About support-interference-free aerodynamic force acting on a sphere with boundary layer trip around its critical Reynolds number

Ⴚ⇇ጀᒝ೙ㆫ⒖ߦ઻߁⥃⇇࡟ࠗࡁ࡞࠭ᢙ೨ᓟߩ⃿ߦ

૞↪ߔࠆᡰᜬᐓᷤߩή޿ⓨ᳇ജߦߟ޿ߡ

Ỉ↰⑲ᄦޔ㗇↰ା৻

ቝቮ⥶ⓨ⎇ⓥ㐿⊒ᯏ᭴✚วᛛⴚ⎇ⓥᧄㇱ

About support-interference-free aerodynamic force acting on a sphere with boundary layer trip around its critical Reynolds number

by

Hideo SAWADA, Shinichi SUDA (JAXA/IAT)

Abstract

Through advanced detail simulation tests, adjusting model mass and control factors made successful measurement of aerodynamic force on a sphere at Reynolds numbers around critical one at the JAXA 60cm magnetic suspension and balance system. The obtained averaged aerodynamic force for 8 seconds shows that the minimum drag coefficient after the critical Reynolds number reaches 0.062 and that any hysteresis phenomenon on drag coefficient with respect to Reynolds number was not observed around the critical one. Through the obtained fluctuations of aerodynamic force, the shrunk force fluctuating around the sphere axis parallel to main flow and some force swirling the sphere about the axis for a short time were observed at Reynolds numbers larger than the critical one. And some oscillating force on a plane including the axis was observed in the test of a sphere with double tapes for boundary layer trip in large Reynolds number region around the critical one.

㧝㧚ߪߓ߼ߦ

⃿ߩᛶ᛫᷹ቯߪฎߊ߆ࠄታᣉߐࠇߡ޿ߡޔ࡟ࠗࡁ࡞࠭

ᢙ㧔৻᭽ᵹㅦ U(m/s)ޔ⃿ߩ⋥ᓘ D(m)ޔേ☼ᕈଥᢙQm²/s ߣߔࠆߣ࡟ࠗࡁ࡞࠭ᢙReߪUDQߣቯ⟵ߐࠇࠆޕ㧕߇3×10⁵

ઃㄭߢᛶ᛫ଥᢙ㧔ᛶ᛫FD(N)ޔ৻᭽ᵹേ࿶q(Pa)ޔ⃿ߩᦨᄢ ᢿ㕙ⓍS(m²)ߣߔࠆߣޔᛶ᛫ଥᢙ C_DߪF_D/(qS)ߣቯ⟵ߐࠇ ࠆޕ㧕߇ᕆߦᷫዋߔࠆߎߣ߇⍮ࠄࠇߡ޿ࠆޕ․ߦޔCD߇0.3 ߦߥࠆᤨߩReࠍ⃿ߩ⥃⇇Reߣ๭߮ޔ㘑ᵢ᳇ᵹੂࠇߩ⒟ᐲ ࠍ␜ߔᜰᮡߣߒߡ߽೑↪ߐࠇߡ޿ࠆޕ⃿ߩ㘑ᵢ⹜㛎ߩᄙߊ ߪᓟᵹ߳ߩᡰᜬⵝ⟎ߩᓇ㗀ࠍ಴᧪ࠆ㒢ࠅዊߐߊߔࠆߚ߼ޔ

⃿ࠍ⚦޿ࠬ࠹ࠖࡦࠣߢᡰ߃ࠆ╬ޔ᭽ޘߥᎿᄦࠍᣉߒߡ޿ࠆ

1-3)ޕߒ߆ߒޔߤߩ႐วߢ߽ᮨဳࠍᡰ߃ߡ޿ࠆᡰᜬㇱ߿ࡢࠗ

ࡗ࡯߇ᮨဳ๟ࠅߩᵹࠇ߿ᓟᵹߦߤߩࠃ߁ߥᓇ㗀ࠍ෸߷ߔ߆ ߪචಽߦ⸃᣿ߐࠇߡ޿ߥ޿ޕᒰὼޔC_Dߦ߽ᐩ㕙࿶ߩ㆑޿╬

ࠍㅢߒߡᓇ㗀ߔࠆߎߣ߇⠨߃ࠄࠇࠆޕ

⏛ജᡰᜬᄤ⒊ⵝ⟎(એ㒠ޔMSBSߣ⸥ߔޕ)ߪ⏛᳇ߩജߢ 㘑ᵢᮨဳࠍᡰᜬߒޔᮨဳߦടࠊࠆⓨ᳇ജࠍ⸘᷹ߔࠆ߽ߩߢޔ ᡰᜬᐓᷤ߇ή޿ޕߎߩߚ߼ޔᓟᵹ߇ᄢ߈ߊᄌൻߔࠆ⥃⇇Re

ઃㄭߢߩ⃿ߩⓨ᳇ജ᷹ቯߦߪㆡߒߡ޿ࠆޕߒ߆ߒޔ⥃⇇Re

ઃㄭߢߪ⃿ߦ૞↪ߔࠆⓨ᳇ജ߇ỗߒߊᄌൻߔࠆߚ߼ޔ⏛ജ ᡰᜬߒߡ޿ࠆ⃿ߩ૏⟎ᄌേ߇ᄢ߈ߊߥࠅޔߎࠇ߹ߢߪᦨ㜞

Re߇3.8×10⁵⒟ᐲߢޔᮨဳࠍ⏛ജᡰᜬߢ߈ߥߊߥߞߡ޿ߚ

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࠹࡯ࡊࠍᮨဳ⴫㕙ߦ⾍ࠅ⹜㛎ࠍታᣉߒߚޕߘߩ⚿ᨐޔ⥃⇇

Re ࠍ⿥߃ޔ⃿߇ߤߩࠃ߁ߥⓨ᳇ജࠍฃߌࠆ߆ޔJAXA ߩ

60cmMSBS ࠍ ↪޿ߡ᷹ቯ ߔ ࠆߎߣ߇಴ ᧪ ߚޕJAXA ߩ

60cmMSBSߣߘࠇࠍⵝ஻ߒߚ㘑ᵢ㧔⏛ജᡰᜬ㘑ᵢ㧕ߩ⹦⚦

ߪᢥ₂5)ࠍෳᾖߐࠇߚ޿ޕ

㧞㧚ᄌേⓨ᳇ജኻ╷

⋥ᓘ 150mm ⃿ߢߪޔ⥃⇇Re ઃㄭߩ᛫ജᄌേߪ⚂0.1

⑽ߩ㑆ߦ 6N ⒟ᐲߩᄌൻ߇⊒↢ߒߡ޿ࠆޕ^6㧕ߒߚ߇ߞߡޔ ࡈࠖ࡯࠼ࡃ࠶ࠢ೙ᓮߪߎࠇߛߌߩᕆߥ᛫ജᄌൻߦኻߒߡ߽

ᮨဳࠍ৻ቯߩ૏⟎ߦ଻ᜬߒ⛯ߌࠆ⢻ജ߇ⷐ᳞ߐࠇࠆޕߘߎ ߢޔߎߩ⃻⽎ࠍᮨᡆߔࠆࡕ࠺࡞ࠍ૞ࠅޔߎߩ᛫ജᄌൻߦኻ ߒߡ᳇ᵹᣇะߩ૏⟎ᄌേߩࠪࡒࡘ࡟࡯࡚ࠪࡦࠍⴕ޿ޔ⥃⇇

Re ࠍ⿥߃ߡᮨဳࠍ቟ోߦ⏛ജᡰᜬߔࠆߚ߼ߩᣇ╷ߦߟ޿

ߡᬌ⸛ߒߚޕߥ߅ޔMSBSߢ೑↪ߒߡ޿ࠆᐳᮡ♽ߪ᷹ቯㇱ ਛᔃࠍᐳᮡේὐߣߒޔ㘑ᵢ᳇ᵹᣇะࠍxゲߦߣࠅޔ㋦⋥਄

ะ߈ࠍzゲߦߒߡޔߎࠇࠄߣ⋥੤ฝᚻ♽ࠍᚑߔࠃ߁ߦyゲ ࠍขߞߡ޿ࠆޕ⃿ߪ᷹ቯㇱਛᔃߦ⸳⟎ߔࠆࠃ߁ߦߒߡ޿ࠆޕ 㧔એ㒠ޔMSBSᐳᮡ♽ߣ๭߱ޕ㧕

JAXA 60cm MSBSߩ೙ᓮ♽ߢߪၮᧄ⊛ߦߪੑ㊀૏⋧ㅴ

ߺઃ߈ߩPI೙ᓮࠍណ↪ߒߡ߅ࠅ⁷⁾ޔᮨဳߩో⾰㊂ࠍmޔߎ ࠇߦ૞↪ߔࠆ⏛᳇ജࠍFmagޔⓨ᳇ജࠍFaeroߣߔࠆߣޔᮨဳ

ߩㆇേᣇ⒟ᑼߪᑼ(1)ߩࠃ߁ߦߥࠆޕ

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᛫ജࠦࠗ࡞ߦᵹߔ㔚ᵹߩᄢ߈ߐࠍ⴫ߔ߽ߩߣߔࠆޕ ࡈࠖ࡯࠼ࡃ࠶ࠢ೙ᓮࠍ฽߼ߚࠪࠬ࠹ࡓో૕ߩવ㆐㑐ᢙ ߪᑼ(2)ߩࠃ߁ߦߥࠆޕ

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ߎߎߢޔkpߪᲧ଀ቯᢙࠍޔTiߪⓍಽᤨ㑆ࠍ⴫ߒޔGcߪ᛫ജ

ࠦࠗ࡞ߩ೙ᓮⷐ⚛ޔHpޔHnޔHsensorߪߘࠇߙࠇ૏⋧ㅴߺⷐ

⚛ޔࡁࠗ࠭ࠞ࠶࠻ࡈࠖ࡞࠲࡯ⷐ⚛ޔx૏⟎ߩ࠮ࡦࠨ࡯ⷐ⚛

ߩવ㆐㑐ᢙࠍ⴫ߒߡ޿ࠆޕJAXA 60cm MSBS೙ᓮ♽ߩࡉࡠ

࠶ࠢ࿑ࠍ࿑㧝ߦ␜ߔޕ

⥃⇇Reࠍ⿧߃ࠆߚ߼ߩኻ╷ߩ৻ߟߣߒߡޔᮨဳ⾰㊂Ⴧ ടߐߖࠆߎߣ߇⠨߃ࠄࠇࠆޕ⾰㊂ࠍჇ߿ߖ߫ᄌേⓨ᳇ജߦ ኻߒߡ૏⟎ᄌേࠍዊߐߊ಴᧪ࠆߣ޿߁ߎߣߪᑼ(1)߆ࠄಽ ߆ࠆޕߘߎߢޔᮨဳߩ᧚⾰ࠍࠕ࡞ࡒ࠾ࡘ࠙ࡓ⵾߆ࠄ㤛㌃⵾

ߦᄌᦝߒޔో૕ߩ⾰㊂ࠍჇ߿ߔߎߣߦߒߚޕ⾰㊂7.0kgߩ రߩᮨဳߢߪޔᕆỗߦ6Nߩᄌേ߇⿠ߎߞߚ႐วޔᦨᄢ

3.5mmߩᄌ૏߇⊒↢ߒߡ޿ߚ߇ޔ଀߃߫⾰㊂ࠍ12.0kgߦჇ

߿ߖ߫ޔ2mm⒟ᐲߦ߹ߢᷫࠄߖࠆߎߣ߇ಽ߆ߞߚޕ

ੑߟ⋡ߩኻ╷ߣߒߡޔࡈࠖ࡯࠼ࡃ࠶ࠢ೙ᓮߦࠃࠆലᨐ

߽೨࿁ࠃࠅᒝൻߔࠆߎߣࠍ࿑ߞߚޕᲧ଀ቯᢙk_pߪࡈࠖ࡯࠼

ࡃ࠶ࠢߦࠃࠆ⏛᳇ജߩᄢ߈ߐࠍ᳿ቯߒޔⓍಽᤨ㑆ߪᮨဳ૏

⟎߇ߕࠇߡ߆ࠄࡈࠖ࡯࠼ࡃ࠶ࠢ߇૞↪ߔࠆ߹ߢߩᤨ㑆ࠍ᳿

ቯߔࠆޕߘߒߡޔߎࠇࠄߩ೙ᓮࡄ࡜ࡔ࡯࠲ࠍ⺞ᢛߔࠇ߫ޔ ᦨᄢᄌ૏ࠍ⚂1.1mmߦㄥᷫࠄߖࠆߎߣ߇್᣿ߒߚޕߎߩࠪ

ࡒࡘ࡟࡯࡚ࠪࡦ⚿ᨐࠍၮߦޔታ㓙ߦ✚⾰㊂10.7kgߩᮨဳࠍ

⵾૞ߒߚޕ

ߒ߆ߒkp߇ᄢ߈ㆊ߉ࠇ߫ޔᚗ޿ߪⓍಽᤨ㑆߇ዊߐㆊ߉ ࠇ߫ᮨဳߩ೙ᓮߪਇ቟ቯߣߥࠅᤃ޿ޕታ㓙ߩ⏛ജᡰᜬߢߪޔ

ᮨဳࠍ⪭ਅߐߖࠆߎߣߩή޿቟ోߥ⏛ജᡰᜬ߇᳞߼ࠄࠇޔ ታ㓙ߩᮨဳߩᔕ╵ࠍⷰኤߒߥ߇ࠄ೙ᓮቯᢙߦ⵬ᱜࠍട߃ࠆ ᔅⷐ߇޽ࠆޕᦨ⚳⊛ߦ೙ᓮቯᢙߩ⺞ᢛߪࠪࡒࡘ࡟࡯࡚ࠪࡦ

ᤨߩ߽ߩߣ⧯ᐓ⇣ߥࠅޔxᣇะߩ೙ᓮߢߪk_pߪ⚂10㧑Ⴧ߿

ߒޔⓍಽᤨ㑆ߪ2⑽ߣߒߚޕ

㧟㧚⹜㛎

⹜㛎ߦ↪޿ߚ੹࿁ߩ⃿ᒻᮨဳߢߪޔᒻ⁁᷹ቯߩ⚿ᨐޔx ゲ߆ࠄ53ᐲߣ233ᐲߩ૏⟎ߢో๟ߦਗ਼ࠅᮨဳធวㇱಽߢᮨ

ဳਔ┵ㇱಽߩᣇ߇⚂0.17mmߛߌ⋥ᓘ߇ᄢ߈ߊޔ೨ᣇߢߪᓟ ࠈะ߈ᲑᏅ߇ޔᓟᣇߢߪ೨ะ߈ᲑᏅ߇ᱷߐࠇߡ޿ࠆߎߣ߇

್ߞߚޕ․ߦ೨ᣇߩᓟࠈะ߈ᲑᏅߪ⥃⇇Reߦߤߩ⒟ᐲޔ߹

ߚߤߩ᭽ߦᓇ㗀ߔࠆ߆ਇ᣿ߢ޽ࠅޔߎ߁ߒߚᓇ㗀ࠍ⍮ࠆߚ

߼ߦធวㇱ⋥ਅᵹㇱಽߦ᏷⚂4mmߩ࠹࡯ࡊߢᲑᏅࠍᄌ߃ߡ 3ㅢࠅߦ⾍ࠅޔ⹜㛎ࠍታᣉߒߚޕ߹ߚޔ㊁⃿ࡏ࡯࡞ߦૃߖޔ

❔޿⋡ߦ⋧ᒰߔࠆㇱಽߦ᏷4mmߩෘ޿ࠪ࡯࡞࠹࡯ࡊ3ᧄࠍ2 ᨎ㊀ߨߢਗߴߡ⾍ߞߚ႐วߦߟ޿ߡ߽⺞ߴߚޕ࿑2ߦߎߩᮨ

ဳࠍ⏛ജᡰᜬߒߡ޿ࠆ᭽ሶࠍ␜ߔޕ

߹ߚޔ⴫1ߦ੹࿁ߩ⹜㛎ߢታᣉߒߚ✚ߡߩ⹜㛎ࠤ࡯ࠬࠍ

␜ߔޕߥ߅ޔ60cmⷺߩ᷹ቯㇱᢿ㕙ߦᲧߴᮨဳ⋥ᓘ߇150mm ߣᄢ߈޿ߩߢ㧔㒖ႧᲧ4.9㧑ޔ⃿ᦨᄢᢿ㕙㕙ⓍS(m²)ޔ᷹ቯ ㇱᢿ㕙ⓍA(m²)ߣߔࠆߣޔ㒖ႧᲧߪS/Aߣቯ⟵ߐࠇࠆޕ㧕ޔ⚂8

⑽㑆ߩᤨ㑆ᐔဋߒߚⓨജଥᢙߩ⹏ଔߢߪㅢᏱߩოᐓᷤ⵬ᱜ ߣߒߡޔ޿ࠊࠁࠆsolid blockage effect ߣ wake blockage effectߩ⵬ᱜࠍᢥ₂8)ߦᓥ޿᷹ቯ⚿ᨐߦᣉߒߚޕ

㧠㧚᷹ቯ⚿ᨐ

㧠㧚㧝 ᤨ㑆ᐔဋ᛫ജଥᢙ

⴫1ߢ␜ߒߚ5⒳㘃ߩ⹜㛎ߢᓧࠄࠇߚC_DߣReߩ㑐ଥ ࠍએ೨ታᣉߒߚ⌀⃿ߩ⚿ᨐ⁴⁾ߣ౒ߦ࿑3ߦ␜ߔޕࠤ࡯ࠬΣ ߢߪጀᵹႺ⇇ጀ߇ᒻᚑߐࠇߡ޿ࠆᚲߦ0.17mmߩᓟࠈะ߈ ᲑᏅ߇ゲኻ⒓ߦ᦭ࠅޔߎߩᲑᏅߪႺ⇇ጀߩᒝ೙ㆫ⒖࿃ሶߣ

ߒߡ௛ߊޕታ㓙ޔએ೨ߩ⌀⃿ߢߪC_Dߩᷫዋ߇ᆎ߹ߞߡ޿ߥ

޿Re߇3.5×10⁵⒟ᐲߢࠤ࡯ࠬΣߢߪCDߩᷫዋ߇ⷰࠄࠇࠆޕ

߹ߚޔReߦ㑐ߔࠆC_Dߩᷫዋ₸ߪએ೨ߩ߽ߩࠃࠅ߽ዊߐ޿ޕ

⥃⇇Reࠍ⿥߃ߚᓟߩCDߪ0.062ߣߥߞߚ߇ޔ੹࿁ߩ⹜

㛎ߢߪ⌀⃿ߣߪ⇣ߥࠅ0.17mmߩᓟࠈะ߈ᲑᏅ߇᦭ࠆ߇ޔ

⥃⇇Re⿥߃ߩCDߦ෸߷ߔߎߩᲑᏅߩᓇ㗀ߪዊߐ޿ߣ⠨߃ ࠄࠇޔ⌀⃿ߩC_Dߪዋߥߊߣ߽0.062એਅߣ⠨߃ࠆޕ

ࠤ࡯ࠬΤߩCDߣReߩ㑐ଥߪ⹜㛎ࠤ࡯ࠬΣߣ߶߷หߓ ߢ޽ࠆ߇ޔ⥃⇇Re⿥߃ߩC_D߇0.09ߣ⧯ᐓᄢ߈޿ޕ⹜㛎ࠤ

࡯ࠬΤߢߪవߩᓟࠈะ߈ᲑᏅ߇࠹࡯ࡊ1ᨎߦࠃࠅ߶߷⸃ᶖ ߐࠇޔᣂߚߦ4mmਅᵹߦߎߩᲑᏅ߇⒖േߒߡ޿ࠆޕߘߩᄖ ߦޔ࠹࡯ࡊࠍ⾍ࠅઃߌࠆ㓙ߦᵹࠇᣇะߩ⊿߇ߢ߈ޔߎࠇ߇ ࡏ࡞࠹࠶ࠢࠬࠫࠚࡀ࡟࡯࠲࡯ߩᓎഀࠍᨐߚߒߡ޿ࠆน⢻ᕈ ߇޽ࠆޕන⚐ߦ4mmߛߌᲑᏅ߇ਅᵹߦᄌ૏ߒߚߛߌߢޔ⥃

⇇Re⿥߃ߩC_D୯߇ᄌൻߒߚߣߪ⠨߃㔍ߊޔᵹࠇᣇะߩ⊿

߆ࠄ⺃⿠ߐࠇߚ❑᷵ߩᓇ㗀߽⠨߃ࠄࠇࠆޕ

ࠤ࡯ࠬΥߪ⚂0.17mmߩ೨ᣇᲑᏅߢޔߒ߆߽4mmਅᵹ

ߢߪ0.35mmߩᓟᣇᲑᏅ߇޽ࠆ႐วߣߥࠆޕߎߩᤨߩCDߣ

Reߩ㑐ଥߢߪ⥃⇇Re߇3.2×10⁵ߦ߹ߢᷫዋߒޔReߦ㑐ߔ ࠆCDߩᷫዋ₸߇ࠤ࡯ࠬΣߣΤߦᲧߴߡዊߐ޿ޕᦝߦޔ⥃⇇

Re⿥߃ߩC_Dߪ0.13ߣࠤ࡯ࠬΤߩ႐วࠃࠅᄢ߈޿ޕ ࠤ࡯ࠬΦߪࠤ࡯ࠬΥࠃࠅ߽ᦝߦ㜞޿ᲑᏅߩ႐วߢޔ⥃

⇇Reߪ1.43×10⁵ߣߥࠅᄢ᏷ߦዊߐ޿ޕ߹ߚޔC_Dߪ⥃⇇Re ࠍ⿥߃ߚᓟ߽ Re ߩჇടߦ઻޿ᄌൻߔࠆޕߘߩਛߢᦨዊߩ C_Dߪ0.16⒟ᐲߢ޽ߞߚޕ

ࠤ࡯ࠬΣ߆ࠄΥߢߪ⥃⇇Reࠍ⿥߃ߚᓟߦޔౣ߮Reࠍ

ᷫዋߐߖߡC_Dࠍ᷹ቯߒߚ߇ޔ⥃⇇ReઃㄭߢC_Dᄌൻߦ㑐 ߔࠆ᦭ᗧߥጁᱧ⃻⽎ߪ᷹ⷰߐࠇߥ߆ߞߚޕ

Achenbachߩታ㛎⁹⁾ߢߪ⃿ߦ࡜ࡈࡀࠬࠍઃߌࠆߣޔRe ߇ჇടߔࠆߦߟࠇߡCDߪᭂዊ୯ࠍขࠅޔᦨ⚳⊛ߦ0.4ㄭ޿

୯ߦ߹ߢ࿁ᓳߔࠆ⃻⽎߇ⷰኤߐࠇߡ޿ࠆ߇ޔᧄ⹜㛎ߢߪో

ߊⷰኤߐࠇߥ߆ߞߚޕReᄌൻߦኻߔࠆCDߩߎ߁ߒߚ᜼േ

ߪ⃿ᓟᣇߢࠬ࠹ࠖࡦࠣᡰᜬࠍߒߡ޿ࠆᓇ㗀ߩน⢻ᕈ߇᦭ࠆޕ ࠤ࡯ࠬΧߪ㊁⃿ߩࡏ࡯࡞ߦૃߖޔ❔޿⋡ߦ⋧ᒰߔࠆㇱ ಽߦ᏷4mmߩෘ޿ࠪ࡯࡞࠹࡯ࡊ3ᧄࠍ2ᨎ㊀ߨߢਗߴߡ⾍

ࠅޔᮨဳߩᛶ᛫ࠍ᷹ቯߒߚ߽ߩߢ޽ࠆޕRe߇0.5×10⁵ߢᣢ ߦ⃿ߩC_Dߣߪ⇣ߥࠆ୯ࠍ␜ߒߡ޿ࠆޕ⥃⇇Reߪ2.5×10⁵ ߢ޽ࠆ߇ޔCDߩᷫዋ㊂߽ઁߩ3⒳ߣᲧߴߡᄢ᏷ߦዊߐ޿ޕ ߎߩߎߣ߆ࠄࠤ࡯ࠬΧߪ⃿๟ࠅᵹࠇߣߪ߆ߥࠅ߆ߌ㔌ࠇߚ

߽ߩߣផቯߐࠇࠆޕ

㧠㧚㧞 ᵹࠇߦ⋥ⷺᣇะߩᤨ㑆ᐔဋⓨ᳇ജ㧔ᮮജ㧕ଥᢙ

ജᚑಽࡌࠢ࠻࡞ࠍ␜ߔߎߣߦߔࠆޕ࠹࡯ࡊߪxゲ๟ࠅߦゲ ኻ⒓ߦ⾍ࠅઃߌߚߩߢޔ⹜㛎ࠤ࡯ࠬΧࠍ㒰߈ޔᮮജᣇะࠍ

․ቯߐߖࠆⷐ⚛ߪήߊޔᮮജߩะ߈ߪ஧ὼߢ޽ࠅޔᐔဋ㊂ ߦ㑐ߒߡߪߘߩᄢ߈ߐߦߩߺᵈ⋡ߔࠆޕ࿑4ߦᮮജଥᢙࡌ

ࠢ࠻࡞㧔⃿ߦ૞↪ߔࠆⓨ᳇ജࡌࠢ࠻࡞ࠍ㧔Fx, Fy, Fz㧕(න૏㧦 N)ߣߔࠆߣޔᮮജଥᢙࡌࠢ࠻࡞ߪ㧔Fy/(qS), Fz/(qS)㧕ߣቯ⟵

ߐࠇࠆޕ㧕ߩᄢ߈ߐߣReߩ㑐ଥࠍ␜ߔޕ

ࠤ࡯ࠬΣߣΤߢߪ⥃⇇Reߦㄭߠߊߦߟࠇߡᮮജଥᢙ߇ Ⴧᄢߒߡ޿ࠆ߇ޔᭂᄢ୯ߪ0.1⒟ᐲߢCDߦᲧߴࠆߣዊߐ޿ޕ

߹ߚޔRe߇3.5×10⁵ࠍ⿥ߔߣࠤ࡯ࠬΣߢߪᮮജଥᢙߪᱴߤ 0ߣߥࠆ߇ޔࠤ࡯ࠬΤߢߪ0߆ࠄ0.1ߩ㑆ߢᄌൻߒ৻ቯߩ௑

ะࠍ␜ߐߥ޿ޕ৻ᣇޔࠤ࡯ࠬΥߢߪRe߇2.1×10⁵ㄝࠅ߆ࠄ ᕆㅦߦᮮജଥᢙ߇Ⴧടߒ0.2એ਄ߣߥࠆޕᦝߦޔRe߇2.8×10⁵ ㄝࠅߢᭂᄢ୯ࠍขࠅޔߘߩᓟᷫዋߔࠆޕ߹ߚޔRe߇2.5×10⁵ ㄝࠅࠍਛᔃߦߒߡᄢ߈ߥጁᱧ߇᷹ⷰߐࠇߡ޿ࠆޕߎߩߎߣ ߆ࠄޔࠤ࡯ࠬΥߢߪ⃿⴫㕙ߩᐔဋ⊛ߥ೸㔌✢ߩxゲ๟ࠅߦ 㑐ߔࠆኻ⒓ᕈ߇ᄢ߈ߊ፣ࠇߡ޿ࠆߣ⠨߃ࠄࠇࠆޕᓟㅀߔࠆ ᄌേⓨ᳇ജߦߟ޿ߡ⺞ߴࠆߣޔRe߇2.5×10⁵ઃㄭߢߪC_D ߪ0.5ㄭ޿୯ࠍ␜ߒߥ߇ࠄޔⓨ᳇ജᄌേ߇ᭂዊߦߥߞߡ߅

ࠅޔᭂ߼ߡ⥝๧ᷓ޿⃻⽎ࠍ␜ߒߡ޿ࠆޕ߹ߚޔRe߇3.5×10⁵ એ਄ߢߪࠤ࡯ࠬΤߣห᭽ߩᄌൻࠍ␜ߒߡ޿ࠆޕ

㧡㧚ᄌേⓨ᳇ജ

MSBS ߢߪࠦࠗ࡞೙ᓮ㔚ᵹ߆ࠄᮨဳߦ૞↪ߒߡ޿ࠆ⏛

᳇ജࠍផቯߢ߈ࠆߩߢޔᮨဳߩ૏⟎ᖱႎ߆ࠄᮨဳߩᘠᕈജ ࠍ⹏ଔߔࠇ߫ޔㆇേᣇ⒟ᑼ߆ࠄⓨ᳇ജߩᤨ㑆ᄌൻࠍផቯ಴

᧪ࠆޕ⹦⚦ߪᢥ₂ 10)ࠍෳᾖߐࠇߚ޿ޕᧄ⹜㛎ߩ೙ᓮ๟ᵄ

ᢙߪ248Hzߢޔᘠᕈജ⹏ଔᤨߦ10Hzߩࡠ࡯ࡄࠬࡈࠖ࡞࠲

࡯ࠍ↪޿ߡ޿ࠆޕ

ⓨ᳇ജଥᢙࡌࠢ࠻࡞㧔⃿ߦ૞↪ߔࠆⓨ᳇ജࡌࠢ࠻࡞ࠍ 㧔Fx, Fy, Fz㧕(න૏㧦N)ߣߔࠆߣޔⓨ᳇ജଥᢙࡌࠢ࠻࡞ߪ 㧔Fx/(qS), F_y/(qS) , F_z/(qS)㧕ߣቯ⟵ߐࠇࠆޕMSBSᐳᮡ♽ߢ

⴫ߒߡ޿ࠆߩߢޔFD=㧙Fxߩ㑐ଥ߇᦭ࠆޕ㧕ࠍxゲߦ⋥੤ߔ ࠆᢿ㕙߳኿ᓇߔࠆߣޔ⃿ߦ૞↪ߔࠆᮮജᄌേߩ᭽ሶࠍ᷹ⷰ

಴᧪ࠆޕ࿑5ߪࠤ࡯ࠬΣߩ႐วߢޔRe߇Ⴧ߃ࠆߦߟࠇߡᮮ ജଥᢙߩⓨ㑆ᄌേ߇ỗߒߊߥࠅޔߘߩᓟ෼߹ࠆ᭽ሶ߇ⷰኤ ߐࠇࠆޕReߦ㑐ߔࠆCDᷫዋ₸߇ᦨᄢߦߥࠆReߢᮮജଥᢙ ߩⓨ㑆ᄌേ߽ᦨᄢߣߥࠆޕᦝߦޔᄌേߪ߶߷ὐኻ⒓ߢᣇะ ᕈߪⷰኤߐࠇߥ޿ޕ߹ߚޔRe߇3.58×10⁵એ਄ߦߥࠆߣޔᮮ ജߩ゠〔ߢਛᔃㇱಽࠍㅢㆊߔࠆ⏕₸߇๟ࠅߦᲧߴߡ⋧ኻ⊛

ߦૐߊߥߞߡ޿ࠆޕߎߩߎߣߪⓨ᳇ജᄌേ߇xゲߦኻߒߡ

௑޿ߡ޿ߥ߇ࠄޔหᤨߦxゲ๟ࠅߦᣓ࿁⊛ߦ૞↪ߒߡ޿ࠆ ߎߣࠍ␜ߒߡ޿ࠆޕߎߩ⃻⽎ߪ⃿ߦㄭ޿ super pressure balloonߩ਄᣹ᤨߦ᷹ⷰߐࠇߡ޿ࠆ”helical motion”ߦኻᔕߒ ߡ޿ࠆߣ⠨߃ࠄࠇࠆ ¹¹⁾ޕ߹ߚޔ⒳ሶ↰ߩታ㛎 ²⁾ߢ 5.0×10⁵ ࠃࠅᄢ߈޿Reߢᾍߦࠃࠆนⷞൻߢⷰኤߐࠇߚᝄ᏷180ᐲ એਅߩᓟᵹߩ࿁ォ⊛ᝄേ⃻⽎ߦૃߡ޿ࠆޕᧄ⹜㛎ߢߎߩ࿁

ォߦኻᔕߔࠆ๟ᵄᢙߪRe߇3.76×10⁵ߢ⚂1.5Hz߇ਥⷐߥ

๟ᵄᢙߢ޽ࠅޔࠬ࠻ࡠ࡯ࡂ࡞ᢙ㧔f㧦ᄌേ๟ᵄᢙ㧔Hz㧕ߣߔ ࠆߣޔࠬ࠻ࡠ࡯ࡂ࡞ᢙStߪf㨯D/Uߣቯ⟵ߐࠇࠆޕ)ߦ឵▚

ߔࠆߣ⒳ሶ↰ߩ᷹ⷰ⚿ᨐߦ߶߷ㄭ޿୯ߦߥߞߡ޿ࠆޕ

ᰴߦޔᮮゲߦC_Dޔ❑ゲߦᮮജଥᢙߩᄢ߈ߐࠍขߞߡޔ หߓReߦኻߒߡឬߊߣ࿑6ߦߥࠆޕⓨ᳇ജ߇xゲ๟ࠅߦᣓ

࿁ߔࠆࠃ߁ߦ૞↪ߔࠆߣޔC_Dߩᄌേߪߘࠇ߹ߢߦᲧߴߡᕆ ߦᄢ߈ߊߥࠅޔᮮജᄌേߣห⒟ᐲߦߥࠆޕᦝߦޔᄌേߪේ

ὐࠍㅢࠅxゲߦኻߒߡ⚂35ᐲ௑޿ߚ⋥✢๟ࠅߦ㓸ਛߒߡ޿

ࠆޕRe ߇ᦝߦჇടߔࠆߣᄌേ⥄૕߇ዊߐߊߥࠅޔCD߽ᷫ

ዋߒߡ޿ߊޕߎߩߎߣߪޔRe߇Ⴧടߔࠆߦߟࠇߡޔ⃿ਛᔃ ࠍ㗂ὐߦߒߚ㗂ⷺ⚂ 70 ᐲߩ౞㍙㕙਄ࠍⓨ᳇ജଥᢙߪᄌേ

ߒߥ߇ࠄᄢ߈ߐࠍᷫዋߐߖߡ޿ߊ߽ߩߣ⠨߃ࠄࠇࠆޕߒ߆ ߒޔCDߩᷫዋ߇෼߹ࠆRe߇3.9×10⁵ઃㄭߢߎߩ௑ะߪⷰኤ ߐࠇߥߊߥࠆޕ

ࠤ࡯ࠬΤߢߪࠤ࡯ࠬΣߩⓨ᳇ജᄌേߩ௑ะߣߪ߶߷ห ߓ௑ะࠍⷰኤߒߚ߇ޔࠤ࡯ࠬΣ߶ߤ᣿⍎ߥᣓ࿁⊛ߥജᄌേ

ߪⷰኤߐࠇߥ߆ߞߚޕ߹ߚޔ⹜㛎ߒߚᦨᄢߩ Re ߢ߽ᮮജ ଥᢙߩᄌേߩᄢ߈ߐߪࠤ࡯ࠬΣ߶ߤዊߐߊߪߥࠄߥ߆ߞߚޕ

৻ᣇޔ࿑7ߣ8ߦ␜ߔࠃ߁ߦޔࠤ࡯ࠬΥߩⓨ᳇ജᄌേ

ߪߘࠇࠄߣోߊ⇣ߥߞߚ௑ะࠍ␜ߒߡ޿ࠆޕRe߇2.1×10⁵

⒟ᐲߢߪᮮജଥᢙߩᄌേߪࠤ࡯ࠬΣߣห᭽ߦゲኻ⒓⊛ߢ޽

ࠆ߇ޔߘߩᓟޔReߩჇടߦ઻޿ᕆߦᮮജ߇⊒↢ߒޔᦝߦᄌ

േ߇߶߷xゲࠍᮮಾࠆࠃ߁ߦ෻ኻ஥߹ߢჇᄢߒޔxゲߦኻ ߒߡኻ⒓ߥᄌേߦᚑ㐳ߒޔߘߩᓟߪޔࠤ࡯ࠬΣߩ႐วߣห

᭽ߦⓨ᳇ജ߇xゲߦኻߒߡ௑޿ߡޔxゲ๟ࠅߦᣓ࿁ߔࠆࠃ ߁ߦ૞↪ߔࠆޕߎߩxゲࠍ฽߻ᐔ㕙ౝߩᝄേ⃻⽎ߪ⃿ߦㄭ

޿super pressure balloonߩ਄᣹ᤨߦᐔ㕙ౝߩ”wavy motion”

ߣߒߡ᷹ⷰߐࠇߡ޿ࠆ߽ߩߦኻᔕߒߡ޿ࠆߣ⠨߃ࠄࠇࠆ¹¹⁾ޕ ߥ߅ޔ࿑9ߦޔ࡟ࠗࡁ࡞࠭ᢙჇടߦ઻߁ߎߩᝄേߩᮮജଥ ᢙߩ᳓ᐔᣇะᚑಽߩᤨ㑆ᄌേߩᄌൻߩ᭽ሶࠍ␜ߔޕ1 ⑽㑆 ߆ࠄ2⑽㑆ߦࠊߚࠅޔ৻ᣇߩ୯ߦṛ⇐ߒޔߘߩᓟᕆߦ෻╓

ภ஥ߩ୯ߦ⒖േߒߡṛ⇐ߔࠆޕᦝߦ࡟ࠗࡁ࡞࠭ᢙ߇Ⴧടߔ ࠆߣޔߎ߁ߒߚṛ⇐ߔࠆᤨ㑆߇⍴ߊߥࠅޔ৻ᣇߩ୯ߦṛ⇐

ߔࠆ௑ะߪ⷗ࠄࠇߥߊߥࠆߩ߇್ࠆޕ

߹ߚޔ࿑ 7 ߆ࠄޔⓨ᳇ജଥᢙߪ⃿ਛᔃࠍ㗂ὐߦߒߚ㗂

ⷺ⚂90ᐲߩ౞㍙㕙਄ࠍᄌൻߒߡ޿ࠆ߇ޔRe߇Ⴧടߒߡ߽ޔ ᮮജଥᢙߩᄌേၞߩᄢ߈ߐߪᷫዋߒߥߊߥࠆὐ߇ࠤ࡯ࠬΣ ߣ⇣ߥߞߡ޿ࠆޕ

㧢㧚߹߹ߣ߼

੐೨ߦ⹦⚦ߥࠪࡒࡘ࡟࡯࡚ࠪࡦࠍታᣉߒޔᮨဳ⾰㊂ߩ

⺞ᢛޔ೙ᓮቯᢙߩౣ⺞ᢛ╬ࠍታᣉߔࠆߎߣߢޔJAXA 60cm MSBSߢ⃿ߩ⥃⇇Re⿥߃ߩⓨ᳇ജࠍ᷹ቯ಴᧪ߚޕߘߩ⚿ᨐޔ

⃿ߩ⥃⇇ Re ೨ᓟߢߩ⃿ߦ૞↪ߔࠆᐔဋⓨ᳇ജޔᄌേⓨ᳇

ജߦ㑐ߔࠆએਅߩ⍮⷗ࠍᓧࠆߎߣ߇಴᧪ߚޕ

1) 8⑽㑆ߦਗ਼ࠆᐔဋⓨ᳇ജ߆ࠄ⥃⇇Re⿥߃ߩᦨዊᛶ᛫୯ ߪ⚂0.062ߢ޽ࠆޕ

2) C_DߣReߩ㑐ଥߢߪޔReᄌൻߦ઻߁᣿⍎ߥጁᱧߪⷰࠄ ࠇߥ޿ޕ

3) C_D߇0.3ᧂḩߢߪ⃿ߩxゲ๟ࠅߦജ߇❗ㅌߒߡ޿ߊ᭽

ሶ߿ޔ⃿ࠍxゲ๟ࠅᣓ࿁ߐߖࠆജ߇⊒↢ߔࠆ᭽ሶࠍ᷹ⷰ

ߒߚޕ

4) ᒝ೙⊛Ⴚ⇇ጀㆫ⒖߇ᒝ޿ߣޔxゲࠍ฽߻ᐔ㕙ౝߢᝄേ⊛

ജ߇૞↪ߔࠆ႐วࠍ᷹ⷰߒߚޕ

޽ߣ߇߈

੹࿁ߩ⹜㛎ߦࠃࠅޔMSBSࠍ↪޿ߚᄌേⓨ᳇ജ᷹ቯߪᄢ ⷙᮨ೸㔌ࠍ઻߁㊰㗡‛૕๟ࠅߩᵹࠇࠍ⎇ⓥߔࠆ਄ߢޔ⾆㊀ ߥᖱႎࠍឭଏߢ߈ࠆߎߣ߇ಽ߆ߞߚޕߎߩߎߣߪޔᄢⷙᮨ

೸㔌ࠍ઻߁㊰㗡‛૕๟ࠅߩᵹࠇߩ CFD ᬌ⸽ߢߪᵹࠇ႐ߩ นⷞൻ⚿ᨐߩᲧセߣ޿ߞߚቯᕈ⊛Ყセ߇⃻࿷ߪਥᵹߢ޽ࠆ ߇ޔ੹ᓟޔMSBSࠍ↪޿᷹ቯߒߚ․㐳⊛ജᄌേࠍᲧセߔࠆ ߎߣߦࠃࠅቯ㊂⊛CFDᬌ⸽߇น⢻ߣߥࠅޔା㗬ᕈࠍ਄ߍࠆ ߎߣ߇ᦼᓙߢ߈ࠆޕ

੹ᓟߪޔ⌀⃿ߩ⥃⇇ Re ⿥߃ߩ⹜㛎ࠍታᣉߔࠆߣ౒ߦޔ MSBSࠍ↪޿ߡᡰᜬᐓᷤߩή޿⁁ᘒߦ߅ߌࠆᓟᵹߩᐔဋᵹ ࠇ႐ޔᄌേᵹࠇ႐⸘᷹ࠍታᣉߔࠆ੍ቯߢ޿ࠆޕߣࠅࠊߌޔ ᵹࠇ႐⸘᷹ߩ㓙ߩ⸘᷹ⵝ⟎ߩᐓᷤࠍㆱߌࠆߦߪPIV⸘᷹߇ ᦸ߹ߒߊޔ੹ᓟߎߩಽ㊁ߩ⎇ⓥ⠪ߣߩදജࠍ᳞߼ߚ޿ޕ

ෳ⠨ᢥ₂

1) Berger, E., Sholtz, D., and Schumm, M. : “Coherent Vortex Structures in the Wake of a Sphere and a Circular Disk at Rest and under Forced Vibrations”, J. Fluid and

Structures(1990), Vol.4, pp.231-257

2) Taneda, S., “Visual Observations of the Flow past a Sphere at Reynolds numbers between 104 and 106,” J. Fluid Mech., Vol. 85, part 1, pp. 187-192, 1978

3) Achenbach,E., “Experiments on the Flow past Spheres at very High Reynolds Numbers,” J. Fluid Mech., Vol. 54, part 3, pp. 565-575, 1972

4) Ỉ↰⑲ᄦޔ࿖⋉ᔀ਽ޔ㗇↰ା৻㧦ޟ⥶ᛛ⎇60cm⏛ജᡰᜬ ᄤ⒊ⵝ⟎ࠍ↪޿ߚ⃿ᒻᮨဳߩ᛫ജ᷹ቯޠޔᣣᧄ㘑Ꮏቇ⺰

ᢥ㓸ޔVol.98ޔ 2004ᐕ1᦬ภ

5) Ỉ↰⑲ᄦޔ࿖⋉ᔀ਽㧦ޟૐㅦ㘑ᵢ↪60cm⏛ജᡰᜬⵝ⟎ߩ 㐿⊒ޠޔᣣᧄ⥶ⓨቝቮቇળ⺰ᢥ㓸ޔ╙50Ꮞޔ╙580ภޔ pp.188-195ޔ2002ᐕ5᦬ภ

6) 㗇↰ା৻ޔỈ↰⑲ᄦ㧦ޟ㘑ᵢ↪⏛ജᡰᜬᄤ⒊ⵝ⟎ޠޔᣣᧄ

⸳⸘Ꮏቇળ⹹ޔ╙41Ꮞޔ╙5ภޔpp.235-241ޔ2006ᐕ 7) Sawada,H., Suda,S., and Kunimasu,T.: “NAL 60cm

Magnetic Suspension and Balance System”, ICAS 2004-3.1.2, August, 2004

8) Pankhurst,R.C. and Holder, D. W., “WIND-TUNNEL TECHNIQUE,” SIR ISAAC PITMAN & SONS, LTD, pp.340-348, 1948

9) Achenbach,E., “The effect of surface roughness and tunnel blockage on the flow past sphere,” J. Fluid Mech., Vol. 65,

part 1, pp. 113-125, 1974

10) Ỉ↰⑲ᄦޔᮘญඳޔട⮮⵨ਯޔ࿖⋉ᔀ਽ޔޟ⏛ജᡰᜬ㘑 ᵢ⹜㛎ߦ߅ߌࠆ㕖ធ⸅⸘᷹ޠޔ╙38࿁ᵹ૕ജቇ⻠Ṷળ೨

೚㓸ޔpp.169-172ޔ2006ᐕ9᦬

11) Soggins,J.R., “Sphere Behavior and Measurement of Wind Profiles,” NASA TN D-3994, 1967

⴫1 ⹜㛎ࠤ࡯ࠬ

⹜㛎 ࠤ࡯ࠬ

࠹࡯ࡊ

ෘ(mm) ᨎ ᢙ

᏷ (mm)

૏⟎ ஻⠨

ḩᴾ ήߒ ធวㇱ ᲑᏅ᦭

Ḫᴾ 0.17 1 4 ធวㇱ

ḫᴾ 0.17 2 4 ធวㇱ

Ḭᴾ 2㨪3 1 4 ធวㇱ

ḭᴾ 2㨪3 2 12 ᡆૃ㊁⃿

ࡏ࡯࡞

࿑㧝 JAXA 60cm MSBSߩ೙ᓮ♽

࿑2 ⏛ജᡰᜬਛߩࠤ࡯ࠬΧߩᮨဳ

0.0 0.1 0.2 0.3 0.4 0.5 0.6

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Reynolds number (million)

drag coefficient

sphere case 㸇 case 㸈 case 㸉 case 㸊 case 㸋

࿑3 C_DߣReߩ㑐ଥ

0.0 0.1 0.2 0.3 0.4 0.5 0.6

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Reynolds number (million)

Cside force

case 㸇 case 㸈 case 㸉

࿑4 ᮮജଥᢙߣReߩ㑐ଥ

䎓 䎓

䎕䎔䎛䎓䎓䎓

䎓 䎓

䎕䎗䎜䎓䎓䎓

䎓 䎓

䎕䎛䎓䎓䎓䎓

䎓 䎓

䎖䎔䎔䎓䎓䎓

䎓 䎓

䎖䎖䎘䎓䎓䎓

䎓 䎓

䎖䎗䎚䎓䎓䎓

䎓 䎓

䎖䎘䎛䎓䎓䎓

䎓 䎓

䎖䎙䎚䎓䎓䎓

䎓 䎓

䎖䎚䎙䎓䎓䎓

䎓 䎓

䎖䎛䎗䎓䎓䎓

䎓 䎓

䎖䎜䎘䎓䎓䎓

䎓 䎓

䎗䎕䎖䎓䎓䎓

࿑5 CASEΣߩᮮജଥᢙᄌേ

㧔⃿ᓟᣇ߆ࠄⷰߚ႐วޕᱜᣇᒻߩ৻ㄝߩ㐳ߐߪⓨജଥᢙߢ 1.0ߦ⋧ᒰޕฦ࿑਄ᣇߩᢙ୯ߪReࠍ␜ߔޕ㧕

䎓䎑䎘 䎓䎑䎘

䎕䎔䎛䎓䎓䎓

䎓䎑䎘 䎓䎑䎘

䎕䎗䎜䎓䎓䎓

䎓䎑䎘 䎓䎑䎘

䎕䎛䎓䎓䎓䎓

䎓䎑䎘 䎓䎑䎘

䎖䎔䎔䎓䎓䎓

䎓䎑䎘 䎓䎑䎘

䎖䎖䎘䎓䎓䎓

䎓䎑䎘 䎓䎑䎘

䎖䎗䎚䎓䎓䎓

䎓䎑䎘 䎓䎑䎘

䎖䎘䎛䎓䎓䎓

䎓䎑䎘 䎓䎑䎘

䎖䎙䎚䎓䎓䎓

䎓䎑䎘 䎓䎑䎘

䎖䎚䎙䎓䎓䎓

䎓䎑䎘 䎓䎑䎘

䎖䎛䎗䎓䎓䎓

䎓䎑䎘 䎓䎑䎘

䎖䎜䎘䎓䎓䎓

䎓䎑䎘 䎓䎑䎘

䎗䎕䎖䎓䎓䎓

࿑6 CASEΣߩ᳇ᵹߦᐔⴕᐔ㕙ౝⓨജଥᢙᄌേ

㧔ᮮゲߪ CDޔ❑ゲߪᮮജଥᢙߩᄢ߈ߐޕᱜᣇᒻߩ৻ㄝߩ㐳 ߐߪⓨജଥᢙߢ1.0ߦ⋧ᒰޕᏀਅࠍේὐߣߒߡ޿ࠆޕฦ࿑਄

ᣇߩᢙ୯ߪReࠍ␜ߔޕ㧕

䎓 䎓

䎕䎔䎚䎓䎓䎓

䎓 䎓

䎕䎖䎚䎓䎓䎓

䎓 䎓

䎕䎜䎕䎓䎓䎓

䎓 䎓

䎖䎓䎙䎓䎓䎓

䎓 䎓

䎖䎔䎙䎓䎓䎓

䎓 䎓

䎖䎕䎚䎓䎓䎓

䎓 䎓

䎖䎗䎓䎓䎓䎓

䎓 䎓

䎖䎘䎘䎓䎓䎓

䎓 䎓

䎖䎙䎛䎓䎓䎓

䎓 䎓

䎖䎚䎚䎓䎓䎓

䎓 䎓

䎗䎓䎕䎓䎓䎓

䎓 䎓

䎗䎔䎘䎓䎓䎓

࿑7 CASEΥߩᮮജଥᢙᄌേ㧔ᐳᮡ઀᭽ߪ࿑4ߣหߓ㧕

䎓䎑䎘 䎓䎑䎘

䎕䎔䎚䎓䎓䎓

䎓䎑䎘 䎓䎑䎘

䎕䎖䎚䎓䎓䎓

䎓䎑䎘 䎓䎑䎘

䎕䎜䎕䎓䎓䎓

䎓䎑䎘 䎓䎑䎘

䎖䎓䎙䎓䎓䎓

䎓䎑䎘 䎓䎑䎘

䎖䎔䎙䎓䎓䎓

䎓䎑䎘 䎓䎑䎘

䎖䎕䎚䎓䎓䎓

䎓䎑䎘 䎓䎑䎘

䎖䎗䎓䎓䎓䎓

䎓䎑䎘 䎓䎑䎘

䎖䎘䎘䎓䎓䎓

䎓䎑䎘 䎓䎑䎘

䎖䎙䎛䎓䎓䎓

䎓䎑䎘 䎓䎑䎘

䎖䎚䎚䎓䎓䎓

䎓䎑䎘 䎓䎑䎘

䎗䎓䎕䎓䎓䎓

䎓䎑䎘 䎓䎑䎘

䎗䎔䎘䎓䎓䎓

࿑8 CASEΥߩ᳇ᵹߦᐔⴕᐔ㕙ౝⓨജଥᢙᄌേ

㧔ᐳᮡ઀᭽ߪ࿑5ߣหߓ㧕

䎓 䎕 䎗 䎙 䎛

䎐䎓䎑䎘 䎓 䎓䎑䎘

䏗䏌䏐䏈䎃䎋䏖䎌

䎦䎼

䎕䎓䎕䎓䎓䎓

䎓 䎕 䎗 䎙 䎛

䎐䎓䎑䎘 䎓 䎓䎑䎘

䏗䏌䏐䏈䎃䎋䏖䎌

䎦䎼

䎕䎕䎜䎓䎓䎓

䎓 䎕 䎗 䎙 䎛

䎐䎓䎑䎘 䎓 䎓䎑䎘

䏗䏌䏐䏈䎃䎋䏖䎌

䎦䎼

䎕䎛䎘䎓䎓䎓

䎓 䎕 䎗 䎙 䎛

䎐䎓䎑䎘 䎓 䎓䎑䎘

䏗䏌䏐䏈䎃䎋䏖䎌

䎦䎼

䎖䎓䎓䎓䎓䎓

䎓 䎕 䎗 䎙 䎛

䎐䎓䎑䎘 䎓 䎓䎑䎘

䏗䏌䏐䏈䎃䎋䏖䎌

䎦䎼

䎖䎔䎓䎓䎓䎓

䎓 䎕 䎗 䎙 䎛

䎐䎓䎑䎘 䎓 䎓䎑䎘

䏗䏌䏐䏈䎃䎋䏖䎌

䎦䎼

䎖䎕䎓䎓䎓䎓

䎓 䎕 䎗 䎙 䎛

䎐䎓䎑䎘 䎓 䎓䎑䎘

䏗䏌䏐䏈䎃䎋䏖䎌

䎦䎼

䎖䎖䎖䎓䎓䎓

䎓 䎕 䎗 䎙 䎛

䎐䎓䎑䎘 䎓 䎓䎑䎘

䏗䏌䏐䏈䎃䎋䏖䎌

䎦䎼

䎖䎗䎜䎓䎓䎓

䎓 䎕 䎗 䎙 䎛

䎐䎓䎑䎘 䎓 䎓䎑䎘

䏗䏌䏐䏈䎃䎋䏖䎌

䎦䎼

䎖䎙䎖䎓䎓䎓

䎓 䎕 䎗 䎙 䎛

䎐䎓䎑䎘 䎓 䎓䎑䎘

䏗䏌䏐䏈䎃䎋䏖䎌

䎦䎼

䎖䎚䎔䎓䎓䎓

䎓 䎕 䎗 䎙 䎛

䎐䎓䎑䎘 䎓 䎓䎑䎘

䏗䏌䏐䏈䎃䎋䏖䎌

䎦䎼

䎖䎜䎘䎓䎓䎓

䎓 䎕 䎗 䎙 䎛

䎐䎓䎑䎘 䎓 䎓䎑䎘

䏗䏌䏐䏈䎃䎋䏖䎌

䎦䎼

䎗䎔䎕䎓䎓䎓

࿑9 CASEΥߩᮮജଥᢙᤨ㑆ᄌേߩ᳓ᐔᣇะᚑಽ