宇宙航空研究開発機構研究開発資料

JAXA Ｒesearch and Development Memorandum

詳細シミュレーションによる水素噴流浮き上がり火炎の構造解析

溝渕 泰寛, 新城 淳史, 松山 新吾, 小川 哲, 竹野 忠夫

宇宙航空研究開発機構研究開発資料

2008年2月

JAXA-RM-07-018宇宙航空研究開発機構研究開発資料

ヲ⣽ࢩ࣑࣮ࣗࣞࢩࣙࣥ࡟ࡼࡿỈ⣲ᄇὶᾋࡁୖࡀࡾⅆ⅖ࡢᵓ㐀ゎᯒ

⁁ῲ Ὀᐶ

^*1

㸪᪂ᇛ ῟ྐ

^*1

㸪ᯇᒣ ᪂࿃

^*1

㸪ᑠᕝ ဴ

^*1

㸪➉㔝 ᛅኵ

^*1

Numerical study of the flame structure of a hydrogen jet lifted flame by detailed simulation

Yasuhiro MIZOBUCHI

^*1

, Junji SHINJO

^*1

, Shingo MATSUYAMA

^*1

Satoru OGAWA

^*1

and Tadao TAKENO

^*1

ABSTRACT

A real-size hydrogen jet lifted flame is successfully reproduced by a highly resolved time-dependent 3-D numerical simulation with detailed chemistry and rigorous transport properties. The analysis based on Flame Index clearly shows that the lifted flame is not a single flame but consists of three flame elements; 1) a stable leading edge flame, 2) diffusion flame islands floating on the outer side of the lifted flame, 3) inner vigorously turbulent rich premixed flames. The stable laminar leading edge flame of ring shape has a triple flame like structure and is stabilized outside the turbulent jet where the incoming flow almost balances with the burning velocity. The combustion in diffusion flame islands can be explained by the conventional laminar flamelet concept, although they take island-like shapes. The island-like shapes are produced by the unsteady turbulent behavior of inner rich premixed flame. In the inner vigorously turbulent rich premixed flames, flame structures that are largely deviated from the laminar flamelet concept are observed. The turbulence scales and the flame structure scales are in the same order and turbulent eddies can easily penetrate into the flame internal structures.

ᴫ せ

ヲ⣽࡞໬Ꮫ཯ᛂ㐣⛬࠾ࡼࡧὶయࡢ㍺㏦≉ᛶࢆ⤌ࡳ㎸ࢇࡔ༑ศ࡞ゎീᗘࢆ᭷ࡍࡿࢩ࣑࣮ࣗࣞࢩࣙࣥ࡟ࡼࡾ㸪ᐇࢫࢣ࣮

ࣝࡢỈ⣲ᄇὶᾋࡁୖࡀࡾⅆ⅖ࢆᩘ್ⓗ࡟࡜ࡽ࠼ࡿࡇ࡜࡟ᡂຌࡋࡓ㸬

Flame Index

ࢆ⏝࠸ࡓゎᯒ࡟ࡼࡾ㸪ᾋࡁୖࡀࡾⅆ⅖ ࡣ༢࡞ࡿ୍ࡘࡢⅆ⅖࡛ࡣ࡞ࡃ㸱ࡘࡢⅆ⅖せ⣲ࢆྵࢇ࡛࠸ࡿࡇ࡜ࡀศ࠿ࡗࡓ㸬ࡍ࡞ࢃࡕ㸪1)୕㔜ⅆ⅖ⓗ࡞ᵓ㐀ࢆࡶࡘࣜ

ࣥࢢ≧ࡢᏳᐃ࡞ඛ➃ⅆ⅖㸪2)ᾋࡁୖࡀࡾⅆ⅖እഃ࡟ᓥ≧࡟ᙧᡂࡉࢀࡿᓥ≧ᣑᩓⅆ⅖㸪3)ᾋࡁୖࡀࡾⅆ⅖ෆഃ࡛ᄇὶࡢ

஘ࢀࡢᙳ㡪ࢆᙉࡃཷࡅ࡚࠸ࡿෆഃ㐣⃰஘ὶணΰྜⅆ⅖㸪࡛࠶ࡿ㸬ඛ➃ⅆ⅖࡟ࡘ࠸࡚ࡣࣜࣥࢢ≧ࡢඛ➃ⅆ⅖୰࡟㸪ⅆ⅖ ࡢఏ᧛㏿ᗘ࡜ⅆ⅖࡟ὶධࡍࡿΰྜẼࡢ㏿ᗘࡀࡘࡾ࠶࠺㒊఩ࡀᏑᅾࡍࡿࡇ࡜࡟ࡼࡾⅆ⅖ࡀᏳᐃ໬ࡉࢀ࡚࠸ࡿࡇ࡜ࡀ᥎ᐃ ࡉࢀࡓ㸬ᓥ≧ᣑᩓⅆ⅖࡟ࡘ࠸࡚ࡣ㸪≉␗࡞ᙧ≧ࢆࡶࡘࡶࡢࡢ㸪ࡑࡢ୰࡛ࡢ⇞↝ࡣᚑ᮶ࡢⅆ⅖ࡢᴫᛕ࡛ㄝ࡛᫂ࡁࡿࡇ࡜㸪 ࡑࡢ⏕ᡂࡣෆഃ࡟࠶ࡿ஘ὶ㐣⃰ணΰྜⅆ⅖ࡢ㠀ᐃᖖࡢᣲື࡟ࡼࡿࡶࡢ࡛࠶ࡿࡇ࡜ࡀ♧ࡉࢀࡓ㸬ෆഃ஘ὶ㐣⃰ணΰྜⅆ

⅖࡛ࡣ㸪ᚑ᮶ࡢⅆ⅖ࡢᴫᛕ࠿ࡽ኱ࡁࡃእࢀࡓⅆ⅖ᵓ㐀ࡀほᐹࡉࢀ㸪ࡑࡇ࡛ࡣ஘ὶ ࡢࢫࢣ࣮ࣝ࡜ⅆ⅖ᵓ㐀ࡢࢫࢣ࣮ࣝ

ࡀྠ⛬ᗘ࡛࠶ࡾὶయࡢ஘ࢀࡀⅆ⅖ෆ㒊ᵓ㐀࡟ᙳ㡪ࢆ୚࠼ࡸࡍ࠸≧ែ࡟࠶ࡿ࡜࠸࠺ࡇ࡜ࡀศ࠿ࡗࡓ㸬

*

ᖹᡂ

19

ᖺ

12

᭶

3

᪥ ཷ௜㸦Received 3 December, 2007㸧

*1

⥲ྜᢏ⾡ᮏ㒊 ィ⟬⛉Ꮫ◊✲ࢢ࣮ࣝࣉ (Computational Science Research Group, Institute of Aerospace Technology)

グྕ

D

㸸ࣀࢬࣝ┤ᚄ(m)

Ds

㸸໬Ꮫ✀

s

ࡢᣑᩓಀᩘ㸦m

²/s㸧

e

㸸ΰྜẼ༢఩య✚࠶ࡓࡾࡢෆ㒊࢚ࢿࣝࢠ㸦J/m

³

㸧

E

㸸ΰྜẼ༢఩య✚࠶ࡓࡾࡢ඲ෆ㒊࢚ࢿࣝࢠ㸦J/m

³

㸧

F.I.

㸸Flame Index㸦1/m

²

㸧

Hs

㸸໬Ꮫ✀

s

ࡢ㸯ࣔࣝ࠶ࡓࡾࡢ࢚ࣥࢱࣝࣆ(J/mol)

'Hfs

㸸໬Ꮫ✀

s

ࡢ㸯ࣔࣝ࠶ࡓࡾࡢ⏕ᡂ࢚ࣥࢱࣝࣆ(J/mol)

k

㸸࣎ࣝࢶ࣐ࣥᐃᩘ㸦J/K㸧

ms

㸸໬Ꮫ✀

s

ࡢศᏊ

1

ಶ࠶ࡓࡾࡢ㉁㔞㸦kg㸧

0_s

㸸໬Ꮫ✀

s

ࡢศᏊ㔞㸦kg/mol㸧

N.F.I. 㸸Normalized Flame Index P

㸸ᅽຊ㸦N/m

²

㸧

Ru

㸸ᬑ㐢Ẽయᐃᩘ㸦J/K/mol㸧

T

㸸 ᗘ㸦K㸧

ui

㸸

i

᪉ྥࡢ㏿ᗘ㸦m/s㸧

Xs

㸸໬Ꮫ✀

s

ࡢࣔࣝศ⋡

Ys

㸸໬Ꮫ✀

s

ࡢ㉁㔞ศ⋡

zs

㸸ΰྜẼ༢఩㉁㔞࠶ࡓࡾࡢ໬Ꮫ✀

s

ࡢࣔࣝᩘ

㸦mol/kg㸧

Hs

㸸໬Ꮫ✀

s

ࡢ࣏ࢸࣥࢩࣕࣝ஭ᡞ῝ࡉ㸦J㸧

N

㸸⇕ఏᑟ⋡㸦W/m/K㸧

P

㸸⢓ᛶಀᩘ㸦N/m

²

㺃s㸧

U

㸸ᐦᗘ㸦kg/m

³

㸧

Vs

㸸໬Ꮫ✀

s

ࡢ⾪✺┤ᚄ㸦m㸧

W

㸸ࡏࢇ᩿ᛂຊ㸦N/m

²

㸧

Zs

㸸 ໬ Ꮫ ✀

s

ࡢ ༢ ఩ య ✚ ࠶ ࡓ ࡾ ࡢ ࣔ ࣝ ⏕ ᡂ ㏿ ᗘ 㸦mol/m

³/s㸧

ࡣࡌࡵ࡟

ᄇὶࡣᇶᮏⓗ࡞ὶࢀࡢ୍ࡘ࡛࠶ࡾ㸪ᒙὶ࠿ࡽ஘ὶ࡬ࡢ 㑄⛣ࡢၥ㢟࠶ࡿ࠸ࡣ஘ὶᄇὶ࡛ࡢ஘ὶΰྜࡢၥ㢟ࡀྂࡃ

࠿ࡽ◊✲ࡉࢀ࡚ࡁ࡚࠸ࡿ㸬ྠᵝ࡟㸪✵Ẽ୰࡟ᄇὶ࡜ࡋ࡚

ᄇฟࡉࢀࡓ⇞ᩱࡢ⇞↝࡟ࡼࡗ࡚ᙧᡂࡉࢀࡿ⇞ᩱᄇὶᣑᩓ ⅆ⅖ࡶᇶᮏⓗ࡞ⅆ⅖ࡢ୍ࡘ࡛࠶ࡾ㸪ᕤᴗⓗ࡟ࡶᗈࡃ฼⏝

ࡉࢀ࡚࠸ࡿⅆ⅖࡛࠶ࡿ㸬ࡇࡢⅆ⅖࡟࠾࠸࡚ࡣ㸪ᄇὶ㏿ᗘ

ࢆᚎࠎ࡟ୖࡆ࡚࠸ࡃ࡜㸪ᒙὶ࠿ࡽ஘ὶ࡬ࡢ㑄⛣ࡀ㉳ࡇࡾ㸪 ࡉࡽ࡟㏿ᗘࢆୖࡆࡿ࡜ࣀࢬࣝ࡟௜╔ࡋ࡚࠸ࡓᣑᩓⅆ⅖ࡀ

ࣀࢬࣝ࠿ࡽ㞳⬺ࡋ㸪ࣀࢬࣝ࠿ࡽ㞳ࢀࡓ఩⨨࡛⇞↝ࡀጞࡲ

ࡿࡇ࡜ࡀ▱ࡽࢀ࡚࠸ࡿ㸬ࡇࡢⅆ⅖ᙧែࢆᾋࡁୖࡀࡾⅆ⅖

࡜࿧ࡪ㸬

ࣀࢬࣝ࠿ࡽ㞳⬺ࡍࡿ๓ࡢᣑᩓⅆ⅖࡜ࡣ␗࡞ࡿᛶ㉁ࢆ

ᣢࡘᾋࡁୖࡀࡾⅆ⅖ࡣ㸪ᇶ♏ⓗ࡞◊✲࡜࠸࠺㠃࠿ࡽぢ࡚

ࡶࡲࡓᐇ⏝ⓗ࡞◊✲ࡢ㠃࠿ࡽぢ࡚ࡶ⯆࿡῝࠸◊✲ᑐ㇟࡛

࠶ࡿ㸬 ᾋࡁୖࡀࡾⅆ⅖ࡢ◊✲࡟࠾ࡅࡿ୺ࡓࡿ◊✲ㄢ㢟ࡣ㸪 ࡑࡢⅆ⅖ᵓ㐀ࡢゎ᫂࠾ࡼࡧࣀࢬࣝ࠿ࡽ㞳⬺ࡋࡓⅆ⅖ࡀୗ

ὶ࡟྿ࡁ㣕ࡤࡉࢀࡎ࡟ᐃᅾⓗ࡞ⅆ⅖࡜ࡋ࡚ಖᣢࡉࢀࡿࡓ

ࡵࡢᏳᐃ໬ᶵᵓࡢゎ࡛᫂࠶ࡿ㸬⌧ᅾࡲ࡛୺࡟ᣑᩓⅆ⅖ࡢ ᾘ⅖[1], ୕㔜ⅆ⅖ᵓ㐀[2,3,4,5]࡜࠸࠺どⅬ࠿ࡽከࡃࡢ◊

✲ࡀ࡞ࡉࢀ࡚࠸ࡿ㸬ࡋ࠿ࡋ࡞ࡀࡽᚑ᮶ࡢ◊✲ࡣᐃᖖ࠶ࡿ

࠸ࡣ஧ḟඖゎᯒࡀ୰ᚰ࡛࠶ࡾ㸪୕ḟඖᛶ࣭㠀ᐃᖖᛶࡀᙉ

࠸ᾋࡁୖࡀࡾⅆ⅖ࡢᵓ㐀ࡢゎ᫂ࡣᮍࡔ༑ศ࡟ࡣ⾜ࢃࢀ࡚

࠾ࡽࡎ㸪ࡲࡓᏳᐃ໬ᶵᵓ࡟ࡘ࠸࡚ࡶ⤖ㄽࡀฟ࡚࠸࡞࠸㸬 ࡑࢀࡣ㸪ᄇὶࡢᙉ࠸஘ࢀࡢᙳ㡪ࢆཷࡅࡿ୕ḟඖⓗ࡛㠀ᐃ ᖖ࡞ෆ㒊ᵓ㐀ࢆィ ࡍࡿࡇ࡜ࡣᴟࡵ࡚ᅔ㞴࡛࠶ࡾ㸪᭱㏆

Ⓨ㐩ࡋ࡚ࡁࡓගᏛィ ᡭἲࢆ⏝࠸࡚ࡶᐜ᫆࡞ࡇ࡜࡛ࡣ࡞

࠸࠿ࡽ࡛࠶ࡿ㸬

ࡇࡢᵝ࡞」㞧࡞⇞↝⌧㇟ࡢゎ᫂࡟ࡣᩘ್ࢩ࣑࣮ࣗࣞ

ࢩࣙࣥࡀ᭷ຠ࡛࠶ࡿ㸬ⅆ⅖ࡢヲ⣽ࢩ࣑࣮ࣗࣞࢩࣙࣥࢆ⾜

࠺ࡓࡵ࡟ࡣ㸪஘ὶ࡟௦⾲ࡉࢀࡿὶయࡢࢫࢣ࣮ࣝ࡟ຍ࠼࡚

⇞ᩱࢆᾘ㈝ࡋ⇕ࢆⓎ⏕ࡍࡿ཯ᛂᖏࢆゎീࡍࡿᚲせࡀ࠶ࡿ㸬

୍⯡࡟㧗 ࡢ⇞↝ὶࢀ࡟࠾࠸࡚ࡣ཯ᛂᖏࡢཌࡉࡣ஘ὶࡢ

᭱ᑠࢫࢣ࣮ࣝࡼࡾࡶᑠࡉ࠸ሙྜࡀከࡃ㸪ⅆ⅖ࡢヲ⣽࡞ࢩ

࣑࣮ࣗࣞࢩࣙࣥ࡟ࡣᴟࡵ࡚⣽࠿࠸᱁Ꮚゎീᗘࡀせồࡉࢀ㸪

⭾኱࡞ィ⟬ᶵ㈨※ࡀᚲせ࡜࡞ࡿ㸬ᚑ᮶ࡑࡢࡼ࠺࡞ࢩ࣑ࣗ

࣮ࣞࢩࣙࣥࡢᐇ᪋ࡣᅔ㞴࡛࠶ࡗࡓࡀ㸪㏆ᖺࡢィ⟬ᶵ⬟ຊ

࠾ࡼࡧィ⟬ᡭἲࡢྥୖ࡟ࡼࡾⅆ⅖ෆ㒊ࡢⷧ࠸཯ᛂᖏෆࢆ

ࡶゎീࡍࡿᩘ್ࢩ࣑࣮ࣗࣞࢩࣙࣥࡀྍ⬟࡜࡞ࡗ࡚ࡁࡓ㸬 ᮏሗ࡛ࡣࢫ࣮ࣃ࣮ࢥࣥࣆ࣮ࣗࢱࢆ⏝࠸ࡓヲ⣽࡞ࢩ࣑ࣗࣞ

࣮ࢩࣙࣥ࡟ࡼࡾ㸪 Ỉ⣲ᄇὶᾋࡁୖࡀࡾⅆ⅖ࡢᵓ㐀࠾ࡼࡧ㸪 ࡑࡢ୰࡟ྵࡲࢀࡿⅆ⅖せ⣲ࡢ≉ᚩ࡟ࡘ࠸࡚ㄪ࡭ࡓ⤖ᯝ࡟

ࡘ࠸࡚ሗ࿌ࡍࡿ㸬

ゎᯒᑐ㇟࡜ࡍࡿⅆ⅖

ィ⟬ᑐ㇟ࡢⅆ⅖ࡣ㟼Ṇ✵Ẽ୰࡟ᄇࡁฟࡉࢀࡓள㡢㏿

Ỉ⣲ᄇὶࡢ⇞↝࡟ࡼࡗ࡚ᚓࡽࢀࡿᾋࡁୖࡀࡾⅆ⅖࡛࠶ࡿ

(ᅗ1)㸬ィ⟬᮲௳ࡣCheng

ࡽࡢᐇ㦂[6]࡟ᚑ࠺㸬ᄇࡁฟࡋ

ཱྀᚄ

D

ࡣ

2mm㸪ᄇࡁฟࡋ㏿ᗘࡣ680m/s㸪ᄇฟࡋཱྀᚄ࡟

ࡶ࡜࡙ࡃࣞ࢖ࣀࣝࢬᩘࡣ

13600

࡛࠶ࡿ㸬㟼Ṇ✵Ẽ㸪ᄇฟ ࡋỈ⣲࡜ࡶᅽຊ

1.01325™10⁵ Pa㸦1atm㸧

㸪 ᗘ

280K

࡜ࡍ

ࡿ㸬ィ⟬᮲௳ࢆ⾲㸯࡟♧ࡍ㸬ᐇ㦂࡛ࡣᾋࡁୖࡀࡾ㧗ࡉ⣙

7D

ࡢᾋࡁୖࡀࡾⅆ⅖ࡀほᐹࡉࢀ࡚࠸ࡿ㸬

⾲

1

ィ⟬᮲௳

㻌 㻌  ᗘ ᅽຊ ㏿ᗘ

Ỉ⣲ᄇὶ

280K 1.01325Pa 680m/s

㟼Ṇ✵Ẽ

280K 1.01325Pa 0m/s

ᅗ

1

ィ⟬ᑐ㇟ࡢᴫほ

ᩘ್ࢩ࣑࣮ࣗࣞࢩࣙࣥ

≀⌮ࣔࢹࣝ

Ẽయࡣ⇕ⓗ࡟ᖹ⾮࡜ࡍࡿ㸬໬Ꮫ཯ᛂࣔࢹࣝ࡜ࡋ࡚ࡣ

9

໬Ꮫ✀( H

2, O2, OH, H2O, H, O, H2O2, HO2, N2 )17

཯ᛂ㸦⾲

㸰㸧ࣔࢹࣝ[7]ࢆ⏝࠸ࡿ㸬༑ศ࡞ᩘࡢ໬Ꮫ✀ࢆ⪃៖ࡋ࡚࠾

ࡾ᪤⇞࢞ࢫࡢ ᗘࢆ⢭ᗘࡼࡃண ࡛ࡁࡿࡇ࡜㸪ࡑࡢ཯㠃 ẚ㍑ⓗᑡ࡞࠸⣲཯ᛂᩘࡍ࡞ࢃࡕᑠࡉ࡞ィ⟬㈇Ⲵ࡛ጇᙜ࡞

ணΰྜⅆ⅖ఏ᧛㏿ᗘࢆ୚࠼ࡿ࡜࠸࠺ࡇ࡜㸪ࡲࡓ╔ⅆࡢၥ 㢟࡟ᑐࡋ࡚ࡶᐇ⦼ࡀ࠶ࡿࡇ࡜࠿ࡽ㸪ࡇࡢࣔࢹࣝࢆ㑅ᢥࡋ ࡓ㸬ศᏊᣑᩓ࡟ࡘ࠸࡚ࡣ㸪⃰ᗘ໙㓄ᣑᩓࢆ௬ᐃࡋ

Fick

ࡢ ἲ๎࡛ホ౯ࡍࡿ㸬✵Ẽࡢ⤌ᡂࡣయ✚ศ⋡࡛

O₂ 22%㸪N2

78%࡜ࡋࡓ㸬

⾲

2

໬Ꮫ཯ᛂࣔࢹࣝ㸦Westbrook[7]㸧

E R T

AT

k_f,b ⁿexp _{a u}

ᨭ㓄᪉⛬ᘧ

ᨭ㓄᪉⛬ᘧࡣ୕ḟඖࢼࣅ࢚ࢫࢺ࣮ࢡࢫ᪉⛬ᘧ࡜㸷໬

Ꮫ✀ࡢಖᏑᘧ࠾ࡼࡧ≧ែ᪉⛬ᘧ࡛࠶ࡿ㸬໬Ꮫ✀ࡢಖᏑᘧ

ࢆ⤌ࡳ㎸ࢇࡔࢼࣅ࢚ࢫࢺ࣮ࢡࢫ᪉⛬ᘧࡣ㸪

x S F x F t q

i iv i

i

w w w w w w

(1)

࡜᭩ࡅࡿ㸬ࡇࡇ࡟㸪

^{0 ,}

0 0 0 0

, 0

, ,

9 1

, 9 9

, 1 1 3 2 1

9 1

3 3

2 2

1 1

9 1 3 2 1

¸¸

¸¸

¸¸

¸¸

¸¸

¸

¹

·

¨¨

¨¨

¨¨

¨¨

¨¨

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¸

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¨

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¸¸

¸¸

¸¸

¸¸

¸¸

¸

¹

·

¨¨

¨¨

¨¨

¨¨

¨¨

¨

©

§

¸¸

¸¸

¸¸

¸¸

¸¸

¸

¹

·

¨¨

¨¨

¨¨

¨¨

¨¨

¨

©

§

Z Z U

U W

W W W

U U

G U

G U

G U

U

U U U U U U

#

# #

#

S

z D

z D

q F u

u z

u z

u p E

p u u

p u u

p u u

u

F

z z E u u u q

j j j k jk

i i i

iv

i i i i i

i i

i i

i

i

, ) (

, ) 2 (

1 ₂

3 2 2 2

1

¦

^'

s zs Hs Hfs p

e u u u e

E U U

, ,

3 )

( , , 2 , ,

¦

,

s s s s j

j j k k ij i j j i

ij P u u G u q NT UD h z

W

࡛࠶ࡾ㸪

h_s {H_s ǻH _fs

㸪

( ),_j{w( )/wx_j

࡛࠶ࡿ㸬

zs

ࡣ໬Ꮫ✀

s

ࡢΰྜẼ༢఩㉁㔞࠶ࡓࡾࡢࣔࣝᩘ㸪

Hs,'Hfs

ࡣࡑࢀࡒࢀ໬Ꮫ✀

s

ࡢ

1

ࣔࣝᙜࡓࡾࡢ࢚ࣥࢱࣝࣆ㸪⏕ᡂ

⇕࡛࠶ࡾ㸪

Ds

ࡣᣑᩓಀᩘ࡛࠶ࡿ㸬ྛ໬Ꮫ✀ࡢ࢚ࣥࢱࣝࣆ

ࡣ

JANAF[8]ࢸ࣮ࣈࣝ࠿ࡽᘬ⏝ࡋ㸪 ᗘࡢ㸲ḟከ㡯ᘧ࡛

㏆ఝࡋࡓ㸬 ከ㡯ᘧࡢಀᩘࢆྛ໬Ꮫ✀࡟ࡘ࠸࡚⾲㸱࡟♧ࡍ㸬

Zs

ࡣ໬Ꮫ✀

s

ࡢ༢య✚࠶ࡓࡾࡢ⏕ᡂ㏿ᗘ(mol/m

³/s)

࡛࠶

ࡾ⾲

2

ࡼࡾồࡵࡿ㸬

≧ែ᪉ᘧࡣୗグ࡜࡞ࡿ㸬

¦

s s

uT z

R

p U

(2)

ࡇࡇ࡟㸪

R_u

ࡣᬑ㐢Ẽయᐃᩘ㸦=8.31447 JK

^-1mol^-1

㸧࡛࠶

ࡿ㸬

ྛ໬Ꮫ✀ࡢ㍺㏦ಀᩘࡣ

Lennard-Jones

ࡢศᏊ㛫࣏ࢸࣥ

ࢩࣕࣝ[9]ࢆ⏝࠸࡚ホ౯ࡋ㸪Wilke ࡢἲ๎[10]࡟ࡼࡗ࡚ΰ

ྜẼయࡢ㍺㏦ಀᩘࢆồࡵࡿ㸬ලయⓗ࡟ࡣ㸪⢓ᛶಀᩘ

P

࠾

ࡼࡧ⇕ఏᑟ⋡

N

ࡣୗグࡢ㏻ࡾồࡵࡿ㸬

¦

s s s s

ij X ȝ

ȝ

(3)

¦

s s s s

ij X ț

ț

¦

¸¸

¹

·

¨¨©

§

»»

¼ º

««

¬ ª

¸¸¹

·

¨¨© §

r r

s s

r r r s

s M

M M

M ȝ X ȝ

ij 1 81

4 2 / 1

(4)

ࡇࡇ࡟

X_s

^㸪

M_s

^{ࡣࡑࢀࡒࢀ໬Ꮫ✀}

s

ࡢࣔࣝศ⋡㸪ศᏊ 㔞࡛࠶ࡿ㸬

P_s

^࠾ࡼࡧ

N_s

^{ࡣࡑࢀࡒࢀ໬Ꮫ✀}

s

ࡢ⢓ᛶಀᩘ࠾

ࡼࡧ⇕ఏᑟ⋡࡛࠶ࡾୗグ࡟ࡼࡾồࡵࡿ㸬

2 1

8

5 w

ʌ T km

ȝ ı ^s

s s

(5)

¸¹

¨ ·

©

§

w w

s u s

s s R

T H

M 4

P 5

N

(6)

ࡇࡇ࡟㸪

k

ࡣ࣎ࣝࢶ࣐ࣥᐃᩘ㸦=1.38065× 10-23 JK-1㸧

࡛࠶ࡾ㸪

ms

㸪

Vs

_{ࡣࡑࢀࡒࢀ໬Ꮫ✀}

_s

_ࡢศᏊ

1

ಶࡢ㉁㔞㸪

⾪✺┤ᚄ࡛࠶ࡿ㸬

໬Ꮫ✀

s

ࡢᣑᩓಀᩘࡣ㸪

2

ᑐᣑᩓಀᩘ

D_sr

^{ࢆ⏝࠸࡚ୗグ} ࡢ㏻ࡾ୚࠼ࡿ㸬

¦

z

s

r sr

r s r

D X D 1 X

(7)

ࡓࡔࡋ㸪໬Ꮫ✀

s

࡜

r

ࡢ㛫ࡢ

2

ᑐᣑᩓಀᩘ

D_sr

^ࡣୗグ࡟

ࡼࡾồࡵࡿ㸬

2 2 2

) (

8

3 w

m m

T m m k D N

s s

s s sr sr

sr V S

(8)

ࡇࡇ࡟

N_sr N_sN_r

㸪

V_sr (V_sV_r)/2

࡛࠶ࡾ㸪

N_s

ࡣ

໬Ꮫ✀

s

ࡢᩘᐦᗘ࡛࠶ࡿ㸬

ᘧ㸦5㸧 㸪 㸦8㸧୰ࡢ

w1

࠾ࡼࡧ

w2

ࡣศᏊ㛫࣏ࢸࣥࢩࣕࣝࣔ

ࢹࣝ࠿ࡽỴࡲࡿ↓ḟඖ㛵ᩘ࡛࠶ࡾ

T/(İ_s/k)

^{ࡢ㛵ᩘ࡛࠶}

ࡿ㸬

H_s

ࡣ໬Ꮫ✀

s

ࡢศᏊ࣏ࢸࣥࢩࣕࣝࣔࢹࣝࡢ஭ᡞࡢ῝

ࡉ࡛࠶ࡾ㸪

İ_s/k

ࡣ ᗘࡢḟඖࢆᣢࡘ㸬ᮏ◊✲࡛ࡣ

w1

㸪

w2

࡜ࡶ

(İ_s/k)/T

ࡢ㸱ḟከ㡯ᘧ࡛㏆ఝࡋࡓ㸬 ࡞࠾

w2

ࢆồࡵ

ࡿ㝿࡟ࡣ஭ᡞࡢ῝ࡉ࡜ࡋ࡚㸰໬Ꮫ✀ࡢ஭ᡞࡢ῝ࡉࡢ┦஌

ᖹᆒࢆ⏝࠸ࡿ㸬໬Ꮫ✀ࡈ࡜ࡢ⾪✺┤ᚄ

V_s

࠾ࡼࡧ

İ_s/k

_ࢆ

⾲㸲 [11]࡟㸪

w₁

^࠾ࡼࡧ

w2

^ࡢ

kT/İs

࡟ᑐࡍࡿ್[9]ࢆ⾲

5

࡟㸪 ࡑࡢከ㡯ᘧ㏆ఝಀᩘࢆ⾲

6

࡟♧ࡍ㸬

࡞࠾㸪≉グࡢ࡞࠸グྕࡣ୍⯡ࡢ౑⏝࡟ᚑ࠺ࡶࡢ࡜ࡍࡿ㸬

⾲

3㸸࢚ࣥࢱࣝࣆከ㡯ᘧಀᩘ࠾ࡼࡧ⏕ᡂ࢚ࣥࢱࣝࣆ

4 4 3 3 2 2 1

0 aT aT aT aT

a

H_s

] K [ : ], J/mol [ :

,H T

H_{s fs}

㻌 㻌

a0 a1 a2 a3 a4 'Hs䡂

H2 -8.1326E+03 2.6663E+01 2.1287E-03 -8.7153E-08 -1.2495E-12 0.0000E+00 O2 -8.7981E+03 2.8524E+01 3.4874E-03 -4.4822E-07 2.5177E-11 0.0000E+00 OH -8.2317E+03 2.6919E+01 2.4185E-03 -1.9602E-07 4.4040E-12 3.9426E+04 H2O -8.8587E+03 2.7196E+01 8.8307E-03 -1.1411E-06 5.8445E-11 -2.4160E+05 H -6.1868E+03 2.0760E+01 3.1743E-06 -6.3343E-10 4.5081E-14 2.1778E+05 O -6.4485E+03 2.1805E+01 -5.9607E-04 1.2975E-07 -7.5884E-12 2.4896E+05 H2O2 -1.0680E+04 2.6514E+01 3.5581E-02 -1.5200E-05 2.6737E-09 -1.3305E+05 HO₂ -1.0338E+04 3.1957E+01 9.6625E-03 -1.6663E-06 1.0667E-10 1.7556E+04 N₂ -8.2271E+03 2.6494E+01 3.9239E-03 -6.3248E-07 3.8992E-11 0.0000E+00

⾲

4㸸⾪✺༙ᚄ㸦V_s

䠅࠾ࡼࡧ

H_s/k

㻌

Vs[10^-10m] Hs/k[K]

H₂ 2.920 38.0

O2 3.548 107.4

OH 2.750 80.0

H2O 2.605 572.4

H 2.050 145.0 O 3.500 80.0

H₂O₂ 3.458 107.4

HO₂ 3.458 107.4

N₂ 3.621 97.53

⾲

6㸸w1,w2

ࡢከ㡯ᘧ㏆ఝ

3 3 2 2 1

0 aR a R a R

a

w

㸪

R (H_s/k)/T

㻌 㻌

a⁰ a¹ a² a³

w1 5.977E-01 1.0752E+00 -2.3769E-01 3.0005E-02 w2 1.3401E+00 2.3472E+00 -3.9074E-01 3.2369E-02

⾲

5㸸kT/İs

࡟ᑐࡍࡿ

w1,w2

ࡢ್[9]

kT/İs w1 w2

0.3 2.648 2.841 0.5 2.066 2.284 0.7 1.729 1.922 1.0 1.440 1.593 1.3 1.274 1.401 1.6 1.168 1.280 2.0 1.075 1.176 2.5 1.0002 1.093 3.0 0.9500 1.0388 4.0 0.8845 0.9699 5.0 0.8428 0.9268 7.0 0.7898 0.8728 10.0 0.7422 0.8244 20.0 0.6640 0.7436 50.0 0.5761 0.6504 100.0 0.5177 0.5869

㞳ᩓ໬ᡭἲ

๓㏙ࡢᨭ㓄᪉⛬ᘧࢆ୍⯡ᗙᶆ⣔࡟ኚ᥮ࡋࡓᚋ㸪᭷㝈య

✚ἲ࡟ࡼࡗ࡚㞳ᩓ໬ࡍࡿ㸬ᘧ(1)ࡣ୍⯡ᗙᶆ⣔࡟࠾࠸࡚

F S F t q

i iv

i

i ˆ ˆ

ˆ ˆ

w w w w w w

[

[

(9)

࡜᭩ࡅࡿ㸬ࡇࡇ࡟㸪

VS S

F n F n F n F

F n F n F n F

Vq q

i v i v v i iv

i i i

i

ˆ ˆ , ˆ ,

, ˆ

3 , 3 2 , 2 , 1 1

3 , 3 2 , 2 1 , 1

࡛࠶ࡾ㸪

V

ࡣィ⟬ࢭࣝయ✚㸪

n_i {(n_1,i,n_2,i,n_3,i)

ࡣࢭࣝቃ⏺

ἲ⥺᪉ྥࡢ㠃✚࣋ࢡࢺ࡛ࣝ࠶ࡿ㸬ᮏ◊✲࡛ࡣィ⟬᱁Ꮚࡢ ኚᙧ⛣ືࡣ࡞࠸ࡶࡢ࡜ࡍࡿ㸬

ᑐὶ㡯࡟ࡘ࠸࡚ࡣ㢼ୖ୕ḟ⢭ᗘࡢ

TVD(Total Variation Diminishing)

ᩘ್ὶ᮰[12,13]࡛ホ౯ࡋ㸪ࡑࡢ㝿㸪≉ᛶ㔞

ࢆእᤄࡍࡿࡇ࡜࡟ࡼࡗ࡚㧗⢭ᗘࡢᩘ್ὶ᮰ࢆᵓ⠏ࡍࡿ㸬 ࢭࣝቃ⏺

j+1/2

࡟࠾ࡅࡿᩘ್ὶ᮰

ˆ_{, 1/2}

j

Fi

ࡣᘧ(10)࡛⾲ࡉ

ࢀࡿ㸬ࡓࡔࡋ㸪

T ^-1AT=/

㸪

A=wFˆ_i/wq

_㸪

/

ࡣ

A

ࡢᅛ᭷್⾜

ิ࡛࠶ࡿ㸬ᐇ㝿ࡢィ⟬࡟ᚲせ࡞⾜ิ

T^-1

㸪

T

㸪

/

ࡢලయⓗ

࡞ᙧ࡟ࡘ࠸࡚ࡣཧ⪃ᩥ⊩[13,14]ࢆཧ↷ࡉࢀࡓ࠸㸬 ከࡃࡢ㧗⢭ᗘ

TVD

ᩘ್ὶ᮰࡛ࡣእᤄࡍࡿኚᩘࡢ໙㓄 ࡢ➢ྕࡀኚ໬ࡍࡿ఩⨨࡛ὶ᮰ไ㝈㛵ᩘࡀാࡁ⢭ᗘࡀ㸯ḟ

⢭ᗘ࡟ⴠࡕ࡚ࡋࡲ࠺࡜࠸࠺ၥ㢟ࡀ࠶ࡿ㸬ࡇࡇ࡛ࡣ≉ᛶ㔞 ࡢ໙㓄ࡢ➢ྕࡀኚ໬ࡍࡿሙᡤ࡛ࡶ㸰ḟ⢭ᗘࢆ⥔ᣢࡍࡿࡼ

࠺࡟タィࡉࢀࡓὶ᮰ไ㝈㛵ᩘ[14]ࢆ⏝࠸ࡿ㸬ᘧ(11)࠾ࡼࡧ

(12)ࡢྑ㎶➨㸰㡯ࡀᩘ್ὶ᮰ࢆ㸰ḟ⢭ᗘ࡜ࡍࡿ௜ຍ㡯㸪

➨㸱㡯ࡀ㸱ḟ⢭ᗘ࡜ࡍࡿࡓࡵࡢ௜ຍ㡯࡛࠶ࡿ㸬ᅗ

2

ࡣኚ

ᩘ໙㓄ኚ໬⋡

R

࡟ᑐࡍࡿ➨㸰㡯ࡢ್࡛࠶ࡿ㸬

Ȍ 1

ࡢ᫬㸪

ᩘ್ὶ᮰ࡣ㸰ḟ⢭ᗘࢆ☜ಖࡍࡿ㸬ᅗ

3

ࡣኚᩘ໙㓄ኚ໬⋡

࡟ᑐࡍࡿ➨㸱㡯ࡢ್࡛࠶ࡾ㸪

Ȍ 1

_{ࡢ᫬㸪ᩘ್ὶ᮰ࡣ㸱} ḟ⢭ᗘ࡜࡞ࡿ㸬

R<0

ࡍ࡞ࢃࡕኚᩘ໙㓄ࡢ➢ྕࡀኚ໬ࡍࡿ

ሙྜ࡟ࡶ

2

ḟ⢭ᗘࢆ☜ಖ࡛ࡁࡿ᮲௳ࡀ࠶ࡿࡇ࡜ࡀศ࠿ࡿ㸬 ᘧ(13)㸪(14)୰ࡢᐃᩘ

D₁

㸪

E₁

㸪

E₂

ࡣὶ᮰ไ㝈㛵ᩘࡢ≉ᛶࢆ

ไᚚࡍࡿṇ್࡛࠶ࡾ㸪

H

ࡣ

0

๭ࢆ㜵ࡄࡓࡵࡢᑠࡉ࡞ṇ್

࡛࠶ࡿ㸬ᮏィ⟬࡛ࡣ㸰ḟ⢭ᗘ௨ୖ࡜࡞ࡿ᮲௳ࢆᗈࡃ☜ಖ ࡍࡿࡓࡵ࡟

D₁=1.5ࠊE₁=1.0㸪E₂=1.5

࡜ࡋࡓ㸬

>

@

_{1/2 , ,1 1/2 1/2 1/2 1/2 1/2}

, ˆ ˆ

2 ˆ 1

j j j

j j j i j i j

i F F T ȁ ı ȁ ı

F

(10)

2 / 1 2 / 2 1

/ 1 2

/ 1 2 /

1 3

) 2

(

j p j p j j

j ı Ȍ R ı Ȍ R ı ı

ı

(11)

1/2 3/2

2 / 3 2

/ 2 1 /

1 3

) 2

(

_j ı_j Ȍ R_m ı_j Ȍ R_m ı_j ı_j

ı

(12)

¿¾

½

¯®

­

) , 2 max(

, 6 1 ), , min(

min 2 )

( ^{2 1}

R İ ȕ R İ

R ȕ

Ȍ

₍₁₃₎

¿¾

½

¯®

­

˜

) , 2 max(

, 6 1 ), 5 . 0 )( , 1 max(

) , 0 max(

min 3 ₁ ¹

R İ Į ȕ

Rİ R R

Ȍ

(14)

q T ǻ

ı ^{1 ,} R_p ı_j1/2/ı_j1/2, R_m ı_j3/2/ı_j1/2

⢓ᛶ㡯࠾ࡼࡧᣑᩓ㡯࡟ࡘ࠸࡚ࡣ㏻ᖖࡢ㸰ḟ⢭ᗘ୰ᚰᕪศ

ࢆ⏝࠸ࡿ㸬ࡓࡔࡋ㸪໬Ꮫ✀ࡢᣑᩓ࡟ࡘ࠸࡚ࡣ㸪Fick ๎࡟

ࡼࡿ໙㓄ᣑᩓࢆ⏝࠸࡚࠸ࡿࡓࡵ㸪໬Ꮫ✀ࡀ

3

✀௨ୖ࡜࡞

ࡿ࡜㸪඲యࡢ㉁㔞ಖᏑ࡜ࡢᩚྜᛶࡀྲྀࢀ࡞ࡃ࡞ࡿ㸬ࡍ࡞

ࢃࡕ໬Ꮫ✀ࡢ㉁㔞ࡢ⥲࿴ࡀ㸪඲㉁㔞࡜୍⮴ࡋ࡞ࡃ࡞ࡿ㸬 ࡑࢀࡣ㸪ࡇࡢࣔࢹࣝ࡟ࡼࡗ࡚ホ౯ࡋࡓྛ໬Ꮫ✀ࡢᣑᩓὶ ᮰ࡀ㸪㉁㔞ὶ᮰ࡢ⥲࿴ࡀ

0

࡟࡞ࡿࡇ࡜ࢆಖドࡋ࡞࠸ࡓࡵ

࡛࠶ࡿ㸬ࡑࡇ࡛㸪௨ୗࡢᡭἲ࡛඲㉁㔞ಖᏑ࡜ࡢᩚྜᛶࢆ

☜ಖࡍࡿࡼ࠺࡟ᣑᩓὶ᮰ࢆಟṇࡋࡓ㸬ࢭࣝቃ⏺࡟࠾ࡅࡿ

ᣑᩓὶ᮰ࢆ୍ᗘィ⟬ࡋ㸪ቃ⏺ࢆṇ࡜㈇ࡢ᪉ྥ࡟㏻㐣ࡍࡿ

㉁㔞ὶ᮰ࢆồࡵࡿ㸬ᮏ᮶㸪ṇ᪉ྥ࡟㏻㐣ࡍࡿ㉁㔞ὶ᮰࡜

㈇ࡢ᪉ྥ࡟㏻㐣ࡍࡿ㉁㔞ὶ᮰ࡢ኱ࡁࡉࡣ➼ࡋࡃ࡞ࡅࢀࡤ

࡞ࡽ࡞࠸ࡀ㸪໙㓄ᣑᩓࢆ⏝࠸ࡿሙྜ࡟ࡣ୧⪅ࡣ୍⮴ࡋ࡞

࠸㸬 ࡑࡇ࡛㸪 ୧⪅ࡢᖹᆒ್ࢆ┿ࡢ㉁㔞ὶ᮰ࡢ್࡜௬ᐃࡋ㸪 ୧⪅ࡀࡑࡢᖹᆒ್࡜࡞ࡿࡼ࠺࡟ྛ໬Ꮫ✀ࡢᣑᩓὶ᮰࡟㔜

ࡳࢆ࠿ࡅㄪᩚࡍࡿ㸬ࡍ࡞ࢃࡕୗグᡭ⥆ࡁ࡟ࡼࡾ㉁㔞ಖᏑ

ࢆ‶㊊ࡍࡿ໬Ꮫ✀

s

ࡢಟṇᣑᩓὶ᮰

f~_s^d

ࢆồࡵࡿ㸬

_s^d

d s d

s f f

f ~ ~

~ (15)

ࡓࡔࡋ㸪

r r

r d

s d

s f

S f S

~

,

S

SS

2 1

,

r r

¦

s d

fs

S

,

s^d

d s d

s f f

f ^r r

2 1

࡛࠶ࡾ㸪

f_s^d

ࡣ໙㓄ᣑᩓ࠿ࡽ┤᥋ィ⟬ࡉࢀࡓ໬Ꮫ✀

s

ࡢᣑ ᩓὶ᮰࡛࠶ࡿ㸬

᫬㛫᪉ྥࡢ✚ศ࡟ࡣ㸰ḟ⢭ᗘࡢ

Runge-Kutta

ἲ࡟ࡼࡿ

㝧ⓗ✚ศࢆ⏝࠸ࡓ㸬㏻ᖖ㸪໬Ꮫ཯ᛂࢆక࠺ᨭ㓄᪉⛬ᘧࢆ

᫬㛫Ⓨᒎⓗ࡟ゎࡃ㝿࡟ࡣ㸪໬Ꮫ཯ᛂ⏕ᡂ㡯ࡢ

stiffness

࡟

ࡼࡿ᫬㛫✚ศᖜࡢไ㝈ࢆྲྀࡾ㝖ࡃࡓࡵ࡟㸪ᵝࠎ࡞⦆࿴ἲ ࡀ⏝࠸ࡽࢀࡿࡇ࡜ࡀከ࠸ࡀ㸪ᮏ◊✲࡛ࡣ≉ู࡞ᥐ⨨ࡣ᪋

ࡋ࡚࠸࡞࠸㸬ᚋ࡟♧ࡍ࡜࠾ࡾィ⟬᱁Ꮚࡀ㠀ᖖ࡟⣽࠿ࡃ㸪 ὶయࡢ᪉⛬ᘧ࠿ࡽࡢせㄳ࡛Ỵࡲࡿ᫬㛫✚ศᖜࡀ཯ᛂࡢ᫬

㛫ࢫࢣ࣮ࣝ࡟ẚ࡭༑ศ࡟ᑠࡉ࠸ࡓࡵ࡛࠶ࡿ㸬

ᅗ

2

ᩘ್ὶ᮰

2

ḟ⢭ᗘ௜ຍ㡯ࡢὶ᮰ไ㝈㛵ᩘ < ( R )

ᅗ

3

ᩘ್ὶ᮰

3

ḟ⢭ᗘ௜ຍ㡯ࡢὶ᮰ไ㝈㛵ᩘ < ( R )

ቃ⏺᮲௳

ィ⟬㡿ᇦእ㒊ቃ⏺࡟ࡣ↓཯ᑕ᮲௳[15,16]ࢆ୚࠼㸪ࣀࢬ

ࣝእቨࡣ⁥ࡾቨ࡜ࡍࡿ㸬ࣀࢬࣝฟཱྀ࡟࠾࠸࡚ࡣ᏶඲஘ὶ

⟶ෆὶࢀࡢᖹᆒ㏿ᗘศᕸ࡟ᑐᛂࡍࡿ඲ ඲ᅽศᕸࢆ୚࠼

ࡿ㸬ලయⓗ࡟ࡣ㸪⾲㸯࡟♧ࡉࢀࡓ᮲௳ࡢ㟼Ṇ✵Ẽ࡟Ỉ⣲

ࢆᄇฟࡋࡓ᫬࡟ᡤᐃࡢ㏿ᗘࢆ୚࠼ࡿ඲ ඲ᅽ࡟ᅛᐃࡍࡿ㸬 ᄇฟ㏿ᗘࢆィ⟬㡿ᇦ࠿ࡽእᤄࡋ㸪୚࠼ࡽࢀࡓ඲ ඲ᅽ࠿

ࡽ᩿⇕᮲௳ࡢ㛵ಀࢆ⏝࠸࡚ᄇฟ ᗘ㸪ᐦᗘࢆồࡵࡿ㸬ᚑ ࡗ࡚㸪ィ⟬㡿ᇦෆࡢᅽຊኚື࡟ᛂࡌ࡚ᄇฟࡋ㏿ᗘࡣኚື

ࡍࡿ㸬 ᄇฟࡋ᮲௳࡜ࡋ࡚㝧ⓗ࡟ࡣ஘ࢀࢆ௜ຍࡋ࡚࠸࡞࠸㸬

ィ⟬᱁Ꮚ࠾ࡼࡧ୪ิィ⟬

ィ⟬㡿ᇦࡣࣀࢬࣝฟཱྀ୰ᚰࢆཎⅬ, ᄇὶ㍈᪉ྥࢆ

y

㍈, ࡑࢀ࡟ᆶ┤࡞᪉ྥࢆ

x, z

㍈࡜ࡋ࡚㸪࠾࠾ࡼࡑ-3D<

y<21D, -12D<x,z<12D

࡛࠶ࡿ㸬ィ⟬᱁Ꮚ⣔ࡣィ⟬㡿ᇦ඲యࢆそ࠺

▴ᙧ᱁Ꮚ⣔࡜ᄇᑕࣀࢬࣝ࿘ࡾࡢ෇⟄᱁Ꮚ⣔࠿ࡽ࡞ࡿ㔜ྜ

᱁Ꮚ⣔࡜࡞ࡗ࡚࠸ࡿ㸬෇⟄᱁Ꮚ⣔ࡢ㡿ᇦࡣ-3D<

y<2D㸪 0.375D<(x²+z²)^1/2<0.75D

࡛࠶ࡿ㸬ᅗ

4

ᕥഃࡣィ⟬㡿ᇦࡢศ

๭ࢆ♧ࡋ࡚࠾ࡾ㸪 ඲యࢆそ࠺▴ᙧ᱁Ꮚ⣔ࡣ

72

ࡢࢧࣈࢻ࣓

࢖ࣥ࠿ࡽ㸪ᄇᑕࣀࢬࣝ࿘ࡾ࡟㉥ࡃグࡉࢀࡓ෇⟄᱁Ꮚ⣔ࡣ

3

ࡘࡢࢧࣈࢻ࣓࢖ࣥ࠿ࡽᵓᡂࡉࢀ࡚࠸ࡿ㸬෇⟄᱁Ꮚ⣔࡜

▴ᙧ᱁Ꮚ⣔ࡣ

y

ᗙᶆࡀ୍⮴ࡋ࡚࠾ࡾ㸪

x-z

ᖹ㠃࡟࠾࠸࡚௨

ୗࡢࡼ࠺࡟ಖᏑ㔞ࡢཷࡅΏࡋࢆ⾜࠺㸬෇⟄᱁Ꮚ⣔ෆഃ࠾

ࡼࡧእഃቃ⏺ࡑࢀࡒࢀ㸰ⅬࡢಖᏑ㔞ࢆ▴ᙧ᱁Ꮚ⣔࠿ࡽ⥺

ᙧෆᤄ⿵㛫ࡍࡿࡇ࡜࡟ࡼࡾᚓ㸪㏫࡟෇⟄᱁Ꮚ⣔ෆ㒊㸦እ

ഃቃ⏺௨እ㸧࡟࠶ࡿ▴ᙧ᱁Ꮚ⣔ࡢ᱁ᏊⅬୖࡢಖᏑ㔞ࡣ෇

⟄᱁Ꮚ⣔ࡢ≀⌮㔞࠿ࡽෆᤄ⿵㛫ࡍࡿࡇ࡜࡟ࡼࡾ୚࠼ࡿ㸬 ࡇࡢసᴗࢆ࢖ࢱ࣮ࣞࢩࣙࣥẖ࡟⾜࠺㸬

ⅆ⅖࠾ࡼࡧᄇὶ࿘㎶࡟࠾ࡅࡿ▴ᙧ᱁Ꮚ⣔ࡢ᱁Ꮚᖜࡣ

0.05mm

࡜ࡋࡓ㸬෇⟄᱁Ꮚ⣔࡟࠾ࡅࡿ᱁Ꮚᖜࡣ༙ᚄ᪉ྥ

࡟ኚ໬ࡍࡿࡀ▴ᙧ᱁Ꮚ⣔ࡢ᱁Ꮚᖜ࡜ྠ࣮࢜ࢲ࡛ࡑࢀࢆ㉸

࠼࡞࠸ࡼ࠺࡟タᐃࡉࢀ࡚࠸ࡿ㸬ᮏ◊✲࡛⏝࠸ࡓࣔࢹࣝࢆ

୍ḟඖᒙὶணΰྜⅆ⅖ゎᯒࢥ࣮ࢻ

PREMIX[17]࡟⤌ࡳ㎸

ࡳ㸪ᙜ㔞ẚ

1

ࡢỈ⣲/✵Ẽ୍ḟඖணΰྜⅆ⅖ࢆィ⟬ࡍࡿ࡜㸪 ࡑࡢ⇞ᩱᾘ㈝ᒙ㸪Ⓨ⇕ᒙ࡜ࡶ⣙

0.5mm

ࡢཌࡳ࡜࡞ࡿ㸬ண ΰྜⅆ⅖ࡢ཯ᛂᖏཌࡉࡣᙜ㔞ẚ

1

௜㏆࡛᭱ࡶ⊃ࡃ࡞ࡿࡢ

࡛㸪ᮏ◊✲࡛⏝࠸ࡓィ⟬᱁Ꮚࡣணΰྜⅆ⅖ࡢෆ㒊ᵓ㐀ࢆ

10

Ⅼ⛬ᗘ௨ୖ࡛ゎീ࡛ࡁࡿ᱁Ꮚᖜ࡜࡞ࡗ࡚࠸ࡿ㸬୍᪉࡛㸪 ࡇࡢ᱁Ꮚᖜࡣᐇ㦂࡛ ᐃࡉࢀࡓⅆ⅖᭱ୖὶ➃࠶ࡓࡾ࡛ࡢ ࢥࣝࣔࢦࣟࣇࢫࢣ࣮ࣝ[6]ࡢ

2~3

ಸ࡜࡞ࡗ࡚࠾ࡾ㸪஘ὶࡢ

᭱ᑠࢫࢣ࣮ࣝࡲ࡛ゎീࡍࡿࡇ࡜ࡣᮇᚅ࡛ࡁ࡞࠸㸬ࡋ࠿ࡋ

࡞ࡀࡽ㸪ᐇ㉁ⓗ࡞஘ὶࡢ࢚ࢿࣝࢠ࣮࢝ࢫࢣ࣮ࢻࢆᢸࡗ࡚

࠸ࡿࡢࡣ᭱ᑠࢫࢣ࣮ࣝࡢ

5

ಸ௨ୖࡢ ࡛࠶ࡾ㸪஘ὶᵓ㐀 ゎീ࡟ᚲせ࡞ゎീᗘࡣࢥࣝࣔࢦࣟࣇࢫࢣ࣮ࣝࡢ

5-8

ಸ࡜

࠸࠺ࡇ࡜ࡀሗ࿌ࡉࢀ࡚࠾ࡾ[18,19]㸪஘ὶᵓ㐀ࡢ኱㒊ศࡣ ゎീࡍࡿࡇ࡜ࡀྍ⬟࡞᱁Ꮚᖜ࡜⪃࠼ࡽࢀࡿ㸬᱁Ꮚ㛫㝸ࡣ

୙➼㛫㝸࡛୰ᚰ㍈࠿ࡽ㞳ࢀࡓ࡜ࡇࢁ㸪ࡲࡓୗὶᇦ࡟࠾࠸

࡚ࡣ⢒ࡃ࡞ࡗ࡚࠸ࡿ㸬⥲ィ⟬᱁ᏊⅬᩘࡣ⣙㸰൨Ⅼ࡛࠶ࡿ.

ィ ⟬ ࡣ Ᏹ ᐂ ⯟ ✵ ◊ ✲ 㛤 Ⓨ ᶵ ᵓ ࡢ

CeNSS(Central Numerical Simulation System)ࢆ⏝࠸࡚⾜ࢃࢀࡓ㸬ᅗ4

ྑ࡟

♧ࡍࡼ࠺࡟㸪ྛࢧࣈࢻ࣓࢖ࣥ࡟

1

ࣉࣟࢭࢫࢆ๭ࡾᙜ࡚㸪

ࣉࣟࢭࢫ㛫㏻ಙࢆ

MPI(Message Passing Interface)࡟ࡼࡗ

࡚⾜࠸㸪 ࣉࣟࢭࢫෆ࡛ࡣ

OpenMP

࡟ࡼࡿ୪ิ໬ࢆ⾜ࡗࡓ㸬 ࡇࡢᡭἲ࡟ࡼࡾ㸪኱㔞ࡢ

CPU

ࢆ⏝࠸ࡓ࡟ࡶ࠿࠿ࢃࡽࡎࣉ

ࣟࢭࢫ㛫ࡢࢹ࣮ࢱ㏻ಙ㔞ࢆపࡃᢚ࠼ࡓຠ⋡ⓗ࡞୪ิィ⟬

ࢆᐇ᪋ࡋࡓ㸬ィ⟬ࡣ

75

ࣉࣟࢭࢫ

291CPU

ࢆ⏝࠸࡚ಸ⢭ᗘ

࡛⾜ࡗࡓࡀ㸪ᐇ⾜᫬ࡢ౑⏝࣓ࣔࣜࡣ⣙

230GB㸪ィ⟬㏿ᗘ

ࡣ⣙

0.13TFlops

࡛࠶ࡗࡓ㸬 ィ⟬࡟࠾ࡅࡿ᫬㛫้ࡳࡣ⣙

6ns

࡛࠶ࡾ㸪 㸯ࢫࢸࢵࣉ࠶ࡓࡾࡢᐇィ⟬᫬㛫ࡣ⣙

30

⛊࡛࠶ࡿ㸬

௒ᅇ㸪⏝࠸ࡓࢹ࣮ࢱࡣⅆ⅖ࡀ‽ᐃᖖ≧ែ࡟࡞ࡗ࡚࠿ࡽ⣙

0.5ms

ࡢ㛫ࡢࢹ࣮ࢱ࡛࠶ࡿࡀ㸪ࢹ࣮ࢱྲྀᚓࡢࡓࡵ࡟⣙

90000

ࢫࢸࢵࣉ㸪750 ᫬㛫/CPU ࡢィ⟬᫬㛫ࢆせࡋࡓ㸬ࡲ

ࡓ㸪ࢹ࣮ࢱࡢಖᏑࡣ༢⢭ᗘ࡛

100

ࢫࢸࢵࣉẖ࡟⾜ࡗࡓ㸬

1

▐㛫࠶ࡓࡾࡢࢹ࣮ࢱࢧ࢖ࢬࡣ⣙

10GB

࡛࠶ࡾ㸪⥲ࢹ࣮ࢱ

㔞ࡣ⣙

9TB

࡜࡞ࡗࡓ㸬

MPI MPI

CP U

CP U

CP U Memory

Process Process

Process

㻻 㼜㼑㼚㻹㻼

CP U

ᅗ

4

㡿ᇦศ๭࡜୪ิィ⟬

ὶࢀሙࡢᴫせ Ỉ⣲ᄇὶ

ᅗ

5

ࡣ࠶ࡿ▐㛫ࡢỈ⣲ᄇὶࡢᵝᏊ࡛࠶ࡿ㸬Ỉ⣲య✚ศ

⋡

70%ࡢ➼್㠃࡛࠶ࡾ㸪⾲㠃ࡢⰍࡣ➼್㠃ୖࡢ ᗘࢆ♧

ࡋ࡚࠸ࡿ㸬Ỉ⣲ᄇὶࡢᙉ࠸

Kelvin-Helmholtz

୙Ᏻᐃᛶ࡟

ࡼࡾᴟࡵ࡚୕ḟඖᛶࡀᙉࡃ஘ࢀࡀ኱ࡁ࡞ᄇὶࡀᙧᡂࡉࢀ

࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿ㸬ࡲࡓᄇὶୖὶᮍ⇞㒊࡟࠾࠸࡚ࡣ㠀 ᖖ࡟ᑠࡉ࡞஘ࢀࡢᵓ㐀ࡀほᐹࡉࢀࡿࡀ㸪᪤⇞㒊࡟࠾࠸࡚

ࡣᑠࡉ࡞ᵓ㐀ࡣほᐹࡉࢀ࡞࠸㸬ࡇࢀࡣ᪤⇞㒊࡟࠾࠸࡚ࡣ 㧗 ࢞ࢫࡢ኱ࡁ࡞⢓ᛶ࠾ࡼࡧᣑᩓ㏿ᗘ࡟ࡼࡾᑠࡉ࡞ᵓ㐀 ࡀᢚᅽࡉࢀࡿࡓࡵ࡛࠶ࡿ㸬

ᅗ

5

Ỉ⣲ᄇὶࠋỈ⣲య✚ศ⋡

70%➼್㠃ࠊ⾲㠃ࡢⰍࡣ 

ᗘࢆ⾲ࡍࠋ

ᾋࡁୖࡀࡾ㧗ࡉ

ᐇ㦂࡟࠾࠸࡚ࡣࢩ࣮ࣗࣜࣞࣥ෗┿ࡸⅆ⅖ࡢ⮬Ⓨගࢆ

ほᐹࡍࡿࡇ࡜࡟ࡼࡾᾋࡁୖࡀࡾ㧗ࡉࢆ᥎ᐃࡋ࡚࠸ࡿ㸬ᅗ

6a

ࡣᩘ್ࢹ࣮ࢱ࠿ࡽᨃఝⓗ࡟సࡗࡓࢩ࣮ࣗࣜࣞࣥ෗┿

࡛࠶ࡾ㸪ᅗ

6b

ࡣⅆ⅖ࡢ⮬Ⓨග※࡛࠶ࡿ

OH

ࡢᑐ⛠㠃ෆࡢ

㉁㔞ศ⋡ศᕸ࡛࠶ࡿ㸬ⅆ⅖ࡢ᭱ୖὶ㒊ࡢ఩⨨ࡣ࿘᪉ྥ࡟

ศᕸࡀ࠶ࡾ᫬㛫ⓗ࡟ࡶኚືࡍࡿࡀ㸪ࡑࡢ㧗ࡉࡣ࠾࠾ࡼࡑ

6-6.5D

࡛࠶ࡿ㸬ᾋࡁୖࡀࡾ㧗ࡉ࡟

0.5-1D

⛬ᗘࡢᕪࡀほᐹ

࡜ࡢ㛫࡟࠶ࡿࡶࡢࡢ㸪࠿ࡘ࡚ࢩ࣑࣮ࣗࣞࢩࣙࣥ࡟ࡼࡗ࡚

෌⌧ࡉࢀࡓ౛ࡀ࡞࠸ⅆ⅖ᙧែࡢ඲యⓗ࡞ጼࢆヲ⣽࡞ࢩ࣑

࣮ࣗࣞࢩࣙࣥ࡟ࡼࡾ෌⌧ࡍࡿࡇ࡜࡟ᡂຌࡋ࡚࠸ࡿ㸬

a㸸ᩘ್ࢹ࣮ࢱ࠿ࡽసᡂࡋࡓࢩ࣮ࣗࣜࣞࣥ෗┿

b㸸ᑐ⛠㠃ෆOH

㉁㔞ศ⋡ศᕸ

ᅗ

6

ⅆ⅖ᾋࡁୖࡀࡾ㧗ࡉ

༙ᚄ᪉ྥࡢศᕸ

ཧ↷ࡋࡓᐇ㦂࡟࠾࠸࡚ࡣ㸪᫬㛫ᖹᆒⓗ࠿ࡘ࿘᪉ྥ࡟ᖹ ᆒⓗ࡞ ᗘศᕸ࠾ࡼࡧ⤌ᡂศᕸࡢィ ࡀヨࡳࡽࢀ࡚࠸ࡿ㸬

໬Ꮫ✀࡟ࡘ࠸࡚ࡣ࣐ࣛࣥᩓ஘࡟ࡼࡾ㸪 ᗘ࡟ࡘ࠸࡚ࡣࣛ

࣐ࣥศගἲ࡟ࡼࡗ࡚ィ ࡉࢀ࡚࠸ࡿ㸬 ィ ࡢᅔ㞴ࡉ࠿ࡽ㸪

࠿࡞ࡾࡢ ᐃㄗᕪࡀ࠶ࡿࡇ࡜ࡣ㑊ࡅࡽࢀ࡞࠸ࡀ㸪኱ࡲ࠿

࡞ഴྥ࡟ࡘ࠸࡚ࡣẚ㍑᳨ドࡢᑐ㇟࡜࡞ࡿ࡜⪃࠼ࡿ㸬ᩘ್

ࢩ࣑࣮ࣗࣞࢩࣙࣥ࡟࠾࠸࡚ࡶ཰㞟ࡋࡓ᫬⣔ิࢹ࣮ࢱࡢ᫬

㛫ᖹᆒࢆ࡜ࡾ㸪࿘᪉ྥ࡟ᖹᆒࢆ࡜ࡿࡇ࡜࡟ࡼࡾ༙ᚄ᪉ྥ

ࡢศᕸࢆィ ࢹ࣮ࢱ࡜ẚ㍑ࡋࡓ㸬ᾋࡁୖࡀࡾ㧗ࡉࡀィ 

ࡼࡾࡶ

0.5-1D

⛬ᗘ▷࠸ࡇ࡜ࢆ⪃៖ࡋ࡚㸪ィ⟬⤖ᯝࡣヨ㦂

࡛ࡢィ Ⅼ࡟࠶ࢃࡏ࡚

0.5D

ୖὶ఩⨨㸪1D ୖὶ఩⨨࡛ࡢ ศᕸࢆ♧ࡋ࡚࠸ࡿ㸬

ᅗ

7

ࡣࣀࢬࣝ࠿ࡽ

7D

ୗὶ㸦ⅆ⅖᭱ୖὶ➃௜㏆㸧࡟࠾

ࡅࡿ㸪a: ᗘ㸪b:Ỉ⣲ࣔࣝศ⋡㸪c:㓟⣲ࣔࣝศ⋡㸪d:OH

ࣔࣝศ⋡㸪e:H

2O

ࣔࣝศ⋡ࡢ༙ᚄ᪉ྥศᕸ࡛࠶ࡿ㸬ࢩ࣑

࣮ࣗࣞࢩࣙࣥ࡟࠾࠸࡚ࡣ㸪ୖୗ఩⨨ࡢഹ࠿࡞㐪࠸࡛ศᕸ ࡀ኱ࡁࡃኚ໬ࡍࡿࡀ㸪ィ ್ࡣ࠾࠾ࡼࡑࢩ࣑࣮ࣗࣞࢩࣙ

ࣥ࡟࠾ࡅࡿ

y=6D

࡜

y=6.5D

ࡢ㛫࡟ศᕸࡋ࡚࠸ࡿ㸬ᐇ㦂࡜

ࡢᑐᛂ࡜࠸࠺ほⅬ࠿ࡽࡶ㸪ᮏࢩ࣑࣮ࣗࣞࢩࣙࣥ࡟࠾ࡅࡿ

ᾋࡁୖࡀࡾ㧗ࡉࡣ

6-6.5D

࡜࠸࠺࡭ࡁ࡛࠶ࢁ࠺㸬ࡲࡓ㸪ᄇ

ὶ୰ᚰ㸦

r=0㸧࡛ࡢ㓟⣲ࣔࣝศ⋡ࡀィ ࡜࡯ࡰ୍⮴ࡋ࡚࠸

ࡿࡇ࡜ࡣ㸪ⅆ⅖ୖὶ࡟࠾ࡅࡿᄇὶ࡬ࡢ㞺ᅖẼ✵Ẽࡢྲྀࡾ

㎸ࡳࢆࢩ࣑࣮ࣗࣞࢩࣙࣥࡀࡼࡃ෌⌧ࡋ࡚࠸ࡿࡇ࡜ࢆ♧ࡋ

࡚࠸ࡿ㸬 ࡋ࠿ࡋ࡞ࡀࡽ

OH

ࡀⓎ⏕ࡋ ᗘࡀୖ᪼ࡍࡿ㡿ᇦ

࡛ࢩ࣑࣮ࣗࣞࢩࣙࣥࡀ㓟⣲ࣔࣝศ⋡ࢆ኱ᖜ࡟పࡃぢ✚ࡶ

ࡿഴྥ࡟࠶ࡾ㸪ࡇࡢⅬࡣ௚ࡢㅖ㔞࡜␗࡞ࡿഴྥࢆ♧ࡋ࡚

࠸ࡿ㸬

ᅗ

8

ࡣࣀࢬࣝ࠿ࡽ

9.5D

ୗὶ࡛ࡢ༙ᚄ᪉ྥศᕸ࡛࠶ࡿ㸬 ࡑࢀࡒࢀࡢศᕸࡣほᐹ⤖ᯝ࡜ఝ㏻ࡗࡓᙧ࡜࡞ࡗ࡚࠸ࡿ㸬 ࡇࡇ࡛ࡶ㍈୰ᚰ࡛ࡢ㓟⣲ࣔࣝศ⋡ࡣィ ࡜ࡼ࠸୍⮴ࢆ♧

ࡋ࡚࠸ࡿࡀ㸪

7D

ୗὶ࡜ྠᵝ࡟཯ᛂࡀ㉳ࡇࡗ࡚࠸ࡿ࡜ᛮࢃ

ࢀࡿ㡿ᇦ࡟࠾࠸࡚ᕪ␗ࡀぢࡽࢀࡿ㸬ࢩ࣑࣮ࣗࣞࢩࣙࣥ࡟

࠾࠸࡚ࡣ

r=5mm

௜㏆ࡢ཯ᛂࡀጞࡲࡾ

OH

ࡀⓎ⏕ࡋ ᗘࡀ

ୖ᪼ࡍࡿ㡿ᇦ࡛㓟⣲ࡀᾘ㈝ࡉࢀࡘࡃࡉࢀࡓ㡿ᇦࡀぢࡽࢀ

ࡿࡢ࡟ᑐࡋ㸪ィ ࡟࠾࠸࡚ࡣ㍈୰ᚰ࡜࡯ࡰྠ୍ࡢ್ࢆ♧

ࡋ࡚࠸ࡿ㸬ୖ㏙ࡢ㏻ࡾⅆ⅖ୖὶ࡛ࡢ㓟⣲ࡢᄇὶ࡬ࡢྲྀࡾ

㎸ࡳࡀࡼࡃ෌⌧ࡉࢀ࡚࠸ࡿ࡜ࡍࡿ࡜㸪཯ᛂ㐣⛬ࡢᕪࡀィ  ࡜ࢩ࣑࣮ࣗࣞࢩࣙࣥ࡜ࡢᕪ࡜࠸࠺ࡇ࡜࡟࡞ࡿࡀ㸪཯ᛂ ࡢ⏕ᡂ≀࡛࠶ࡿ

H₂O

ࡢࣔࣝศ⋡ศᕸࡣィ ࡜ࢩ࣑ࣗࣞ

࣮ࢩ࡛ࣙࣥࡼ࠸୍⮴ࢆぢࡏ࡚࠸ࡿ㸬ࡲࡓ

9.5D

ୗὶ࡟࠾࠸

࡚ࡣෆഃỈ⣲㐣⃰᪤⇞࢞ࢫ࡜እഃ✵Ẽ୰ࡢ㓟⣲ࡢ㛫࡟ᣑ ᩓⅆ⅖ࡀᙧᡂࡉࢀ࡚࠸ࡿࡓࡵ⌮ㄽΰྜẚࡢ఩⨨௜㏆࡛ࡣ 㓟⣲ࡀ࡯ࡰᾘ㈝ࡋࡘࡃࡉࢀ㸪㓟⣲⃰ᗘࡀ㠀ᖖ࡟ᑠࡉ࡞㡿 ᇦࡀᙧᡂࡉࢀ࡚ࡋ࠿ࡿ࡭ࡁ࡜ࡶ⪃࠼ࡽࢀࡿ㸬㓟⣲ࣔࣝศ

⋡ࡢศᕸࡢᕪ␗࡟ࡘ࠸࡚⌮ゎࡍࡿࡓࡵ࡟ࡣ཯ᛂࣔࢹࣝ࠾

ࡼࡧィ ㄗᕪࡢ୧㠃࠿ࡽ᳨ウࡍࡿᚲせࡀ࠶ࡿ࡜⪃࠼ࡿࡀ㸪 ࡇࡇ࡛ࡣ௒ᚋࡢㄢ㢟࡜ࡍࡿ㸬

㓟⣲ࣔࣝศ⋡ศᕸ࡟ࡘ࠸࡚ࡣ᳨ウㄢ㢟ࡀ࠶ࡿࡶࡢࡢ㸪 ࡑࢀࢆ㝖ࡃㅖ㔞ࡢ༙ᚄศᕸ࡟࠾࠸࡚ࢩ࣑࣮ࣗࣞࢩࣙࣥࡣ ほᐹ⤖ᯝ࡟㏆࠸ศᕸࢆ෌⌧ࡋ࡚࠸ࡿ㸬

a)

b)

c)

d)

e)

ᅗ

7

 ᗘ࠾ࡼࡧ໬Ꮫ✀㉁㔞ศ⋡ࡢ༙ᚄ᪉ྥศᕸ㸦ࣀࢬࣝࡼࡾ

7D

ୗὶ㸧 㸬

a㸸 ᗘ㸪b㸸Ỉ⣲ࣔࣝศ⋡㸪c㸸㓟⣲ࣔࣝศ⋡㸪d㸸OH

ࣔࣝศ⋡㸪e㸸H

2O

ࣔࣝศ⋡㸬

a)

b)

c)

d)

ⅆ⅖඲యᵓ㐀

ᅗ

9 a, b

ࡣࡑࢀࡒࢀ㸪࠶ࡿ▐㛫ࡢᑐ⛠㠃ෆ࡛ࡢỈ⣲ᾘ

㈝㏿ᗘ࡜Ⓨ⇕⋡ࡢศᕸ࡛࠶ࡿ㸬ࣀࢬࣝ࠿ࡽᘏࡧ࡚࠸ࡿᐇ

⥺ࡣ⌮ㄽΰྜẚࡢ఩⨨ࢆ♧ࡋ࡚࠸ࡿ㸬⇞ᩱᾘ㈝㸪Ⓨ⇕࡜

ࡶ」㞧࡞ศᕸ࡜࡞ࡗ࡚࠸ࡿࡀ㸪኱㒊ศࡣⅆ⅖ඛ➃௜㏆࡛

㉳ࡇࡗ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿ㸬ࡲࡓⅆ⅖ୗὶ࡟࠾࠸࡚ࡣ㸪

⌮ㄽΰྜẚࡢ⥺࡟ἢࡗ࡚⇞ᩱᾘ㈝࠾ࡼࡧⓎ⇕ࡀࢫ࣏ࢵࢺ

≧࡟⌧ࢀ࡚࠸ࡿ㸬௨ୗ࡟࠾࠸࡚㸪ࡇࡢ」㞧࡞ⅆ⅖ᵓ㐀ࡢ

⌮ゎࢆヨࡳࡿ㸬

)ODPH,QGH[

ⅆ⅖ࡢ඲యⓗ࡞ᵓ㐀ゎᯒࡢࡓࡵ࡟㸪➉㔝ࡽ࡟ࡼࡗ࡚ᥦ

᱌ࡉࢀࡓ

Flame Index [20]ࢆ⏝࠸ࡓ㸬Flame Index (௨ୗF.I.)

ࡣୗグࡢ࡜࠾ࡾᐃ⩏ࡉࢀࡿ㸬

O

F.I. ’YF˜’Y (16)

ࡇࡇ࡟㸪

YF

࠾ࡼࡧ

YO

ࡣ⇞ᩱ࠾ࡼࡧ㓟໬๣ࡢ㉁㔞ศ⋡

࡛࠶ࡾ㸪ᮏࢩ࣑࣮ࣗࣞࢩࣙࣥࡢሙྜ㸪F ࡀỈ⣲㸪O ࡀ㓟

⣲࡜࡞ࡿ㸬

ⅆ⅖ࡢ⇞↝ᙧែ࡜ࡋ࡚ࡣ኱ࡁࡃศࡅ࡚㸪ணΰྜⅆ⅖࡜

ᣑᩓⅆ⅖ࡀ࠶ࡿ㸬ணΰྜⅆ⅖࡜ࡣ⇞ᩱ࡜㓟໬๣ࡀ཯ᛂࡍ

ࡿ๓࠿ࡽ༑ศΰྜࡋࡓⅆ⅖࡛࠶ࡾ㸪Ἴࡢࡼ࠺࡞ఏ᧛ᛶࢆ

ᣢࡘ㸬ࡇࡢⅆ⅖ࡢෆ㒊࡛ࡣ㸪ᅗ

10a

࡟♧ࡍࡼ࠺࡟㸪⇞ᩱ

࡜㓟໬๣ࡣྠࡌ᪉ྥ࠿ࡽ཯ᛂᖏ࡟౪⤥ࡉࢀࡿ㸬୍᪉㸪ᣑ ᩓⅆ⅖ࡣ⇞ᩱ࡜㓟໬๣ࡀูࠎ࡟౪⤥ࡉࢀศᏊᣑᩓ࡟ࡼࡾ

ΰࡊࡾ࡞ࡀࡽ཯ᛂࡍࡿⅆ⅖࡛࠶ࡾ㸪⌮ㄽΰྜẚ࡜࡞ࡿ఩

⨨௜㏆࡛⇞↝཯ᛂࡀ㉳ࡇࡿ㸬ࡇࡢⅆ⅖࡛ࡣ㸪ᅗ

10b

࡟♧

ࡍࡼ࠺࡟⇞ᩱ࡜㓟໬๣ࡀ஫࠸࡟ྥࡁྜ࠺ᙧ࡛཯ᛂᖏ࡟౪

⤥ࡉࢀࡿ㸬ᚑࡗ࡚

F.I.ࡀṇࡢ᫬ࡍ࡞ࢃࡕ㸪⇞ᩱ⃰ᗘ໙㓄

࡜㓟໬๣⃰ᗘ໙㓄ࡢྥࡁࡀྠࡌሙྜࡣⅆ⅖ࡢ⇞↝ᙧែࡣ ணΰྜⅆ⅖㸪㏫࡟㈇ࡢሙྜࡣᣑᩓⅆ⅖࡜ุ᩿ࡍࡿࡇ࡜ࡀ

࡛ࡁࡿ㸬

e)

ᅗ

8 :

 ᗘ࠾ࡼࡧ໬Ꮫ✀㉁㔞ศ⋡ࡢ༙ᚄ᪉ྥศᕸ㸦ࣀࢬࣝࡼࡾ

9D

ୗὶ㸧 㸬

a㸸 ᗘ㸪b㸸Ỉ⣲ࣔࣝศ⋡㸪c㸸㓟⣲ࣔࣝศ⋡㸪d㸸OH

ࣔࣝศ⋡㸪e㸸H

2O

ࣔࣝศ⋡㸬

ᅗ

9

㸰ḟඖ᩿㠃ෆࡢ a㸸⇞ᩱᾘ㈝㏿ᗘศᕸ, b㸸Ⓨ⇕ศ

ᕸ㸬ࣀࢬࣝ࠿ࡽࡢᐇ⥺ࡣ⌮ㄽΰྜẚࡢ఩⨨ࢆ⾲ࡍ㸬

ᅗ

10

௦⾲ⓗ࡞ⅆ⅖ᙧែ㸪

a㸸ணΰྜⅆ⅖㸪b㸸ᣑᩓⅆ⅖㸬

1RUPDOL]HG)ODPH,QGH[

F.I.ࡣணΰྜⅆ⅖࡜ᣑᩓⅆ⅖ࡢุูࢆྍ⬟࡜ࡍࡿ㸬ࡇࡢ

F.I.ࢆ↓ḟඖ໬ࡍࡿࡇ࡜࡟ࡼࡾ᪂ࡋ࠸ព࿡ࢆ௜ࡅຍ࠼ࡿ

ࡇ࡜ࡀ࡛ࡁࡿ㸬ṇࡢ

F.I.࡟ࡘ࠸࡚ࡣ㸪ྠࡌᙜ㔞ẚࡢ୍ḟ

ඖᒙὶணΰྜⅆ⅖ࡢ

F.I.࡛↓ḟඖ໬ࡋ㸪㈇ࡢF.I.࡟ࡘ࠸࡚

ࡣᑐྥὶ୍ḟඖᣑᩓⅆ⅖࡟࠾࠸࡚ṍࡳ㏿ᗘࢆ኱ࡁࡃࡋ࡚

࠸ࡗࡓ᫬࡟ᾘ⅖ࡍࡿ㝿ࡢ

F.I.࡛↓ḟඖ໬ࡍࡿ㸬ࡇࡢ↓ḟ

ඖ໬ࡉࢀࡓ

F.I.ࡍ࡞ࢃࡕNormalized Flame Index (N.F.I.)ࡣ㸪

ணΰྜⅆ⅖࡟ᑐࡋ࡚ࡣᒁᡤࡢⅆ⅖㏿ᗘࡢᣦᶆ࡜࡞ࡾ㸪ᒁ ᡤࡢⅆ⅖㏿ᗘࡀ୍ḟඖᒙὶⅆ⅖ࡢⅆ⅖㏿ᗘࡢ࠾࠾ࡼࡑ

(N.F.I.)^1/2

࡜᥎ᐃࡍࡿࡇ࡜ࡀ࡛ࡁࡿ㸬ᣑᩓⅆ⅖࡟ᑐࡋ࡚ࡣ ᾘ⅖ࡲ࡛ࡢవ⿱ࢆ♧ࡍࡇ࡜࡟࡞ࡿ㸬

ⅆ⅖ᵓᡂせ⣲

ᅗ

11

ࡣỈ⣲ᾘ㈝㏿ᗘ

10⁴mol/m³/s

ࡢ➼್㠃࡛࠶ࡿ㸬➼

್㠃ୖࡢⰍࡣ

F.I.࠾ࡼࡧᒁᡤࡢẼయ⤌ᡂࢆ⏝࠸ุ࡚ᐃࡋ

ࡓ⇞↝࣮ࣔࢻࢆ♧ࡋ࡚࠸ࡿ㸬㉥㸸㐣⃰ணΰྜⅆ⅖㸪㟷㸸 ᕼⷧணΰྜⅆ⅖㸪⥳㸸ᣑᩓⅆ⅖࡟ศ㢮࡛ࡁࡿ㸬㐣⃰࡜ࡣ

⌮ㄽΰྜẚࡼࡾࡶ⇞ᩱࡢ๭ྜࡀከ࠸ሙྜ࡛㸪ᕼⷧ࡜ࡣࡑ ࡢ㏫࡛࠶ࡿ㸬

ࡇࡢᅗ࠿ࡽ㸪ᑐ㇟ࡢᾋࡁୖࡀࡾⅆ⅖ࡣ༢࡞ࡿ୍ࡘࡢⅆ

⅖࡛ࡣ࡞ࡃ㸪㸱ࡘࡢⅆ⅖せ⣲ࢆྵࢇ࡛࠸ࡿࡇ࡜ࢆ♧ࡋ࡚

࠸ࡿ㸬ࡍ࡞ࢃࡕ㸪

࣭㐣⃰㸭ᕼⷧணΰྜⅆ⅖࡜ᣑᩓⅆ⅖ࡀΰᅾࡋࡓ୕㔜ⅆ⅖

ⓗ࡞ᵓ㐀ࢆࡶࡘⅆ⅖ඛ➃㒊

࣭ⅆ⅖እഃ࡟ᓥ≧࡟ศᕸࡍࡿᣑᩓⅆ⅖

࣭ⅆ⅖ෆഃࡢ」㞧࡞ᙧ≧ࡢ㐣⃰ணΰྜⅆ⅖

࡛࠶ࡿ㸬ࡉࡽ࡟ⅆ⅖ࡢ㠀ᐃᖖ࡞ືࡁࢆほᐹࡍࡿ࡜㸪ⅆ⅖ ඛ➃㒊ࡣ୕ḟඖᛶࡀᙉ࠸ᵓ㐀ࢆᣢࡕ⦆ࡸ࠿࡟ື࠸࡚࠸ࡿ

ࡀ㠀ᖖ࡟Ᏻᐃ࡛ᾋࡁୖࡀࡾⅆ⅖඲యࡢᏳᐃᛶࢆࢥࣥࢺࣟ

࣮ࣝࡋ࡚࠸ࡿࡇ࡜㸪እഃࡢᣑᩓⅆ⅖ࡣ⌮ㄽΰྜẚࡢ㠃࡟

ἢࡗ࡚ࡺࡗࡃࡾ࡜ୗὶ࡟ὶࢀ࡚࠸ࡃࡇ࡜㸪ෆഃࡢ㐣⃰ண ΰྜⅆ⅖ࡣᄇὶࡢ஘ࢀࡢᙳ㡪ࢆᙉࡃཷࡅࡿ஘ὶⅆ⅖࡛࠶

ࡿࡇ࡜ࡀ᫂ࡽ࠿࡜࡞ࡗࡓ㸬

ḟ❶࡟࠾࠸࡚㸪ྛⅆ⅖せ⣲࡟ࡘ࠸࡚᫂ࡽ࠿࡜࡞ࡗࡓࡇ

࡜㸪௒ᚋゎ᫂ࡋ࡚࠸ࡃ࡭ࡁࡇ࡜࡟ࡘ࠸࡚㏙࡭ࡿ㸬

ᅗ

11

ⅆ⅖඲యᵓ㐀ࠋ Ỉ⣲ᾘ㈝㏿ᗘ

10⁴mol/s/m³

ࡢ➼್㠃㸬

⾲㠃ࡢⰍࡣ⇞↝࣮ࣔࢻࢆ⾲ࡍ㸪㉥㸸㐣⃰ணΰྜ⇞

↝㸪㟷㸸ᕼⷧணΰྜ⇞↝, ⥳㸸ᣑᩓ⇞↝㸬

ⅆ⅖ᵓᡂせ⣲ࡢ≉ᚩ࡜◊✲ㄢ㢟 ඛ➃ⅆ⅖

ඛ➃ⅆ⅖ࡣ㸪㐣⃰㸭ᕼⷧணΰྜⅆ⅖࠾ࡼࡧᣑᩓⅆ⅖ࡀ ΰᅾࡋࡓ୕㔜ⅆ⅖ⓗ࡞ᵓ㐀ࢆᣢࡗ࡚࠸ࡿ㸬ᾋࡁୖࡀࡾⅆ

⅖ୖὶ➃࡟఩⨨ࡍࡿࡇࡢⅆ⅖せ⣲ࡀⅆ⅖඲యࡢᏳᐃᛶࢆ

ᨭ㓄ࡋ࡚࠸ࡿ㸬 ࡇࡢඛ➃㒊ࡢ㠀ᐃᖖ࡞ືࡁࢆほᐹࡍࡿ࡜㸪 ᄇὶ࠿ࡽࡶࡗ࡜ࡶ㞳ࢀࡓ఩⨨࡟࠶ࡿᕼⷧணΰྜⅆ⅖ࡀ᭱

ࡶᏳᐃ࡛఩⨨ࡢኚືࡀᑠࡉ࠸㒊఩࡜࡞ࡗ࡚࠸ࡿ㸬 ࡓࡔࡋ㸪 ᖖ࡟࠶ࡿ఩⨨ࡢᕼⷧணΰྜⅆ⅖ࡀᏳᐃ࡛࠶ࡿࢃࡅ࡛ࡣ࡞

ࡃ㸪Ᏻᐃ࡞఩⨨ࡣ᫬ࠎ้ࠎ⛣ືࡋ࡚࠸ࡿ㸬ᅗ

12 a

ࡣ࠶ࡿ

▐㛫࡟࠾ࡅࡿᏳᐃ࡞ᕼⷧணΰྜⅆ⅖࡟࠾ࡅࡿ

N.F.I.ࢆ♧

ࡋ࡚࠸ࡿ㸬ࡓࡔࡋᅗࢆぢࡸࡍࡃࡍࡿࡓࡵ࡟㸪 ᗘࡀ

400K

ᮍ‶ࡢ㡿ᇦ࡛ࡣ

N.F.I.=0

࡜ࡋ࡚࠸ࡿ㸬ṇࡢ

N.F.I.ࡣᐇ⥺࡛

0.4

࠿ࡽ

0.4

้ࡳ࡛㸪㈇ࡢ

N.F.I.ࡣ◚⥺࡛0.001

้ࡳ࡛➼

್⥺ࢆᥥ࠸࡚࠸ࡿ㸬㯮࠸ᐇ⥺ࡣ⌮ㄽΰྜẚࡢ఩⨨ࢆ♧ࡋ

࡚࠸ࡿ㸬 ᅗ୰ࡢᕼⷧணΰྜⅆ⅖㒊࡟࠾࠸࡚

N.F.I.ࡣ0.8-1.6

ࡢ್࡜࡞ࡗ࡚࠸ࡿ㸬ⅆ⅖ࡀᏳᐃ࡞㛫ࡣ㸪

N.F.I.ࡢ್ࡣ᫬㛫

ⓗ࡟ኚືࡍࡿࡶࡢࡢᅗ

12a

࡟௦⾲ࡉࢀࡿࡼ࠺࡟

1

๓ᚋ࠿

ࡽ

2

๓ᚋࡢ್ࢆ♧ࡍ㸬ࡍ࡞ࢃࡕணΰྜⅆ⅖ࡢఏ᧛㏿ᗘࡣ

୍ḟඖᒙὶணΰྜⅆ⅖࡜ྠ⛬ᗘ࠿ࡽ

1.5

ಸ⛬ᗘ࡛࠶ࡿࡇ

࡜ࡀ᥎ᐃࡉࢀࡿ㸬⌮ㄽΰྜẚ㏆ࡃࡢᙜ㔞ẚࡢணΰྜⅆ⅖ ࡢఏ᧛㏿ᗘࡀ

2m/s

࡛࠶ࡿࡇ࡜࠿ࡽ(ᅗ

12 b)㸪ᒁᡤࡢⅆ⅖

ࡢఏ᧛㏿ᗘࡣ

2-3m/s

࡜᥎ᐃࡉࢀࡿ㸬୍᪉㸪㍈᪉ྥࡢᖹᆒ

㏿ᗘࡣ⣙

2.9m/s

࡛࠶ࡗࡓ㸬ࡍ࡞ࢃࡕ㸪Ᏻᐃ࡞ᕼⷧணΰྜ

ⅆ⅖࡟࠾࠸࡚ࡣ㸪ⅆ⅖ࡢఏ᧛㏿ᗘ࡜ὶධࡍࡿᮍ⇞ΰྜẼ ࡢ㏿ᗘࡀ࠾࠾ࡼࡑࡘࡾ࠶ࡗ࡚࠸ࡿ࡜࠸࠼ࡿ㸬

ୖグࡢࡼ࠺࡞Ⅼࡀࣜࣥࢢ≧ࡢඛ➃ⅆ⅖࡟ᖖ࡟Ꮡᅾࡍ

ࡿࡇ࡜࡟ࡼࡾ㸪ⅆ⅖఩⨨ࡀᏳᐃ໬ࡉࢀ࡚࠸ࡿࡶࡢ࡜᥎  ࡉࢀࡿࡀ㸪ゎᯒࡣඛ➃ⅆ⅖඲య࡜ࡋ࡚ࡢᏳᐃᛶࡢ⌮ゎࡲ

࡛ࡣ⮳ࡗ࡚࠸࡞࠸㸬௒ᚋ㸪」㞧࡞୕ḟඖᵓ㐀ࢆᣢࡘඛ➃ ⅆ⅖ࡀ඲య࡜ࡋ࡚࡝ࡢᵝ࡟Ᏻᐃ໬ࡉࢀ࡚࠸ࡿ࠿㸪୕ḟඖ ᵓ㐀ࡢ㠀ᐃᖖ࡞ືࡁࢆほᐹࡋ࡚᫂ࡽ࠿࡟ࡋ࡚࠸ࡃᚲせࡀ

࠶ࡿ㸬

ࡲࡓ㸪ⅆ⅖ఏ᧛㏿ᗘ࡜ᮍ⇞ΰྜẼὶධ㏿ᗘࡢࣂࣛࣥࢫ

࡟ࡼࡗ࡚ඛ➃ⅆ⅖఩⨨ࡀỴࡲࡗ࡚࠸ࡿ࡜ࡍࡿ࡜㸪௒ᅇࡢ ࢩ࣑࣮ࣗࣞࢩࣙࣥ࡟࠾࠸࡚ᾋࡁୖࡀࡾ㧗ࡉࡀほᐹࡼࡾࡶ

0.5-1D

ప࠸ཎᅉ࡜ࡋ࡚㸪Ỉ⣲ᄇὶ࡜✵Ẽࡢ㐠ື㔞ࡢΰྜ

࠾ࡼࡧணΰྜⅆ⅖ࡢఏ᧛㏿ᗘࡢホ౯ㄗᕪࡀ⪃࠼ࡽࢀࡿ㸬

௒ᚋࡇࡢ஧ࡘࡢホ౯᪉ἲࡢ⢭ᗘ᳨ウ࠾ࡼࡧ㧗⢭ᗘ໬ࢆᅗ ࡗ࡚࠸ࡃᚲせࡀ࠶ࡿ㸬

ᅗ

12 a)ඛ➃௜㏆ࡢN.F.I.ศᕸ࡜b)Ỉ⣲✵Ẽணΰྜⅆ⅖ࡢ

ఏ᧛㏿ᗘ㸬

a)୰ࡢ㯮ᐇ⥺ࡣ⌮ㄽΰྜẚࡢ఩⨨ࢆ♧ࡍ

ᓥ≧ᣑᩓⅆ⅖

እഃࡢᣑᩓⅆ⅖࡟ࡘ࠸࡚ࡣ㸪ࡲࡎ㏻ᖖࡢⅆ⅖࡜ࡣ␗࡞

ࡿᓥ≧ࡢᙧែࡢ୰࡛࡝ࡢᵝ࡞⇞↝ࡀ㉳ࡇࡗ࡚࠸ࡿ࠿ࡀ⯆

࿡῝࠸㸬ᅗ

13

ࡣ஧ࡘࡢᓥ≧ᣑᩓⅆ⅖࡟ᑐࡋ࡚㸪ࡑࡢᖜ࡜

ࡑࡢⅆ⅖࡟࠾ࡅࡿ᭱኱⇞ᩱᾘ㈝㏿ᗘࡢ㛵ಀࢆࣉࣟࢵࢺࡋ ࡓࡶࡢ࡛࠶ࡿ㸬ⅆ⅖ࡢ㍯㒌ࢆᾘ㈝㏿ᗘࡀ

10⁴mol/m³/s

ࡢ➼

್㠃࡜ᐃ⩏ࡋ㸪ࡑࡢᖜࢆⅆ⅖ᖜ࡜ࡋ࡚ィ ࡋࡓ㸬ⅆ⅖ࡢ ᖜࡣ࠾࠾ࡼࡑศᏊᣑᩓࡢ᫬㛫ࢫࢣ࣮ࣝࢆ⾲ࡍࡢ࡛㸪ᣑᩓ ࡢ᫬㛫ࢫࢣ࣮ࣝ࡜໬Ꮫ཯ᛂࡢ᫬㛫ࢫࢣ࣮ࣝࡢẚ㍑࡜࡞ࡿ㸬

࡝ࡕࡽࡢⅆ⅖࡟࠾࠸࡚ࡶ㸪ศᏊᣑᩓࡢ᫬㛫ࢫࢣ࣮ࣝ࡜໬

Ꮫ཯ᛂࡢ᫬㛫ࢫࢣ࣮ࣝࡣ࡯ࡰ⥺ᙧ࡞㛵ಀ࡟࠶ࡾ㸪໬Ꮫ཯

ᛂࡀศᏊᣑᩓ࡟ᨭ㓄ࡉࢀ࡚࠸ࡿࡇ࡜ࢆ♧၀ࡋ࡚࠸ࡿ㸬ࡍ

࡞ࢃࡕ㸪ᓥ≧ࡢ≉␗࡞ᙧ≧ࢆ࡜ࡿࡶࡢࡢ㸪ࡑࡢ୰࡛ࡢ⇞

↝ࡣ㸪ⷧ࠸཯ᛂᖏ࡛㉳ࡁࡿ⇞ᩱᾘ㈝ࡀࡑࡢ࿘ࡾࡢศᏊᣑ ᩓ࡟ࡼࡿ⇞ᩱ౪⤥࡟ᨭ㓄ࡉࢀ࡚࠸ࡿ࡜࠸࠺㏻ᖖࡢᒙὶⅆ

⅖∦ࡢᴫᛕ[21]࡛ㄝ࡛᫂ࡁࡿᛶ㉁ࢆᣢࡗ࡚࠸ࡿࡇ࡜ࡀศ

࠿ࡿ㸬

ຍ࠼࡚㸪ᓥ≧ࡢᙧែࡀ࡝ࡢࡼ࠺࡟ᙧᡂࡉࢀ࡚࠸ࡿ࠿ࡶ

⯆࿡῝࠸㸬ࡍ࡞ࢃࡕ㸪࿘㎶ࡼࡾࡶᙉ࠸ᣑᩓ⇞↝ࡀ㉳ࡇࡗ

࡚࠸ࡿ㡿ᇦࡀᒁᡤⓗ࡟Ꮡᅾࡍࡿࡢࡣ࡞ࡐ࠿࡜࠸࠺ࡇ࡜࡛

࠶ࡿ㸬௨ୗ࡟ⅆ⅖ࡢᣲືࢆほᐹࡍࡿࡇ࡜࡟ࡼࡗ࡚᫂ࡽ࠿

࡟࡞ࡗࡓᙧᡂ㐣⛬ࢆ♧ࡍ㸬

ᾋࡁୖࡀࡾⅆ⅖እഃ࡟ࡣ⌮ㄽΰྜẚ➼್㠃እഃ࠶ࡓ

ࡾ࡟㓟⣲ศᏊᣑᩓᒙࡀᙧᡂࡉࢀ࡚࠸ࡿ㸬ࡇࢀࡣඛ➃ⅆ⅖

࡟ὶධࡍࡿ㐣⃰ΰྜẼ୰ࡢ㓟⣲ࡢ኱㒊ศࡀඛ➃ⅆ⅖࡛ᾘ

㈝ࡉࢀ࡚ࡋࡲ࠺ࡓࡵ࡟࡛ࡁࡿඛ➃ⅆ⅖ᚋὶࡢ㓟⣲ࡀṤ࡝

↓࠸㡿ᇦ࡜እഃࡢ✵Ẽࡢ㛫࡟ฟ᮶ࡿ㓟⣲ศᏊᣑᩓᒙ࡛࠶

ࡿ㸬ࡑࡢෆഃ࡟࠶ࡿ㐣⃰ணΰྜⅆ⅖ࡣᴟࡵ࡚஘ࢀࡢᙉ࠸

ⅆ⅖࡛࠶ࡾ㸪 ᫬࡟ࡼࡾእഃ࡟኱ࡁࡃᙇࡾฟࡍሙྜࡀ࠶ࡿ㸬 ࡇࡢෆഃணΰྜⅆ⅖ࡀእഃ࡟࠶ࡿ㓟⣲ศᏊᣑᩓᒙ࡟᥋ゐ ࡍࡿ᫬࡟ᓥ≧ᣑᩓⅆ⅖ࡀᙧᡂࡉࢀ㸪ࡲࡓ᪤Ꮡࡢᓥ≧ᣑᩓ ⅆ⅖࡟᥋ゐࡍࡿሙྜࡣࡑࡢ⇞↝ࢆάᛶ໬ࡉࡏࡿ㸬

ᅗ

14

ࡣ⏕ᡂ㐣⛬ࡢ୍౛࡛࠶ࡿ㸬እഃ࡟ᥥ࠿ࢀ࡚࠸ࡿ

➼್⥺ࡣ࠶ࡿᖹ㠃ෆࡢ㓟⣲㉁㔞ศ⋡ศᕸ࡛࠶ࡾ㸪㓟⣲ศ Ꮚᣑᩓᒙࢆ⾲ࡋ࡚࠸ࡿ㸬᫬้

a

࡟࠾࠸࡚ۑ࡛ᅖࡲࢀࡓ㒊 ศࡀ㠀ᐃᖖ࡞ືࡁ࡟ࡼࡾ᫬้

b

࡟࠾࠸࡚እഃ㓟⣲ᣑᩓᒙ

࡟᥋ࡍࡿࠋࡑࡢ᫬࡟ணΰྜⅆ⅖࡟᥋ࡋ࡚ᣑᩓⅆ⅖ࡀᙧᡂ ࡉࢀࡿ㸬ࡑࡢᚋ᫬้

c

࡟ぢࡽࢀࡿࡼ࠺࡟ணΰྜⅆ⅖࡜ᣑ ᩓⅆ⅖ࡢ᥋ྜ㒊ࡀ⇞ᩱࡢᾘ㈝࡟ࡼࡗ࡚཰⦰ࡋ࡚ࡺࡁ㸪ࡘ

࠸࡟ࡣ᫬้

d

࡟࠾࠸࡚᥋ྜ㒊࡛ᾘ⅖ࡀ㉳ࡇࡾᣑᩓ⇞↝㒊 ࡣෆഃ㐣⃰ணΰྜⅆ⅖࠿ࡽศ㞳ࡉࢀ㸪ᓥ≧ࡢᣑᩓⅆ⅖࡜

࡞ࡿ㸬

ෆഃ஘ὶ㐣⃰ணΰྜⅆ⅖

ෆഃ㐣⃰ணΰྜⅆ⅖ࡣỈ⣲ᄇὶࡢ஘ࢀࡢᙳ㡪ࢆ᭱ࡶ

ᙉࡃཷࡅࡿⅆ⅖せ⣲࡛࠶ࡿ㸬ࡑࡢᙳ㡪ࡀ㢧ⴭ࡟⌧ࢀࡓ⤖

ᯝ࡜ࡋ࡚㸪 ᅗ

15

ࡢୖ༙ศ࡟ぢࡽࢀࡿࡼ࠺࡞Ⓨ⇕ᒙࡀ⇞ᩱ

ᾘ㈝ᒙ࠿ࡽ኱ࡁࡃ஋㞳ࡋ࡚࠸ࡿ㡿ᇦࡢᏑᅾࡀ࠶ࡆࡽࢀࡿ㸬 ࡇࢀࡣ㸪⌧ᅾከࡃࡢⅆ⅖ࣔࢹࣝࡢᇶ♏࡜࡞ࡗ࡚࠸ࡿᒙὶ

ⅆ⅖∦ࡢᴫᛕ[21]࠿ࡽࡣ኱ࡁࡃእࢀࡓ≉ᚩ࡛࠶ࡿ㸬 ࡑࡢࡼ࠺࡞≉ᚩࡀ㢧ⴭ࡞㒊ศ࡟࠾ࡅࡿ஘ࢀࡢࢫࢣ࣮

ࣝࢆࢩ࣑࣮ࣗࣞࢩࣙࣥࡢ᫬⣔ิࢹ࣮ࢱࢆ⤫ィฎ⌮ࡍࡿ஦

࡟ࡼࡾ᥎⟬ࡋࡓ㸬ィ ࡋࡓⅬࡣࣀࢬࣝ࠿ࡽ

16mm㸪ᄇὶ

୰ᚰ࠿ࡽ

2.8mm

ࡢ఩⨨࡛࠶ࡾ㸪ᖹᆒ㏿ᗘ࠾ࡼࡧ㏿ᗘኚື

ࡣ

71.7m/s

࠾ࡼࡧ 43.4m/s㸪 ᒁᡤⓗ࡞ᙜ㔞ẚࡣ⣙

4

࡛࠶ࡿ㸬 ලయⓗ࡟ࡣ

x

㸪

y

㸪

z

᪉ྥࡑࢀࡒࢀ࡟࠾ࡅࡿ㏿ᗘኚືࡢ

2

Ⅼ┦㛵࠿ࡽᚓࡽࢀࡿྛ᪉ྥࡢ✚ศ㛗ࡢᖹᆒࢆ✚ศ㛗࡜ࡋ㸪 ᩓ㐓⋡➼ࢆ⏝࠸࡚ࢥࣝࣔࢦࣟࣇࢫࢣ࣮ࣝࢆ᥎⟬ࡋࡓ㸬ࡑ ࡢ⤖ᯝ㸪✚ศ㛗࠾ࡼࡧࢥࣝࣔࢦࣟࣇࢫࢣ࣮ࣝࡣࡑࢀࡒࢀ

2.8mm

࠾ࡼࡧ

0.03mm

࡜ᚓࡽࢀࡓ㸬ཧ⪃ࡲ࡛࡟㸪ᐇ㦂࡛

ィ ࣭᥎⟬ࡉࢀࡓ㸪࡯ࡰྠ఩⨨࡟࠾ࡅࡿᖹᆒ㏿ᗘࡣ

70m/s㸪

✚ศ㛗ࡣ

1.3mm㸪ࢥࣝࣔࢦࣟࣇࢫࢣ࣮ࣝࡣ0.03mm

࡛࠶

ࡿ[6]㸬⤫ィฎ⌮࡛ࡣࢥࣝࣔࢦࣟࣇࢫࢣ࣮ࣝࡀ

0.03mm

࡜

ᅗ

13

ᓥ≧ᣑᩓⅆ⅖ࡢᖜ࡜⇞ᩱᾘ㈝㏿ᗘ

ᅗ

14

ෆഃ㐣⃰ணΰྜⅆ⅖ࡢ㠀ᐃᖖᣲື࡟ࡼࡿᓥ≧ᣑᩓⅆ⅖ࡢ⏕ᡂࠋෆഃ㐣⃰ணΰྜⅆ⅖ࡀⅆ⅖እഃ࡟࠶ࡿ㓟⣲ศᏊ

ᣑᩓᒙ࡟᥋ゐࡋࡓ㝿࡟ᓥ≧ᣑᩓⅆ⅖ࡀ⏕ᡂࡉࢀࡿ㸬➼್⥺ࡣ㓟⣲ศᏊᣑᩓᒙࢆ♧ࡍ.

ᅗ

16

ෆഃ㐣⃰஘ὶணΰྜⅆ⅖ࡢ

Borghi Diagram

ୖ࡛ࡢศ㢮㸬㉥࠸Ⅼࡀィ Ⅼ㸬

᥎⟬ࡉࢀࡓࡀ㸪ィ⟬᱁Ꮚᖜࡀ

0.05mm

࡛࠶ࡿࡇ࡜ࢆ⪃៖

ࡍࡿ࡜ࢩ࣑࣮ࣗࣞࢩ࡛ࣙࣥ෌⌧ࡉࢀ࡚࠸ࡿ ࡢࢫࢣ࣮ࣝ

ࡣ

0.2mm

⛬ᗘ࠿ࡽ

2.8mm

ࡢ㛫࡟ศᕸࡋ࡚࠸ࡿ࡜⪃࠼ࡽ

ࢀࡿ㸬୍᪉࡛ᙜ㔞ẚ

4.0

࡛ࡢᒙὶỈ⣲ணΰྜⅆ⅖ࡣ㠀ᖖ

࡟ཌࡃ㸪⇞ᩱᾘ㈝ᒙࡀ⣙

1mm㸪Ⓨ⇕ᒙࡣ᭦࡟ࡑࢀࡼࡾࡶ

ᑡࡋཌ࠸㸬ࡍ࡞ࢃࡕ㸪ࡇࡢෆഃ㐣⃰ணΰྜⅆ⅖࡟࠾࠸࡚

ࡣⅆ⅖ཌࡉ࡜ྠ࣮࢜ࢲ࡛㸪ࡑࢀࡼࡾࡶᑠࡉ࠸ ࡀᏑᅾࡍ

ࡿࡓࡵ㸪 ࡀⅆ⅖ෆ㒊࡟౵ධࡋⅆ⅖ᵓ㐀࡟ᙳ㡪ࢆ୚࠼ࡸ

ࡍ࠸≧ែࡀᙧᡂࡉࢀ࡚࠸ࡿ㸬ࡑࡢ⤖ᯝ㸪Ⓨ⇕ᒙࡀ⇞ᩱᾘ

㈝ᒙ࠿ࡽ኱ࡁࡃ஋㞳ࡍࡿ࡟⮳ࡗ࡚࠸ࡿ࡜⪃࠼ࡽࢀࡿ㸬஘

ὶணΰྜⅆ⅖ࡢ≉ᛶࢆ㸪ⅆ⅖ཌࡉ

lF

࡜✚ศ㛗

l

ࡢẚ࠾ࡼ

ࡧᒙὶⅆ⅖ఏ᧛㏿ᗘ

SL

࡜஘ࢀࡢ㏿ᗘ

v’

ࡢẚࢆࣃ࣓࣮ࣛࢱ

࡜ࡋ࡚ᩚ⌮ࡍࡿᅗࡢ୍ࡘ࡟

Borghi

ࢲ࢖࢔ࢢ࣒ࣛ[22]ࡀ࠶

ࡿ(ᅗ

16)㸬ᅗ16

୰

Ka{l_F² Ș²

ࡣⅆ⅖ཌࡉ࡜ࢥࣝࣔࢦࣟ

ࣇࢫࢣ࣮ࣝ

K

ࡢẚ㸦ࡢ⮬஌㸧ࢆ⾲ࡍ࢝ࣝࣟࣅࢵࢶᩘ࡛࠶

ࡾ㸪

Da{S_Ll vcl_F

ࡣ஘ὶ࡜⇞↝ࡢ᫬㛫ࢫࢣ࣮ࣝࡢẚࢆ

⾲ࡍ஘ὶࢲ࣒ࢣ࣮ࣛᩘ࡛࠶ࡿ㸬ⅆ⅖࠾ࡼࡧ஘ࢀࡢࢫࢣ࣮

ࣝࢆ┤᥋

Borghi

ࢲ࢖࢔ࢢ࣒ࣛୖ࡟ࣉࣟࢵࢺࡍࡿ࡜㸪஘ࢀ

ࡀ㠀ᖖ࡟ᙉ࠸࠺࠼㸪

Da<1

ࡍ࡞ࢃࡕ஘ࢀࡢ᫬㛫ࢫࢣ࣮ࣝࡀ

⇞↝ࡢ᫬㛫ࢫࢣ࣮ࣝࡼࡾࡶᑠࡉ࠸

well-stirred reactors

࡟ ศ㢮ࡉࢀ㸪㠀ᖖ࡟≉␗࡞⇞↝≧ែࡀᙧᡂࡉࢀ࡚࠸ࡿࡇ࡜

ࡀศ࠿ࡿ㸬

௒ᚋࡣࡇࡢᵝ࡞㏻ᖖࡢⅆ⅖ࡢᴫᛕࢆ㐺⏝࡛ࡁ࡞࠸⇞

↝ࡢᵓ㐀ࢆゎ᫂ࡋ㸪ࡑࡢ⇞↝ࡀ࠸࠿࡟⥔ᣢࡉࢀ࡚࠸ࡿ࠿

ࢆ⌮ゎࡋ㸪ࡑࡢ▱ぢࢆ⇞↝ࣔࢹࣝᵓ⠏࡬࡜ά࠿ࡋ࡚࠸ࡃ ࡇ࡜ࡀᚲせ࡛࠶ࡿ㸬

ᅗ

15

Ⓨ⇕ᒙࡢ⇞ᩱᾘ㈝ᒙ࠿ࡽࡢ஋㞳, a : ஧ḟඖ᩿㠃ෆ

⇞ᩱᾘ㈝㏿ᗘศᕸ, b : Ⓨ⇕ศᕸ.

ࡲ࡜ࡵ

ヲ⣽࡞໬Ꮫ཯ᛂ㐣⛬࠾ࡼࡧὶయࡢ㍺㏦≉ᛶࢆ⤌ࡳ㎸ࢇ

ࡔ㸪ⅆ⅖཯ᛂᖏᵓ㐀࠾ࡼࡧ஘ࢀࡢ୺せᵓ㐀ࢆ࡜ࡽ࠼ࡿࡇ

࡜ࡀ࡛ࡁࡿゎീᗘࢆ᭷ࡍࡿᩘ್ࢩ࣑࣮ࣗࣞࢩࣙࣥ࡟ࡼࡾ㸪 Ỉ⣲ᄇὶᾋࡁୖࡀࡾⅆ⅖ࢆ࡜ࡽ࠼ࡿࡇ࡜࡟ᡂຌࡋࡓ㸬 ྲྀᚓࡉࢀࡓࢹ࣮ࢱࢆゎᯒࡍࡿࡇ࡜࡟ࡼࡾ㸪ᾋࡁୖࡀࡾ

ⅆ⅖ࡣ༢࡞ࡿ୍ࡘࡢⅆ⅖࡛ࡣ࡞ࡃ㸪㸱ࡘࡢⅆ⅖せ⣲ࢆྵ

ࢇ࡛࠸ࡿࡇ࡜ࡀศ࠿ࡗࡓ㸬ࡍ࡞ࢃࡕ㸪

࣭୕㔜ⅆ⅖ⓗ࡞ᵓ㐀ࢆࡶࡘᏳᐃ࡞ඛ➃ⅆ⅖

࣭ᾋࡁୖࡀࡾⅆ⅖እഃ࡟ᓥ≧࡟ᙧᡂࡉࢀࡿᓥ≧ᣑᩓⅆ⅖

࣭ᾋࡁୖࡀࡾⅆ⅖ෆഃ࡛ᄇὶࡢ஘ࢀࡢᙳ㡪ࢆᙉࡃཷࡅ࡚

࠸ࡿෆഃ㐣⃰஘ὶணΰྜⅆ⅖

࡛࠶ࡿ㸬

ඛ➃ⅆ⅖࡟ࡘ࠸࡚ࡣ㸪ࣜࣥࢢ≧ࡢඛ➃ⅆ⅖୰࡟㸪ⅆ⅖ ࡢఏ᧛㏿ᗘ࡜ὶධΰྜẼࡢ㏿ᗘࡀࡘࡾ࠶࠺㒊఩ࡢᏑᅾ࡟

ࡼࡾⅆ⅖఩⨨ࡀᏳᐃ໬ࡉࢀ࡚࠸ࡿࡇ࡜ࡀ᥎ᐃࡉࢀࡓ㸬 ᓥ≧ᣑᩓⅆ⅖࡟ࡘ࠸࡚ࡣ㸪≉␗࡞ᙧ≧ࢆࡶࡘࡶࡢࡢ㸪 ࡑࡢ୰ࡢ⇞↝ࡣᚑ᮶ࡢⅆ⅖ࡢᴫᛕ࡛ㄝ࡛᫂ࡁࡿࡇ࡜ࡀ♧

ࡉࢀࡓ㸬ࡲࡓ㸪ࡑࡢ⏕ᡂࡣෆഃ࡟࠶ࡿ஘ὶ㐣⃰ணΰྜⅆ

⅖ࡢ㠀ᐃᖖ࡞ᣲື࡟ࡼࡿࡶࡢ࡛࠶ࡿࡇ࡜ࡀ♧ࡉࢀࡓ㸬 ෆഃ஘ὶ㐣⃰ணΰྜⅆ⅖࡟ࡘ࠸࡚ࡣ㸪ᚑ᮶ࡢⅆ⅖ࡢᴫ ᛕ࠿ࡽ኱ࡁࡃእࢀࡓⅆ⅖ᵓ㐀ࡀほᐹࡉࢀࡓ㸬ࡑࡇ࡛ࡣ஘

ὶ ࡢࢫࢣ࣮ࣝ࡜ⅆ⅖ᵓ㐀ࡢࢫࢣ࣮ࣝࡀྠ⛬ᗘ࡛࠶ࡾ㸪 ὶయࡢ஘ࢀࡀⅆ⅖ෆ㒊ᵓ㐀࡟ᙳ㡪ࢆ୚࠼ࡸࡍ࠸≧ែ࡟࠶

ࡿ࡜࠸࠺ࡇ࡜ࡀศ࠿ࡗࡓ㸬

௨ୖࡢ㏻ࡾ㸪ᾋࡁୖࡀࡾⅆ⅖ࡢ඲యᵓ㐀࠾ࡼࡧⅆ⅖ᵓ ᡂせ⣲࡟ࡘ࠸࡚㸪ࡑࡢ≉ᚩࡀ࠶ࡿ⛬ᗘ᫂ࡽ࠿࡜࡞ࡗࡓ㸬 ࡋ࠿ࡋ࡞ࡀࡽṧࡉࢀࡓㄢ㢟ࡶከ࠸㸬≉࡟㸪」㞧࡞୕ḟඖ ᵓ㐀ࢆᣢࡘඛ➃ⅆ⅖ࡀ඲య࡜ࡋ࡚࡝ࡢᵝ࡟Ᏻᐃ໬ࡉࢀ࡚

࠸ࡿ࠿㸪ᚑ᮶ࡢⅆ⅖⌮ㄽࢆ㐺⏝࡛ࡁ࡞࠸ෆഃ஘ὶணΰྜ

ⅆ⅖ࡢᵓ㐀ࢆ࠸࠿࡟⌮ゎࡋ㸪ࡑࡢ▱ぢࢆ஘ὶⅆ⅖⌮ㄽ࡬

Ⓨᒎࡉࡏ࡚࠸ࡃ࠿㸪࡜࠸࠺ࡇ࡜ࡀ௒ᚋࡢ㔜せ࡞ㄢ㢟࡜⪃

࠼ࡿ㸬ࡲࡓ,ࢩ࣑࣮ࣗࣞࢩࣙࣥ࡟ࡼࡗ࡚෌⌧ࡉࢀࡓᾋࡁୖ

ࡀࡾ㧗ࡉࡀほᐹࡼࡾࡶ

0.5-1D

ప࠸࡜࠸࠺ၥ㢟ࡶ࠶ࡿ㸬ࡑ ࡢཎᅉ࡜ࡋ࡚ࡣ㸪Ỉ⣲ᄇὶ࡜✵Ẽࡢ㐠ື㔞ΰྜ࡜ணΰྜ

ⅆ⅖ఏ᧛㏿ᗘࡢホ౯⢭ᗘࡀ⪃࠼ࡽࢀ㸪௒ᚋࡇࢀࡽࡢホ౯

⢭ᗘࡢ᳨ウ࠾ࡼࡧ⢭ᗘࢆྥୖࡉࡏࡿィ⟬ᡭἲࢆ㏣ồࡋ࡚

࠸ࡃᚲせࡀ࠶ࡿ㸬

ㅰ㎡

ᮏ◊✲ࡣᩥ㒊⛉Ꮫ┬㛤ᨺⓗ⼥ྜ◊✲ไᗘࠕ஘ὶไᚚ࡟ࡼ

ࡿ᪂ᶵ⬟⇕ὶయࢩࢫࢸ࣒ࡢ๰ฟࠖࡢ୍⎔࡜ࡋ࡚⾜ࢃࢀࡓ

ཧ⪃ᩥ⊩

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