THE SCIENCE AND ENGINEERING REVIEW OF DOSHISHA UNIVERSITY, VOL. 50, NO.3October2009
Characteristics of Flow Rate Control by Using Magneto-Rheological Elastomers
Kazuhiko M
ATSUMURA*, Masashi K
AWAGUCHI**, Yuki S
ASATANI**, Hiroshi Y
AMAGUCHI**(Received July 9, 2009)
The purpose of this study is to verify the characteristics of a flow control device when the structure is actually installed in a section of pipe. In the present a magneto-rheological elastomers is prepared by mixing ferromagnetism fine particles and the silicone gel. The magneto-rheological elastomers with a tiny hole inherited from the manufacturing process is then installed in a section of a pipe. The flow rate, especially water in the present study, is controlled by applying magnetic field. The flow of water, represented with flow coefficient through the whole of elastomers, is effectively controlled by imposing magnetic field. In this flow control structure, the shape of the magneto-reological elastomers becomes an especially important factor. The influence on the flow of the working fluid when the length of the magneto-rheological elastomers passed the throttle is also investigated in the present research. It is found, with an assistance of CFD, that the elastomer is deformed to the down stream in the controlling section, resulting in strong effect on the flow coefficient.
-G[9QTFU : flow rate control㧘magneto-reological elastomers㧘ferromagnetism fine particles㧘magnetic field
ࠠࡢ࠼㧦
ᵹ㊂ᓮ⏛᳇☼ᒢᕈᒝ⏛ᕈᓸ☸ሶ⏛႐⏛᳇☼ᒢᕈߦࠃࠆᵹ㊂ᓮ․ᕈ
᧻ᒾ* 㧘Ꮉญᱜ༹** 㧘╣⼱㓶ၮ** 㧘ጊญඳม**
✜⸒
㧘ᄙߊߩᾲ㧘ᵹࠪࠬ࠹ࡓߢ↪ߐࠇߡࠆ ᯏ᪾ᑼᵹ㊂ᓮᑯߪ㧘৻⥸⊛ߦ᭴ㅧࠆߪᓮᯏ
᭴߇ⶄ㔀ߢࠅ㧘ᦝߦᵹߦࠃࠆ㛍㖸߇⊒↢ߔࠆ1-4)
╬ߩ㗴ࠍᛴ߃ߡࠆ㧚߹ߚ㧘ㆊߩ⎇ⓥߢᣂߒ
⹜ߺߣߒߡ⏛ᕈᵹ⤑5)ࠍ↪ߚᵹ㊂ᓮ6)߳ߩᔕ
↪߇น⢻ߢࠆߎߣ߇⍮ࠄࠇߡࠆ㧚ߒ߆ߒߎߩᯏ
᭴ߢߪ⏛ᕈᵹߩ⏛႐ᜬജ߇ዊߐߚ㧘ᵹ㊂߇ ᄙߊߥࠆߣ㧘⏛ᕈᵹ⤑ߩ৻ㇱ߇㘧ᢔߒ㧘ߎࠇߦࠃ ࠅ⛉ࠅലᨐ߇ᷫዋߔࠆ㗴ὐ߇ࠆ㧚ߘߎߢᧄ⎇ⓥ
ߢߪߎࠇࠄߩ㗴ὐࠍ⸃ߔࠆߚߦ㧘⏛ᕈᵹ⤑
ߩઍࠊࠅߦ㧘ᒝ⏛ᕈᓸ☸ሶߣಽᢔᇦߢࠆࠪࠦ
ࡦࠥ࡞ࠍᷙวߒߚ⏛᳇☼ᒢᕈࠍ↪ߚᣂߚߥᵹ㊂
ᓮᯏ᭴ࠍឭ᩺ߒ㧘ශട⏛႐߇ᵹࠇߩ․ᕈ㧘․ߦᵹ
㊂ᓮᑯߣߒߡߩᵹ㊂ᓮ․ᕈߦ߷ߔᓇ㗀ߦߟ
ߡᬌ⸛ࠍⴕߞߚ㧚
ᧄ⎇ⓥߢߪ㧘ߎߩᵹ㊂ᓮᯏ᭴ࠍ㊂↥᭽ߩᵹ㊂
ᓮᑯ߳ㆡ↪ߔࠆߚߩ㊀ⷐߥᬌ⸛㗄⋡ߩ৻ߟߣߒ ߡ㧘⏛᳇☼ᒢᕈߩᒻ⁁ࠍขࠅߍ㧘ߘߩਛߢ߽⛉
ࠅᯏ᭴ㇱࠍ᭴ᚑߔࠆ⏛᳇☼ᒢᕈߩ㐳ߐ߇㧘⛉ࠅᯏ
᭴ㇱߩᒻ⁁ᄌൻ߮⛉ࠅᯏ᭴ㇱࠍㅢㆊߔࠆ㓙ߩേ
ᵹߩᵹࠇߦ߷ߔᓇ㗀ߦߟߡ⺞ᩏߒߚ㧚 ߘߎߢ㧘ᦨೋߦή⽶⩄ᤨߦ߅ߡ㧘ශട⏛႐ᒝߐ ࠍᄌൻߐߖߚ႐วߩゲᣇะ߆ࠄߚ⛉ࠅᯏᓟㇱߩᒻ
⁁ߩนⷞൻࠍⴕ㧘ශട⏛႐ᒝߐߣ㐿ญᢿ㕙Ⓧߣߩ 㑐ଥߦߟߡ⺞ᩏߒߚ㧚ᰴߦ㧘ታ㛎߮ᢙ୯⸃ᨆࠃ ࠅᓧࠄࠇߚേᵹᵹേᤨߦ߅ߌࠆࠗࡁ࡞࠭ᢙ
* Pacific Industrial Co., Ltd , Godo-cho, Anpachi, Gifu
Telephone: +81-584-28-0144, Fax: +81-584-28-0130, E-mail: kzmatsum@pacific-ind.co.jp
**Department of Mechanical and Systems Engineering, Doshisha University, Kyoto
Telephone: +81-774-65-6462, Fax: +81-774-65-6831, E-mail: hyamaguc@mail.doshisha.ac.jp
Reߣᵹ㊂ଥᢙCvߣߩ㑐ଥࠍᲧセߔࠆߎߣߦࠃࠅඨ ᓘᣇะ߆ࠄߚ⛉ࠅᯏ᭴ㇱߩᒻ⁁߇േᵹߩᵹࠇ ߩേߦ߷ߔᓇ㗀ߦߟߡ⺞ᩏߒߚ㧚ᦨᓟߦ㧘ߎ ࠇࠄߩ⚿ᨐ߆ࠄ⏛᳇☼ᒢᕈߩᵹ㊂ᓮᑯ߳ߩᔕ↪
ߩน⢻ᕈߦߟߡᬌ⸛ߒߚ㧚
ᵹ㊂ᓮᯏ᭴ߩේℂ
Fig.1
ߦᧄ⎇ⓥߦ߅ߌࠆᵹ㊂ᓮᯏ᭴ߩේℂ࿑ࠍ␜ߔ㧚ߎࠇߪᵹ㊂ᓮታ㛎ߦ߅ߡ
Fig.2
ߩ࠹ࠬ࠻࡚ࠢࠪࡦࠍᒻᚑߔࠆ߽ߩߢࠅ㧘ਥߦࡄࠗࡊ㧘⏛
᳇☼ᒢᕈ㧘㔚⏛⍹߆ࠄ᭴ᚑߐࠇࠆ㧚ߎߩ࠹ࠬ࠻
࡚ࠢࠪࡦߩߦߚߞߡߪ㧘ࠄ߆ߓゲᣇะߦ
⛉ࠅᯏ᭴ㇱߣߥࠆዊⓣߩߚ⏛᳇☼ᒢᕈࠍ
ߒ㧘ߘࠇࠍࡄࠗࡊߩਛߦࠇ࿕ቯߒߚ㧚⏛᳇☼ᒢᕈ
ߩ⛉ࠅᯏ᭴ㇱߪ㧘㔚⏛⍹ߦࠃࠅ⏛႐ࠍශടߔࠆߎ ߣߢ㧘ᒝ⏛ᕈᓸ☸ሶߦඨᓘᣇะߩ⏛᳇Ⓧജ߇↪
ߒ㧘ߘࠇߦࠃࠅ⏛᳇☼ᒢᕈ߇㔚⏛⍹ߦᒁ߈ነߖ ࠄࠇࠆߎߣߢ㐿ญߔࠆ㧚ߎߎߢ⏛᳇☼ᒢᕈߦ↪
ߔࠆනⓍᒰߚࠅߩ⏛᳇Ⓧജࡌࠢ࠻࡞fߪ㧘⏛
ൻࡌࠢ࠻࡞Mߣ⏛႐൨㈩ШHߣߩౝⓍ7)ߢએਅߩᑼ ߢߐࠇࠆ㧚
f =MШШH
(1)
߹ߚ࠹ࠬ࠻࡚ࠢࠪࡦߢߩ⏛᳇☼ᒢᕈߦ↪ߔ ࠆജߪ㧘㐿ᑯᤨߦ߅ߡߪශട㔚ᵹࠍߍࠆߎߣߢ㧘 ᐔဋ⏛ൻࡌࠢ࠻࡞Mߩᒝߐ߇Ⴧടߒ㧘⏛᳇Ⓧജ߇ Ⴧߔߎߣߦࠃࠅ⊒↢ߔࠆ㧚ߔߥࠊߜ⏛᳇☼ᒢᕈߦ ߪඨᓘᣇะߩᐔဋ⏛႐൨㈩㺂H߇↪ߒ㧘⏛᳇☼ᒢ ᕈߦߊඨᓘᣇะߩᐔဋ⏛᳇Ⓧജfߦࠃࠅ㐿ญ ᢿ㕙Ⓧ߇Ⴧടߔࠆ㧚ㅒߦ㐽ᑯᤨߦߪශട⏛႐ࠍᷫዋ ߐߖࠆߎߣߦࠃࠅ㧘ࠪࠦࡦࠥ࡞ߩᓳరജࠍ↪
ߒ㧘⛉ࠅᯏ᭴ㇱߩ㐿ญᢿ㕙Ⓧߪᷫዋߔࠆ㧚ߘߩ⚿ᨐ㧘 ᵹࠇ႐ߦ⸳⟎ߐࠇߚ࠹ࠬ࠻࡚ࠢࠪࡦߢߪ⛉ࠅᯏ᭴
ㇱߩᵹߣਅᵹߦᏅ߇↢ߓ㧘ᵹ㊂ᓮ6)߇น
⢻ߣߥࠆ㧚
ᧄታ㛎ߢߪ
Fig.1
ߦ␜ߔ᭽ߦ㧘⏛᳇☼ᒢᕈߩ㐳 ߐࠍߘࠇߙࠇ5[mm]
㧘10[mm]
㧘15[mm]
ߩ3
⒳㘃ߦ⸳ቯߒߚ㧚
(a)5[mm]
Pipe
Electromagnet Magneto-rheological elastomers
Throttle Magnetic field lines
Fig. 1. Principle of flow rate control structure Flow
5[mm]
(c)15[mm]
(b)10[mm]
10[mm]
15[mm]
ታ㛎ⵝ⟎
Fig.2
ߦታ㛎ⵝ⟎ߩ⇛࿑ࠍ␜ߔ㧚േᵹߦߪ᳓ࠍ↪㧘⸳ቯ᷷ᐲߪ
20[
͠]
ߣߒߚ㧚․ߦ⛉ࠅᯏ᭴ㇱᵹߢߪ㧘࠹ࠬ࠻࡚ࠢࠪࡦญߦ߅ߡ⊒㆐ߒ ߚᵹࠇߣߥࠆࠃ߁ߦ㧘ࡉࠫࡀߩℂ⺰8)ߦၮߠߡഥ
㑆ࠍ⸳ߌߚ㧚ࡐࡦࡊߦࠃࠅേᵹࠍ㚟േߐߖ㧘 ࡈࡠ࠻ᵹ㊂⸘ઃዻߩᑯߦࠃࠅᚲቯߩᵹ㊂ߦ⸳ቯߒ ߚ㧚߹ߚ㧘㔚⏛⍹ߦࠃࠅ⏛᳇☼ᒢᕈߦ⏛႐ࠍශട ߒᵹ㊂ᓮ߇ⴕࠊࠇࠆ㧚ߥ߅㔚⏛⍹ߪㅢ㔚ᤨߩ⊒ᾲ ߦࠃࠆ⛘✼⎕უࠆߪ⏛ജߩૐਅࠍ㒐ᱛߔࠆߚ
㧘಄ළⵝ⟎ߦࠃࠅᏱᤨᒝ಄ළࠍⴕߞߚ㧚߹ߚ㧘
⛉ࠅᯏ᭴ㇱ೨ᓟߦജ࠻ࡦࠬ࠺ࡘࠨࠍขࠅઃ
ߌ㧘ኻ⽎ߣߔࠆ⛉ࠅᯏ᭴ㇱߩᏅࠍ㧘ᦝߦ㔚⏛ᑼ♖
ኒᵹ㊂⸘ࠍ⛉ࠅᯏ᭴ㇱਅᵹߦ⸳⟎ߒ㧘ᵹ㊂ߩ♖ኒ
᷹ቯࠍⴕߞߚ㧚
4
⏛᳇☼ᒢᕈߣ࠹ࠬ࠻࡚ࠢࠪࡦ ᒝ⏛ᕈᓸ☸ሶߣࠪࠦࡦࠥ࡞ߦࠃࠆ⛉ࠅᯏ
᭴ㇱ
⏛᳇☼ᒢᕈࠍ᭴ᚑߔࠆ᧚ᢱߣߒߡᒝ⏛ᕈᓸ☸ሶࠍ
ࠪࠦࡦࠥ࡞ࠍណ↪ߒߚ㧚ᧄ⎇ⓥߢ↪ߚಽᢔᒝ⏛
ᕈᓸ☸ሶߪ
Carbonyl SQ(BASF
␠㧕ߢࠆ㧚☸ሶᒻ⁁ߪ⁁ߢ㧘ᐔဋ☸ᓘߪ࿁↪ߚࠨࡦࡊ࡞ࠍ᷹ቯߒߚ⚿ᨐ
5.4[P m]
ߢࠆ㧚߹ߚಽᢔᇦߪ⏛᳇Ⓧജߦࠃࠆᄢᄌᒻࠍ ᓧ ࠆ ߚ ߦ 㧘 ࠪ ࠦ ࡦ ࠥ ࡞ ߦ ߪ
TSE3062
㧔
MOMENTIVE
␠㧕ࠍ↪ߚ㧚ߥ߅㊎ᐲߪ55
ߢࠆ㧚⏛᳇☼ᒢᕈߩᣇᴺߪ㧘ኈེߦᒝ⏛ᕈᓸ☸ሶߣ
ࠪࠦࡦࠥ࡞ࠍⷙቯߩⓍᲧ₸㧘ᧄ⎇ⓥߢߪઍ୯ߣ ߒߡ
5:5
ߣߥࠆ᭽ߦᛩߒ㧘⌀ⓨ⣕ᵃᡬᜈⵝ⟎ࠍ↪ߡ⌀ⓨ⣕ᵃߒߥ߇ࠄᡬᜈߔࠆ㧚ߘࠇࠍࡄࠗࡊߦᵹߒㄟࠎߛ ᓟ㧘ᕡ᷷ᮏߢടᾲ⎬ൻߐߖࠆ㧚
ߎߎߢ㧘ታ㛎ߦ↪ߔࠆ೨ߦ⏛᳇☼ᒢᕈߩဋ৻ᕈࠍ ᬌ⸽ߔࠆߚ㧘ᷓᐲ
3D
ᒻ⁁᷹ቯ㗼ᓸ㏜ࠍ↪ߡ㧘ട ᾲ⎬ൻᓟߩౝㇱ⁁ᘒࠍ⏕ߒߚ㧚ߘߩ⚿ᨐ㧘☸ሶߪ╬ᣇ ߦဋ৻ಽᢔߒ㧘ಝ㓸߽ࠄࠇߕ㧘᳇ᵃ߽⏕ߐࠇߥ߆ߞ ߚ㧚ࠃߞߡᒝ⏛ᕈᓸ☸ሶߩಽᢔ⁁ᘒߪ⦟ᅢߢࠆߎߣ߇⏕ߐࠇߚ㧚߹ߚᧄ⎇ⓥߦ߅ߌࠆ⛉ࠅᯏ᭴ㇱߩೋᦼ㐿ญ ᢿ㕙ⓍߪS
=4.9[mm
2] 㧔
I2.5[mm]㧕ࠍណ↪ߒߚ㧚
ή⽶⩄ᤨߦ߅ߌࠆශട⏛႐ߦኻߔࠆ⛉ࠅᯏ᭴
ㇱߩᒻ⁁ᄌൻߩนⷞൻߣ㐿ญᢿ㕙Ⓧ
ή⽶⩄ᤨߦ߅ߌࠆ⛉ࠅᯏ᭴ㇱߩ㐿ญᢿ㕙Ⓧࠍ⹏ଔ ߔࠆߚ㧘⛉ࠅᯏ᭴ㇱ߇ශട⏛႐ߦኻߒߡ㐿㐽ߔࠆ 㓙ߩ㐿ญᢿ㕙Ⓧߩ᷹ቯࠍⴕߞߚ㧚᷹ቯᣇᴺߪ㧘⏛᳇
☼ᒢᕈߩ⛉ࠅᯏ᭴ㇱਅᵹ߆ࠄ㧘㜞ຠ࠺ࠫ࠲࡞
ࡆ࠺ࠝࠞࡔߦࠃࠅ⛉ࠅᯏ᭴ㇱᵹ߆ࠄ㐿ญㇱߩ
⁁ᘒࠍᓇߒߚᓟ㧘㐿ญᢿ㕙Ⓧߩ▚ࠍⴕߞߚ㧚
5
ታ㛎⚿ᨐ߮⠨ኤ
ή⽶⩄ᤨߦ߅ߌࠆශട⏛႐ߦኻߔࠆ⛉ࠅᯏ᭴
ㇱߩᒻ⁁ᄌൻߩนⷞൻߣ㐿ญᢿ㕙Ⓧ
Fig.3(a)
ߦ⏛᳇☼ᒢᕈߩฦ㐳ߐߦ߅ߌࠆශട⏛႐ᒝߐHߣ㐿ญᢿ㕙Ⓧ
S
ߩ㑐ଥࠍ␜ߔ㧚ߎߎߢශട⏛႐ᒝߐ H ߪゲᣇะ⏛႐ߩᦨᄢ୯ߣߒߚ㧚߹ߚ
Fig.3(b)
ߦઍߣߒߡ⏛᳇☼ᒢᕈߩ㐳ߐ߇10[mm]
ߢ 㧘 ශ ട ⏛ ႐ ߇ H=0[MA/m]ߣ H=0.282 Fig. 2. Experimental apparatusPump Reserve tank
Flow direction Float flow meter Pressure sensor
Flow meter
Pressure sensor Test section (Fig.1(a)(b)(c))
Valve Electromagnet
㨇
MA/m
㨉ߩᤨߩ㧘ή⽶⩄ᤨߦ߅ߌࠆゲᣇะ߆ࠄߚ⛉ࠅᯏ᭴ㇱߩนⷞൻ౮⌀ࠍ␜ߔ㧚
Fig.3(a)
߆ࠄ㧘㐳ߐ߇10[mm]
ߩ⏛᳇☼ᒢᕈ߇ᦨ߽㐿ญᢿ㕙Ⓧ߇ᄢ߈ߊ㧘ߘߩᦨᄢ㐿ญ㕙ⓍᲧߪ㧘ශ ട⏛ ႐
0
҇H҇0.282[MA/m]
ߩ ▸ ࿐ߦ߅ ߡ㧘21/4.9=4.3
ߣߥߞߚ㧚߹ߚFig.3(b)
ߩ⚿ᨐ߆ࠄ㧘⛉ࠅ ᯏ᭴ㇱߩᒻ⁁ߪශട⏛႐ߩჇടߦหᔃ⁁ߦ㐿 ญߒߡࠆߎߣ߇ಽ߆ߞߚ㧚ࠗࡁ࡞࠭ᢙ
Reߣᵹ㊂ଥᢙ
Cvߣߩ㑐ଥ
േᵹᵹേᤨߦ߅ߌࠆ㧘⛉ࠅᯏ᭴ㇱߩᵹ㊂ᓮ
․ᕈࠍ⹏ଔߔࠆߚ㧘ࠗࡁ࡞࠭ᢙReߣᵹ㊂ଥᢙ Cvߣߩ㑐ଥߦߟߡ⺞ᩏߒߚ㧚ߥ߅ࠗࡁ࡞࠭ᢙߣ ᵹ㊂ଥᢙߪฦޘ㧘ᑼ
(2)
ߣᑼ(3)
9-11)ߢቯ⟵ߐࠇࠆ㧚
Re
=UUD/
P(2)
(3)
ߎߎߢUߪേᵹ㧔᳓㧕ߩኒᐲ㧘Uߪേᵹ
㧔᳓㧕ߩઍㅦᐲ㧘Dߪࠕࠢ࡞ࡄࠗࡊߩౝᓘ㧘P ߪേᵹ㧔᳓㧕ߩ☼ᐲ㧘㧽ߪ⛉ࠅᯏ᭴ㇱㅢㆊᓟߩ ᵹ㊂㧘dߪ⛉ࠅᯏ᭴ㇱߩౝᓘ㧘ӠPߪ࠹ࠬ࠻ࠢࠪ
࡚ࡦ೨ᓟߩᏅߢࠆ㧚
Fig.4
ߦ⛉ࠅᯏ᭴ㇱߩᵹ㊂ᓮ․ᕈߩታ㛎⚿ᨐࠍ␜ߔ㧚ߎߎߢᮮゲ߇ࠗࡁ࡞࠭ᢙRe㧘❑ゲߪᵹ㊂ଥ ᢙCvߢࠆ㧚ߎߩ⚿ᨐ߆ࠄ⏛᳇☼ᒢᕈߩ㐳ߐߩ ᅤߦ㑐ࠊࠄߕශട⏛႐ߩჇടߦᵹ㊂ଥᢙ߇ᄢ ߈ߊߥߞߡࠆߎߣ߇ಽ߆ࠆ㧚߹ߚශട⏛႐ߩჇട ߦ㧘
3
⒳㘃ߩ⏛᳇☼ᒢᕈߩᵹ㊂ଥᢙߩ୯ߩᏅ ߇ᄢ߈ߊߥࠆߎߣ߇ಽ߆ࠆ㧚ߎࠇߪශട⏛႐ߩჇട ߦ㧘⏛᳇☼ᒢᕈߩ㐿ญᢿ㕙Ⓧߩᄌᒻ㊂߇Ⴧട ߒ㧘ᦝߦߪേᵹߩ᳓ߦࠃࠆᄌᒻߩᓇ㗀ࠍࠃࠅ ฃߌ߿ߔߎߣࠍ␜ߒߡࠆ߽ߩߣᕁࠊࠇࠆ㧚ᦝߦ⏛᳇☼ᒢᕈߩ㐳ߐ߇
10[mm], 5[mm], 15[mm]
ߩ㗅 ߦᵹ㊂ଥᢙ߇㜞ߎߣ߇ಽ߆ߞߚ㧚ߎࠇߪ㐳ߐ10[mm]
ߩ⏛᳇☼ᒢᕈ߇3
⒳㘃ߩਛߢߪᦨ߽㜞ᵹ㊂ᓮ․ᕈࠍߒߡ߅ࠅ㧘
Fig.3(a)
ߢ␜ߒߚะߣ৻⥌ߒߡࠆ㧚ߎߩߎߣ߆ࠄή⽶⩄ᤨߦ߅ߌࠆශട⏛
႐ߣ㐿ญᢿ㕙Ⓧߣߩ㑐ଥߪ㧘േᵹߦ᳓ࠍ↪ߚ ႐วߩࠗࡁ࡞࠭ᢙߣᵹ㊂ଥᢙߣߩ㑐ଥߣ⋧㑐㑐ଥ ߇ࠆߎߣ߇ಽ߆ߞߚ㧚
ߎߎߢ
Fig.4
ߦ߅ߌࠆฦශട⏛႐ߦߟߡ⠨ኤࠍߔࠆߣ
Fig.4(a)
ߦ߅ߡ㧘ශട⏛႐ H=0.070[MA/m]ߢߪ㧘
5[mm]
ߩ⏛᳇☼ᒢᕈ߇ࠗࡁ࡞࠭ᢙRe㧪500
ߩ㗔ၞߢߪᵹ㊂ࠍ᷹ቯߔࠆߎߣ߇ߢ߈ߥ߆ߞߚ㧚ߎ ࠇߪ⏛᳇☼ᒢᕈߩ⛉ࠅᯏ᭴ㇱᵹ┵㕙߇᳓ߦ ࠃߞߡᄌᒻߒ㧘⛉ࠅᯏ᭴ㇱߩⓣ߇Ⴇ߇ߞߡߒ߹ߞߚ ߚ ߣᕁ ࠊࠇ ࠆ
. Fig.4(b)
ߦ ߅ ߡ 㧘ශ ട ⏛႐ H=0.141[MA/m]ߢߪ㧘3
⒳㘃ߩ⏛᳇☼ᒢᕈߣ߽ࠗࡁ࡞࠭ᢙߩჇടߦ㧘ᵹ㊂ଥᢙߪ߶߷ቯߒߚ Ⴧടะࠍ␜ߒߡࠆ㧚
Fig.4(c)
ߦ߅ߡ㧘ශട⏛႐ H=0.282[MA/m]ߢߪ㧘15[mm]
ߩ⏛᳇☼ᒢᕈߪ㧘ࠗࡁ࡞࠭ᢙߩჇടߦᵹ㊂ଥᢙߪ✭߿߆ߦჇടߒߡࠆ߽ߩߩ㧘
10[mm]
ߩ⏛᳇☼ᒢᕈߦߟߡߪ㧘ૐࠗࡁ࡞࠭ᢙ㗔ၞ
㧔Re҇
800
㧕ߦ߅ߡᵹ㊂ଥᢙ߇ᕆỗߥჇടะߦ0 5 10 15 20 25
0.0 0.1 0.2 0.3
H[ MA/m]
S [mm
2]
5mm 10mm 15mm
(a) Opening area due to applied magnetic field Fig.3(b)-1
Fig.3(b)-2
(b)-1 0[MA/m] (b)-2 0.282[MA/m]
U p D
d Q d
Cv 2'
) / ( 1
/ޓ㧙 2
Fig. 3. Visualization of throttle control section
ࠆߩߦኻߒ㧘㜞ࠗࡁ࡞࠭ᢙ㗔ၞߦ߅ߡᵹ㊂ଥ ᢙߪ✭߿߆ߥჇടะߦࠆߎߣ߇ಽ߆ࠆ㧚ߎࠇߪ㧘 ශട⏛႐ H=0.282[MA/m]ߩ᭽ߥ㜞ශട⏛႐ਅߦ ߅ߡߪ㧘⛉ࠅᯏ᭴ㇱߩ㐿ญᢿ㕙Ⓧ߇ᄢ߈ߊ㧘৻⥸
ߦࠝࡈࠖࠬࠍ↪ߚᵹ㊂ᓮᑯߦࠄࠇࠆࠃ߁ߦ
,
ࠗࡁ࡞࠭ᢙ߇ૐ㗔ၞߢߪ㧘ጀᵹ߇ᡰ㈩⊛ߣߥࠅ
⛉ࠅᯏ᭴ㇱߦ߅ߌࠆ᷵ߩᓇ㗀ࠍᒝߊฃߌࠆߚߢ
ࠆߣᕁࠊࠇࠆ㧚߹ߚᵹ㊂ଥᢙߩᕆỗߥᄌൻߩะߪ㧘
⏛᳇☼ᒢᕈߩ⛉ࠅᯏ᭴ㇱ೨ᓟߢ↢ߓࠆജᏅ'P ߦࠃࠆᄌᒻ߇ේ࿃ߣ⠨߃ࠄࠇࠆ㧚߹ߚ
5[mm]
ߩ⏛᳇☼ᒢᕈߦ߅ߡߪࠗࡁ࡞࠭ᢙߩჇടߦ৻⽾
ߒߡᵹ㊂ଥᢙ߇Ⴧടߒߡࠆ㧚ߎࠇߪࠗࡁ࡞࠭ᢙ ߩჇടߦ㧘⛉ࠅᯏ᭴ㇱᵹߩ┵㕙߇᳓ߦࠃ ߞߡᓟᣇ߳ߒ߿ࠄࠇ㧘⛉ࠅᯏ᭴ㇱߩ㐿ญᢿ㕙Ⓧ
߇ࠗࡁ࡞࠭ᢙߩჇടߦ㧘ᓢޘߦᄢ߈ߊߥࠅߎ ߩࠃ߁ߥ⚿ᨐߦߥߞߚ߽ߩߣ⠨߃ࠄࠇࠆ㧚
6 ᢙ୯ᵹ⸃ᨆ
⸃ᨆᣇᴺ
ᧄ⎇ⓥߦ߅ߡ㧘ᢙ୯ᵹ⸃ᨆߦ↪ߚ࠰ࡈ࠻࠙
ࠚࠕߪ
SCRYU/Tetra
㧔ࢃ࠰ࡈ࠻࠙ࠚࠕࠢࠗ࠼࡞␠㧕ࠆ㧚േᵹߢࠆ᳓ߩ‛ᕈ୯ߪ㧘᳓᷷
20[
͠]
ߦ ߅ ߡ 㧘 ኒ ᐲ ߪU 998.07[kg/m3]
㧘 ☼ ᐲ ߪP㧩1.016×10
-3[Pa
s]
ߣߒߚ㧚ߎߎߢ㧘⛉ࠅᯏ᭴ㇱࠍㅢㆊ ߔࠆᵹࠇߪ㧘ญߢߩࠗࡁ࡞࠭ᢙߪૐ߽ߩߩ㧘⛉ࠅᯏ᭴ㇱߩ⋥ᓘࠍၮḰߣߒߚ႐วߩࠗࡁ࡞࠭ᢙ ߪ㜞ߊߥࠅ㧘ੂᵹߦㆫ⒖ߔࠆ 9)ߣ⠨߃ࠄࠇࠆ㧚ᓥߞ ߡᧄ⸘▚ߦ߅ߡߪ㧘⛉ࠅᯏ᭴ㇱߢߩᵹࠇߪੂᵹߣ
ቯߒ㧘ੂᵹࡕ࠺࡞ߦߪᮡḰk-H12)ᴺࠍ↪ߚ㧚߹ߚ
ജᱜᑼߩ⸃ᴺߦߪୃᱜ
SIMPLEC
ᴺࠍ↪ߚ㧚⸃ᨆᣇᴺߩᬌ⸽⚿ᨐ
⸃ᨆᣇᴺߩᅷᒰᕈࠍᬌ⸽ߔࠆߚ㧘㐿ญᢿ㕙Ⓧ
S=4.9[mm2
]
ߩ࿕ቯࠝࡈࠖࠬࠍ↪㧘ታ㛎ߦࠃࠅࠗࡁ࡞࠭ᢙReߣᵹ㊂ଥᢙCvߣߩ㑐ଥࠍ᳞㧘೨⸥
6.1
ߩ⸃ᨆᣇᴺࠍ↪ߡࠗࡁ࡞࠭ᢙRe=200㧘400, 800
㧘1200
㧘1600
㧘1800
ߩว⸘6
ὐߢᢙ୯ᵹ⸃ᨆ ࠍⴕߞߚ㧚Fig.5
ߦߘߩ⚿ᨐࠍ␜ߔ㧚ߎߩ⚿ᨐ߆ࠄታ 㛎୯ߣ⸃ᨆ୯ߪ߶߷৻⥌ߒߡࠆߎߣ߇⏕ߐࠇߚ㧚 ࠃߞߡ࿁⸳ቯߒߚᢙ୯ᵹ⸃ᨆᣇᴺߩᅷᒰᕈ߇ᬌ⸽ߐࠇߚ㧚
0
2 4 6 8 10
0 500 1000 1500 2000
Re[-]
Cv[-]
5mm
䋨Exp.䋩10mm
䋨Exp.䋩15mm
䋨Exp.䋩0
2 4 6 8 10
0 500 1000 1500 2000
Re[-]
Cv[-]
5mm 䋨 Exp. 䋩 10mm 䋨 Exp. 䋩 15mm 䋨 Exp. 䋩
0 2 4 6 8 10
0 500 1000 1500 2000
Re[-]
Cv [-]
5mm 䋨 Exp. 䋩 10mm 䋨Exp.䋩 15mm 䋨 Exp. 䋩
(a) H=0.070[MA/m]
(b) H=0.141[MA/m]
(c) H=0.282[MA/m]
Fig.. 4. Flow coefficient Cv
◲ᤃ⸃ᨆࡕ࠺࡞ߩ⸳ቯ
ᢙ୯ᵹ⸃ᨆߦ߅ߌࠆ⸃ᨆ᧦ઙߣߒߡ㧘ශട⏛႐ ߇H=0.070[MA/m]ߩᤨߦߪ㧘ࠗࡁ࡞࠭ᢙRe=300 ߣ Re=800㧘 ශ ട ⏛ ႐ ߇ H=0.141[MA/m]ߣ H
=0.282[MA/m]ߩ႐วߦߪࠗࡁ࡞࠭ᢙ
Re=300 ߣRe=1200ߣߒߚ㧚
⏛᳇☼ᒢᕈ߇⛉ࠅᯏ᭴ㇱ೨ᓟߦ↪ߔࠆജᏅࠍ ฃߌߚ㓙ߦᄌᒻߔࠆᒻ⁁ࠍ㧘◲ᤃ⊛ߦࡕ࠺࡞ൻߔࠆߚ㧘
◲ᤃ⏕ታ㛎ࠍⴕߞߚ㧚ౕ⊛ߦߪFig.2ߢ␜ߔ࠹ࠬ࠻
࡚ࠢࠪࡦ߆ࠄᵹ㊂ᓮᑯࠍขࠅߒ㧘ή⏛႐⁁ᘒߦߡ⛉
ࠅᯏ᭴ㇱᵹ߆ࠄ᳓ࠍㅢㆊߐߖࠆߎߣߦࠃࠅ⏛᳇☼ᒢ ᕈߩᒻ⁁ࠍ⋡ⷞߦߡ◲ᤃ⊛ߦ⏕ߒߚ㧚ߘߩ⚿ᨐ㧘⏛
᳇☼ᒢᕈߩ⛉ࠅᯏ᭴ㇱᵹ┵㕙߇᳓ࠍฃߌߡᓟᣇ
߳ߣᄌᒻߒ㧘߆ߟ⛉ࠅᯏ᭴ㇱᵹߩ㐿ญᢿ㕙Ⓧ߇ዊߐ ߊߥࠅ㧘⛉ࠅᯏ᭴ㇱਅᵹ߳ⴕߊߦᓥߞߡ㐿ญᢿ㕙Ⓧ߇
ᄢ߈ߊߥࠆߎߣ߇⏕ߐࠇߚ㧚ࠃߞߡ◲ᤃ⸃ᨆࡕ࠺࡞ߩ
ᚑߦ߅ߡߪ㧘ߎࠇࠄߩ⽎ࠍ⠨ᘦߒ㧘ή⽶⩄ᤨߦ߅ ߌࠆゲᣇะ߆ࠄߚ㐿ญᢿ㕙ⓍࠍၮḰߣߒ㧘⏛᳇☼ᒢᕈ
ߩⓍ߇৻ቯߣߥࠆࠃ߁⠨ᘦߒߥ߇ࠄ㧘߭ߕߺⷺᐲT1 ߣ࠹ࡄⷺᐲT2ࠍ
5°
㧘10°
㧘15°
ߩ3
⒳㘃ߦ⸳ቯߒߚ㧚7 ⚿ᨐ߮⠨ኤ
7.1 ታ㛎୯ߣ⸃ᨆ୯ߣߩᲧセ
Fig.7
ߦࠗࡁ࡞࠭ᢙReߣᵹ㊂ଥᢙCvߣߩ㑐ଥߦߟߡ㧘ታ㛎୯ߣ⸃ᨆ୯ߩᲧセࠍⴕߞߚ⚿ᨐࠍ␜ߔ㧚
(a)
߇ H =0.070[MA/m]㧘(b)
߇ H =0.141[MA/m]㧘(c)
߇ H= 0.282[MA/m]ߢࠆ㧚߹ߚFig.4
ߣห᭽ߦ㧘ᮮ ゲߪࠗࡁ࡞࠭ᢙRe㧘❑ゲߪᵹ㊂ଥᢙCvߢࠆ㧚 ߎߩ⚿ᨐ㧘ශട⏛႐H =0.141[MA/m]ߩ႐วߦ߅ߡࠗࡁ࡞࠭ᢙRe=300ߣ
1200
ߩ႐ว㧘ߕࠇߩ㐳 ߐߦ߅ߡ߽㧘ታ㛎୯ߣ⸃ᨆ୯ߪ߶߷৻⥌ߒߡࠆ㧚߹ߚH =0.282[MA/m]ߩ႐ว㧘⏛᳇☼ᒢᕈߩ㐳ߐ߇
15[mm]
ߩ႐วߦ߅ߡߪ㧘ታ㛎୯ߣ⸃ᨆ୯ߪ߶߷৻⥌ߒߡࠆ㧚߹ߚ
5[mm]
ߣ10[mm]
ߩ႐ว㧘ࠗࡁ࡞࠭ᢙRe=1200ߦ߅ߡߪ㧘ታ㛎୯ߣ
CFD
ߩ୯ߪ߶߷৻⥌ߒߡࠆ߇㧘ࠗࡁ࡞࠭ᢙRe=300ߢߪ⸃ᨆ ୯ߩᣇ߇ታ㛎୯ࠃࠅ߽㜞୯ߣߥߞߡࠆߎߣ߇⏕
ߢ߈ߚ㧚ߎࠇࠄߩශട⏛႐߮ࠗࡁ࡞࠭ᢙߩ▸
࿐ߦ߅ߡࠇࠆታ㛎୯ߣ⸃ᨆ୯ߩਇ৻⥌ߦߟߡ
⠨ኤߔࠆߣ㧘ᧄ⎇ⓥߢ↪ߚ⏛᳇☼ᒢᕈ߇㐳ዤߩ
⛉ࠅᯏ᭴ㇱߢࠆߎߣߣ㧘⏛᳇☼ᒢᕈߩᄌᒻߦࠃ ࠆ⋧ਸ਼ലᨐߦ㧘㕖Ᏹߦⶄ㔀ߥᵹࠇߦߥߞߡࠆ ߣ⠨߃ࠄࠇࠆ㧚߃߫⛉ࠅᯏ᭴ㇱ೨ᓟߢ㧘⏛᳇☼ᒢ ᕈߩᄌᒻߦࠃࠆ᷵߇⊒↢ߒߡࠆߎߣ߇⠨߃ࠄࠇ ࠆ߇㧘ᓟᦝߦߒᬌ⸛߇ᔅⷐߣ⠨߃ࠆ㧚
0 2 4 6 8 10
0 500 1000 1500 2000
Re䌛-䌝
Cv䌛-䌝
5mm䋨Exp.䋩 10mm䋨Exp.䋩 15mm䋨Exp.䋩 5mm䋨CFD.䋩 10mm䋨CFD.䋩 15mm䋨CFD.䋩 0.0
0.5 1.0 1.5 2.0
0 500 1000 1500 2000
R e[-]
Cv[-]
Fixed orifice CFD
Fig.5 Flow coefficient Cv for fixed orifice
Fig. 6. Computational model
Magneto-rheological elastomers
Flow T
T
(a) H=0.070[MA/m]
8
ᢙ୯ᵹ⸃ᨆߦࠃࠆജಽᏓ
⛉ࠅᯏ᭴ㇱౝㇱ߮ߘߩ೨ᓟߢߩജಽᏓ⸃ᨆ
⚿ᨐߩઍߣߒߡ㧘
Fig.8(a)
ߦශട⏛႐ H=0.141
[MA/m]
㧘⏛᳇☼ᒢᕈߩ㐳ߐ߇5[mm]
㧘ࠗࡁ࡞࠭ᢙRe=1200㧘ᵹ㊂ଥᢙCv=2.96ߩ႐วߩ⚿ᨐࠍ㧘
Fig.8(b)
ߦශട⏛႐H=0.141[MA/m]
㧘⏛᳇☼ᒢᕈߩ㐳ߐ߇
10[mm]㧘ࠗࡁ࡞࠭ᢙ
Re=1200㧘ᵹ㊂ଥᢙCv=4.17ߩ႐วߩ⚿ᨐࠍ㧘
Fig.8(c)
ߦශട⏛႐H
=0.282[MA/m]㧘⏛᳇☼ᒢᕈߩ㐳ߐ߇ 15[mm]㧘
ࠗࡁ࡞࠭ᢙRe=1200㧘ᵹ㊂ଥᢙCv=2.25ߩ႐วߩ⚿
ᨐࠍߘࠇߙࠇ␜ߔ㧚
ߎߩ⚿ᨐ߆ࠄ㧘⏛᳇☼ᒢᕈ߇ߕࠇߩ㐳ߐߦ߅
ߡ߽⛉ࠅᯏ᭴ㇱญઃㄭߢ㧘ജ߇ૐ▎ᚲ߇
ࠄࠇࠆ㧚ߎࠇߪ⏛᳇☼ᒢᕈߩญㇱߩᒻ⁁߇ࠪࡖ
ࡊࠛ࠶ࠫߣߥߞߡࠆߚߢࠆߣ⠨߃ࠄࠇࠆ㧚
߹ߚ
3
⒳㘃ߩ⏛᳇☼ᒢᕈߩਛߢߪ㧘㐳ߐ߇10[mm]
ߩ႐ว߇㧘⛉ࠅᯏ᭴ㇱญㇱߣญㇱߢߩᏅ߇ૐ ߊ㧘⛉ࠅᯏ᭴ㇱㅢㆊᓟ㧘ᱜߦ࿁ᓳߔࠆ〒㔌߇
18
㨇mm
㨉ߣᦨ߽⍴ߎߣ߇ಽ߆ߞߚ㧚0
2 4 6 8 10
0 500 1000 1500 2000
Re䌛-䌝
Cv䌛-䌝
5mm䋨Exp.䋩 10mm䋨Exp.䋩 15mm䋨Exp.䋩 5mm䋨CFD.䋩 10mm䋨CFD.䋩 15mm䋨CFD.䋩
Fig. 7. Comparison between experimental results and Computational Fluid Dynamics results
Flow 㨇Pa㨉 Pressure
1200
800
1200 400 0
800 Magneto-
rheological elastomers
400
23[mm]
Flow 㨇Pa㨉 Pressure
700
467
700 234 0
467 Magneto-
rheological elastomers
234
18[mm]
(a) H=0.141[MA/m], Re=1200, sample length=5[mm], Cv=2.96
(b) H=0.141[MA/m]
(c) H=0.282[MA/m]
(b) H =0.141[MA/m], Re=1200, sample length=10[mm], Cv=4.17
0 2 4 6 8 10
0 500 1000 1500 2000
Re[-]
Cv[-]
5mm䋨Exp.䋩 10mm䋨Exp.䋩 15mm䋨Exp.䋩 5mm䋨CFD.䋩 10mm䋨CFD.䋩 15mm䋨CFD.䋩
⚿⺰
⏛᳇☼ᒢᕈࠍ↪ߚᵹ㊂ᓮᑯߩᵹ㊂ᓮᯏ᭴ߦߟ
ߡᣂߚߦឭ᩺ߔࠆߎߣࠍ⋡⊛ߣߒ㧘േᵹᵹേᤨߦ ߅ߡ⛉ࠅᯏ᭴ㇱߩో㐳߇⛉ࠅᯏ᭴ㇱߩᒻ⁁ᄌൻ߮ᵹ ࠇߩേߦ߷ߔᓇ㗀ߦߟߡ⺞ᩏߒ㧘⠨ኤߒߚ⚿ᨐ㧘 એਅߩ⍮ࠍᓧߚ㧚
(1)
ශട⏛႐Hࠍᄌൻߐߖࠆߎߣߦࠃࠅ㧘⏛᳇☼ᒢ ᕈ⛉ࠅᯏ᭴ㇱߩೋᦼ㐿ญᢿ㕙Ⓧߩ㐿ญᓮ߇ น⢻ߢࠅ㧘⏛᳇☼ᒢᕈߩ㐳ߐߦࠃߞߡ㐿ญᓮ▸࿐߇⇣ߥࠆߎߣ߇⏕ߢ߈ߚ㧚
(2) 3
⒳㘃ߩ⏛᳇☼ᒢᕈߩਛߢߪ㧘㐳ߐ߇10[mm]
ߩ߽ߩ߇ᦨ߽㐿ญᢿ㕙Ⓧ߇ᄢ߈ߊ㧘ߘߩᦨᄢ㐿 ญ㕙ⓍᲧߪ㧘ශട⏛႐
0
҇H҇0.282
㨇MA/m
㨉ߩ▸࿐ߦ߅ߡ㧘
21/4.9=4.3
ߢߞߚ㧚߹ߚ㧘ࡅࠬ࠹ࠪࠬ߇ᦨ߽ዊߐߎߣ߇ಽ߆ߞߚ㧚
(3) ࠗࡁ࡞࠭ᢙRe
ߣᵹ㊂ଥᢙCvߣߩ㑐ଥ߆ࠄᓧࠄࠇߚታ㛎⚿ᨐߪ㧘ή⽶⩄ᤨߦ߅ߌࠆශട⏛႐ߣೋᦼ 㐿ญᢿ㕙Ⓧߣߩ㑐ଥߣ⋧㑐㑐ଥߦࠆߎߣ߇ಽ ߆ߞߚ㧚
(4)
ታ㛎୯߮CFD
ߦࠃࠆ⸃ᨆ୯ߩ⚿ᨐ߆ࠄ3
⒳㘃 ߩ⏛᳇☼ᒢᕈߩਛߢߪో㐳߇10[mm]߇ᦨ߽
ᵹ㊂ᓮ․ᕈ߇⦟ߎߣ߇ಽ߆ߞߚ㧚
ෳ⠨ᢥ₂
1) ⷰ㖸┙ਃ, ንჇብ, ⮮ᒄ,“▤ౝ᳇ᶧੑ⋧಄ᇦᵹ
ߩ⊒↢ߩ੍᷹ߣૐᷫ”, ਃ⪉㊀Ꮏᛛႎ , 28 , No.2, 135-142 (1991).
2) ᪢↰⍮Ꮘ, ਛᤘਃ, ዊ࿖⎇, ፉᢅᒾ, ਅᣂ৻, 㐳⺈, ഞಷ⢻ᢥ,“⤘ᒛᑯߦ࿃ߔࠆ಄ᇦ᳇ᶧੑ⋧ᵹ ߩᵹേૐᷫ”,ᣣᧄᯏ᪾ቇળ⺰ᢥ㓸(B✬), 59-557, 243-248 (1993).
3) ᪢↰⍮Ꮘ, ፉᢅᒾ, ਛᤘਃ, ⮮⦟ᰴ, ᷓ㊁ᔀ, દ
⮮ᱜ,“න৻ᄢ᳇⎔߇⛉ࠅࠍㅢㆊߔࠆߣ߈ߩ᳇ᶧੑ⋧
ᵹߩᵹേ㖸”, ᣣᧄᯏ᪾ቇળ⺰ᢥ㓸(B✬), 60-574, 56-63 (1994).
4) ⮮ᐽᒾ, ᧁ❥↵, 㥲⮮㓉ਯ, ᧁ✎㓉ᒄ, ᧻ᒾ,
“⤘ᒛᑯࠍㅢㆊߒߚ಄ᇦߩ᳇ᶧੑ⋧ᵹേ⽎ߩนⷞൻ, 㧙╙2ႎ⤘ᒛᑯ⛉ࠅᯏ᭴ㇱߩૐ㛍㖸ൻ”, ᣣᧄ಄ಓⓨ
⺞ቇળ⺰ᢥ㓸, 23-4, 67-78 (2006).
5) H. Yamaguchi, Y. Suzuki and S. Shuchi, “Membrane Formation Process in Magnetic Fluid and Application for Aperture Control”㧘Journal of Thermophysics and Heat Transfer, 17-1, 82-88 (2002).
6) H. Yamaguchi, Y. Suzuki and S. Shuchi, “Application of Magnetic Fluid Membrane for Flow Control”㧘Journal of Thermophysics and Heat Transfer, 17-1, 89-94(2002).
7) R. E. Rosensweig, “Ferrohydrodynamics”, University Press, Cambridge, 13 (1985).
8) ਛጊᵏ༑, ᵹߩജቇ, (㙃⾫ၴ㧘᧲੩㧘2005)㧘p.101.
9)
Miki, M., Yamaguchi, H. and Honda, N., Flow Characteristics of a Spool Valve (1st Report, Evaluation of Flow Behavior by Experimentation with an Aid of Three Dimensional Numerical Analysis) (in Japanese), Transactions of Japan Society of Mechanical Engineers, Series B, .69-679, 561-567 (2003).10) Miki, M., Yamaguchi, H., Tokunaga, H. and Ueno, D., Flow Characteristics of a Spool Valve (2nd Report, Modeling Method by Three-Dimensional Numerical Analysis and Evaluation of Flow Characteristics)(in Japanese), Transactions of Japan Society of Mechanical Engineers, Series B, 71-701, 38-39 (2005).
11) ᏒᎹᏱ㓶㧘᳓ജቇᵹജቇ, (ᦺୖᦠᐫ, ᧲੩, 2004), p.29.
12) SCRYU/Tetra User's Guide Basic Edition (in Japanese), (2007), p.3-10.
(c) H=0.141[MA/m], Re=1200, sample length=15[mm], Cv=2.25
Fig. 8. Pressure distribution Flow
㨇Pa㨉 Pressure
2000 1333
2000 -668 0
1333 Magneto-
rheological elastomers
25[mm] 668
