Fiber-Concentration Distributions of Pulp Liquid in the Wake of Dispersion Promoter

ࣃࣝࣉ⧄⥔ศᩓಁ㐍ࣉ࣮ࣟࣔࢱᚋὶ㡿ᇦ࡟࠾ࡅࡿ⧄⥔⃰ᗘศᕸ

ゅ⏣ ຾^*1㸪⸨ᮏ ኴ㑻^*2

Fiber-Concentration Distributions of Pulp Liquid in the Wake of Dispersion Promoter

The flow characteristics of a pulp liquid in the wake of a dispersion promoter were investigated to explore the feasibility of improving the hydraulic headbox of a papermaking machine. This research was undertaken as a basic test of a screen-type model, in which a circular cylinder has been inserted in a channel. The test was performed using a pulp liquid with a fiber concentration ranging from 0.3 to 1.0 wt% under flow velocity conditions of Ua = 0.016 0.74 m/s.

The distributions of the fiber concentration were measured by transmitted light attenuation method. The obtained results are illustrated, and the influence of the flow velocity on the characteristics of the wake behind the cylinder are argued with reference to findings previously reported (Sumida and Fujimoto, 2010). The fiber-concentration distribution changes in the flow direction were large in the section from the cylinder to four times its diameter. The findings provide useful information for the development of hydraulic headboxes.

Keywords: Pulp Liquid Flow, Fiber-Concentration Distribution, Wake, Dispersion Promoter, Headbox, Flow Visualization

㸬ࡣࡌࡵ࡟

⣬ࡢཎᩱ࡛࠶ࡿࣃࣝࣉᾮࡣᮌᮦ≀㉁ࢆỈ࡟⦩⃮ࡋ ࡓࡶࡢ࡛㸪ᢒ⣬ᶵ࡛ࡣᮌᮦ⧄⥔ࢆࡼࡾศᩓࡉࡏࡓ≧ែ

࡛⣬ᖜ᪉ྥ࡟ᆒ୍࡟ὶ㏿࡜ὶྥࢆᥞ࠼࡚࣊ࢵࢻ࣎ࢵࢡ ࢫ㸦ᅗ1ཧ↷㸧࠿ࡽᄇฟࡉࡏࡿࡇ࡜ࡀồࡵࡽࢀ࡚࠸ࡿ㸬

ࡲࡓ㸪࢚ࢿࣝࢠ࣮኱ᾘ㈝⏘ᴗ࡛࠶ࡿ〇⣬ᴗ⏺࡟ࡣ୍ᒙ ࡢ࢚ࢿࣝࢠ࣮๐ῶࡀྉࡤࢀ㸪ฟ᮶ࡿࡔࡅ㧗⃰ᗘᢒ⣬ྍ

⬟࡞࣊ࢵࢻ࣎ࢵࢡࢫࡢ㛤Ⓨࡀᙉࡃᮃࡲࢀ࡚࠸ࡿ㸬ࡑࡢ ࡓࡵ㸪࣊ࢵࢻ࣎ࢵࢡࢫࡢὶ㊰ᵓ㐀࡟ࡘ࠸࡚ࡣ㸪ࣃࣝࣉ

ࡢ⧄⥔ศᩓࢆ㧗ࡵࡿࡓࡵࡢດຊࡸᨵၿࡀᵝࠎ࡞ᙧ࡛ヨ

⾜ࡉࢀ࡚࠸ࡿ^(1)~(4)㸬ࡋ࠿ࡋ࡞ࡀࡽ㸪ࣃࣝࣉᾮࡣప⃰ᗘ

࡛࠶ࡗ࡚ࡶὶື୰࡟ࡣ⧄⥔ྠኈࡀ⤡ࡲࡗ࡚ࣇࣟࢵࢡࢆ

ᙧᡂࡍࡿ࡜࠸࠺จ㞟ᛶࢆ᭷ࡋ࡚࠾ࡾ㸪㧗⃰ᗘ௙ᵝ࡟ྥ

ࡅ࡚ࡢᨵၿࡣ㞴ࡋ࠸ࡢࡀ⌧≧࡛࠶ࡿ⁽⁵⁾㸬

ࡑࡇ࡛㸪࣊ࢵࢲ࣮࠿ࡽ౪⤥ࡉࢀࡿࣃࣝࣉᾮࢆከᏍ⟶

࠿ࡽ࡞ࡿࢳ࣮ࣗࣈࣂࣥࢡࢆ⤒࡚࣊ࢵࢻ࣎ࢵࢡࢫෆࡢศ ᩓ㒊࡬ᑟࡃ㐣⛬࡟࠾࠸࡚ࡶ㸪⧄⥔ศᩓࢆྥୖࡉࡏࡼ࠺

࡜ࡍࡿྲྀࡾ⤌ࡳࡀ 1990 ᖺ௦࡟⾜ࢃࢀ࡚࠸ࡿ^{(1), (6)}㸬 Hauptmannࡽࡢ◊✲⁽⁶⁾࡛ࡣ㸪≀యᚋὶ࡛ࡢ஘ࢀࢆ฼⏝

ࡍࡿࡇ࡜࡬ࡢᴫᛕᅗࡀ✵Ẽὶ࡛ࡢ᪤ ࡢ⤖ᯝࢆᇶ࡟ᥦ

♧ࡉࢀ࡚࠸ࡿ㸬ࡋ࠿ࡋ㸪ࡑࡢᚋ㸪ᙼࡽࡢᴫᛕ᱌ࢆࣇ࢛

࣮ࣟ࢔ࢵࣉࡋࡓ◊✲౛ࡣ㸪ṧᛕ࡞ࡀࡽ⌧ᅾ࡟࠾࠸࡚ࡶ

ぢ࠶ࡓࡽ࡞࠸㸬

ࡇࡢࡼ࠺࡞⌧ἣ࡟㚷ࡳ㸪ᮏ◊✲࡛ࡣὶ㊰ධࡾཱྀ๓࡟

ࢫࢡ࣮ࣜࣥ㸦᱁Ꮚ≧ࡢ㝽㛫㸧ࢆ㏻ࡍࢫࢡ࣮ࣜࣥᆺࢆᛕ 㢌࡟㸪ࡲࡎࡣ᭱ࡶᇶᮏⓗ࡞᱁Ꮚᙧ≧࡛࠶ࡿ෇ᰕࢆ⧄⥔

ศᩓಁ㐍ࣉ࣮ࣟࣔࢱ࡜ࡋ࡚▴ᙧ᩿㠃ࢳࣕࢿࣝෆ࡟༢୍

タ⨨ࡋࡓὶࢀሙ࡟ࡘ࠸࡚㸪ᐇ㝿ࡢࣃࣝࣉᾮࢆ⏝࠸࡚ࡑ ࡢ⃰ᗘศᕸ≉ᛶࢆㄪᰝࡋࡓ㸬

ཎ✏ཷ௜ 2018ᖺ4᭶5᪥

*¹ ㏆␥኱ᏛᕤᏛ㒊 ᶵᲔᕤᏛ⛉ ᩍᤵ㸪ḟୡ௦ᇶ┙ᢏ⾡◊✲ᡤ ᩍᤵ㸦ࠛ739-2116 ᮾᗈᓥᕷ㧗ᒇ࠺ࡵࡢ㎶1␒㸧 E-mail [email protected]

*² ඖ㏆␥኱Ꮫ኱Ꮫ㝔 ࢩࢫࢸ࣒ᕤᏛ◊✲⛉ ࢩࢫࢸ࣒ᕤᏛᑓᨷ ༤ኈ๓ᮇㄢ⛬㸦ࠛ739-2116 ᮾᗈᓥᕷ㧗ᒇ࠺ࡵࡢ㎶1␒㸧 㐃⤡ඛ㸸ゅ⏣ ຾㸦◊✲௦⾲⪅㸧

近畿大学次世代基盤技術研究所報告 Vol. 9（2018）71－75

㸬ᐇ㦂⿦⨨࠾ࡼࡧ᪉ἲ

ᮏᐇ㦂࡛⏝࠸ࡓ⿦⨨ࡢᴫ␎^{(7), (8)}ࢆᅗ2࡟㸪ࡲࡓࢸࢫ ࢺࢭࢡࢩࣙࣥࡢᴫ␎ཬࡧᗙᶆ⣔ࢆᅗ3࡟ࡑࢀࡒࢀ♧ࡍ㸬 ヨ㦂ὶ㊰ࡣ㏱᫂࢔ࢡࣜࣝ〇ࡢᖜ B=70 mm㸪㧗ࡉ H

=20 mmࡢ▴ᙧ᩿㠃ࢆ᭷ࡍࡿ㛗ࡉ⣙2000 mmࡢࢳࣕ

ࢿ࡛ࣝ࠶ࡿ㸬ࡇࡢࢳࣕࢿࣝ࡟ࡣ㸪ධࡾཱྀࡼࡾ1200 mm ࡢ᩿㠃୰ኸ࡟༢୍᱁Ꮚ࡜ࡋ࡚┤ᚄd=15 mmࡢ෇ᰕᆺ ࡢศᩓࣉ࣮ࣟࣔࢱࡀᤄධࡉࢀ࡚࠸ࡿ㸬ࡇࢀࡽࡢㅖඖࡣ㸪

࠶ࡿᐇ⏝ᢒ⣬ᶵࡢᙧ≧ࢆᇶ࡟ࡋ࡚࠸ࡿ㸬

ࣃࣝࣉᾮὶࢀࡢྍど໬࡟ࡣ㸪ග㏱㐣ῶ⾶ἲࢆ⏝࠸ࡓ㸬

ྍど໬⏝ᖹ⾜ග⥺ࡢග※࡜ࡋ࡚ࡣᾮᬗࣉࣟࢪ࢙ࢡࢱ (150W)ࢆ⏝࠸㸪ヨ㦂ὶ㊰ࡢୗ᪉࠿ࡽ ᐃ㒊࡟ᆒ୍࡟↷

ᑕࡋ㸪㏱㐣ῶ⾶ࡋࡓගࢆࢳࣕࢿࣝୖ᪉࠿ࡽࣁ࢖ࢫࣆ

࣮ࢻ࣓࢝ࣛ㸦Photoron〇, FASTCAM-1024PCI㸧࠾ࡼ

ࡧࢹ࢕ࢪࢱ࣓ࣝ࢝ࣛ㸦Nikon〇㸪D100㸧࡛᧜ᙳࡋࡓ㸬

᧜ᙳ⏬ീࡣPC࡟ࡼࡗ࡚グ㘓ࡉࢀࡿ࡜࡜ࡶ࡟㸪ᚋ㏙ࡍ

ࡿ᪉ἲ࡟ࡼࡗ࡚ࣃࣝࣉ⧄⥔⃰ᗘCࡀ⟬ฟࡉࢀࡿ㸬 ౪ヨࣃࣝࣉᾮ࡟ࡣ㸪୍⯡ⓗ࡞ୖ㉁⣬⏝ࡢࢡࣛࣇࢺࣃ

ࣝࣉ(LBKP) ࢆ౑⏝ࡋࡓ㸬ᐇ㦂᮲௳ࡣ㸪ᐇ㝿ࡢᢒ⣬ᶵ

࡛౑⏝ࡉࢀ࡚࠸ࡿࣃࣝࣉ⧄⥔㔜㔞⃰ᗘ Csࢆཧ⪃࡟ Cs

=0.3㹼1.0wt㸣㸪ࢳࣕࢿࣝධཱྀ࡛ࡢ᩿㠃ᖹᆒὶ㏿Ua 㸻

0.016㹼0.74 m/s ࡛⾜ࡗࡓ㸬ࢳࣕࢿࣝෆ࡟タ⨨ࡉࢀ࡚

࠸ࡿࣉ࣮ࣟࣔࢱࡢ෇ᰕ┤ᚄd࡟ᇶ࡙ࡃࣞ࢖ࣀࣝࢬᩘ࡛

ࡣ㸪Red =Ua࣭d/ν =240㹼11000 㸦ν㸸Ỉࡢື⢓ᛶಀᩘ㸧

࡛࠶ࡿ㸬

㸬ග㏱㐣ἲ࡟ࡼࡿࣃࣝࣉ⧄⥔⃰ᗘศᕸࡢホ౯᪉ἲ ᮏ❶࡛ࡣ㸪㏱㐣ගῶ⾶ἲ࡟ࡼࡗ࡚ࣃࣝࣉὶࢀᾮ୰ࡢ

⧄⥔⃰ᗘࢆホ౯ࡍࡿ⡆౽࡞᪉ἲ࡟ࡘ࠸࡚㏙࡭ࡿ㸬ࡇࡢ ᪉ἲࡣ㸪ග㊰୰࡟Ꮡᅾࡍࡿࣃࣝࣉ⧄⥔ࡢᩓ஘࡜྾཰࡟

ࡼࡿῶ⾶≉ᛶ࡟ᇶ࡙࠸࡚࠾ࡾ㸪㏱㐣ࡋࡓගࡢᙉᗘࢆ㍤

ᗘ࡜ࡋ࡚ ᐃࡍࡿࡇ࡜࡟ࡼࡗ࡚㸪ࡑࡢග㊰࡟ࢃࡓࡿ㔜 㔞⃰ᗘࡀᚓࡽࢀࡿ㸬

ᅗ4ࡣ㸪ࢳࣕࢿࣝ୰ᚰ㍈ࢆྵࡴx㸫y㠃ෆ࡟ᖜ60 mm

×㛗ࡉ100 mmࡢ᳨ᰝ㡿ᇦࢆ࡜ࡗ࡚㸪඘ศ᧠ᢾࡉࢀࡓ

౪ヨࣃࣝࣉᾮ⃰ᗘCs࡜᳨ᰝ㡿ᇦෆࡢ㍤ᗘ್Iࡢᖹᆒ್

IA࡜ࡢ㛵ಀࢆ♧ࡋࡓࡶࡢ࡛࠶ࡿ㸬ᅗࡣCs = 0.3wt㸣࡛

ࡢᖹᆒ㍤ᗘࡢ್IA,0.3࡛ࡶࡗ࡚㝖ࡋ࡚♧ࡉࢀ࡚࠸ࡿ㸬ࡇ ࡢ㛵ಀࡣ㸪౪ヨࣃࣝࣉᾮ⃰ᗘࡢ ᐃ⠊ᅖ㸦0.03 ≤ Cs≤ 3wt%㸧࡟࠾࠸࡚ࡣ㸪ᅗ୰ࡢᐇ⥺࡛♧ࡍḟᘧࡢࡼ࠺࡞⡆

༢࡞ᐇ㦂ᘧ࡛⾲ࡉࢀࡿࡇ࡜ࡀศ࠿ࡿ㸬

IA /IA,0.3㸻(Cs /Cs,0.3)^-b (1)

࡞࠾㸪b ࡢ್ࡣ ᐃ⣔࠾ࡼࡧග㊰㛗࡞࡝࡟౫Ꮡࡍࡿಀ

ᩘ࡛࠶ࡿ㸬

10^-2 10^-1 10⁰ 10¹ 10^-1

10⁰ 10¹

C /Cs s,0.3

I /IA A,0.3

ᅗ1㸬ࣁ࢖ࢻࣟࣜࢵࢡᆺ࣊ࢵࢻ࣎ࢵࢡࢫ

ᅗ2㸬ᐇ㦂⿦⨨ᴫ␎ᅗ^{(7), (8)}

ᅗ3㸬ヨ㦂ὶ㊰࡜ᗙᶆ⣔ ᅗ4㸬ග㏱㐣ῶ⾶ἲ࡟ࡼࡿ㍤ᗘ࡜⃰ᗘࡢ㛵ಀ

ᮏホ౯᪉ἲ࡟࠾࠸࡚ࡣ㸪࠶ࡿⅬ(x㸪y)࡛ࡢᒁᡤ⃰ᗘ

C(x㸪y)࡜㍤ᗘ್ I(x㸪y)࡜ࡢ㛵ಀ࡟ࡣ㸪ୖᘧ࡜඲ࡃྠ

ࡌ㛵ಀࡀᡂࡾ❧ࡘࡶࡢ࡜ࡋ࡚

C (x, y)/Cs㸻㹹I (x, y)/Is㹻^-1/㹠 (2)

࡜࠾ࡃ㸬ࡇࡇ࡛㸪IsࡣCs್࡟ᑐᛂࡍࡿィ⟬㡿ᇦෆࡢ㍤

ᗘࡢᖹᆒ್࡛࠶ࡿ㸬ࡕ࡞ࡳ࡟㸪ᅗ 4 ࡟♧ࡍ Cs 㸻 0.3wt㸣ࡢሙྜ㸪bࡢ್ࡣ0.53࡛࠶ࡿ㸬

㸬⤖ᯝ࡜⪃ᐹ

ⴭ⪅ࡽࡣඛࡢሗ࿌⁽⁷⁾࡟࠾࠸࡚㸪┿┤࡞ࢳࣕࢿࣝෆࡢ

ࣃࣝࣉᾮࡢὶࢀ≉ᛶࡣ㸪⧄⥔ᣲືࡢほⅬ࡟ࡼࡾ5ࡘࡢ

ࣃࢱ࣮ࣥ(PatternϨ㹼Ϭ)࡟኱ู࡛ࡁࡿࡇ࡜ࢆ᫂ࡽ࠿

࡟ࡋ࡚࠸ࡿ㸬ᅗ5ࡣ㸪୍㎶ࡢ㛗ࡉࡀ20 mmࡢṇ᪉ᙧ

᩿㠃ࢳࣕࢿࣝෆࡢὶࢀࢆ኱ูࡋࡓࡶࡢ࡛࠶ࡿ㸬ࢳࣕࢿ

ࣝෆ࡟࠾ࡅࡿࣃࣝࣉᾮࡢὶࢀᵝᘧࡣ㸪᩿㠃ᖹᆒὶ㏿Ua

࡜౪ヨࣃࣝࣉᾮࡢ⃰ᗘCs࡟౫Ꮡࡋ࡚ኚ໬ࡍࡿ⁽⁸⁾㸬

ᚋὶࡢ⃰ᗘศᕸ࡟ཬࡰࡍᖹᆒὶ㏿ࡢᙳ㡪 ᮏሗ࿌࡛ࡣ㸪Cs=0.3wt%ࡢࣃࣝࣉᾮࢆྲྀࡾୖࡆ㸪≉

ᚩⓗ࡞ᚋὶࣃࢱ࣮ࣥࡀ⏕ࡌࡓ 3 ࡘࡢᖹᆒὶ㏿ Ua࡟ࡘ

࠸࡚ࡢ⤖ᯝࢆᅗ♧ࡍࡿ㸬ࡇࢀࡽࡢὶ㏿᮲௳ࡣ㸪ᅗ5୰

࡟ࡣ۔ࡢグྕ࡛♧ࡉࢀ࡚࠸ࡿ㸬ᅗ6࠾ࡼࡧᅗ7ࡣ㸪ࡇ

ࢀࡽࡢ᮲௳ୗ࡟࠾ࡅࡿ⃰ᗘศᕸ࡞ࡽࡧ࡟y㍈ୖ࡟࠾ࡅ

ࡿ⃰ᗘࡢ᫬㛫ᖹᆒ್Ctaࡢศᕸࢆ♧ࡋࡓࡶࡢ࡛࠶ࡿ㸬

ࡲࡎ㸪ࢳࣕࢿࣝෆࢆపὶ㏿࡛ࣃࣝࣉ⧄⥔ࡀࣇࣟࢵࢡ

࡜ ࡋ ࡚ ୍ య ࡜ ࡞ ࡗ ࡚ ὶ ࢀ ࡿ ࡼ ࠺ ࡞ ሙ ྜ 㸦 ᅗ6(a)㸪 7(a):Ua =0.016 m/s, Red =250㸹Case A㸧㸪ࣉ࣮ࣟࣔࢱ

෇ᰕ๓᪉࡛ࡣࣃࣝࣉ⧄⥔ሢࡀࡸࡸワࡲࡗ࡚ࣃࣝࣉᾮ⃰

ᗘࡣ㧗ࡃ࡞ࡿ(x/d=-1)㸬ࡇࡢ㧗⃰ᗘࣃࣝࣉᾮࡣ෇ᰕ๓ 㠃࡛ࡣ⾲㠃࡟ἢࡗ࡚ὶࢀ㸪y ㍈ୖ෇ᰕഃ㠃ቨ㏆ࡃ࡛

Cta/Csࡢศᕸࡣ✺ฟࡋࡓᙧ≧ (x/d=0) ࢆ♧ࡋ࡚ὶୗ

ࡍࡿ㸬୍᪉㸪෇ᰕ⾲㠃ࡢ๓᪉࠿ࡽࡣ⃰ᗘࡢప࠸Ỉ⎔㒊 ࡢὶయࡀ㸪෇ᰕࡢᚋ⦕㒊࡟ὶࢀ㎸ࢇ࡛ࡼ࡝ࡳ㡿ᇦࢆᙧ ᡂࡍࡿ(x/d≈0.5㹼1)㸬ࡑࡢࡓࡵ㸪෇ᰕ┤ᚋ࡛ࡣ Ctaࡣ

࠿࡞ࡾప࠸್ࢆ♧ࡋ㸪㹷㍈ୖࡢศᕸࡣ኱ࡁࡃ❑ࢇࡔᙧ

≧࡜࡞ࡿ(ᅗ 7(a))㸬ࡇࡢࡼ࡝ࡳ㡿ᇦࡢ࿘㎶࡛ࡣ㸪จ㞟 ࡋࡓ㧗⃰ᗘࣃࣝࣉ⧄⥔ሢࡀࢳࣕࢿࣝ୰ᚰ㍈࡟ᐤࡾྜࡗ

࡚ὶୗࡍࡿࡓࡵ㸪Ctaศᕸᙧ≧ࡣࡸࡸᖹᆠ໬ࡍࡿ㸦ᅗ 7(a)㸪x/d=1.5㸧㸬ࡋ࠿ࡋ㸪ప⃰ᗘࡢࡼ࡝ࡳὶయࡣ➽≧

࡜࡞ࡗ࡚x㍈࡟ἢࡗ࡚ᦂࡽࡂ࡞ࡀࡽὶࢀ㸪x/d>2ࡢx

㍈ୖ࡛ࡣCta /Csࡣ࡯ࡰ0.9ࡢ್ࢆྲྀࡗ࡚ὶࢀ᪉ྥኚ໬

ࡣᑠࡉࡃ࡞ࡿ㸬

ᅗ5㸬ࢳࣕࢿࣝෆࣃࣝࣉᾮࡢὶࢀࣃࢱ࣮ࣥ

ࡢᶍᘧ⁽⁷⁾㸦۔㸸ᅗ♧᮲௳㸧

Flow

(a) Case A (Ua =0.016 m/s)

(b) Case B (Ua =0.067 m/s)

ᅗ 㸬ᚋὶࡢ⃰ᗘศᕸ

0 0.3 0.6 wt% (c) Case C (Ua =0.74 m/s)

ᖹᆒὶ㏿ࢆḟ➨࡟ቑࡍ࡜㸪෇ᰕ๓ഃ⾲㠃ୖࡢỈ⎔㒊 ࡢప⃰ᗘὶయ㔞ࡶቑ኱ࡋ㸪ὶࢀࡣ෇ᰕ⾲㠃࠿ࡽ๤ࡀࢀ

࡚ࡃࡿ㸬࡜ྠ᫬࡟㸪ഃቨᐤࡾࡢ㧗⃰ᗘࣃࣝࣉ⧄⥔ࡣỈ

⎔ὶయࡢ๤㞳ὶࢀ࡟ἢࡗ࡚ᚋ᪉࡬㐠ࡤࢀ㸪࠶ࡿ✀ࡢ๤

㞳ὶ⥺㸦➽⥺㸧ࢆᙧᡂࡍࡿࡼ࠺࡟࡞ࡿ(Ua =0.027㹼 0.044 m/s,Red =400㹼700)㸬ࡑࡋ࡚㸪෇ᰕᚋ᪉ࡢ➽⥺

ࡣᚋὶ㡿ᇦࢆᙧᡂࡋ㸪ࡑࡢᖜࡣx=4d௜㏆ࡲ࡛ࡣ⣙1d

࡜࠶ࡲࡾᗈࡀࡽ࡞࠸ࡀ㸪4d௨㝆ࡢୗὶ࡛ࡣ኱ࡁࡃᗈࡀ

ࡿ㸦ᅗ6(b)㸪7(b)㸸Ua =0.067 m/s㸹Case B㸧㸬ࡇࡢ➽

⥺ࡣ≧ἣࢆ෇ᰕᚋὶ㡿ᇦ࡜እഃࡢࢳࣕࣥࣝ୺ὶ࡜࡟஧

ศ໬ࡍࡿࡼ࠺࡟࡞ࡿ㸬ࡍ࡞ࢃࡕ㸪෇ᰕᚋ⦕࡟ࡣࣃࣝࣉ

⧄⥔ࡀሁ✚ࡋࡓ㧗⃰ᗘࡼ࡝ࡳ㡿ᇦࡀᙧᡂࡉࢀ㸪x/d= 0.5࡛ࡣCtaࡀCsࡢ1.5ಸࢆ㉸ࡍ್ࢆ♧ࡍ㸬௨㝆ࡢୗ

ὶ㒊࡛ࡣ ิࡀⓎ⏕ࡋ࡚࠾ࡾ㸪ࡇࡢ 㐠ືࡣࣃࣝࣉ⧄

⥔ࢆᕳࡁ㎸ࢇ࡛ࡺࡗࡃࡾὶୗࡋ㸪ὶࢀ୰ᚰ㍈ୖࡢ Cta

ࡣ௚ࡢὶ㏿᮲௳࡟ẚ࡭࡚᭱ࡶ኱ࡁ࠸್ࢆ♧ࡍ㸬ࡋࡓࡀ ࡗ࡚㸪y㍈ୖࡢCtaࡢศᕸࡣ㸪෇ᰕࡢ┤ᚋ࡛➽⥺ࡀỈ⎔

ὶయ࠿ࡽ࡞ࡿx/d≈0.5㹼1࡛ࡣy/d≈±0.6࡛ᒁᡤⓗ࡟❑

ࡳ㸪୰ᚰ㍈ୖ࡛✺ฟࡋࡓᙧ≧ࢆ♧ࡍ㸬ࡑࡋ࡚㸪ࡑࡢୗ

ὶ㒊࡛ࡣ➽⥺ࡢ㡿ᇦࡀ㧗⃰ᗘὶయ࡜ΰࡊࡾྜࡗ࡚㸪⃰

ᗘࡢCtaࡣCs್࡟㏆࡙࠸࡚ᚋὶ㒊ࡢእഃ࡛ࡣẚ㍑ⓗᖹ ᆠ࡞㸪ෆഃࡢ୰ኸ㒊࡛ࡣ⭾ࡽࢇࡔᙧ≧࡟⛣⾜ࡍࡿ(x/d= 3.5)㸬ࡉࡽ࡞ࡿୗὶ㒊࡛ࡢศᕸࡣ㸪Ⓨ㐩ࡋࡓࢳࣕࢿࣝ

ෆࡢ⃰ᗘศᕸ⁽⁷⁾࡟ḟ➨࡟ኚࢃࡿ㸬

ࡉࡽ࡟ὶ㔞ࢆቑࡍ࡜㸦ᅗ6(c)㸪7(c)㸸Ua =0.74 m/s,Red

=11000㸹Case C㸧㸪ࢳࣕࢿࣝ඲యࡢὶࢀࡣ஘ὶ໬ࡍࡿ

࡜࡜ࡶ࡟㸪ࣃࣝࣉ⧄⥔ࡣࢳࣕࢿࣝෆ࡛࡯ࡰ୍ᵝ࡟ศᩓ ࡍࡿࡼ࠺࡟࡞ࡿ㸬ࡋࡓࡀࡗ࡚㸪x㍈ୖࡢCta/Csࡢ್ࡣ㸪

෇ᰕᚋ⦕┤ᚋ(x/d≈0.5)࡛ࡣ 1 ࡼࡾࢃࡎ࠿࡟ᑠࡉ࠸್

ࢆ♧ࡍࡀ㸪1dୗὶ࡛ࡣ࡯ࡰ1࡟㏆࠸್ࢆ♧ࡋ㸪y㍈ୖ

ࡢCtaࡣᖹᆠ࡞ᙧ≧࡜࡞ࡿ㸬 ⃰ᗘࡴࡽ

ᐇᶵࡢᢒ⣬ᶵ࡟࠾࠸࡚ࡣ㸪⣬ࡢရ㉁ྥୖࡢࡓࡵ࡟ࡣ

ࣃࣝࣉᾮࢆ⃰ᗘࡴࡽࡢᑠࡉ࠸≧ែ࡛㸪ࡋ࠿ࡶὶ㏿ࢆᖜ ᪉ྥ࡟୍ᵝ࡞ศᕸ࡛࣊ࢵࢻ࣎ࢵࢡࢫ࠿ࡽ࣡࢖࣮ࣖࣃ࣮

ࢺ࡬㏦ฟࡍࡿࡇ࡜ࡀᮃࡲࡋ࠸㸬ࡑࡇ࡛㸪ࢳࣕࢿࣝෆ࡟

෇ᰕࢆタ⨨ࡋࡓࡇ࡜࡟ࡼࡿࡇࢀࡽࡢᖜ᪉ྥࡢࡴࡽࡢᗘ

ྜ࠸࡟ࡘ࠸᳨࡚ウࡍࡿ㸬ࡑࡢᗘྜ࠸ࢆy ㍈ୖࡢCtaศ ᕸࢆ⏝࠸࡚㸪ḟᘧ࡛ホ౯ࡍࡿ㸬

ܧ_௖ ൌ ͳ

ܤܥ_௦න ȁܥ_௧௔െ ܥ_௦ȁ݀ݕ

஻ ଶΤ

ି஻Ȁଶ

ᅗ8࡟㸪ୖᘧࡢ⤖ᯝࢆ♧ࡍ㸬Ecࡣ㸪ࡑࡢ್ࡀᑠࡉ࠸

࡯࡝ࢳࣕࢿࣝᖜ᪉ྥࡢᆒ୍ᛶࡀ㧗࠸ࡇ࡜ࢆ♧ࡋ࡚࠸ࡿ㸬 Ecࡢὶࢀ᪉ྥኚ໬ࡣ෇ᰕᚋ᪉x≈4dࡲ࡛ࡢ༊㛫࡛኱ࡁ ࡃ㸪௨㝆ࡢୗὶ࡛ࡣࡑࡢኚ໬ࡣᑠࡉ࠸ࡇ࡜ࡀศ࠿ࡿ㸬

ࡲࡎ㸪పὶ㏿ࡢCase A࡛ࡣὶయࡣ๛యⓗ࡟ὶୗࡍࡿ

ᰦὶ࡜࡞ࡗ࡚࠾ࡾ㸪෇ᰕᚋ᪉┤ࡄ࡟Ecࡣᛴῶࡋ㸪ศᕸ ࡣᖹᆠ໬ࡍࡿ㸬୰ὶ㏿ࡢCase B࡛ࡣ㸪෇ᰕ┤ᚄ࡟┦

ᙜࡍࡿᖜࡢᚋὶࡀ࠿࡞ࡾᚋ᪉ࡲ࡛Ꮡᅾࡋ㸪௚ࡢὶࢀ

Case࡜ẚ࡭࡚Ecࡣࡶࡗ࡜ࡶ኱ࡁ࠸್ࢆ࡜ࡿ㸬ὶ㏿ࡢ 㧗࠸Case C࡛ࡣ㸪Ecࡣᮏᐇ㦂ࡢሙྜCtaศᕸ࡟೫ࡾ

ࡀ⏕ࡌ࡚x=3dୗὶ࡛ࡣⓎ㐩ࡋࡓࢳࣕࢿࣝෆࡢ್ࡼ

ࡾࡶ኱ࡁ࠸್ࢆ♧ࡋ࡚࠸ࡿ㸬

-2 -1 0 1 2

3

1 1.5 2 4 5 6 7

-1 0 0.5

C_ta/C_s

x/d

y/d

0 1 2

x/d 0

7 2

0.5 1

=-1 1.5 3 4 5 6

(a) Case A (Ua =0.016 m/s)

-2 -1 0 1 2

3

1 1.5 2 4 5 6 7

-1 0 0.5

C_ta/C_s

x/d

y/d

0 1 2 x/d 5

3 4 2 1 1.5 0.5

-1 =0 6 7

(b) Case B (Ua =0.067 m/s)

-2 -1 0 1 2

3

1 1.5 2 4 5 6 7

-1 0 0.5

C_ta/C_s

x/d

y/d

0 1 2

4 3 1.5 2

1 -1 0.5

x/d=0

7

5 6

(c) Case C (Ua = 0.74 m/s) ᅗ7㸬᫬㛫ᖹᆒ⃰ᗘCtaࡢy㍈ୖศᕸ

ᅗ8㸬⃰ᗘศᕸࡢ୍ᵝᛶ

(3)

㸬࠾ࢃࡾ࡟

ᢒ⣬ᶵ࣊ࢵࢻ࣎ࢵࢡࢫὶ㊰࡛⧄⥔ศᩓࢆᅗࡿࡓࡵ࡟

タࡅࡿࢫࢡ࣮ࣜࣥᆺࡢࣔࢹࣝᇶ♏ᐇ㦂࡜ࡋ࡚㸪෇ᰕᆺࣉ

࣮ࣟࣔࢱࢆタ⨨ࡋࡓࢳࣕࢿࣝෆࣃࣝࣉᾮὶࢀ࡟ࡘ࠸࡚

ග㏱㐣ῶ⾶ἲ࡟ࡼࡿ⃰ᗘศᕸ㏿ᗘ ᐃ࡟ࡼࡗ࡚ᚋὶ≉

ᛶࢆㄪᰝࡋࡓ㸬ࡑࡢ⤖ᯝ㸪ࣇ࣮ࣟࢩ࣮ࢺ࠿ࡽ࡞ࡿศᩓ㒊 ධࡾཱྀ࡟タ⨨ࡍࡿࢫࢡ࣮ࣜࣥᆺࡢሙྜ㸪㐺ᗘ࡞஘ࢀస⏝

࡛⧄⥔ࣇࣟࢵࢡࢆࡲࡎࡣศゎࡋ㸪ࣇ࣮ࣟࢩ࣮ࢺ㛫࡛ศᩓ

≧ែ࡜ὶ㏿ࢆᩚ࠼ࡿࡇ࡜ࢆ⪃࠼ࡿ࡜㸪ὶࢀ᪉ྥኚ໬ࡀẚ

㍑ⓗ⦆ࡸ࠿࡞Case Bࡢࡼ࠺࡞ὶࢀ᮲௳ୗ࡛ຠᯝࡀ㧗࠸

࡛࠶ࢁ࠺࡜᥎ᐹࡉࢀࡿ㸬

ࡲࡓ㸪ᮏ◊✲࡛ࡣࢫࢡ࣮ࣜࣥᆺࡢᇶ♏◊✲࡜ࡋ࡚༢୍

෇ᰕࢆᤄධࡋࡓᚋὶ≉ᛶࢆㄪᰝࡋࡓࡶࡢ࡛࠶ࡿࡀ㸪௒ᚋ ࡣ」ᩘࡢ෇ᰕࢆタ⨨ࡋࡓὶ㊰࡟ࡘ࠸࡚ࡶ㸪ᘬࡁ⥆ࡁㄪᰝ ࡍࡿࡇ࡜ࡀᚲせ࡛࠶ࡿ㸬

ㅰ㎡

ᮏ◊✲࡟ᙜึ㸪᥼ຓࢆ㡬࠸ࡓ୕⳻㔜ᕤᴗओᗈᓥ◊✲ᡤ㸪 ヨ㦂ࣃࣝࣉᾮࢆᥦ౪㡬࠸ࡓ⋤Ꮚ〇⣬ओ㉺๓࿴ᗈẶ࡞ࡽ

ࡧ࡟⋤Ꮚ࣐ࢸࣜ࢔ओᖹᑿྩ⏕Ặ㸪᭷┈࡞ຓゝࢆ㡬࠸ࡓ Valmetओ㕥ᮌ⠇ኵẶࢆࡣࡌࡵ㉥⃝㈗ᚿ࣭⸨ᮌᜨ୍ࡢ୧Ặ

࡟ㅰពࢆ⾲ࡍࡿ㸬ࡲࡓ㸪ᮏᐇ㦂࡟ᦠࢃࡗࡓᙜ᫬ࡢ◊✲ᐊ Ꮫ⏕ࡢኴ⏣₶࣭㜿㒊ᚁྐࡢ୧ྩ࡟ࡶឤㅰࡋࡲࡍ㸬࡞࠾㸪 ᮏ◊✲ࡢ୍㒊ࡣ㸪⛉Ꮫᢏ⾡᣺⯆ᶵᵓ(JST)ᆅᇦ࢖ࣀ࣮࣋

ࢩࣙࣥ๰ฟ⥲ྜᨭ᥼஦ᴗࠕࢩ࣮ࢬⓎ᥀ヨ㦂ࠖ࡞ࡽࡧ࡟⛉

Ꮫ◊✲㈝⿵ຓ㔠㸦ㄢ㢟␒ྕ26420127㸧ࡢຓᡂ࡟ࡼࡗ࡚

ᐇ᪋ࡉࢀࡓࡶࡢ࡛࠶ࡿࡇ࡜ࢆグࡋ㸪ឤㅰࡢពࢆ⾲ࡍࡿ㸬

ཧ⪃ᩥ⊩

(1)

(2)

(3)

(4)

Hauptmann, E., Vyse, R. and Mardon, J., ͆The Wake Effect as Applied to Modern Hydraulic Headboxs: Part 2͇, Pulp & Paper Canada, Vol.

91 (10), 369-376 (1990)

Lundell, F., S¸derberg, L. D. and Alfredsson, P.

H.,͆Fluid Mechanics of Papermaking͇, Ann.

Rev. Fluid Mech., Vol. 43, 195-217 (2011)

Cotas, C., Asendrych, D., Garcia, F., Faia, P. and Rasteiro, M. G., ͆CFD Simulation of a Turbulent Fiber Suspension Flow: A Modified Near-Wall Treatment͇, Eng. Appl. Comput.

Fluid Mech., Vol. 9 (1), 233-246 (2015)

Takano, Y., ͆History and State-of-the-Art Technology of Paper Machine Wet Section͇, Japan Tappi J., Vol. 69 (9), 920-936 (2015)

(5)

(6)

(7)

(8)

H¦m¦l¦inen, J., Lindstr¸m, S. B., H¦m¦l¦inen, T.

and Niskanen, H., ͆Papermaking Fibre-Suspension Flow Simulations at Multiple Scales͇, J. Eng.

Math., Vol. 71, 55-79 (2011)

Hauptmann, E., Vyse, R. and Mardon, J., ͆The Wake Effect as Applied to Modern Hydraulic Headboxs: Part 1͇, Pulp & Paper Canada, Vol.

91 (9), 357-364 (1990)

Sumida, M. and Fujimoto T., ͆Measurement of Fiber-Concentration and Flow Characteristics of Pulp-Suspension in a Duct͇, Trans. Jpn. Soc.

Mech. Eng. Ser. B, Vol. 76 (761), 35-41 (2010) Sumida, M. and Fujimoto T., ͆Flow Properties of Wood Pulp-fiber Suspensions in Circular Pipes͇, Trans. Jpn. Soc. Mech. Eng., Vol. 81 (823), (2015) (doi: 10.1299/transjsme.14-00242)