宇宙航空研究開発機構研究開発資料

JAXA Ｒesearch and Development Memorandum

ノズルに発生するキャビテーション気泡群に作用する熱力学的効果

新井山 一樹, 長谷川 敏, 渡邉 光男, 吉田 義樹

宇宙航空研究開発機構研究開発資料

2011年2月

JAXA-RM-10-018宇宙航空研究開発機構研究開発資料

018

10

ࡁ࠭࡞ߦ⊒↢ߔࠆࠠࡖࡆ࠹࡯࡚ࠪࡦ᳇ᵃ⟲ߦ૞↪ߔࠆᾲജቇ⊛ലᨐ

ᣂ੗ጊ㩷 ৻᮸

^㪁㪈

㪃㩷 㐳⼱Ꮉ㩷 ᢅ

^㪁㪈

㪃㩷 ᷰㆺ㩷 శ↵

^㪁㪈

㪃㩷 ศ↰㩷 ⟵᮸

^㪁㪈

㩷 㩷

Thermodynamic Effects on Cavitation Bubble Cluster in a Nozzle ^*

Kazuki NIIYAMA

^㪁㪈

, Satoshi HASEGAWA

^㪁㪈

, Mitsuo WATANABE

^㪁㪈

and Yoshiki YOSHIDA

^㪁㪈

Abstract

Thermodynamic effects on cavitation occurred in a nozzle flow were experimentally investigated with liquid nitrogen. The aspect visualization of cavitating flows shows that the quantity of cavity bubbles increased gradually with the decrease of cavitation number but the size of cavity bubbles did not so change then. And, the temperature measurement of cavitating flows shows that the temperature depression in the cavitating point increased with the decrease of cavitation number. It can be cleared that the temperature of the cavitating point decreases and decreases due to the evaporative latent heat of the increasing cavity bubbles. Furthermore, the size distribution obtained by image analysis on the visualized images shows that cavity bubbles did not grow up easily in the contracted section of the nozzle when the cavitation number is small. However, it also shows that the cavity bubbles did not shrink easily in the diverging section then. These features can be considered because the thermodynamic effects become strong due to the dramatic growth of bubbles at the beginning of cavitation.

Key Words: Cavitation, Thermodynamic effect, Cryogenic fluid, Nozzle flow, Flow visualization

✜ ⸒

ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ߩ ᾲ ജ ቇ ⊛ ല ᨐ ߪ 㧘 ࠗ ࡦ ࠺ ࡘ ࡯ ࠨ ᕈ ⢻ ࠍ ะ ਄ ߐ ߖ 㧘 ࠗ ࡦ ࠺ ࡘ ࡯ ࠨ ߦ ⊒ ↢ ߔ ࠆ ࠠ ࡖ ࡆ

࠹ ࡯ ࠪ ࡚ ࡦ ਇ ቟ ቯ ࠍ ᛥ ೙ ߔ ࠆ ߎ ߣ ߇ ᣿ ࠄ ߆ ߦ ߥ ߞ ߡ

޿ ࠆ㧚 ߎ ߩ ᾲ ജ ቇ ⊛ ല ᨐ ߪ ᭂ ૐ ᷷ ᵹ ૕ ਛ ߢ 㗼 ⪺ ߢ޽ ࠆ ߎߣ ߆ ࠄ㧘ᶧ૕ ᳓ ⚛ 㨯ᶧ ૕㉄ ⚛ࠍ ૞േ ᵹ ૕ߣ ߔ ࠆ ࡠ ࠤ ࠶ ࠻ ࠛ ࡦ ࠫ ࡦ ↪ ࠲ ࡯ ࡏ ࡐ ࡦ ࡊ ߦ ߅ ޿ ߡ 㧘 ᅢ ߹ ߒ ޿ ᾲ ജ ቇ ⊛ ല ᨐ ࠍ ㆡ ಾ ߦ ૞ ↪ ߐ ߖ ࠆ ߎ ߣ ߇ ߢ ߈ ࠇ

߫ 㧘 ࠗ ࡦ ࠺ ࡘ ࡯ ࠨ ᕈ ⢻ ࠍ ะ ਄ ߐ ߖ ࠆ ߎ ߣ ߇ ߢ ߈ ࠆ 㧚 ߎ ߩ ߚ ߼ ߦ ߪ 㧘 ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ߦ ૞ ↪ ߔ ࠆ ᾲ ജ ቇ

⊛ ല ᨐ ߩ ⒟ ᐲ ࠍ ቯ ㊂ ⊛ ߦ ᛠ ី ߒ 㧘 ⸳ ⸘ ߦ ㆡ ↪ ߒ ߁ ࠆ ᜰ㊎ ࠍ ⏕┙ ߔ ࠆߎ ߣ ߇ᔅ ⷐ ߣߥ ࠆ 㧚

᳓ ߣ 6JGTOQUGPUKDNG ߥ ᵹ ૕ ߣ ߩ ๆ ޿ ㄟ ߺ ᕈ

⢻ߩ Ꮕ ߆ ࠄ㧘 5VGRCPQHHߪࠠ ࡖ ࡆ ࠹࡯ ࡚ࠪ ࡦ ߩ ᾲ ജ ቇ⊛ ല ᨐߩ ᜰ ᮡߣ ߒ ߡ $ ࡈ ࠔࠢ ࠲ ࠍឭ ᩺ ߒߡ ޿ ࠆ㧚

ߎߎ ߢ 㧘

ӹ

^˟ޔ

ӹ

^˩ޔ㧯ˣʿ˟ޔ㧸ޔ Ǎ

˧

ߪߘ ࠇߙ ࠇ 㧘 ᶧ⋧

ኒᐲ =MIO?㧘᳇⋧ ኒ ᐲ=MIO?㧘ᶧ ⋧ ቯ࿶ Ყ ᾲ=,MI㨯 -?㧘 ⫳ ⊒ ẜ ᾲ =,MI?㧘 ᷷ ᐲ 㒠 ਅ ㊂ =-?ࠍ ⴫ ߔ 㧚

T

ߪ ᵹ

૕ߩ ‛ ᕈߦ ኻ ߔࠆ ․ ᕈ᷷ ᐲ =-?ߢ޽ ࠅ㧘⴫ ߦ ␜ߔ ࠃ ߁ߦ 㧘6ߪ ᶧ ૕㉄ ⚛ ߢ᳓ ߩ ⚂ ୚ 㧘 ᶧ ૕᳓ ⚛ ߢߪ ᳓ ߩ ୚ એ਄ ⒟ᐲ ߣ ߥࠆ ߚ ߼㧘ᭂૐ ᷷ ᵹ ૕ߢ ߪ ᾲജ ቇ

⊛ ല ᨐ ߦ ࠃ ࠆ ᷷ ᐲ 㒠 ਅ ߇ 㗼 ⪺ ߣ ߥ ࠆ 㧚 ߹ ߚ 㧘 ห ৻ ᵹ

૕ ߢ ޽ ࠇ ߫ ᷷ ᐲ ߇ 㜞 ޿ ߶ ߤ ․ ᕈ ᷷ ᐲ ߪ ᄢ ߈ ߊ 㧘 ᾲ ജ ቇ⊛ ല ᨐߦ ࠃ ࠆ᷷ ᐲ 㒠ਅ ߇ 㗼⪺ ߣ ߥࠆ 㧚

Table 1 Thermodynamic parameter of several fluids

Fluid T[K] T* [K] Ȉ

Hydrogen

(Normal boiling point) 20 0.80 779,440 Nitrogen

(Experimental point) 86 1.25 135,240 Nitrogen

(Normal boiling point) 77 0.54 25,670 Oxygen

(Normal boiling point) 90 0.48 15680 Water

(Room temperature) 300 0.015 8.16

৻ ᣇ ߢ㧘$TGPPGPߪ 4C[NGKIJ2NGUUGV ᣇ ⒟ᑼ ߩ ࿶ ജ 㗄 ߦ ኻ ߒ ߡ ᷷ ᐲ 㒠 ਅ ߦ ࠃ ࠆ 㘻 ๺ ⫳ ᳇ ࿶ ߩ ᄌ ൻ ࠍ ⠨

* ,

T T L

T B C

V L p

L

' '

U U

L p L

V

C T L

,

*

U

U

2

宇宙航空研究開発機構研究開発資料　

JAXA-RM-10-018

ᘦ ߒ 㧘 ߐ ࠄ ߦ ᳇ ᶧ ⇇ 㕙 ㄭ ற ߦ ߅ ߌ ࠆ ᾲ વ ዉ ࠍ ⠨ ᘦ ߔ ࠆߎ ߣ ߢ㧘 Ǜ ࡄ ࡜ ࡔ࡯ ࠲=OU?ࠍ ឭ᩺ ߒ ߡ޿ ࠆ 㧚

ߎ ߎ ߢ 㧘

ө

^˟ߪ ᶧ ⋧ ߩ ᷷ ᐲ ᜛ ᢔ ₸ =OU?ߢ ޽ ࠆ 㧚 Ǜ ࡄ ࡜ ࡔ ࡯ ࠲ ߪ න ৻ ᳇ ᵃ ߩ ᚑ 㐳 ࠍ ᛥ ೙ ߔ ࠆ ⒟ ᐲ ࠍ ⃻ ߔ ᜰᮡ ߢ ޽ࠅ㧘Tห᭽㧘ᶧ ૕ ᳓⚛ ߥ ߤߩ ᭂ ૐ᷷ ᵹ ૕ߢ ᄢ ߈ ߊ 㧘 ห ৻ ᵹ ૕ ߢ ߪ ᷷ ᐲ ߇ 㜞 ޿ ߶ ߤ ᄢ ߈ ߊ ߥ ࠆ 㧚 ߐ ࠄߦ -CVQ߿ 9CVCPCDG㧘(TCPEߪ ߘࠇ ߙ ࠇ㧘ห ᭽ ߦ ᳇ ᶧ ⇇ 㕙 ๟ ࿐ ߩ ᾲ વ ዉ ޽ ࠆ ޿ ߪ ᾲ વ ㆐ ࠍ ⠨ ᘦ ߒ 㧘

๟ ࿐ ᵹ ૕ ߩ ᵹ ㅦ ߩ ᓇ 㗀 ࠍ ⠨ ᘦ ߒ ߚ ࡄ ࡜ ࡔ ࡯ ࠲ ࠍ ឭ ᩺ ߒ 㧘 ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ᵹ ࠇ ߩ ᵹ ㅦ ߇ ᳇ ᵃ ߩ ᚑ 㐳 ㆊ ⒟ ߦ ᓇ 㗀 ߔ ࠆ ߎ ߣ ࠍ ᣿ ࠄ ߆ ߦ ߒ ߡ ޿ ࠆ 㧚 ߎ ߎ ߢ ߪ 㧘 9CVCPCDG ߦ ࠃ ࠆ Ǜࡄ ࡜ ࡔ ࡯ ࠲ ࠍ ᑼ 㧠 ߣ ߒ ߡ ␜ ߔ 㧚

ߎ ࠇ ࠄ ߩ ߎ ߣ ߆ ࠄ 㧘 ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ߩ ᾲ ജ ቇ ⊛ ല ᨐ ࠍ ቯ ㊂ ൻ ߔ ࠆ ߚ ߼ ߦ ߪ 㧘 ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ᵹ ࠇ ߩ ᷷ ᐲ 㒠 ਅ ㊂ ߣ ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ᳇ ᵃ ⟲ ߩ ․ ᓽ ㊂

᳇ ᵃ ᓘ 㧘 ᢙ 㧘 ಽ Ꮣ ߥ ߤ ߣ ߩ ⋧ 㑐 ᕈ ࠍ ታ 㛎 ⊛ ߦ ᛠ ី ߔ ࠆ ᔅ ⷐ ߇ ޽ ࠆ 㧚 ߎ ߁ ߒ ߚ ᭂ ૐ ᷷ ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ߩታ 㛎 ࠺ ࡯࠲ ߣߒ ߡ *QTF ࠄ߇ ታᣉ ߒ ߚᶧ ૕ ᳓ ⚛㨯 ᶧ ૕ ⓸ ⚛ ߩ ታ 㛎 ߇ ޽ ࠆ ߇ 㧘 ୘ ޘ ߩ ᳇ ᵃ ߇ ್ ೎ ߢ ߈ ࠆ

࡟ ࡌ ࡞ ߩ น ⷞ ൻ ↹ ௝ ߪ ᓧ ࠄ ࠇ ߥ ޿ 㧚 ߘ ߎ ߢ ᧄ ⎇ ⓥ ߢ ߪ 㧘 ࡁ ࠭ ࡞ ࠍ ଏ ⹜ ૕ ߣ ߔ ࠆ ᭂ ૐ ᷷ ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ น ⷞ ൻ ታ 㛎 ࠍ ታ ᣉ ߒ 㧘 ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ߩ ᷷ ᐲ 㒠 ਅ

㊂ ߩ ⋥ ធ ⸘ ᷹ ߣ ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ߩ น ⷞ ൻ ⷰ ኤ ෸ ߮

↹ ௝ ⸃ ᨆ ߦ ࠃ ߞ ߡ 㧘 ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ᳇ ᵃ ⟲ ߩ ᚑ 㐳 ㆊ⒟ ߦ ኻߔ ࠆ ᾲജ ቇ ⊛ല ᨐ ߩ⒟ ᐲ ࠍ⠨ ኤ ߒߚ 㧚

ታ㛎 ⵝ⟎

࿑ ߦᧄ ⎇ⓥ ߢ ૶↪ ߒ ߚᭂ ૐ ᷷ࠠ ࡖ ࡆ࠹ ࡯ ࡚ࠪ ࡦ

࠲ࡦ ࡀ ࡞ߩ ࠪࠬ ࠹ ࡓ᭎ ⷐ ࿑ࠍ ␜ ߔ㧚ᧄ ⸳஻ ߢ ߪ㧘૞

േ ᵹ ૕ ߢ ޽ ࠆ ᶧ ૕ ⓸ ⚛ ࠍ ࡜ ࡦ ࠲ ࡦ ࠢ ߆ ࠄ ࠠ ࡖ ࠶ ࠴ ࠲ ࡦ ࠢ ߳ ߣ ᵹ േ ߐ ߖ 㧘 ㅜ ਛ ߦ ⸳ ⟎ ߒ ߚ ࠹ ࠬ ࠻ ࠮ ࠢ ࠪ ࡚ ࡦ ߢ ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ࠍ ⊒ ↢ ߐ ߖ ࠆ 㧚 ૞ േ ᵹ ૕ ߩ 㚟

േ ߦ ߪ 㜞 ࿶ ߩ ⓸ ⚛ ࠟ ࠬ ࠍ ↪ ޿ ߡ ޿ ࠆ 㧚 ߹ ߚ 㧘 ࡜ ࡦ ࠲

ࡦ ࠢ ߦ ᶧ ૕ ⓸ ⚛ ࠍ ల Ⴏ ߒ 㧘 ⓸ ⚛ ࠟ ࠬ ߢ ࡜ ࡦ ࠲ ࡦ ࠢ ࠍ 㘻 ๺ ⫳ ᳇ ࿶ એ ਄ ߦ ᣹ ࿶ ߔ ࠆ ߎ ߣ ߢ 㧘 ಝ ❗ ᾲ ࠍ ೑ ↪ ߒ ߡ ᶧ ૕ ⓸ ⚛ ߩ ᷷ ᐲ ࠍ ਄ ᣹ ߐ ߖ ࠆ ߎ ߣ ߇ ߢ ߈ ࠆ 㧚 ᧄ ታ 㛎ߢ ߪ ૞േ ᵹ ૕᷷ ᐲ ࠍ - ߣ ߒߚ 㧚 ࠹ ࠬ࠻ ࠮ ࠢࠪ ࡚ ࡦ ߩ ਄ ᵹ ߦ ⸳ ⟎ ߒ ߚ ᵹ ㊂ ⸘ ߣ ਅ ᵹ ߦ ⸳ ⟎ ߒ ߚ ᵹ ㊂ ⺞

▵ᑯ ࠍ ↪޿ ߡ 㧘ଏ ⹜ ㇱߩ ᵹ ㊂߿ ࿶ ജࠍ ⺞ ▵ߒ ߚ 㧚 ࿑ ߦߪ ଏ⹜ ㇱ ߩ᭎ ⷐ ࿑ࠍ ␜ ߔ㧚 ᧄ ⸳஻ ߩ ਥ㈩ ▤ ߪࠬ ࠹ ࡦ࡟ ࠬ ▤ౝᓘ OOࠍ↪ ޿ߡ ߅ࠅ 㧘ߘ ߩ ㈩

▤ߦ ❗ ᵹㇱ ౝ ᓘ߇ OO ߣߥ ࠆ ࡁ࠭ ࡞ࠍ ข ࠅઃ ߌ ߡ ޿ ࠆ 㧚 ଏ ⹜ ࡁ ࠭ ࡞ ߪ ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ߩ ᭽ ⋧ ࠍ น ⷞ ൻ ߔ ࠆ ߚ ߼ 㧘 ㅘ ᣿ ࡐ ࡝ ࠞ ࡯ ࡏ ࡀ ࡯ ࠻ ߢ ⵾ ૞ ߒ ߡ ߅ ࠅ 㧘 ߐ ࠄ ߦ 㧘 ૐ ᷷ ߦ ࠃ ࠆ ㅘ ⷞ ▤ ߳ ߩ 㔮 ઃ ߈ ࠍ 㒐 ߋ ߚ

߼ 㧘 ࡁ ࠭ ࡞ ࠍ ⷒ ߁ ⌀ ⓨ ᢿ ᾲ ᮏ ࠍ ⸳ ߌ 㧘 ⷞ ⇇ ࠍ ⏕ ଻ ߒ ߡ޿ ࠆ 㧚

Fig.1 Schematic diagram of cryogenic cavitation tunnel

Fig.2 Schematic diagram of the test section

ଏ ⹜ ૕ߢ ޽ ࠆࡁ ࠭ ࡞ߩ ਄ ᵹ+0㧘❗ᵹ ㇱ01<㧘ਅ ᵹ176ߦ࿶ ജ࠮ ࡦ ࠨ෸ ߮ ᷷ᐲ ࠮ ࡦࠨ ࠍ ⸳⟎ ߒ ߚ㧚ࠠ

ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ᵹ ࠇ ߩ ᷷ ᐲ 㒠 ਅ ㊂ ࠍ 㜞 ♖ ᐲ ߦ ⸘ ᷹ ߔ

L L p V

V

T C

L D U

U

, 2

2 2

6

2 ,

2 2 2

*

U D T

C L

L L p V

V

D U

6 U

ࠆߚ ߼ 㧘ࡁ ࠭ ࡞਄ ᵹ ෸߮ ❗ ᵹㇱ ߦ ߪ࿑ ߦ␜ ߔ ዊဳ

࠳ ࠗ ࠝ ࡯ ࠼ ࠮ ࡦ ࠨ ࠍ ↪ ޿ ߚ ᷷ ᐲ ࡊ ࡠ ࡯ ࡉ ࠍ ↪ ޿ ߚ 㧚 ᧄ ࠳ ࠗ ࠝ ࡯ ࠼ ࠮ ࡦ ࠨ .CMGUJQTG&65&ߪ - ߦ ߅ ޿ ߡ 㧘 セ ᱜ ᷣ ߩ ᾲ 㔚 ኻ ߩ ⺋ Ꮕ ࠃ ࠅ ߽ ⚂ ৻ ߌ ߚ ዊ ߐ ޿rO- ߩ ⺋ Ꮕߢ ⸘ ᷹ ߇ น ⢻ߢ ޽ ࠆ 㧚 ߥ ߅㧘 ᷷ ᐲ ࡊ ࡠ ࡯ ࡉ ߪ 㧘 ࠠ ࡖ ࡆ ࠹ ࠖ ߇ ⊒ ↢ ߔ ࠆ ო 㕙 ㄭ ற ߩ ᷷ ᐲ ࠍ ⸘ ᷹ ߢ ߈ ࠆ ࠃ ߁ ߦ Ꮕ ߒ ㄟ ߺ ᷓ ߐ ࠍ ⺞ ▵ ߒ ߚ 㧚 ࠮ ࡦ ࠨ ߪ ⊒ ↢ ߔ ࠆ ࠠ ࡖ ࡆ ࠹ ࠖ ߩ ᳇ ᵃ ᓘ ߦ ኻ ߒ ߡ ච ಽ ߦ ᄢ ߈ ޿ ߎ ߣ ߆ ࠄ 㧘 ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ⊒ ↢ ㇱ ߢ ⸘ ᷹ ߔ ࠆ

᷷ ᐲ ߪ 㧘 ᷷ ᐲ 㒠 ਅ ߒ ߚ Ⴚ ⇇ ጀ ߩ ዪ ᚲ ᤨ ⓨ 㑆 ᐔ ဋ ᷷ ᐲ ߣ⠨ ߃ ࠄࠇ ࠆ 㧚

ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ߩ น ⷞ ൻ ⷰ ኤ ߦ ߪ 㧘 ࠺ ࠫ ࠲ ࡞ ৻

⌒࡟ ࡈ ࠞࡔ ࡜ 0KMQP& ࠍ ૶↪ ߒ 㧘 㐹శ ᤨ 㑆 Ǵ ⑽ ߩ ࡈ ࡜ ࠶ ࠪ ࡘ ߢ ᠟ ᓇ ߒ ߚ 㧚 น ⷞ ൻ ↹ ௝ ࠃ ࠅ ▚ ಴ ߒ ߚ

᠟ᓇ ⸃ ௝ᐲ ߪ ⚂ ǴORKZGN ߢ ޽ ࠆ㧚

Fig.3 Temperature probe with cryogenic miniature diode sensor (Lakeshore DT-670-SD: height 1.1 mm, width 1.9 mm, length 3.2 mm).

ታ㛎 ⚿ᨐ

ታ 㛎 ᤨߦ ߪ 㧘࡜ ࡦ ࠲ࡦ ࠢ ࠍ /2C ߦട ࿶ ߒߚ ⁁ ᘒ ߢ ᶧ ૕ ⓸ ⚛ ࠍ ᵹ േ ߐ ߖ 㧘 ଏ ⹜ ㇱ ਅ ᵹ ߩ ᵹ ⺞ ᑯ ࠍ Ბ 㓏 ⊛ ߦ 㐿 ߊ ߎ ߣ ߢ ଏ ⹜ ㇱ ߩ ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ᢙ ࠍ 㒠 ਅߐ ߖ 㧘ࠠ ࡖ ࡆ࠹ ࡯ ࡚ࠪ ࡦ ࠍ⊒ ↢ ߐߖ ߚ 㧚࿑ ߦታ 㛎ᤨ ߩ ࡜ࡦ ࠲ ࡦࠢ

R

₄₇₀㧘ࠠࡖ ࠶ ࠴࠲ ࡦ ࠢ

R

_%#6%*ߩ ࿶ ജ ෸ ߮ ᵹ ⺞ ᑯ 㐿 ᐲ (%8㧘 ૕ Ⓧ ᵹ ㊂

3

ߩ ᤨ 㑆 ጁ ᱧ ࠍ

␜ ߔ 㧚 ᵹ ⺞ ᑯ ࠍ Ბ 㓏 ⊛ ߦ 㐿 ߊ ߎ ߣ ߢ ᓢ ޘ ߦ ᵹ ㊂ ߇ ਄

᣹ߒ ߡ ޿ࠆ ߎ ߣ߇ ಽ ߆ࠆ 㧚 ߐࠄ ߦ 㧘࿑ ߦߪ ଏ ⹜ㇱ

౉ญ ࠠ ࡖࡆ ࠹ ࡯ࠪ ࡚ ࡦᢙ ǻ₊₀ᑼ㧡㧘౉ ญ̆ ❗ ᵹ ㇱ 㑆 ߩ ᷷ ᐲ 㒠 ਅ ㊂ Ǎ

6

ᑼ 㧢 ਗ ߮ ߦ ᠟ ᓇ ᤨ ೞ ߩ ࡑ ࡯

ࠞ࡯ ࠍ ␜ߒ ߡ ޿ࠆ 㧚

R

₊₀㧘

R

_5#6㧘

7

_6*㧘

6

₊₀㧘

6

_01<ߪ ߘࠇ ߙ ࠇ 㧘 ଏ ⹜ ㇱ ౉ ญ ࿶ 㧘 ౉ ญ ᷷ ᐲ ߦ ኻ ߔ ࠆ 㘻 ๺ ⫳ ᳇ ࿶ 㧘

❗ᵹ ㇱ ᵹㅦ 㧘 ౉ญ ᷷ ᐲ㧘 ❗ ᵹㇱ ᷷ ᐲߢ ޽ ࠆ㧚 ࿑ ߣ ࿑ ߩ Ყセ ߆ࠄ 㧘ᵹ ⺞ ᑯࠍ 㐿 ߈ᵹ ㊂ ߇਄ ᣹ ߔ ࠆ ߦ ߟ ࠇ ߡ 㧘 ଏ ⹜ ㇱ ౉ ญ ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ᢙ ߇ 㒠 ਅ ߒ 㧘 ߘ ࠇ ߣ ߣ ߽ ߦ ᷷ ᐲ 㒠 ਅ ㊂ ߇ Ⴧ ᄢ ߒ ߡ ޿ ࠆ ߎ ߣ ߇ಽ ߆ ࠆ㧚

Fig.4 Time evolution of the pressures in run tank and catch tank, the opening of flow control valve and the volumetric flow rate.

Fig.5 Time evolution of the inlet cavitation number and the temperature difference between the inlet flow and the nozzle throat.

㧔㧕

㧔㧕

࿑ ߦߪ ઍ ⴫⊛ ߥ ࠠࡖ ࡆ ࠹࡯ ࠪ ࡚ࡦ ᵹ ࠇߩ ᭽ ⋧ߩ

2

) (

2

TH L

SAT

IN IN

U

p p

V U

NOZ IN

T T

T

'

4

宇宙航空研究開発機構研究開発資料　

JAXA-RM-10-018

นⷞ ൻ ౮⌀ ࠍ ␜ߔ 㧚౮⌀ ߩ C㧘Dߪ ߘ ࠇߙ ࠇ 㧘࿑

ߦ ߅ ߌ ࠆ ᠟ ᓇ ᤨ ೞ ߅ ࠃ ߮ ߦ ኻ ᔕ ߒ ߡ ޿ ࠆ 㧚 ࠠ ࡖ ࡊ ࠪ ࡚ ࡦ ߣ ߒ ߡ 㧘 ฦ ᠟ ᓇ ᤨ ೞ ߦ ߅ ߌ ࠆ ౉ ญ ࠠ ࡖ ࡆ

࠹࡯ ࠪ ࡚ ࡦ ᢙ ǻ₊₀㧘 ᑼ㧠ߩ Ǜࡄ ࡜ࡔ ࡯ ࠲ 㧘ᑼ ߩ $ ࡈ ࠔࠢ ࠲ ߩᤨ 㑆 ᐔဋ ୯ ࠍ␜ ߒ ߡ޿ ࠆ 㧚ߥ ߅㧘$ ࡈ ࠔ ࠢ ࠲ ߩ ⸘ ▚ ߦ ߪ ᑼ 㧢 ߩ ᷷ ᐲ 㒠 ਅ ㊂ ࠍ ↪ ޿ ߡ ޿ ࠆ 㧚

࿑ CߣDߣߩ Ყ セ߆ ࠄ 㧘ࠠ ࡖࡆ ࠹ ࡯ ࡚ࠪ ࡦ ᢙߩ 㒠 ਅ ߦ ઻ ߞ ߡ ࠠ ࡖ ࡆ ࠹ ࠖ ߩ ⊒ ↢ ㊂ ߇ Ⴧ ട ߒ ߡ ࡁ ࠭ ࡞ ో

૕ߦ ᜛ ᢔߒ 㧘߆ߟ 㧘$ ࡈ ࠔ ࠢ࠲ ߇ Ⴧᄢ ߒ ߡ޿ ࠆ ߎߣ ߇ ಽ ߆ ࠆ 㧚 ߹ ߚ 㧘 ᳓ ߢ ⊒ ↢ ߔ ࠆ ࠠ ࡖ ࡆ ࠹ ࠖߦ Ყ ߴ ߡ ᶧ ૕ ⓸ ⚛ ߦ ⊒ ↢ ߔ ࠆ ࠠ ࡖ ࡆ ࠹ ࠖ ߪ ⚦ ߆ ߥ ᳇ ᵃ ߢ ᭴ ᚑ ߐ ࠇ ߡ ޿ ࠆ ߎ ߣ ߇ ಽ ߆ ࠆ 㧚 ߥ ߅ 㧘 ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ᢙߩ 㒠 ਅߣ ߣ ߽ߦ Ǜࡄ࡜ ࡔ࡯ ࠲ ߪᷫ ዋ ߒߡ ޿ ࠆ߇ ߘ ߩ ᄌ ൻ ₸ ߇ ዊ ߐ ޿ ߎ ߣ ߆ ࠄ 㧘 ᧄ ታ 㛎 ⚿ ᨐ ߦ ߅ ߌ ࠆ ᵹ ㅦߩ ᓇ 㗀ߪ ዊ ߐ޿ ߣ ⠨߃ ࠄ ࠇࠆ 㧚

Fig.6 Typical aspect of the cavitating nozzle flows with the inlet cavitation number ı

IN

, the thermodynamic parameter Ȉ

^*

and the Stepanoff's B-factor.

ߎ ߎ ߢ㧘ฦ ᤨೞ ߩ ࠠࡖ ࡆ ࠹ࠖ ߩ ᭽⋧ ߦ ⌕⋡ ߔ ࠆߣ㧘

ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ᢙ ߩ 㒠 ਅ ߦ ઻ ޿ ࠠ ࡖ ࡆ ࠹ ࠖ ߩ ⊒ ↢

㊂ ߪ Ⴧ ട ߒ ߡ ޿ ࠆ ߽ ߩ ߩ 㧘 ᳇ ᵃ ࠨ ࠗ ࠭ ߘ ߩ ߽ ߩ ߪ ᄢ ߈ ߊ ᄌ ൻ ߒ ߡ ޿ ߥ ޿ ߎ ߣ ߇ ↹ ௝ ߆ ࠄ ផ ᷹ ߢ ߈ ࠆ 㧚 ߘ ߎ ߢ 㧘 ࠠ ࡖ ࡆ ࠹ ࠖ ߩ ᭽ ⋧ ࠍ ࠃ ࠅ ቯ ㊂ ⊛ ߦ ᛠ ី ߔ ࠆ ߚ

߼ 㧘 น ⷞ ൻ ↹ ௝ ߦ ኻ ߒ ߡ ࠺ ࠫ ࠲ ࡞ ಣ ℂ ࠍ ⴕ ޿ 㧘 ࠠ ࡖ ࡆ ࠹ ࠖ ߩ ․ ᓽ ㊂ ࠍ ᛽ ಴ ߒ ߚ 㧚 ߚ ߛ ߒ 㧘 ᧄ ႎ ๔ ߢ ߪ ◲ ᤃ ⊛ ߦ 㧘 ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ߩ น ⷞ ൻ ↹ ௝ ߆ ࠄ ⢛ ᥊ ↹

௝ࠍ Ꮕ ಽߒ 㧘 ߐࠄ ߦ ߘߩ Ꮕ ಽ↹ ௝ ࠍㆡ ಾ ߦ ୯ ൻߔ ࠆߎ ߣ ߢ᳇ ᵃ ߩ․ ᓽ ㊂ࠍ ᛽ ಴ߔ ࠆ ᣇᴺ ࠍ ណߞ ߚ 㧚 ࿑ ߪ᠟ ᓇᤨ ೞߣ ߦ ߅ ߌࠆ ᳇ ᵃඨ ᓘ ߩᐲ ᢙ ಽ Ꮣ ߢ ޽ ࠆ 㧚 ৻ ⥸ ⊛ ߥ ᳓ ߩ ᳇ ᵃ ᢙ ಽ Ꮣ ߣ ห ᭽ 㧘 ᳇ ᵃ ᓘ ߇ ዊ ߐ ߊ ߥ ࠆ ߶ ߤ ᳇ ᵃ ᢙ ߇ ᄙ ߊ ߥ ߞ ߡ ޿ ࠆ 㧚 ᠟ ᓇ

ᤨ ೞ ߦ ࠃ ࠆ ㆑ ޿ ߦ ⌕ ⋡ ߒ Ყ セ ߔ ࠆ ߣ 㧘 ᤨ ೞ ߆ ࠄ ߦ ߥ ߞ ߡ ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ᢙ ߇ 㒠 ਅ ߔ ࠆ ߎ ߣ ߦ ࠃ ߞ ߡ 㧘 ో ૕ ⊛ ߦ ᳇ ᵃ ᢙ ߇ Ⴧ ട ߒ ߡ ޿ ࠆ ߎ ߣ ߇ ಽ ߆ ࠆ㧚 ߥ ߅㧘Ǵ O ߩ ඙ಽ ߦዊ ߐ ߥࡇ ࡯ ࠢ߇ ޽ ࠆ߇ 㧘 ߎ ࠇ ߪ น ⷞ ൻ ↹ ௝ ߆ ࠄ ⋡ ⷞ ߢ ್ ೎ ߒ ߚ ႐ ว ߩ ઍ ⴫ ⊛ ߥ ᳇ ᵃ ᓘ ߣ ߅ ߅ ࠃ ߘ ৻ ⥌ ߒ ߡ ߅ ࠅ 㧘 ߹ ߚ 㧘 ߎ ߩ ࡇ ࡯

ࠢ ૏ ⟎ ߪ ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ᢙ ߇ ᄌ ൻ ߒ ߡ ߽ ᄌ ࠊ ࠄ ߥ

޿ 㧚 ߚ ߛ ߒ 㧘 ᳇ ᵃ ᢙ ߇ Ⴧ ട ߔ ࠆ ഀ ว ߪ ߎ ߩ ࡇ ࡯ ࠢ ૏

⟎ઃ ㄭ ߢ㜞 ߊ ߥߞ ߡ ޿ࠆ 㧚

Fig.7 Typical histogram of the diameter of cavity bubbles estimated from the binarized image of (1) and (6) shown in Fig. 5.

࿑ ߪ ࡁ ࠭ ࡞ౝ ߦ ߅ߌ ࠆ ᐔဋ ᳇ ᵃᓘ ߩ ᄌൻ ࠍ ␜ߔ㧚 ᐔဋ ᳇ ᵃᓘ ߪ 㧘࿑ ߦ ␜ ߔ ࠃ߁ ߦ ࡁ࠭ ࡞ ౝࠍ ୘ߩ 㗔 ၞ ߦ ಽ ഀ ߒ 㧘 ฦ 㗔 ၞ ߦ ߅ ߌ ࠆ ᳇ ᵃ ᢙ ಽ Ꮣ ߆ ࠄ ⓨ 㑆

⊛ ߥ ᐔ ဋ ᳇ ᵃ ᓘ ࠍ ▚ ಴ ߒ 㧘 ߐ ࠄ ߦ ߘ ߩ ᤨ 㑆 ᐔ ဋ ࠍ ข ߞߚ ߽ ߩߢ ޽ ࠆ㧚

ᐔ ဋ ᳇ ᵃ ᓘ ߪ ࡁ ࠭ ࡞ ࠬ ࠻ ࡟ ࡯ ࠻ ㇱ #㨪 #ߢ ߪ ᓢ ޘ ߦ ᄢ ߈ ߊ ߥ ࠅ 㧘 ᜛ ᄢ ㇱ #㨪 #ߦ ౉ ߞ ߡ ߆ ࠄ ᓢ ޘ ߦ ዊ ߐ ߊ ߥ ߞ ߡ ޿ ࠆ ߎ ߣ ߇ ಽ ߆ ࠆ 㧚 ߚ ߛ ߒ 㧘 ᠟

ᓇᤨ ೞ㨪 ǻ₊₀ψ ߩ ࠠࡖ ࡆ ࠹࡯ ࠪ

࡚ ࡦ ᢙ ߇ ᄢ ߈ ޿ ᤨ ߦ ߪ ᜛ ᄢ ㇱ ߦ ౉ ࠆ ߣ ห ᤨ ߦ ᳇ ᵃ ᓘ

߇ዊ ߐ ߊߥ ࠅ ᆎ߼ ߡ ޿ࠆ ߩ ߦኻ ߒ ߡ㧘᠟ ᓇᤨ ೞ㨪 ǻ₊₀ψߢ ߪ ᓢ ޘ ߦ ᐔ ဋ ᳇ ᵃ ᓘ ߇ ᦨ ᄢ ߣ ߥ ࠆ ૏ ⟎ ߇ ਅ ᵹ ஥ ߦ ࠪ ࡈ ࠻ ߒ ߡ ޿ ࠆ 㧚 ߹ ߚ 㧘 ᐔ ဋ ᳇ ᵃ ᓘ ߪ ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ᢙ ߩ 㒠 ਅ ߣ ߣ ߽ ߦ ో ૕

⊛ߦ ዊ ߐߊ ߥ ߞߡ ޿ ࠆߎ ߣ ߇ಽ ߆ ࠆ㧚

ૐ ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ᢙ ߩ ႐ ว ߦ 㧘 ᐔ ဋ ᳇ ᵃ ᓘ ߇ ዊ ߐ ߊ ߥ ߞ ߚ ේ ࿃ ߪ એ ਅ ߩ ࠃ ߁ ߦ ⠨ ߃ ࠄ ࠇ ࠆ 㧚 ߹ ߕ 㧘

ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ᢙ ߇ ᄢ ߈ ޿ ႐ ว ߦ ߪ 㧘 4C[NGKIJ2NGUUGV ߩ ᑼ߆ ࠄࡁ ࠭ ࡞ߩ ᳇ ᵃ⊒ ↢ 㐿ᆎ ὐ ߦ ߅ ߌ ࠆ ࠠ ࡖ ࡆ ࠹ ࠖ ߩ ᚑ 㐳 ㅦ ᐲ ߇ ዊ ߐ ߊ ߥ ࠆ ߣ ⠨ ߃ ࠄ ࠇ ࠆ 㧚 ߎ ߩ ⚿ ᨐ 㧘 ⫳ ⊒ ẜ ᾲ ߦ ࠃ ࠆ ᷷ ᐲ 㒠 ਅ ㊂ ߇ ዊ ߐ ߊ ߥ ࠅ ᾲ ജ ቇ ⊛ ല ᨐ ߩ ⒟ ᐲ ߇ ᒙ ߊ ߥ ࠆ ߚ ߼ 㧘 ୘ ޘ ߩ ᳇ ᵃ ߇ ᄢ ߈ ߊ ᚑ 㐳 ߒ 㧘 ᐔ ဋ ᳇ ᵃ ᓘ ߇ ᄢ ߈ ߊ ߥ ߞ ߚ

߽ ߩ ߣ ⠨ ߃ ࠄ ࠇ ࠆ 㧚 ৻ ᣇ 㧘 ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ᢙ ߇ ዊ ߐ ޿ ᤨ ߦ ߪ 㧘 ࡁ ࠭ ࡞ ߩ ᳇ ᵃ ⊒ ↢ 㐿 ᆎ ὐ ߦ ߅ ߌ ࠆ ࠠ ࡖ ࡆ࠹ ࠖ ߩ⊒ ↢ 㨯ᚑ 㐳ㅦ ᐲߪ ᄢ߈ ߊ ߥࠆ 㧚ߎߩ ⚿ ᨐ 㧘᷷

ᐲ 㒠 ਅ ㊂ ߇ ᄢ ߈ ߊ ߥ ࠅ ᾲ ജ ቇ ⊛ ല ᨐ ߩ ⒟ ᐲ ߇ ᒝ ߊ ߥ ࠆ ߚ ߼ 㧘 ୘ ޘ ߩ ᳇ ᵃ ߩ ᚑ 㐳 ߇ ᛥ ೙ ߐ ࠇ 㧘 ᐔ ဋ ᳇ ᵃ ᓘ ߇ዊ ߐ ߊߥ ߞ ߚ߽ ߩ ߣ⠨ ߃ ࠄࠇ ࠆ㧚࿑ ߿ ࿑ ࠃ ࠅ㧘

ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ᢙ ߇ ዊ ߐ ߊ ߥ ࠆ ߦ ߟ ࠇ ߡ ᾲ ജ ቇ ⊛ ല ᨐ ߩ ᜰ ᮡ ߣ ߥ ࠆ ᷷ ᐲ 㒠 ਅ ㊂ ߇ Ⴧ ᄢ ߒ ߡ ޿ ࠆ ߎ ߣ ߆ ࠄ 㧘 ᾲ ജ ቇ ⊛ ല ᨐ ߩ ⒟ ᐲ ߇ ᒝ ߊ ߥ ߞ ߡ ޿ ࠆ ߎ ߣ ߇ ಽ ߆ ࠆ 㧚 ᧄ ታ 㛎 ⚿ ᨐ ࠃ ࠅ 㧘 ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ߩ ᾲ ജ ቇ

⊛ ല ᨐ ߇ 㗼 ⪺ ߣ ߥ ࠆ ᭂ ૐ ᷷ ᵹ ૕ ߦ ߅ ޿ ߡ ߪ 㧘 ࠗ ࡦ ࠺ ࡘ ࡯ ࠨ ߩ ౉ ญ ߢ ࠊ ߕ ߆ ߥ ࠠ ࡖ ࡆ ࠹ ࠖ ࠍ ᗧ ࿑ ⊛ ߦ ⊒ ↢ ߐ ߖ ࠆ ߎ ߣ ߢ ᵹ ૕ ߩ ᷷ ᐲ ࠍ 㒠 ਅ ߐ ߖ 㧘 ㆊ ᄢ ߥ ࠠ ࡖ ࡆ

࠹ࠖ ߩ ᚑ㐳 ࠍ ᛥ೙ ߢ ߈ࠆ น ⢻ᕈ ߇ ␜ໂ ߐ ࠇࠆ 㧚

Fig.8 Mean diameter of cavity bubbles in each analyzed area at several inlet cavitation numbers.

Fig.9 Locations of A01-A10 with the flip horizontal image.

⚿⸒

ᶧ ૕ ⓸ ⚛ ࠍ ૞ േ ᵹ ૕ ߣ ߔ ࠆ ࡁ ࠭ ࡞ ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ น ⷞ ൻ ታ 㛎 ࠍ ታ ᣉ ߒ 㧘 ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ᵹ ࠇ ߦ ߅ ߌࠆ ᷷ ᐲ㒠 ਅ ㊂ߣ ↹ ௝⸃ ᨆ ߆ࠄ એ ਅߩ ⍮ ⷗ࠍ ᓧ ߚ㧚

ࠠ ࡖࡆ ࠹࡯ ࠪ ࡚ࡦ ᢙ ߩ㒠 ਅ ߦ઻ ޿ 㧘ࠠ ࡖࡆ ࠹ ࠖ ߩ⊒ ↢ ㊂߇ Ⴧ ᄢߒ㧘ࠠ ࡖࡆ ࠹࡯ ࠪ ࡚ࡦ ᵹ ࠇߩ ᷷ ᐲ 㒠ਅ ㊂ ߪჇ ᄢ ߒߚ 㧚

ࠠ ࡖࡆ ࠹࡯ ࠪ ࡚ࡦ ᢙ ߩ㒠 ਅ ߣߣ ߽ ߦ㧘⊒↢ ߔ ࠆ

ࠠࡖ ࡆ ࠹ࠖ ߩ ᳇ᵃ ᢙ ߪჇ ᄢ ߔࠆ ߽ ߩߩ㧘ઍ⴫ ᳇ ᵃ ᓘߪ ᄢ ߈ߊ ᄌ ൻߒ ߥ ޿㧚

ૐ ࠠ ࡖ ࡆ ࠹ ࡯ ࠪ ࡚ ࡦ ᢙ ߩ ႐ ว ߦ ᐔ ဋ ᳇ ᵃ ᓘ ߇ ዊߐ ߊ ߥߞ ߚ ߩߪ㧘᳇ ᵃߩ ೋᦼ ᚑ 㐳ㅦ ᐲ ߇ᄢ ߈ ޿ ߚ ߼ ࠠ ࡖ ࡆ ࠹ ࠖ ⊒ ↢ 㐿 ᆎ ὐ ߢ ᷷ ᐲ 㒠 ਅ ㊂ ߇ ᄢ ߈ ߊߥ ࠅ㧘ࡁ࠭ ࡞ߦ ߅ ߌࠆ ᾲ ജቇ ⊛ ലᨐ ߩ ૞↪ ߇ ᒝ ߊߥ ߞ ߚߎ ߣ ߢ㧘୘ ޘ ߩ᳇ ᵃߩ ᚑ 㐳߇ ᛥ ೙ߐ ࠇ ߚ ߚ߼ ߣ ⠨߃ ࠄ ࠇࠆ 㧚

㩷

ෳ⠨ᢥ₂

(1) Kikuta, K., et al., 2008, “Thermodynamic Effect on Cavitation Performances and Cavitation Instabilities in an Inducer,” Trans. of ASME J Fluids Eng. 130, 111302.

(2) Yoshida, Y., et al., 2009, "Thermodynamic Effect on Rotating Cavitation in an Inducer," Trans. of ASME J Fluids Eng. 131, 091302.

(3) Stepanoff, A. J., 1964, “Cavitation Properties of Liquids,”

J Eng. Power, 86, pp.195-200.

(4) Brennen, C.E., 1995, "Cavitation and Bubble Dynamics," Oxford University Press.

(5) Kato, H., 1984, "Thermodynamic Effect on Incipient and Developed Sheet Cavitation," Proceedings of ASME FED-Vol.16, International Symposium on Cavitation, pp.127-136.

(6) Watanabe, S., et al., 2007, “Steady Analysis of the

6

宇宙航空研究開発機構研究開発資料　

JAXA-RM-10-018

Thermodynamic Effect of Partial Cavitation Using the Singularity Method,” Trans. of ASME J. Fluids Eng., 129(2), pp.121-127.

(7) Franc, J. P., 2004, "Fundamentals of Cavitation," Fluid Mechanics and its Applications, Vol.76, Kluwer Academic Publishers.

(8) Hord, J., et al., 1972-1974, “Cavitation in Liquid Cryogens: I-Venturi, II-Hydrofoil, III-Ogives, IV-Combined Correlations for Venturi, Hydrofoil, Ogives, and Pumps,” NASA CR-2054, 2156, 2242, 2448.

(9) Niiyama, K., et al., 2010, “Thermodynamic Effects on Cavitation in a Cryogenic Nozzle Flow,” Proceedings of the 7th International Conference on Multiphase Flow ICMF2010, Tampa, FL.

(10)

ᄢ႐ࠄ㧘

1973

㧘

“

ࡌࡦ࠴ࡘ࡝ߩࠠࡖࡆ࠹࡯࡚ࠪࡦⴣ᠄

࿶ߩ⸃᣿

(

╙

2

ႎ

)

㧘

”

ㅦ⎇ႎ๔ ╙

33

Ꮞ㧘╙

326

ภ㧘

pp.37-50

㧚