Clarification of Cavitation Influence on Spray Atomization (2nd Report, Modeling of Cavitation inside Nozzle Based on Bubble Dynamics)

Clarification of Cavitation Influence on Spray Atomization (2nd Report, Modeling of Cavitation inside Nozzle Based on Bubble Dynamics)

Masashi MATSUMOTO *¹, Yoshimitsu KOBASHI *², Eriko MATSUMURA *³, Jiro SENDA *⁴ (Received May 27, 2010)

In this research, it is purpose to understand the cavitation effects on fuel spray atomization. In this report, the numerical model predicted bubble behavior was proposed. The proposed numerical model treats that cavitation bubble grows or shrinks following to the pressure distribution inside nozzle hole. The calculation was carried out by use of estimated pressure distributions inside nozzle hole based on experimental measurements. Primary, for each injection pressure and test fuel, cavitation bubble behavior was calculated. Secondary, for various initial bubble radiuses, bubble growth and shrinkage processes were calculated. As results of these calculations, this model predicts the key points of bubble behavior adequately for various pressure history bubble undergoing and each initial bubble radiuses.

.

.H\ZRUGV㸸cavitation, atomization, spray, bubble dynamics, cavitation model

࣮࣮࢟࣡ࢻ㸸࢟ࣕࣅࢸ࣮ࢩࣙࣥ㸪ᚤ⢏໬㸪ᄇ㟝㸪ẼἻືຊᏛ㸪࢟ࣕࣅࢸ࣮ࢩࣙࣥࣔࢹࣝ

ᄇ㟝ᚤ⢏໬࡟ᑐࡍࡿ࢟ࣕࣅࢸ࣮ࢩࣙࣥࡢᙳ㡪ࡢゎ᫂

( ➨ ሗ㸪ẼἻຊᏛ࡟❧⬮ࡋࡓࣀࢬࣝෆ࢟ࣕࣅࢸ࣮ࢩࣙࣥࡢࣔࢹࣜࣥࢢ )

ᯇᮏ 㞞⮳*¹㸪ᑠᶫ ዲ඘*²㸪ᯇᮧ ᜨ⌮Ꮚ*³㸪༓⏣ ஧㑻*⁴

ࡣࡌࡵ࡟

᫖௒ࡢ┠ぬࡲࡋ࠸ィ⟬ᶵჾࡢ⢭ᗘྥୖ࡟క࠸㸪◊

✲࣭㛤Ⓨศ㔝࡟࠾ࡅࡿᩘ್ゎᯒࡢ㔜せᛶࡀ㧗ࡲࡗ࡚

࠸ ࡿ 㸬 ෆ ⇞ ᶵ 㛵 ศ 㔝 ࡟ ࠾ ࠸ ࡚ ࡶ ౛ እ ࡛ ࡞ ࡃ 㸪 CFD(Computational Fluid Dynamics)࡟ࡼࡿຠ⋡ⓗ࡞

ᶵ㛵タィࡸ⌧㇟ࡢヲ⣽ゎ᫂࡟ᑐࡍࡿ㈉⊩ࡀᮇᚅࡉࢀ

࡚࠸ࡿ㸬

୍⯡ࡢᩘ್ゎᯒࢥ࣮ࢻࡣᗄከࡢࢧࣈࣔࢹࣝ࡟ࡼࡾ

ᵓᡂࡉࢀ㸪ಶࠎࡢ≀⌮㐣⛬࡟ᑐࡍࡿࣔࢹࣝ໬ᡭἲࡀ ゎᯒ⤖ᯝ࡟኱ࡁ࡞ᙳ㡪ࢆཬࡰࡍ㸬≉࡟㸪⇞ᩱᄇ㟝ࢆ

ᩘ್ⓗ࡟ྲྀࡾᢅ࠺㝿࡟ࡣ㸪⇞ᩱᄇᑕ᫬ࡢึᮇ᮲௳࠾

ࡼࡧᾮ⁲ศ⿣ࣔࢹࣝࡀィ⟬⤖ᯝ࡟ᑐࡋ࡚ᨭ㓄ⓗ࡜࡞

ࡿࡓࡵ㸪ࡇࢀࡽ࡟㛵ࡍࡿㅖ⌧㇟ࡢせⅬࢆⓗ☜࠿ࡘ⡆

₩࡟グ㏙ࡋᚓࡿᩘ್ࣔࢹࣝࡢᵓ⠏ࡀᮃࡲࢀࡿ㸬ᄇ㟝 ィ⟬࡟࠾ࡅࡿᾮ⁲ศ⿣㐣⛬ࢆグ㏙ࡍࡿࣔࢹࣝ࡜ࡋ࡚㸪 WAVEࣔࢹࣝ¹⁾㸪TABࣔࢹࣝ²⁾ࡸKH-RTࣔࢹࣝ³⁾ࡀ ᖜᗈࡃ౑⏝ࡉࢀ࡚࠸ࡿ㸬ࡇࢀࡽࡢࣔࢹࣝ࡟ඹ㏻ࡍࡿ

Ⅼ࡜ࡋ࡚㸪ᄇᑕࡉࢀࡓᚋࡢ⇞ᩱᣲືࢆゎࡃࣔࢹ࡛ࣝ

࠶ࡿࡇ࡜㸪ᐃᩘࡢኚ᭦࡟ࡼࡿィ⟬⤖ᯝ࡬ࡢᙳ㡪ࡀᴟ

ࡵ࡚኱ࡁ࠸ࡇ࡜ࡀᣲࡆࡽࢀࡿ㸬୍᪉㸪㏆ᖺ࡛ࡣᄇ㟝

*¹ Department of Mechanical and Engineering, Graduate School of Doshisha University, Kyoto Telephone:+ 81-774-65-7742, Fax:+81-774-65-7743, E-mail: [email protected]

*² Department of Mechanical Engineering, Kanazawa Institute of Technology, Ishikawa

*³ Power Train Engineering Div.2 TOYOTA MOTOR CORPORATION, Shizuoka

*⁴ Department of Mechanical and Engineering, Doshisha University, Kyoto

ᚤ⢏໬࡟ᑐࡋ࡚ࣀࢬࣝෆࡢὶືࡸࡑࡇ࡟⏕ࡌࡿ࢟ࣕ

ࣅࢸ࣮ࢩࣙࣥ⌧㇟ࡢᙳ㡪ࢆ⪃៖ࡍ࡭ࡁ࡜ࡢᣦ᦬ࡶከ ࡃ^4-6)㸪ࡇࢀࡽࢆ⪃៖ࡋࡓᩘ್ࣔࢹࣝࡶࡲࡓᥦ᱌ࡉࢀ

࡚࠸ࡿ^7-9)㸬ࡋ࠿ࡋ࡞ࡀࡽ㸪࠸ࡎࢀࡶࣀࢬࣝෆࡢ≧ἣ

ࢆึᮇ᮲௳࡜ࡋ࡚⡆᫆ⓗ࡟⪃៖ࡍࡿࡶࡢ࡛࠶ࡾ㸪ᐇ 㦂⤖ᯝ࡜ẚ㍑᳨࣭ドࡍࡿ㝿࡟ࡣᐃᩘኚ᭦࡟ࡼࡿࣇ࢕

ࢵࢸ࢕ࣥࢢࡣචࢀ࡞࠸㸬ࡍ࡞ࢃࡕ㸪࠶ࡽࡺࡿ᮲௳࡟

ᑐࡋ࡚ᐃᩘࡢኚ᭦࡞ࡋ࡟⇞ᩱᄇ㟝ࢆண ࡋᚓࡿᩘ್

ࣔࢹࣝࡣᮍࡔᵓ⠏ࡉࢀ࡚࠸࡞࠸㸬ࡇࡢࡇ࡜ࡣ㸪࢟ࣕ

ࣅࢸ࣮ࢩࣙࣥ⌧㇟ࡀᄇ㟝ᚤ⢏໬࡟ཬࡰࡍᙳ㡪ࡀヲ⣽

࡟ᢕᥱࡉࢀ࡚࠸࡞࠸ࡇ࡜࡟㉳ᅉࡍࡿ㸬

ࡑࡇ࡛㸪ᮏ◊✲࡛ࡣ⇞ᩱᄇ㟝࡟ᑐࡍࡿ࢟ࣕࣅࢸ࣮

ࢩࣙࣥࡢᙳ㡪ࢆゎ᫂ࡍࡿࡇ࡜ࢆ┠ⓗ࡜ࡍࡿ㸬ᮏሗ࡛

ࡣ㸪➨1ሗ࡟࠾࠸࡚ᐇ㦂ⓗ࡟ᚓࡽࢀࡓᅽຊศᕸࢆࡶ

࡜࡟㸪Rayleigh-Plessetᘧࢆゎࡃࡇ࡜࡛ẼἻᣲືࢆ⡆

᫆ⓗ࡟෌⌧ࡍࡿࡇ࡜ࢆヨࡳࡓ㸬ᐇ㦂⤖ᯝ࡜ࡢẚ㍑࣭

᳨ドࢆ⾜࡞࠸㸪࢟ࣕࣅࢸ࣮ࢩࣙࣥ⌧㇟ࢆᩘ್ⓗ࡟ྲྀ

ࡾᢅ࠺㝿࡟⪃៖ࡍ࡭ࡁⅬ࡟ࡘ࠸᳨࡚ウࡋࡓ㸬

ィ⟬᪉ἲ ẼἻ༙ᚄᒚṔࡢ⟬ฟ

↓㝈ᾮయ୰࡟࠾ࡅࡿ⌫ᙧẼἻࡢᡂ㛗࣭཰⦰㐣⛬ࡣ

ḟࡢRayleigh-Plessetࡢᘧࡼࡾ⟬ฟࡉࢀࡿ㸬

) 1 (

2 3 2

r w l

P P R

R

R

U

࣭࣭࣭(1)

(1)ᘧ࡟࠾࠸࡚㸪R㸪Ul࠾ࡼࡧPrࡣࡑࢀࡒࢀẼἻ༙ᚄ㸪 ᾮయࡢᐦᗘ࠾ࡼࡧ↓㝈㐲ࡢὶయᅽຊ࡛࠶ࡿ㸬ࡲࡓ㸪

R࠾ࡼࡧRࡣ᫬㛫ࢆt࡜ࡋࡓሙྜ࡟ࡑࢀࡒࢀdR/dt㸪

2 2R/dt

d ࢆព࿡ࡍࡿ㸬୍᪉㸪PwࡣẼἻቨ࡟࠾ࡅࡿὶ యᅽຊ࡛࠶ࡾ㸪(2)ᘧ࡛୚࠼ࡽࢀࡿ㸬

R R R

R R P R

P

P ^{l l}

n l

r v w

P V

V 2 4

2 ₀ ³

0

0 ¸

¹

¨ ·

©

¸¸§

¹

¨¨ ·

©

§

^࣭࣭࣭(2)

ࡇࡇ࡛㸪n ࡣ࣏ࣜࢺ࣮ࣟࣉᣦᩘ㸪Vlࡣᾮయࡢ⾲㠃ᙇ ຊ㸪Plࡣᾮయࡢ⢓ᗘ㸪Pvࡣὶయࡢ㣬࿴⵨Ẽᅽ㸪Pr0

ࡣึᮇࡢ࿘ᅖὶయᅽຊ㸪R₀ࡣึᮇẼἻ༙ᚄ࡛࠶ࡿ㸬

ẼἻ཰⦰࣭ᔂቯ᫬࡟⏕ࡌࡿ࢚ࢿࣝࢠࡢ⟬ฟ ᔂቯ┤๓࡟ẼἻࡀ཰⦰ࡍࡿ㏿ᗘࡣᴟࡵ࡚㧗ࡃ㸪ᮏ

ࣔࢹ࡛ࣝࡣࡇࡢ್ࢆホ౯ࡍࡿ㸬཰⦰㐣⛬࡟࠾࠸࡚⏕

ᡂࡉࢀࡿ࢚ࢿࣝࢠࢆ(3)ᘧ࡛ᐃ⩏ࡍࡿ㸬

¦³

¦

˜ ^j

i R r

R R r

l shrink

i

i

dr r v R

N

E 1

2 24 )

2 ( S

U ࣭࣭࣭(3)

(3)ᘧ࡟࠾࠸࡚㸪i ࡣẼἻࡀ᭱኱༙ᚄ࡟㐩ࡍࡿ㝿ࡢ᫬

้㸪jࡣᔂቯࡍࡿ㝿ࡢ᫬้ࢆ♧ࡍ㸬࡞࠾㸪N(R)ࡣ࢟ࣕ

ࣅࢸ࣮ࢩࣙࣥẼἻࡢᩘ࡛࠶ࡾ㸪ᮏሗ࡛ࡣ N(R)=1 ࡜ ࡋࡓ㸬ࡲࡓ㸪཰⦰᫬࡟࠾ࡅࡿẼἻ㏿ᗘV࠾ࡼࡧ࿘ᅖ ὶయࡢ㏿ᗘvࡣࡑࢀࡒࢀࡢ⾲㠃✚࡟㛵ࡋ㏫ẚ౛ࡢ㛵 ಀ࡟࠶ࡿࡇ࡜࠿ࡽ㸪(4)ᘧࡀᑟ࠿ࢀࡿ㸬

2 2 max

r R V

v

࣭࣭࣭(4) (4)ᘧ࡟࠾ࡅࡿ Rmax㸪r ࡣࡑࢀࡒࢀ᭱኱ẼἻ༙ᚄ࠾ࡼ

ࡧྛ᫬้ࡢẼἻ༙ᚄ࡛࠶ࡿ㸬(3)ᘧ࡟(4)ᘧࢆ௦ධࡍࡿ

ࡇ࡜࡛(5)ᘧࢆᚓࡿ㸬

¦³

¦

¹

·

¨¨

©

˜ ^j §

i R r

R r

i R

l shrink

i

i

dr r r V

R R N E

1

2 2

2 2

4 )

2 ( S

U _࣭࣭(5)

ࡲࡓ㸪ᓥࡽ¹⁰⁾࡟ࡼࢀࡤ㸪㠀ᅽ⦰ᛶὶయ࡟࠾࠸࡚ẼἻ ࡀᔂቯࡍࡿ㝿࡟⏕ࡌࡿ᭱኱⾪ᧁἼᅽຊ Pmaxࡣ (6)ᘧ

࡛⾲ࡉࢀࡿ㸬

brk l

brk R

R P R

P ₀ ^3N 2V

0

max ¸¸

¹

¨¨ ·

©

§ ࣭࣭࣭(6)

ࡇࡇ࡛㸪P0ࡣึᮇࡢẼἻෆᅽຊ㸪Rbrkࡣᔂቯ᫬࡟࠾

ࡅࡿẼἻ༙ᚄ㸪Nࡣ᩿⇕ᣦᩘ࡛࠶ࡿ㸬࡜ࡇࢁ࡛㸪(6) ᘧࡣึᮇẼἻ༙ᚄ࠾ࡼࡧᔂቯ᫬࡟࠾ࡅࡿẼἻ༙ᚄࡢ 㛵ಀࡼࡾᵓᡂࡉࢀࡿ㸬ࡋ࠿ࡋ㸪(2)ᘧ࡟࠾࠸࡚㣬࿴⵨

Ẽᅽ Pvࢆ⪃៖ࡋ࡚࠸ࡿࡇ࡜࠿ࡽࡶ᫂ࡽ࠿࡞ࡼ࠺࡟㸪 ᐇ㝿࡟ࡣẼἻࡢᡂ㛗㐣⛬࡟࠾࠸࡚⇞ᩱ⵨ẼࡀẼἻෆ 㒊࡟⵳✚ࡉࢀࡿ㸬ࡇࡢࡇ࡜ࢆ⪃៖ࡍࡿ࡜㸪(6)ᘧ࡟ࡼ

ࡿᅽຊ್࡜ẚࡋ࡚ࡉࡽ࡟㧗࠸⾪ᧁἼᅽຊࡀ⟬ฟࡉࢀ

ࡿࡓࡵ㸪ᮏሗ࡛ࡣ(6)ᘧࢆ(7)ᘧࡢࡼ࠺࡟ኚᙧࡍࡿ㸬

brk l brk

R R R

P R

P _max ^3N 2V

max

max ¸¸¹

¨¨ ·

©

§ ࣭࣭࣭(7)

ࡇࡇ࡛㸪PRmaxࡣẼἻࡀ᭱኱ẼἻᚄ࡟㐩ࡋࡓ㝿ࡢẼἻ ෆᅽຊ࡛࠶ࡾ㸪ᮏࣔࢹ࡛ࣝࡣ⇞ᩱࡢ㣬࿴⵨Ẽᅽ࡜ࡋ ࡓ㸬࡞࠾㸪ᮏࣔࢹ࡛ࣝࡣẼἻᔂቯ᫬ࢆ᩿⇕ኚ໬࡜௬ ᐃࡋ㸪N=1.4 ࡜ࡋࡓ㸬ࡓࡔࡋ㸪ẼἻࡢ཰⦰㐣⛬࡟㉳

ࡇࡿ⵨Ẽࡢจ⦰ࡣ↓どࡋࡓ㸬ࡇࢀࡣẼἻᔂቯࡢ᭱⤊

ẁ㝵࡟࠾࠸࡚཰⦰㏿ᗘࡀᴟࡵ࡚㧗㏿࡜࡞ࡿሙྜ㸪⵨

Ẽࡢจ⦰ࡀẼἻ཰⦰࡟㏣࠸ࡘ࠿࡞࠸ሙྜࡶ࠶ࡿ࡜⪃

࠼ࡓࡓࡵ࡛࠶ࡿ㸬ᔂቯ᫬ࡢᅽຊࡀ࿘ᅖὶయࡢ஘ࢀࢆ

ㄏⓎࡍࡿ࡜⪃࠼ࡓሙྜ࡟࠾ࡅࡿ࢚ࢿࣝࢠࡣ(8)ᘧ࡛

⾲ࡉࢀࡿ㸬

¦

R

brk

collapse N R P R R

E ( ) _max( ) ³

3

4S _࣭࣭࣭(8)

౪ヨᾮయ

ᮏィ⟬࡛ࡣ㸪➨1ሗ࡟♧ࡋࡓᄇᏍ㒊ࡢ᧜ᙳ⤖ᯝ࡜

ẚ㍑ࡍࡿࡓࡵ㸪Table 1࡟♧ࡍ3✀㢮ࡢ౪ヨᾮయࢆィ

⟬ᑐ㇟࡜ࡋࡓ㸬

ẼἻ༙ᚄࡢィ⟬᪉ἲ

ᮏィ⟬࡟ࡣ㸪➨1ሗ࡟♧ࡋࡓ25ಸᣑ኱ࣀࢬࣝࢆ⏝

࠸ࡓᐇ㦂⤖ᯝࡼࡾ᥎ᐃࡋࡓᅽຊศᕸࢆ⏝࠸ࡿ㸬ᐇ㦂

࡟⏝࠸ࡓ౪ヨࣀࢬࣝᙧ≧࠾ࡼࡧྛ㒊ᑍἲࢆ Fig.1㸪

Table 2࡟ࡑࢀࡒࢀ♧ࡍ㸬ࡲࡓ㸪ᐇ㦂⤖ᯝࡼࡾᚓࡽࢀ

ࡓᅽຊศᕸࢆ Fig.2 ࡟♧ࡍ㸬ᐇ㦂ࡼࡾᚓࡽࢀࡓᅽຊ ศᕸࡢ᥎ᐃ᪉ἲ࡞࡝㸪ヲ⣽࡟㛵ࡋ࡚ࡣ➨1ሗࢆཧ↷

ࡉࢀࡓ࠸㸬ᮏሗ࡛ࡣᄇᏍධཱྀ㒊ࡢὶయᅽຊࢆᾮయࡢ 㣬࿴⵨Ẽᅽ㸪ฟཱྀࡢᅽຊࢆ኱Ẽᅽ࡜௬ᐃࡋ㸪ࡇࢀࡽ

࡜ Fig.2 ࡟♧ࡋࡓ⤖ᯝ࡜ࢆ⤌ࡳྜࢃࡏ࡚ከ㡯㏆ఝࡍ

ࡿࡇ࡜࡛ᄇᏍ㒊ࡢᅽຊศᕸࢆ⟬ฟࡋࡓ㸬௨ୖࡢ⤖ᯝ

ࡼࡾ㸪ᮏィ⟬࡟⏝࠸ࡿᅽຊᒚṔࢆ Fig.3 ࡟♧ࡍ㸬࡞

࠾㸪Fig.2(a)ࡢPinj=0.30MPa࠾ࡼࡧFig.2(b)ࡢC5/C11 ࡢ஧᮲௳ࡣhydraulic flipࢆ࿊ࡍࡿࡓࡵ㸪ᮏሗࡢィ⟬

ᑐ㇟ࡼࡾ㝖እࡋࡓ㸬ィ⟬࡟㝿ࡋ㸪ẼἻࡣ࣋ࣝࢾ࣮࢖

ᘧࡼࡾᚓࡽࢀࡿᖹᆒὶ㏿Vave࡜➼㏿࡛ᄇᏍෆࢆὶࢀ

ࡿ࡜࠸࠺௬ᐃࡢࡶ࡜㸪ྛࢱ࢖࣒ࢫࢸࢵࣉࡢᅽຊࢆ୚

࠼ࡓ㸬ࡲࡓ㸪ẼἻࡣ㣬࿴⵨Ẽᅽ௨ୗ࡜࡞ࡗࡓ᫬Ⅼ࡛

ᡂ㛗ࢆ㛤ጞࡍࡿ࡜ࡋ࡚࠾ࡾ㸪ᮏሗ࡛ࡣ඲࡚ࡢ᮲௳࡟

࠾࠸࡚ẼἻࡣᄇᏍධཱྀ㒊ࡼࡾᡂ㛗ࢆጞࡵࡿࡇ࡜࡜࡞

ࡿ㸬ィ⟬ࡣẼἻ༙ᚄࡀẼἻᔂቯ᫬ࡢ༙ᚄ Rbrkࢆୗᅇ

ࡿࡲ࡛⾜࡞࠸㸪ᮏሗ࡛ࡣRbrk=0.5Pm࡜ࡋࡓ㸬

Table 1. Test fuel properties.

3.6㽢10⁴ 2.4㽢10⁴

2.3㽢10⁴ [Pa]

Saturated vapor pressure

n-C5H12/n-C7H16

n-C5H12/n-C6H14

2-Methylpentane

[N/m]

[Pa䞉s]

[kg/m³]

1.8㽢10^-2 1.8㽢10^-2

1.8㽢10^-2 Surface tension

2.9㽢10^-4 2.9㽢10^-4

3.0㽢10^-4 Viscosity

6.5㽢10² 6.6㽢10²

6.5㽢10² Density

6䠖4 - 2䠖8

Mixture ratio (mole fraction)

iC6 C5/C6 C5/C7

Fuel Component

P_v: at bubble point U

P V

Pv [Pa] 2.3㽢10⁴ 2.4㽢10⁴ 3.6㽢10⁴

Saturated vapor pressure

n-C5H12/n-C7H16

n-C5H12/n-C6H14

2-Methylpentane

[N/m]

[Pa䞉s]

[kg/m³]

1.8㽢10^-2 1.8㽢10^-2

1.8㽢10^-2 Surface tension

2.9㽢10^-4 2.9㽢10^-4

3.0㽢10^-4 Viscosity

6.5㽢10² 6.6㽢10²

6.5㽢10² Density

6䠖4 - 2䠖8

Mixture ratio (mole fraction)

iC6 C5/C6 C5/C7

Fuel Component

P_v: at bubble point U

P V Pv

Table 2. Dimensions of actual and enlarged nozzle.

ws

wh

lh

[mm]

[mm]

[mm]

20.00 0.80

Sac width

3.75 0.15

Hole width

17.50 0.70

Hole length

25-times Actual nozzle

enlarged nozzle (Slit type)

ws

wh

lh

[mm]

[mm]

[mm]

20.00 0.80

Sac width

3.75 0.15

Hole width

17.50 0.70

Hole length

25-times Actual nozzle

enlarged nozzle (Slit type)

iC6 C5/C6

C5/C7 C5/C11

Distance from hole inlet [mm]

0.0 14.0 17.5

(b) For each fuel (P_inj= 0.20MPa)

P_inj= 0.15MPa P_inj= 0.20MPa

P_inj= 0.25MPa P_inj= 0.30MPa

(a) For each P_inj(Fuel : iC6)

Pressure [kPa]

Distance from hole inlet [mm]

0.0 50

0 100 200

3.5 7.0 10.5 14.0 17.5

Pressure [kPa]

50 0 100 250 200

iC6 C5/C6

C5/C7 C5/C11

Distance from hole inlet [mm]

0.0 14.0 17.5

(b) For each fuel (P_inj= 0.20MPa)

P_inj= 0.15MPa P_inj= 0.20MPa

P_inj= 0.25MPa P_inj= 0.30MPa P_inj= 0.15MPa

P_inj= 0.20MPa

P_inj= 0.25MPa P_inj= 0.30MPa

(a) For each P_inj(Fuel : iC6)

Pressure [kPa]

Distance from hole inlet [mm]

0.0 50

0 100 200

3.5 7.0 10.5 14.0 17.5

j j

0 0 0 0 0 0 0 0 0 0 0 0

3 5

3 5 7 07 0 10 510 5 14 014 0 1717

0 0 0 0 0

C5/C6

0 0

0 0 14 014 0 1717

Pressure [kPa]

50 0 100 250 200

Fig. 2. Pressure distribution inside nozzle.

ws

wh

lh

䈜thickness : 5mm

ws

wh

lh

䈜thickness : 5mm

Fig. 1. Nozzle configuration.

ィ⟬⤖ᯝ

ᅽຊᒚṔࡢᕪ␗࡟ࡼࡿẼἻ༙ᚄ࡬ࡢᙳ㡪

Fig.3 ࡟♧ࡋࡓᅽຊศᕸࢆẼἻࡀ⤒㦂ࡍࡿᅽຊᒚ

Ṕ࡜ࡋ㸪Rayleigh-Plessetᘧࢆ⏝࠸ࡓẼἻᚄィ⟬ࢆ⾜

࡞ࡗࡓ㸬ึᮇẼἻ༙ᚄR0ࢆ10Pm࡜ࡋࡓ㝿ࡢẼἻ༙

ᚄࡢᒚṔࢆᅽຊᒚṔ࡜࡜ࡶ࡟Fig.4࡟♧ࡍ㸬Fig.4ࡼ

ࡾ㸪ẼἻࡢ⤒㦂ࡍࡿᅽຊᒚṔࡀపᅽ࡛࠶ࡿ࡯࡝㸪᭱

኱ẼἻ༙ᚄࡣ኱ࡁࡃ࡞ࡾ㸪ࡑࡢᔂቯ఩⨨ࡣᄇᏍ㒊ࡢ

ୗὶ᪉ྥ࡬࡜᥎⛣ࡍࡿࡇ࡜ࡀࢃ࠿ࡿ㸬ࡲࡓ㸪ẼἻࡢ ᡂ㛗㏿ᗘ࡜ẚࡋ࡚཰⦰ࡍࡿ㝿ࡢẼἻቨ㏿ᗘࡣ㠀ᖖ࡟

㧗࠸ࡇ࡜ࡸ㸪࿘ᅖὶయࡢᅽຊࡀ㣬࿴⵨Ẽᅽࢆୖᅇࡗ ࡓᚋࡶẼἻࡣ័ᛶຊࡢᙳ㡪࡟ࡼࡾ࠶ࡿᮇ㛫ࡣᡂ㛗ࢆ

⥆ࡅࡿ࡞࡝㸪ẼἻ༙ᚄࡢኚ໬࡟㛵ࡍࡿᐃᛶⓗ࡞≉ᚩ ࡀᚓࡽࢀࡿࡇ࡜ࡀ☜ㄆࡉࢀࡿ㸬ࡇࡇ࡛㸪ẼἻᔂቯ఩

⨨ࡢẚ㍑ᑐ㇟࡜ࡋ࡚㸪Fig.5࡟♧ࡍᐇ㦂ࡼࡾᚓࡽࢀࡓ

᧜ᙳ⏬ീࢆ⏝࠸ࡿ㸬࡞࠾㸪⫼ᬒග᧜ᙳ࡟ࡼࡾᚓࡽࢀ

ࡓ⏬ീ࡛࠶ࡿࡓࡵ㸪㯮ࡃ᧜ᙳࡉࢀࡓ㡿ᇦࡀẼἻ㡿ᇦ

3.0 2.0

1.0

0.5 1.5 2.5

0.0 100

80 60 40 20 0 10^-2 10^-3 10^-4 10^-5 10^-6

Pressure [kPa]Bubble radius [m] ^{Vave= 12.2m/s} V_ave= 17.4m/s

= 24.7m/s

Distance from nozzle hole inlet [mm]

(a) For each V_ave(fuel : iC6)

iC6

8.0 4.0

2.0 6.0 10.0

0.0 150 120 90 60 30 0 10^-2 10^-3 10^-4 10^-5 10^-6

Pressure [kPa]Bubble radius [m]

Distance from nozzle hole inlet [mm]

(b) For each test fuel (V_ave= 17.4m/s)

-2 -3 -4 -5 -6

0

-2 -3 -4 -5 -6

Vave

V

V = 12.2m/s V_ave V

V = 17.4m/s

= 24.7m/s

0 iC6 0 0 0 0 0 0 0

0 0 0 0 0 0

3.0 2.0

1.0

0.5 1.5 2.5

0.0 100

80 60 40 20 0 10^-2 10^-3 10^-4 10^-5 10^-6

Pressure [kPa]Bubble radius [m] ^{Vave= 12.2m/s} V_ave= 17.4m/s V_ave= 24.7m/s

Distance from nozzle hole inlet [mm]

(a) For each V_ave(fuel : iC6)

iC6 C5/C6 C5/C7

8.0 4.0

2.0 6.0 10.0

0.0 150 120 90 60 30 0 10^-2 10^-3 10^-4 10^-5 10^-6

Pressure [kPa]Bubble radius [m]

Distance from nozzle hole inlet [mm]

(b) For each test fuel (V_ave= 17.4m/s) Fig. 4. Histories of bubble radius and pressure (initial bubble radius R0=10Pm).

0.0 3.5 7.0 10.5 14.0 17.5

Distance from nozzle hole inlet [mm]

Fuel [MPa]

[m/s]

0.15 12.2 iC6

0.20 17.4 iC6

0.25 21.3 iC6 Pinj

Vave

0.20 17.4 C5/C6

0.20 17.4 C5/C7

0.0 3.5 7.0 10.5 14.0 17.5

Distance from nozzle hole inlet [mm]

Fuel [MPa]

[m/s]

0.15 12.2 iC6

0.20 17.4 iC6

0.25 21.3 iC6 Pinj

Vave

0.20 17.4 C5/C6

0.20 17.4 C5/C7

Fig. 5. Cavitation image inside nozzle hole for each condition.

V_ave= 12.2m/s Vave= 17.4m/s Vave= 24.7m/s 200

150 100 50 0

0.0 3.5 7.0 10.5 14.0 17.5

Pressure [kPa]

Distance from hole inlet [mm]

(a) For each V_ave(fuel : iC6)

iC6 C5/C6 C5/C7 200

150 100 50 0

0.0 3.5 7.0 10.5 14.0 17.5

Pressure [kPa]

Distance from hole inlet [mm]

(b) For each test fuel (V_ave= 17.4m/s)

iC6 C5/C6 C5/C7 0

0 0 0 0

V_ave V

V = 12.2m/s Vave

V

V = 17.4m/s Vave

V

V = 24.7m/s 0

0 0 0 0

V_ave= 12.2m/s Vave= 17.4m/s Vave= 24.7m/s 200

150 100 50 0

0.0 3.5 7.0 10.5 14.0 17.5

Pressure [kPa]

Distance from hole inlet [mm]

(a) For each V_ave(fuel : iC6)

iC6 C5/C6 C5/C7 200

150 100 50 0

0.0 3.5 7.0 10.5 14.0 17.5

Pressure [kPa]

Distance from hole inlet [mm]

(b) For each test fuel (V_ave= 17.4m/s) Fig. 3. Pressure distribution used for calculation.

࡛࠶ࡿ㸬⏬ീࡼࡾ᫂☜࡞ᔂቯ఩⨨ࡣᢕᥱ࡛ࡁ࡞࠸ࡀ㸪

࠾࠾ࡼࡑࡢ఩⨨ࡣ᥎ᐃྍ⬟࡛࠶ࡿ࡜ุ᩿ࡋ㸪ᮏࣔࢹ

ࣝࡢẚ㍑ᑐ㇟࡜ࡋ࡚⏝࠸ࡓ㸬Fig.4㸪5 ࡼࡾ㸪࠸ࡎࢀ

ࡢᅽຊᒚṔ࡟ᑐࡋ࡚ࡶ㸪ẼἻィ⟬ࡼࡾᚓࡽࢀࡓᔂቯ

఩⨨ࡣ᫂ࡽ࠿࡟ᐇ㦂⤖ᯝࡼࡾࡶᄇᏍ㒊ࡢୖὶഃ࡟఩

⨨ࡋ࡚࠸ࡿࡇ࡜ࡀࢃ࠿ࡿ㸬௨ୖࡢ⤖ᯝࡼࡾ㸪ẼἻࡢ ᔂቯ఩⨨ࡇࡑ኱ࡁࡃ␗࡞ࡿࡶࡢࡢ㸪ᮏࣔࢹ࡛ࣝࡣẼ Ἳࡢᅽຊሙ࡟ᑐࡍࡿᐃᛶⓗ࡞ᣲືࢆ⾲⌧ࡍࡿࡇ࡜ࡀ

ྍ⬟࡛࠶ࡿ࡜࠸࠼ࡿ㸬

ึᮇẼἻ༙ᚄࡀẼἻᣲື࡟ཬࡰࡍᙳ㡪

ึᮇẼἻ༙ᚄ R0ࢆኚ໬ࡉࡏࡿࡇ࡜࡟ࡼࡾẼἻᣲ

ື࣭ᔂቯ఩⨨ࡀዴఱ࡟᥎⛣ࡍࡿ࠿ࢆ᳨ドࡍࡿ㸬Fig.3 ࡢᅽຊᒚṔ࡟ᑐࡋ㸪ึᮇẼἻ༙ᚄR0ࢆ 5㹼25Pm࡜ ኚ໬ࡉࡏࡓሙྜࡢẼἻ༙ᚄᒚṔࢆFig.6࡟♧ࡍ㸬Fig.6

ࡼࡾ㸪C5/C7 ΰྜ⇞ᩱࡢ᮲௳ࢆ㝖ࡃ࠸ࡎࢀࡢᅽຊᒚ

Ṕ࡟ᑐࡋ࡚ࡶ㸪ึᮇẼἻ༙ᚄR0ࢆቑຍࡉࡏࡿࡇ࡜࡟

ࡼࡾ฿㐩ࡍࡿ᭱኱ẼἻ༙ᚄࡣ኱ࡁࡃ࡞ࡿࡇ࡜ࡀࢃ࠿

ࡾ㸪ึᮇẼἻ༙ᚄ࡟ࡼࡿẼἻᣲື࡬ࡢᙳ㡪ࢆᐃᛶⓗ

࡟ᤊ࠼࡚࠸ࡿ࡜࠸࠼ࡿ㸬ࡋ࠿ࡋ࡞ࡀࡽ㸪R₀ࡢቑຍ࡟

క࠸ẼἻᔂቯ఩⨨ࡣୗὶ᪉ྥ࡬࡜⛣ືࡍࡿࡶࡢࡢ㸪 ᐇ㦂⤖ᯝࡢᔂቯ఩⨨࡟ࡣ฿㐩ࡋ࡞࠸ࡇ࡜ࡀ☜ㄆࡉࢀ

ࡿ㸬୍᪉㸪C5/C7ΰྜ⇞ᩱࡢᅽຊᒚṔ࡟ᑐࡋ࡚ᚓࡽ

ࢀࡓึᮇẼἻ༙ᚄ R0ࡢᙳ㡪ࡣ௚ࡢ᮲௳࡜␗࡞ࡗ࡚

࠸ࡿ㸬ࡍ࡞ࢃࡕ㸪R0ࢆ5㹼25Pmࡢ⠊ᅖ࡛ኚ໬ࡉࡏ࡚

ࡶ᭱኱ẼἻ༙ᚄ࣭ᔂቯ఩⨨࡟࠾࠸࡚ᕪ␗ࡀぢࡽࢀ࡞

࠸㸬ࡇࢀࡣ㸪ẼἻࡢᡂ㛗㏿ᗘࡀ኱࡞ࡿ࡯࡝㸪ึᮇẼ Ἳ༙ᚄࡀᚋࡢẼἻᣲື࡟ཬࡰࡍᙳ㡪ࡣᑠࡉࡃ࡞ࡿࡇ

࡜ࢆ♧ࡋ࡚࠸ࡿ㸬࠸ࡎࢀ࡟ࡋ࡚ࡶ㸪ึᮇẼἻ༙ᚄࢆ

ኚ໬ࡉࡏࡿࡢࡳ࡛ࡣᐇ㦂⤖ᯝࡢᔂቯ఩⨨ࢆ෌⌧ࡋᚓ

࡞࠸ࡇ࡜ࡀ♧ࡉࢀࡓ㸬

0.0 0.1 0.2 0.3 0.4 0.5

0.10 0.08 0.06 0.04 0.02 0.00

Distance from nozzle hole inlet [mm]

Bubble radius [mm]

0.0 0.4 0.8 1.2 1.6 2.0

0.10 0.08 0.06 0.04 0.02 0.00

Distance from nozzle hole inlet [mm]

Bubble radius [mm]

0.0 0.6 1.2 1.8 2.4 3.0

0.20 0.16 0.12 0.08 0.04 0.00

Distance from nozzle hole inlet [mm]

Bubble radius [mm]

0.0 0.2 0.4 0.6 0.8 1.0

0.10 0.08 0.06 0.04 0.02 0.00

Distance from nozzle hole inlet [mm]

Bubble radius [mm]

0.0 2.0 4.0 6.0 8.0 10.0

1.00 0.80 0.60 0.40 0.20 0.00

Distance from nozzle hole inlet [mm]

Bubble radius [mm]

(a) iC6,V_ave=12.2m/s

(b) iC6,V_ave=17.4m/s

(c) iC6,V_ave=21.3m/s

(d) C5/C6,V_ave=17.4m/s

(e) C5/C7,V_ave=17.4m/s R0 = 5Pm R0 = 10Pm R0 = 15Pm R₀ = 20Pm R₀ = 25Pm

0 0 2 0 4 0 6 0 8 0 10 0

0 0 0 0 0 0

0 0 0 2 0 4 0 6 0 8 1 0

0 8 6 4 2 0

0 0 0 6 1 2 1 8 2 4 3 0

0 6 2 8 4 0

0 0 0 4 0 8 1 2 1 6 2 0

0 8 6 4 2 0

0 0 0 1 0 2 0 3 0 4 0 5

0 8 6 4 2 0

0.0 0.1 0.2 0.3 0.4 0.5

0.10 0.08 0.06 0.04 0.02 0.00

Distance from nozzle hole inlet [mm]

Bubble radius [mm]

0.0 0.4 0.8 1.2 1.6 2.0

0.10 0.08 0.06 0.04 0.02 0.00

Distance from nozzle hole inlet [mm]

Bubble radius [mm]

0.0 0.6 1.2 1.8 2.4 3.0

0.20 0.16 0.12 0.08 0.04 0.00

Distance from nozzle hole inlet [mm]

Bubble radius [mm]

0.0 0.2 0.4 0.6 0.8 1.0

0.10 0.08 0.06 0.04 0.02 0.00

Distance from nozzle hole inlet [mm]

Bubble radius [mm]

0.0 2.0 4.0 6.0 8.0 10.0

1.00 0.80 0.60 0.40 0.20 0.00

Distance from nozzle hole inlet [mm]

Bubble radius [mm]

(a) iC6,V_ave=12.2m/s

(b) iC6,V_ave=17.4m/s

(c) iC6,V_ave=21.3m/s

(d) C5/C6,V_ave=17.4m/s

(e) C5/C7,V_ave=17.4m/s R0 = 5Pm R0 = 10Pm R0 = 15Pm R₀ = 20Pm R₀ = 25Pm

Fig. 6. Effect of initial bubble radius on growth and shrinkage processes of cavitation bubbles.

௒ᚋࡢ᳨ウ஦㡯

๓⠇ࡲ࡛࡟ᚓࡽࢀࡓ⤖ᯝࢆ⥲ྜࡍࡿ࡜㸪ᮏࣔࢹࣝ

ࢆ⏝࠸ࡓィ⟬⤖ᯝࡣẼἻࡢ⤒㦂ࡍࡿᅽຊᒚṔ࡟኱ࡁ ࡃᕥྑࡉࢀࡿ࡜࠸࠼ࡿ㸬ࡑࡇ࡛㸪ᮏィ⟬࡟⏝࠸ࡓᅽ ຊᒚṔ࡟ࡘ࠸᳨࡚ウࡍࡿ㸬ୖ㏙ࡢ㏻ࡾ㸪ᮏሗ࡛ࡣᐇ 㦂ࡼࡾᚓࡽࢀࡓᅽຊศᕸࢆẼἻࡢ⤒㦂ࡍࡿᅽຊᒚṔ

࡜ࡋ࡚ィ⟬ࢆ⾜࡞ࡗࡓ㸬ࡋ࠿ࡋ࡞ࡀࡽ㸪ẼἻࡀᚠ⎔

ὶࢀ࡟ᅾࡋ࡞࠸࡜௬ᐃࡍࡿ࡜㸪ᐇ㝿࡟ࡣ୺ὶ࡟ἢ ࡗ࡚ᄇᏍୗὶ㒊࡬࡜⛣ືࡍࡿ࡜⪃࠼ࡽࢀࡿ㸬ࡇࢀࡼ

ࡾ㸪୺ὶ㒊࡟࡚ẼἻࡢ⤒㦂ࡍࡿᅽຊᒚṔࡣᮏィ⟬࡟

⏝࠸ࡓࡑࢀ࡜␗࡞ࡿࡓࡵ㸪ィ⟬⤖ᯝ࡜ᐇ㦂⤖ᯝࡢ୙

୍⮴ࡀ⏕ࡌࡓྍ⬟ᛶࡀ࠶ࡿ࡜᥎ᐹࡉࢀࡿ㸬ࡲࡓ㸪௒

ᅇࡣ༢୍ẼἻ࡟ࡘ࠸࡚ィ⟬ࢆ⾜࡞ࡗࡓࡀ㸪ᐇ㝿࡟ࡣ ከᩘࡢẼἻࡀྠ᫬ከⓎⓗ࡟ⓎἻ࣭ᡂ㛗࠾ࡼࡧ཰⦰㐣

⛬ࢆ♧ࡍ࡜⪃࠼ࡽࢀࡿ㸬ࡇࡢࡇ࡜࠿ࡽ㸪ከᩘࡢẼἻ ᣲືࡀ஫࠸࡟ᙳ㡪ࢆཬࡰࡍྍ⬟ᛶࡀ㧗࠸࡜࠸࠼ࡿ㸬 ࡍ࡞ࢃࡕ㸪ⓎἻẼἻᩘࡢቑຍ࡟క࠺ᄇᏍෆ࡛ࡢᅽຊ ኚືࡢ⦆࿴¹¹⁾ࡸ⾲㠃⢓ᛶࡢᙳ㡪¹²⁾࡞࡝㸪௚ࡢᅉᏊ࡟

ࡘ࠸࡚ࡶ᳨ウࡍࡿᚲせࡀ࠶ࡿ㸬௒ᚋࡣࡇࢀࡽࡢࡇ࡜

ࢆ㋃ࡲ࠼㸪ᐇ㦂⤖ᯝ࡜ࡢẚ㍑᳨࣭ドࢆ㔜ࡡࡿࡇ࡜࡛

ண ⢭ᗘࡢྥୖࢆᅗࡿ㸬

⤖ゝ

ᮏ◊✲࡛ࡣከᵝ࡞ᄇᑕ᮲௳࡟ᑐࡍࡿᄇ㟝≉ᛶࢆண  ࡍࡿࡓࡵ㸪࢟ࣕࣅࢸ࣮ࢩࣙࣥ⌧㇟ࢆ⪃៖࡟ධࢀࡓ ィ⟬ᡭἲࡢᵓ⠏ࢆ┠ⓗ࡜ࡍࡿ㸬ᮏሗ࡛ࡣ㸪࢟ࣕࣅࢸ

࣮ࢩࣙࣥࣔࢹࣝ࡟ࡘ࠸࡚ᴫㄝࡋ㸪ᐇ㦂ⓗ࡟ᚓࡽࢀࡓ ᅽຊᒚṔࢆࡶ࡜࡟㸪ẼἻᣲືࢆ⡆᫆ⓗ࡟෌⌧ࡍࡿࡇ

࡜ࢆヨࡳࡓ㸬௨ୗ࡟ᚓࡽࢀࡓ▱ぢࢆ♧ࡍ㸬

(1) ᮏࣔࢹࣝࡣẼἻ༙ᚄࡢኚ໬࡟㛵ࡍࡿᐃᛶⓗ࡞≉

ᚩࢆグ㏙ࡍࡿ㸬

(2) ẼἻࡢᡂ㛗㏿ᗘࡀ኱ࡁࡃ࡞ࡿ࡯࡝㸪ึᮇẼἻ༙

ᚄࡀẼἻࡢᡂ㛗࣭཰⦰㐣⛬࠾ࡼࡧᔂቯ఩⨨࡟ཬ

ࡰࡍᙳ㡪ࡣᑠࡉࡃ࡞ࡿ㸬

(3) ᐇ㦂⤖ᯝࢆ㐺ษ࡟෌⌧ࡍࡿࡓࡵ㸪ẼἻࡢ⤒㦂ࡍ

ࡿᅽຊᒚṔࡢぢ┤ࡋࡸẼἻྠኈࡢ┦஫ᖸ΅ࢆ⪃

៖ࡍࡿ࡞࡝㸪ᮏࣔࢹࣝࡣ௒ᚋࡢᨵၿࢆせࡍࡿ㸬

ཧ⪃ᩥ⊩

1) Pope, S. B., Computationally Efficient Implementation of

Combustion Chemistry using in Situ Adaptive Tabulation, Combustion and Theory Modeling, Vol.1, pp.41-63, (1997).

2) O’Rouke, P. J. and Amsden, A. A., The Tab Method for Numerical Calculation of Spray Droplet Breakup, SAE paper, No.872089, (1987).

3) Patterson, M. A., Reitz, R. D., Modeling the Effects of Fuel Spray Characteristics on Diesel Engine Combustion and Emission, SAE paper, No.980131, (1998).

4) ⋢ᮌఙⱱ, す⏣ᜨဢ, ΎỈṇ๎, ᘅᏳ༤அ, ࣀࢬࣝෆ ᄇᏍෆࡢ࢟ࣕࣅࢸ࣮ࢩࣙࣥࡀᾮయᄇὶࡢᚤ⢏໬࡟ཬ

ࡰ ࡍ ᙳ 㡪, ᪥ ᮏ ᶵ Ე Ꮫ ఍ ㄽ ᩥ 㞟 B ⦅, 63(614), pp.3447-3454, (1997).

5) ኱㯮ṇᩄ, ྂ㤋ோ, ✄ᮧ㝯ኵ, ࣀࢬࣝෆ࢟ࣕࣅࢸ࣮ࢩ

ࣙࣥࡀᾮయศ⿣ᶵᵓ࡟ཬࡰࡍᙳ㡪(➨3ሗ㸪2Dࣀࢬࣝ

ෆࡢᅽຊኚື), ᪥ᮏᶵᲔᏛ఍ㄽᩥ㞟 B ⦅, 71(703), pp.811-816, (2005).

6) ᑠ➟ཎៅ, ኱㯮ṇᩄ, ࣀࢬࣝෆᾮయࡢ஘ࢀࡀᄇὶ࡟ཬ

ࡰࡍᙳ㡪, ᪥ᮏᶵᲔᏛ఍ᮾ໭ᨭ㒊⛅Ꮨㅮ₇఍ㅮ₇ㄽ

ᩥ㞟, 20060930, pp.71-72, (2006).

7) Arcoumanis, C., Gavaises, M., Linking the Nozzle Flow with Spray Characteristics in a Diesel Fuel Injection System, Atomization and Sprays, Vol.8, pp.179-197, (1998).

8) Nishimura, A. and Assanis, D. N., A Model for Primary Diesel Atomization Based on Cavitation Bubble Collapse Energy, Proc. ICLASS-2000, pp.1249-1256, (2000).

9) Baumgarten, C., Shi, Y., Bush, R. and Merker, G. P., Numerical and Experimental Investigations of Cavitation Flow in High Pressure Diesel Nozzles, ILASS-Europe, (2001).

10) ᓥ❶, ⸨ཎᚨ୍, ᅽ⦰ᛶἜᅽసືἜ୰ࡢẼἻࡢᔂቯ, ᮾ໭኱Ꮫ㧗㏿ຊᏛ◊✲ᡤሗ࿌, 46(407), pp.129-144, (1981).

11) ➉୰฼ ኵ, ᾆ ⏣ⱥ୕, ἜຊᏛ, 㣴㈼ᇽ, pp.206-223, (1968).

12) Ἳࡢ࢚ࣥࢪࢽ࢔ࣜࣥࢢ, ࢸࢡࣀࢩࢫࢸ࣒, pp.19-29, (2005).