸ࡃ㸬ᩥ   ⊩(1) Murthy, S.S., ͆Heat and mass transfer in solid state hydrogen storage: A review͇, Journal of Heat Transfer, Vol.134 (2012),
pp.031020-0312030.
(2) ᯇୗᨻ⿱㸪㛛ฟᨻ๎㸪ගṊ㞝୍㸪͆Ỉ⣲྾ⶶྜ㔠ࡢ⭾ᙇ࣭཰⦰ࡢྍど໬ヨ㦂⿦⨨͇㸪బ㈡኱Ꮫᾏὒ࢚ࢿࣝࢠ࣮◊✲ࢭࣥࢱ࣮ሗ࿌ OTEC㸪No㸬15㸦2010㸧㸪pp㸬37㸫40㸬(3) ᯇୗᨻ⿱㸪㛛ฟᨻ๎㸪ගṊ㞝୍㸪͆Ỉ⣲྾ⶶᨺฟ࡟ࡼࡿỈ⣲྾ⶶྜ㔠ࡢయ✚ኚ໬ࡢྍど໬ィ ͇㸪బ㈡኱Ꮫᾏὒ࢚ࢿࣝࢠ࣮◊✲ࢭࣥࢱ࣮ሗ࿌ OTEC㸪No㸬16㸦2011㸧㸪pp㸬77㸫84㸬(4) ᯇୗᨻ⿱㸪㛛ฟᨻ๎㸪ගṊ㞝୍㸪 ͆Ỉ⣲྾ⶶྜ㔠ࡢ⢏Ꮚᔂቯ࡟ࡼࡿ඘ሸ≧ែࡢኚ໬࡟㛵ࡍࡿ◊✲͇㸪᪥ᮏᶵᲔᏛ఍
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(5) Matsusita, M., Monde, M. and Mitsutake, Y., ͆Experimental formula for estimating porosity in a metal hydride packed bed”
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(6) ᯇୗᨻ⿱㸪㛛ฟᨻ๎㸪ගṊ㞝୍㸪 ͆Ỉ⣲྾ⶶྜ㔠ࡢ᭷ຠ⇕ఏᑟ⋡ࡢィ⟬͇㸪᪥ᮏᶵᲔᏛ఍ㄽᩥ㞟 B ⦅㸪㸦ᢞ✏୰ᥖ㍕Ỵᐃ῭㸧㸬(7) ᯇୗᨻ⿱㸪㛛ฟᨻ๎㸪ගṊ㞝୍㸪͆㞳ᩓせ⣲ἲ࡟ࡼࡿỈ⣲྾ⶶྜ㔠ࡢ඘ሸ≧ែィ⟬͇㸪బ㈡኱Ꮫᾏὒ࢚ࢿࣝࢠ࣮◊✲ࢭࣥࢱ࣮ሗ࿌ OTEC㸪No㸬17㸦2012㸧㸪pp㸬47㸫55㸬(8) ⢊యᕤᏛ఍⦅, ⢊యᕤᏛྀ᭩ ➨㸵ᕳ ⢊యᒙࡢ᧯స࡜ࢩ࣑࣮ࣗࣞࢩࣙࣥ, (2009), ᪥หᕤᴗ᪂⪺♫.
(9) ⢊యᕤᏛ఍⦅, ⢊యࢩ࣑࣮ࣗࣞࢩࣙࣥධ㛛, (1998), ⏘ᴗᅗ᭩ᰴᘧ఍♫.