Analysis of Shallow Water Flow in Curved Channel Using Dispersion Stresses Method

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**** ᕽᬙ⦺Ʊ Õᖅ⪹ĞŖ⦺ᇡ ၶᔍ ⬥ ᩑǍᬱ ([email protected])

Received February 13, 2013/ revised March 14, 2013/ accepted April 17, 2013

Copyright ⵑ 2013 by the Korean Society of Civil Engineers

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0)

ǣǣȀȀǤǤȀͳͲǤͳʹ͸ͷʹȀǤʹͲͳ͵Ǥ͵͵ǤͷǤͳ͹ͺͷ

ǤǤǤ

⍂♮ⴏᷣ≓ⴂ#ⴲⱧ㬚#ኟ⛞⟖Ḛ⮎⛚ⴖ#㉚⟖㴎ὂ#㬲⛛

৉ఢֽȵছଵ଀ȵ׌೾଀ȵੲ୨ָ

Song, Chang Geun, Seo, Il Won, Kim, Tae Won, Ahn, Jungkyu****

Analysis of Shallow Water Flow in Curved Channel Using Dispersion Stresses Method

ABSTRACT

Most of the previous models for analysis of shallow water flow assumed the uniform velocity distributions over the flow depth so that they produced incorrect velocity prediction at meandering part due to the ignorance of secondary current. In this study, the vertical velocity profiles in longitudinal and transverse direction were decomposed as the mean and variation components, which resulted in additional dispersion stresses terms in momentum equations. The proposed model were applied at the channels with 30 ô , 90 ô , 270 ô bends, and shallow water flow in curved channel was analyzed using dispersion stresses. The dispersion stresses acted as a sink or source in the momentum equations, which caused the transverse convection of momentum to shift from the inner bank to the outer bank.

Key words : Curved channel, Secondary current, Velocity profile, Dispersion stresses method, Shallow water equations, Finite element model

Ⅹಾ

ʑ᳕ݡᇡᇥ᮹⃽ᙹ⮱෥⧕ᕾ༉⩶ᨱᕽ۵ᩑḢႊ⨆ᮝಽɁᯝ⦽ᮁᗮᮥaᱶ⦹ᩡʑভྙᨱ⦹⃽อłᇡᨱᕽᯕ₉ඹ᮹ᩢ⨆ᮥŁಅ⦹ḡ༜⦹Łᇡ ᱶ⪶⦽⮱෥⧕ᕾđŝෝࠥ⇽⦹ᩡ݅. ᅙᩑǍᨱᕽ۵᳦⬂ႊ⨆ᮁᗮ᮹ᩑḢᇥ⡍ෝ⠪Ɂsŝᯕಽᇡ░᮹ᄡ࠺పᮝಽᇥ⧁⦹ᩍᯕsॅᮥᬕ࠺ప

ႊᱶ᜾ᨱݡ᯦⦹ᩍᔾᖒࡹ۵⇵aᱢᯙ⧎ᯙᇥᔑ᮲ಆᮥ⡍⧉⦹۵ᙹ⊹༉⩶ᮥ}ၽ⦹ᩡ݅. ᱽᦩࡽ༉⩶ᮥ30 ô , 90 ô , 270 ô ᮹łශᮥaḡ۵ᙹಽ ᨱᱢᬊ⦹ᩍᇥᔑ᮲ಆᮥᯕᬊ⦽łᖁᙹಽᨱᕽ᮹⃽ᙹ⮱෥ᮥᙹ⊹༉᮹⦹ᩡ݅. ༉᮹đŝ, ᬕ࠺పႊᱶ᜾ᨱ⡍⧉ࡽᇥᔑ᮲ಆ⧎ᮡᔾᖒ/ᗭ໙ŝz

ᮡᩎ⧁ᮥ⦹ᩍ, อł᮹ԕ⊂ᨱᕽ᫙⊂ᮝಽ⬂ႊ⨆ᬕ࠺పᮥᯕ࠺᜽┅íࡹအಽᇥᔑ᮲ಆᮥ⡍⧉⦹ḡᦫ۵Ğᬑᅕ݅ᱶ⪶⦽ᙹ⊹༉᮹đŝෝᱽ

᜽⦹۵äᮝಽၾ⩡Ჭ݅.

áᔪᨕ łᖁᙹಽ, ᯕ₉ඹ, ᮁᗮᇥ⡍, ᇥᔑ᮲ಆჶ, ⃽ᙹႊᱶ᜾, ᮁ⦽᫵ᗭ༉⩶

1. ᕽು

ᯱᩑ⦹⃽᮹อłᇡᨱᕽ۵ᬱᝍಆ, ⬂ႊ⨆ᙹ໕Ğᔍᨱ᮹⦽ᦶಆ₉, ӽඹᨱ᮹⦽ᱥ݉ಆ॒᮹ᔢ⪙᯲ᬊᮝಽᯙ⧕ᙹ⢽໕ᨱᕽ᮹⬂ႊ⨆

ᮁᗮᮡłශ᮹ ᫙⊂ᮥ⨆⦹Ł, ၵ݆ ᇡɝᨱᕽ᮹⬂ႊ⨆ᮁᗮᮡ อł᮹ԕ⊂ᮥ⨆⦹ᩍ, ᵝ⮱෥ႊ⨆ᨱ ᩑḢᯙ݉໕ᮥ঑௝ Fig. 1ŝ

zᮡ ӹᖁ⩶ ⮱෥ᯙ ᯕ₉ඹa ၽᔾ⦽݅. Tominaga᪡ Nezu(1991)۵ ⦹⃽ ḢᖁǍe ԕᨱᕽ᮹ ᯕ₉ඹ۵ ᳦ႊ⨆ ᮁᗮ᮹ ↽ݡ 4%

սėॡ

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Fig. 1. Velocity Structure for Curved Open-Channel Flow (Song et al., 2012)

ᱶࠥ᮹Ⓧʑෝaḥ݅Łᱽ᜽⦹ᩡŁ, Shiono᪡Muto(1998)۵

ᔍ⧪⦹⃽ ԕᨱᕽ᮹ ᳦ႊ⨆ ᮁᗮŝ እƱ⦹ᩍ ᯕ₉ඹ᮹ Ⓧʑa

ݡఖ10-16% ᱶࠥ᮹sᮥw۵݅Łᵝᰆ⦹ᩡ݅. ᯕ᪡zᯕᯕ₉ ඹ۵ ᵝ ⮱෥ᨱ እ⧕ ə Ⓧʑa ᯲ḡอ ᵝ ⮱෥ ᮁᗮ Ǎ᳑ෝ

ᄡ⪵᜽┅໑ᮁᔍᯕᘂ, ⦹ᔢၰᱽႊ⋉᜾, ⦹ᔢḡ⩶ᄡ⪵॒ᨱ

ⓑᩢ⨆ᮥၙ⊽݅. ੱ⦽᪅ᩝ⪶ᔑ᮹Ğᬑ⦹⡎ႊ⨆ᮝಽ᪥ᱥ⯩

⪝⧊ࡹʑᱥʭḡ᮹ᇥᔑŝᱶᨱᕽᯕ₉ඹaၙ⊹۵ᩢ⨆ᮡๅᬑ

ᵲ᫵⦹݅.

ʑ᳕ݡᇡᇥ᮹⃽ᙹ⮱෥⧕ᕾ༉⩶ᨱᕽ۵ᩑḢႊ⨆ᮝಽɁᯝ⦽

ᮁᗮᮥaᱶ⦹ᩡʑভྙᨱ⦹⃽อłᇡᨱᕽᯕ₉ඹ᮹ᩢ⨆ᮥŁಅ

⦹ḡ༜⦹Łᇡᱶ⪶⦽⮱෥⧕ᕾđŝෝࠥ⇽⦹ᩡ݅. ঑௝ᕽʑ᳕᮹

༉⩶ᨱᕽ۵ྜྷญᱢᮝಽ᪽łࡽӽඹ࠺ᱱᖒĥᙹෝ᯦ಆ⦹ᩍłᖁ ᇡᨱᕽ᮹ᮁᗮǍ᳑ෝ฿⇵ಅ۵᜽ࠥaኩჩ⦹ᩡ݅. ੱ⦽ᱶƱ⦽

ӽඹ༉⩶ᮥᯕᬊ⦹ᩍ౩ᯕסᷩ᮲ಆᮥĥᔑ⦹ᩡḡอᯕ₉ඹ᮹⬉

ŝෝၹᩢ⦹ḡᦫᦥอłᇡᨱᕽ᮹ᝅᱽᮁᗮᮥ᪍ၵ෕í༉᮹⦹ḡ

༜⦹۵2₉ᬱ༉⩶ࠥ݅ᙹ᳕ᰍ⦽݅(Ye᪡McCorquodale, 1997;

Jia᪡ Wang, 1998; Wilson ॒, 2002).

ᅙᩑǍᨱᕽ۵3₉ᬱReynolds ႊᱶ᜾ᮥᙹᝍᱢᇥ⦹۵ŝᱶᨱ ᕽ Ɂᯝ⦽ ᮁᗮᇥ⡍ෝ aᱶ⦹ᩍ อłᇡᨱᕽ ᯕ₉ඹa ᵝ ⮱෥

ᮁᗮᨱ ၙ⊹۵ ᯕᘂ᮹ ᩢ⨆ᮥ ྕ᜽⦽ ʑ᳕ ݡᇡᇥ᮹ ᩑǍ᪡۵

ݍญ, ᳦⬂ႊ⨆ᮁᗮ᮹ᩑḢᇥ⡍ෝ⠪Ɂsŝᯕಽᇡ░᮹ᄡ࠺పᮝ ಽᇥ⧁⦹ᩍᯕsॅᮥᬕ࠺పႊᱶ᜾ᨱݡ᯦⦹ᩍᔾᖒࡹ۵⇵aᱢ ᯙ ⧎ᯙ ᇥᔑ᮲ಆᮥ ⡍⧉⦹۵ ᙹ⊹༉⩶ᮥ }ၽ⦹ᩡ݅. ᱽᦩࡽ

༉⩶ᮥ 30

^o

, 90

^o

, 270

^o

᮹ อłᇡෝ ⡍⧉⦹۵ ᙹಽᨱ ᱢᬊ⦹ᩍ

ᇥᔑ᮲ಆᮥᯕᬊ⦽łᖁᙹಽᨱᕽ᮹⃽ᙹ⮱෥ᮥᙹ⊹༉᮹⦹Ł༉

᮹đŝෝᙹญᝅ⨹ᨱ᮹⦽⊂ᱶsၰ┡༉⩶᮹༉᮹sŝእƱ⦹

ᩡ݅.

2. ᯕುᱢᩑǍ

2.1 ଲఙࠑକুंඑ

ᯕ₉ඹᮁᗮᇥ⡍ᨱݡ⦽ᯕು᜾ᮡᩍ్ᩑǍᯱॅᨱ᮹⧕ᱽ᜽ࡹ

ᨩ݅. Rozovskii(1961)۵ᵝ⮱෥ႊ⨆ᮁᗮ᮹ᩑḢᇥ⡍ෝಽə⧉

ᙹෝᯕᬊ⦹ᩍᱶ᮹⦹Łอłᇡᨱᕽӹ┡ӹ۵ᯕ₉ඹ᮹᪥ᱥၽݍ

⬂ႊ⨆ᮁᗮᩑḢᇥ⡍᜾ᮥ⦹ᔢ᮹᳑ࠥᨱ঑௝Ǎᇥ⦹ᩍᱽᦩ⦹ᩡ

݅. ੱ⦽อłᇡᨱᕽᵝ⮱෥ႊ⨆ᯕ࠺Ñญᨱ঑௝ᯕ₉ඹ᮹Ⓧʑa

᷾aၰqᗭ⦹۵Ğ⨆ᮥḡᙹ⧉ᙹෝᯕᬊ⦹ᩍӹ┡ԩ݅. Kikkawa

॒(1976)ᮡᙹᝍ⠪Ɂ⦽ӽඹ࠺ᱱᖒĥᙹෝᱢᬊ⦹ᩍĥᔑ⦹ʑ

ᛍᬕ⩶┽᮹⬂ႊ⨆ᮁᗮᇥ⡍᜾ᮥᱽᦩ⦹ᩡŁ, de Vriend(1977)۵

ᯕ₉ඹ᮹3₉ᬱᱢᩢ⨆ᮥ⃽ᙹ⮱෥⧕ᕾ༉⩶ᮝಽʑᚁ⦹ʑ᭥⦽

ᙹ⊹༉⩶ᮥ}ၽ⦹ᩍ, ᵝ⮱෥ŝᔢ⪙᯲ᬊ⦹۵ᯕ₉ඹ᮹ᮁᗮǍ᳑

ᨱݡ⦽༉⩶ᮥᱽᦩ⦹ᩡ݅. Odgaard(1986)۵໒⧉ᙹෝᯕᬊ⦹ᩍ

ᵝ⮱෥ႊ⨆ᮁᗮ᮹ᩑḢᇥ⡍ෝӹ┡ԩᮝ໑, อłᇡᨱᕽ⩶ᖒࡹ۵

ᯕ₉ඹᖡᵲᝍᨱᕽᇡ░ၽᔾ⦹۵ᬱᝍಆᮥŁಅ⦹ᩍ, ᩑḢႊ⨆ᮥ

঑௝ ᖁ⩶ᱢᮝಽ ᄡ⪵⦹۵ ⬂ႊ⨆ᮁᗮ ᇥ⡍ෝ ᱽᦩ⦹ᩡ݅.

Rozovskii(1961)aᱽᦩ⦽᜾ᮡ⧕ᕾᱢᮝಽᱢᇥ⦹ʑᨕಅᬕ

⩶┽᮹⧉ᙹෝ⡍⧉⦹໑, Kikkawa ॒(1976)ᯕᱽᦩ⦽᜾ᮥᝅ⨹ᙹ ಽᨱᕽ ⊂ᱶ⦽ ᮁᗮᯱഭ᪡ እƱ⧕ ᅕ໕ ⬂ႊ⨆ ᮁᗮ᮹ Ⓧʑෝ

ŝݡᔑᱶ⦹۵Ğ⨆ᮥᅕᯕŁᯩᮝ໑, ᮁࠥŝᱶᨱᯩᨕᕽĞĥ᳑Õ ᨱݡ⦽ฯᮡaᱶᮥ⡍⧉⦹ŁᯩŁᝅᱽᯱᩑ⦹⃽᮹ᅖᰂ⦽ḡ⩶ᨱ

ᱢᬊ⦹۵ߑ⦽ĥa᳕ᰍ⦽݅. ᯕ₉ඹ᮹ᮁᗮǍ᳑ᨱݡ⦽Odgaard (1986)᮹ᱽᦩ᜾ᮡ⦹ᔢ᳑ࠥ᮹ᩢ⨆ᮝಽᅖᰂ⦹íӹ┡ӹ۵⬂ႊ

⨆ᮁᗮ᮹ᩑḢᇥ⡍ෝӹ┡ԕḡ༜⦹໑, ၵ݆໕ᨱᕽ᮹ྕ⪽(no-slip condition)ᮥ อ᳒⦹ḡ ᦫ۵ ⦽ĥᱱᮥ ḡܩŁ ᯩ݅.

2.2 ଲఙࠑઽේැজࢺ࣑

อłᇡᨱᕽ᮹ᯕ₉ඹᮁᗮǍ᳑ෝ⃽ᙹ⮱෥⧕ᕾᨱၹᩢ⦹ʑ

᭥⦹ᩍࢱaḡႊჶᯕձญᔍᬊࡹŁᯩ݅. ℌჩṙႊჶᮡVAM (2D Vertically Averaged and Moment) ༉ߙᨱ᮹⦽ႊჶ(Ghamry, 1999; Ghamry᪡ Steffler, 2002; Ghamry᪡ Steffler, 2005;

Vasquez ॒, 2006)ᯕŁ, ࢱჩṙႊჶᮡᅙᩑǍᨱᕽᯕᬊ⦽ᇥᔑ᮲ ಆ⧎ᮥ⡍⧉⦹۵ႊჶ(de Vriend, 1977)ᯕ݅. VAM ႊჶᮡFig.

2᪡ zᯕ x, y, zႊ⨆ ᮁᗮ᮹ ᩑḢ ᇥ⡍᪡ ᦶಆ ᇥ⡍ෝ ݉ᙽ⦽

ᖁ⩶ ⩶┽ಽ aᱶ⦹ᩍ ᯕ bb᮹ ᇥ⡍ෝ ⇵aᱢᯙ ๅ}ᄡᙹ (moments)ෝᯕᬊ⦹ᩍ༉ߙย⦹۵ʑჶᯕ݅. ঑௝ᕽᯕႊჶᮡ

᜾(1)ŝzᮡᙹᝍ⠪Ɂࡽᩑᗮႊᱶ᜾, ᜾(2)᮹ᬕ࠺పႊᱶ᜾ŝ

޵ᇩᨕ᜾(3)᮹ᬕ࠺పႊᱶ᜾ᨱᩑḢႊ⨆ᄡᙹෝŒ⦹ᩍ⇵aᱢᮝಽ

ᔾᖒࡹ۵ᬕ࠺ప༉ູ✙ႊᱶ᜾(moment of momentum equations)

ᮥ ᩑĥ ⧕ᕾ⦹ᩍ ᯕ₉ඹ ᮁᗮǍ᳑ෝ ၹᩢ⦹۵ ႊჶᯕ݅.

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Fig. 2. Linear Vertical Distributions of Horizontal Velocities Used in Moment of Momentum Method

ć ŞƆ â Şƒ ć ŞƖ _ƈ

ŞƏ ƈ á ×

(1)

ć Şƒ ŞƏ ƈ

â ć ŞƖ Ş _ƈ Þ ^ć ^Ə ^Ɔ ^Ƈ ^Ə ^ƈ ß ^âƅƆć ^ŞƖ Ş ÞƆâ¡ß Ƈ

(2)

à ćƎ Î

ć ŞƖ ƈ

Şŉ Ƈƈ

â ćƎ Î ŉ _ƀƇ à ćÐ Î ć ŞƖ ƈ

Ş Þ ^ƆƓ̂ Ƈ Ɠ̂ _ƈ ß ^{á ×}

ć Şƒ ŞƓ̂ _Ƈ

â ć ŞƖ ƈ

Ş Þ ^ć ^Ə ^ƈ ^Ɔ ^Ɠ̂ ^Ƈ ß ^âƓ̂ ^Ɖ ^ć ^ŞƖ Ɖ

Ş Þ ^ć ^Ɔ ^Ə ^Ƈ ß

á ćÏ Ð ƙ

Ɯ ƚ _ć ^Ñŉ _ƆƎ ^Ƈƈ _ć _ŞƖ

ƈ

ŞƘ _Ƌ à ć ƆƎ

Ñŉ _ƇƘ â ć ƆƎ Ï ŉ ƀƇ

ƛ

Ɲ ƞ

(3)

ᩍʑᕽ, i۵ 1, 2; t۵ ᜽e ;

^{q q} ¹ ^, ²

۵ bb x, yႊ⨆ᮝಽ᮹

݉᭥⡎ݚᮁప ; g۵ᵲಆaᗮࠥ ; h۵ᙹᝍ; H۵ၵ݆Ł; τ ۵

ij

ijႊ⨆ᮝಽ᯲ᬊ⦹۵ᩑḢ⠪Ɂӽඹᱥ݉᮲ಆ;

τ bi

_{۵ၵ݆ᱥ݉ಆ;}

1 2

ˆ ˆ ,

u u

۵bbᙹ໕ᨱᕽx, yႊ⨆ᮝಽ⠪Ɂᮁᗮᨱእ⧕Ⅹŝࡽ

ᮁᗮ᮹Ⓧʑ; z ᮡ⠪Ɂᙹᝍᮥӹ┡ԙ݅. ᭥᜾ᨱᕽᦥ௹℉ᯱ

^m

j᪡k۵ᦥᯙᛩ┡ᯙ⧊⢽᜽Ƚ⊺ᮥ঑෕໑k۵i᪡zḡᦫ݅. ə్ӹ

ᯕႊჶᮡ⃽ᙹႊᱶ᜾ᯕ᫙ᨱEq. (3)ŝzᮡ⇵aᱢᯙࢱ}᮹

ᙹᘂႊᱶ᜾ᮥ ޵ ⣡ᨕ᧝ ⦹အಽ, ĥᔑపᯕ ฯŁ ⬂ႊ⨆ ᮁᗮ᮹

ӹᖁ⩶ᩑḢᇥ⡍ෝ᯹ၹᩢ⦹ḡ༜⦹໑, ၵ݆ᨱᕽ᮹ྕ⪽᳑Õᮥ

อ᳒⦹ḡ ༜⦹۵ ݉ᱱᯕ ᯩ݅.

อłᇡᨱᕽ᮹ᯕ₉ඹᮁᗮǍ᳑ෝ⃽ᙹ⮱෥ᙹ⊹༉᮹ᨱၹᩢ⦹

ʑ᭥⦽ࢱჩṙႊჶᯙᇥᔑ᮲ಆჶᮡ݅ᮭŝz݅. 3₉ᬱNavier- Stokes ႊᱶ᜾ᮥ᜽e⠪Ɂ⦹໕3₉ᬱReynolds ႊᱶ᜾ᮥ᨜í

ࡹ໑, ᯕෝᙹᝍ⠪Ɂ⦹໕ᦥ௹᪡zᮡᩑḢႊ⨆ᮝಽ⠪Ɂࡽႊᱶ᜾

ᯕ ࠥ⇽ࡽ݅.

ć Şƒ Ş

õ

_¡ ^¡âƆ ^Ɠ ^Ƈ ^{ÞƘßƂƘ â ć} ŞƖ Ş _ƈ

õ

_¡ ^¡âƆ ^Ɠ ^Ƈ ^ÞƘßƓ ^ƈ ^ÞƘßƂƘ

⁽⁴⁾

âƅƆć ŞÞ¡ âƆß à ŞƖ Ƈ

õ

_¡ ^¡âƆ ^Ɣć ^Ş _ŞƖ ^Ï ^Ɠ _ƈ ^Ƈ _ŞƖ ^ÞƘß _ƈ ^{ƂƘ âƅƌ} ^Ï ^ć ^ö

^Ɠ^Ƈ

_Ɔ ^ć ^Ɠ ^ÎîÐ ^ƈ ^Ɠ ^ƈ ^{á ×}

ᩍʑᕽ, h۵ ᙹᝍ; t۵ ᜽e, x

i

۵ i = 1ᯙ Ğᬑ xႊ⨆, 2ᯙ

Ğᬑyႊ⨆ ;

^u ⁱ

۵ᙹᝍ⠪Ɂᮁᗮ ; H۵⦹ᔢŁ; v۵ӽඹ࠺ᱱᖒ

ĥᙹ ; g۵ᵲಆaᗮࠥ ; nᮡ᳑ࠥĥᙹෝ᮹ၙ⦽݅. ʑ᳕᮹⃽ᙹ⮱

෥༉⩶ᮡᩑḢႊ⨆ᮝಽɁ॒⦽ᮁᗮᇥ⡍ෝaᱶ⦹အಽ, Eq. (4)᮹

ᙹᝍᱢᇥ⧎ᯕ⡍⧉ࡽℌჩṙ, ࢱჩṙၰօჩṙ⧎ᯕᩑḢ⠪Ɂ

ᮁᗮŝᙹᝍᮝಽ⢽⩥ࡹᨕᯝၹᱢᯙᬕ࠺పႊᱶ᜾ᯕࡽ݅. ə్ӹ

łᖁᇡᨱᕽ᮹

u i

᮹ᩑḢႊ⨆ᇥ⡍۵Ɂᯝ⦹ḡᦫᮝအಽᯕෝၹᩢ

⦹ʑ᭥⧕᳦⬂ႊ⨆ᮁᗮ( ( )u z )ᮥ⠪Ɂ(

i ^u ⁱ

)ŝᯕಽᇡ░᮹ᄡ࠺ప (

u z _i ′ ( )

)᮹ ⧊ᮝಽ ᱶ᮹⦹Ł Eq. (4)ᨱ ݡ᯦⦹໕ ࢱ ჩṙ ⧎ᯙ

ᯕᘂ aᗮࠥ⧎ᯕ ݅ᮭŝ zᯕ ⢽⩥ࡽ݅.

ć ŞƖ Ş _ƈ

õ

_¡ ^¡âƆ ^Ɠ ^Ƈ ^ÞƘßƓ ^ƈ ^{ÞƘßƂƘ á}

⁽⁵⁾

ć ŞƖ Ş _ƈ Þ ^ƆƓ Ƈ Ɠ _ƈ ß _{â ć} _ŞƖ

ƈ

Ş

õ

_¡ ^¡âƆ ^Þ ^Ɠ ^Ƈ ^{ÞƘß àƓ} ^Ƈ ^ßÞ ^Ɠ ^ƈ ^{ÞƘß àƓ} ^ƈ ^ß ^ƂƘ

᭥᜾᮹ᬑᄡ᮹ℌჩṙ⧎ᮡᙹᝍ⠪Ɂ⮱෥ᨱ᮹⦽ᯕᘂaᗮࠥ⧎

ᯕ໑, ᬑᄡ᮹ࢱჩṙ⧎ᮡᙹᝍ⠪ɁᮁᗮŝᩑḢႊ⨆ᮥ঑௝ᄡ⪵⦹

۵ᮁᗮᇥ⡍₉ᨱ᮹⧕ᔾᖒࡹ۵ᇥᔑ᮲ಆ⧎ᨱ⧕ݚ⦽݅. ঑௝ᕽ

⇵aᱢᮝಽᔾᖒࡽᇥᔑ᮲ಆ⧎ᮥ^S^ijಽ⢽⩥⦹໕Eq. (4)۵݅ᮭŝ

zᮡ ⩶┽ಽ ӹ┡ӽ݅.

ć Şƒ ŞƓ _Ƈ

âƓ _ƈ ć ŞƖ _ƈ ŞƓ _Ƈ

âƅć ŞƖ Ş¡ âƅć _ƈ ŞƖ ŞƆ _Ƈ

(6a)

à ć ŞƖ Ş _ƈ Þ ^Ɣć ^ŞƖ ^ŞƓ ^ƈ ^Ƈ ß ^âƅƌ ^Ï ^ć ^Ɠ ^Ƈ ^ö ^Ɔ ^ÑîÐ ^ć ^Ɠ ^ƈ ^Ɠ ^ƈ ^{â ć} ^Ş¬ ^ŞƖ ^Ƈƈ ^ƈ ^{á ×}

¬ _Ƈƈ á ć ŞƖ Ş _ƈ

õ

_¡ ^¡âƆ ^Þ ^Ɠ ^Ƈ ^{ÞƘß à Ɠ} ^Ƈ ^ßÞ ^Ɠ ^ƈ ^{ÞƘß à Ɠ} ^ƈ ^ß ^ƂƘ

^(6b)

᭥᜾ᨱӹ┡ӽၵ᪡zᯕᯕ₉ඹ᮹ᩢ⨆ᮥၹᩢ⦹ʑ᭥⧕ᇥᔑ᮲ ಆႊჶᮥᔍᬊ⦹۵Ğᬑᮁᗮ᮹ᩑḢ⠪Ɂsŝᄡ⪵ప᮹₉a

(4)

ᱢᇥ a܆⦹݅໕ ᨕਁ⦽ ᮁᗮᇥ⡍ᨱࠥ ᱢᬊ⧁ ᙹ ᯩ۵ ᯕᱱᯕ

ᯩᮝ໑, ੱ⦽VAMŝzᮡᯕ₉ඹ⧕ᕾ༉⩶ᨱᕽᯕᬊ⦹۵ᇡᙹᱢ ᯙ ᙹᘂႊᱶ᜾ᮥ ⣡ ⦥᫵a ᨧ۵ ᰆᱱᯕ ᯩ݅.

⃽ᙹ⮱෥⧕ᕾᨱᕽᯕ₉ඹ᮹ᩢ⨆ᮥŁಅ⦹ʑ᭥⧕ᇥᔑ᮲ಆჶ

ᮥ᯦ࠥ⦽ǎԕ᮹ᩑǍಽ۵Kim ॒(2009), KimŝChoi(2009) ၰSong ॒(2012)ᮥΞᮥᙹᯩ݅. ᯕॅᮡ༉ࢱde Vriend(1977)a

ᱽᦩ⦽ಽə⧉ᙹ⩶┽᮹᳦ႊ⨆ᮁᗮ᮹ᩑḢᇥ⡍᜾ŝእᖁ⩶ಽə

⧉ᙹ᮹ᱢᇥ᳑⧊⩶⬂ႊ⨆ᮁᗮ᮹ᩑḢᇥ⡍᜾ᮥ⃽ᙹႊᱶ᜾ᨱ

ݡ᯦⦹ᩍ⇵aᱢᮝಽၽᔾ⦹۵ᇥᔑ᮲ಆ⧎ᨱ᮹⧕ᯕ₉ඹ᮹ᩢ⨆

ᮥ ၹᩢ⦹ᩡ݅. Kim ॒(2009)ŝ Kimŝ Choi(2009)۵ ᅕ᳕⩶

⃽ᙹႊᱶ᜾ᨱCDG ʑჶ(Ghanem, 1995)ᮥᱢᬊ⦹ᩍᇥᔑ᮲ಆ

ᮁྕᨱ঑ෙRozovskii᮹180ࠥอłᙹಽၰ10 m ʙᯕ᮹อłᇡ a3}᳕ᰍ⦹۵Kinoshita ᙹಽᨱᕽ}ၽࡽ༉⩶ᮥá᷾⦹ᩡ݅.

Song ॒(2012)ᮡ࠺ᯝ⦽de Vriend᮹ᙹ⦺ᱢ༉⩶ᮥእᅕ᳕⩶

⃽ᙹႊᱶ᜾ᨱᱢᬊ⦹ŁSU/PG ʑჶᨱ᮹⧕ᯕᔑ⪵⦹ᩍ, Rozovskii ᮹อłᙹಽ, ᅙඹ᪡ḡඹa90ࠥಽ⧊ඹ⦹۵ᝅ⨹ᙹಽၰԉvݱ

⦹ඹᇡ4.7 km ᔍ⧪Ǎeᨱ}ၽࡽ༉⩶ᮥᱢᬊ⦹Łᬕ࠺పႊᱶ᜾

᮹b⧎ᨱእ⧕ᇥᔑ᮲ಆ⧎ᯕaḡ۵Ⓧʑၰḡ႑ಆᮥᱽ᜽⦹ᩡ݅.

ə్ӹSong ॒(2012)᮹ᩑǍᨱᕽ۵݅᧲⦽ᔍ⧪bࠥෝaḡ۵

ᝅ⨹ᙹಽᨱᕽᇥᔑ᮲ಆ༉⩶᮹ᮁ⬉ᖒၰᱢᬊᖒᮥá᷾⦹ḡ༜⦹

ᩡ݅. ᇥᔑ᮲ಆᮥᯕᬊ⦹ᩍᯕ₉ඹ᮹ᩢ⨆ᮥ⧕ᕾ⦽ǎ᫙ᩑǍ۵

Flokstra(1977)ᮥ᜽᯲ᮝಽMolls᪡Chaudhry(1995), Hsieh᪡

Yang(2003), Begnudelli ॒(2010) ॒ᯕᯩᮝ໑, ᯕॅᮡ᳦⬂ႊᮝ ಽ ᧞eᦊ݅ෙ ᩑḢ ᮁᗮᇥ⡍᜾ᮥ ᯕᬊ⦹ᩍ ᇥᔑ᮲ಆʑჶᮥ

ᱢᬊ⦹ᩡ݅. de Vriend(1977)᮹ᙹ⦺ᱢ༉⩶ᨱʑⅩ⦽ᇥᔑ᮲ಆჶ

ᮡ┥┥⦽ᯕುᱢʑၹᮥaḡŁᯩᮝ໑, ၵ݆ᨱᕽ᮹ྕ⪽᳑Õᮥ

᯹ อ᳒᜽┅Ł, ʑ᳕᮹ ᝅ⨹đŝ᪡ࠥ ᯹ ᯝ⊹⦹۵ ᰆᱱᯕ ᯩ݅

(Song ॒, 2012).

3. ᇥᔑ᮲ಆ༉⩶

ᅙᩑǍᨱᕽ۵Eq. (6a)ᨱᔩ೎í⇵aࡽ

^S

^ijෝ༉⩶⪵⦹ʑ᭥⧕

ᕽde Vriend(1977)aᖎ࠺ჶᮥᱢᬊ⦹ᩍᮁࠥ⦽ᙹ⦺ᱢ༉⩶ᮥ

ᯕᬊ⦹ᩡ݅. de Vriend(1977)ᨱ᮹⧕ᱽᦩࡽḢƱ᳭⢽ĥᨱᕽ᮹

᳦⬂Ⴢ⨆ ᮁᗮ᮹ ᩑḢ ᮁᗮ ᇥ⡍᜾ᮡ ݅ᮭŝ z݅.

Ɠ Î Þļßá Ɠ _Î Ƅ Ƌ ÞļßàƆ® _Î Ƅ Ƒ Þļß

(7a)

Ɠ _Ï Þļßá Ɠ _Ï Ƅ _Ƌ ÞļßàƆ® _Ï Ƅ _Ƒ Þļß

(7b)

ᩍʑᕽ

u 1

ᮡ

x−

ႊ⨆᮹ᙹᝍᱢᇥࡽᮁᗮ;

u 1 ( ) ζ

ᮡ

x−

ႊ⨆ᮁᗮ ᮹ᩑḢᇥ⡍;

u 2

۵

^{y −}

ႊ⨆ᙹᝍ⠪Ɂᮁᗮ;

u 2 ( ) ζ

۵

^{y −}

ႊ⨆ᮁᗮ᮹

ᩑḢᇥ⡍; h۵ᙹᝍ;ζ

= − ( z H h ) /

۵ၵ݆ᮝಽᇡ░᮹ྕ₉ᬱÑญ

ෝ ᮹ၙ⦹໑, U1ŝ

U

2۵ ᦥ௹᪡ zᯕ ⢽⩥ࡽ݅.

® _Î á ć Ïŀ ^Ï Ɠ ^Ð

ĺ

(8a)

ƙ

Ɯ ƚÞ Ɠ ^Ï âƓ _Ï ^Ï ß Þ ^Ɠ ^Î ^ć ^ŞƓ ^ŞƖ ^Î ^âƓ ^Ï ^ć ^ŞƓ ^ŞƗ ^Î ß ^{à Ɠ} ^Î ^Ɠ ^Ï Þ ^Ɠ ^Î ^ć ^ŞƓ ^ŞƖ ^Ï ^âƓ ^Ï ^ć ^ŞƓ ^ŞƗ ^Ï ß ^ƛ ^Ɲ ^ƞ

® _Ï á ć Ïŀ ^Ï Ɠ ^Ð

ĺ

(8b)

ƙ

Ɯ ƚÞ ^Ɠ ^Ï ^âƓ Î Ï ß Þ ^Ɠ ^Î ^ć ^ŞƓ ^ŞƖ ^Ï ^âƓ ^Ï ^ć ^ŞƓ ^ŞƗ ^Ï ß ^{à Ɠ} ^Î ^Ɠ ^Ï Þ ^Ɠ ^Î ^ć ^ŞƓ ^ŞƖ ^Î ^âƓ ^Ï ^ć ^ŞƓ ^ŞƗ ^Î ß ^ƛ ^Ɲ ^ƞ

᭥᜾ᨱᕽ

δ

۵ᙹᝍݡłශၹĞ᮹እಽᯝၹᱢᮝಽ1 ᯕ⦹᮹

sᮥ aḡ໑, ^u۵ ᮁᗮ᮹ Euclidian normᯕ݅.

ᵝ⮱෥⧉ᙹ(

f m ^{( )} ζ

)᪡ᯕ₉⮱෥⧉ᙹ(

f s ^{( )} ζ

)۵ᦥ௹᪡zᯕ

ᱶ᮹ࡹ໑Chézy ĥᙹCᨱ঑௝Fig. 3ŝzᯕᩑḢႊ⨆ᮁᗮᇥ⡍a

ᄡ⪵ࡽ݅.

Ƅ Ƌ Þļßá Î â ć

ö

ŀ ćƅ ÞÎ âļß

(9a)

Ƅ _Ƒ Þļßá Ï _Î Þļß â ć ŀ

ö

^ć ƅ _Ï Þļß àÏ Þ ^{Î à ć}

^ö

^ŀ ^ćƅ ß ^Ƅ ^Ƌ ^Þļß

^(9b)

᭥᜾ᨱᕽk۵von Karman ᔢᙹ(0.4)ᯕŁ ( )F1ζ ŝ ( )

F

2 ζ ۵

݅ᮭŝ zᮡ ᜾ᮝಽ ⢽⩥ࡽ݅.

_Î Þļß á

õ

_× ^Î ^ć ļà Î ļ Ƃļ

Ï Þļß á

õ

_× ^Î ^ć _{ļà Î} ^Ï ^{ļ Ƃļ}

⁽¹⁰⁾

Eq. (7)ŝ Eq. (9)ᨱ ঑෕໕, ᩑḢႊ⨆ ᮁᗮᇥ⡍۵ ᵝ ⮱෥

ᮁᗮ᮹ಽəᇥ⡍᪡Chézy ၰvon Karman ᔢᙹෝ⡍⧉⦹۵እᖁ⩶

ᯕ₉ ⮱෥ ⧉ᙹ᮹ đ⧊ᮝಽ ᯕ൉ᨕᲙ ᯩᮭᮥ ᦭ ᙹ ᯩ݅. ੱ⦽

ᯕ₉⮱෥⧉ᙹ۵ ᔍ⧪ᨱ ᮹⦽ᵝ ⮱෥᮹ ႊ⨆ᨱᙹḢᯙ ᖒᇥŝ

ᵝ⮱෥᮹᳦ႊ⨆aᗮᨱ᮹⧕ၽᔾ⦹۵ᵝ⮱෥ႊ⨆ᯕ₉ඹᖒᇥᮝ ಽǍᖒࡹᨕᯩ݅. ᯕ۵ᮁᖁႊ⨆ᬕ࠺పᮥอłᇡԕ⊂ᮝಽᇡ░

᫙⊂ᮝಽᯕ࠺᜽⍽᫙⊂ᨱᕽ᮹ᵝ⮱෥ᮁᗮᯕ ᷾aࡹ۵⩥ᔢᮥ

ၹᩢ⦹ʑ ᭥⦽ äᯕ݅.

Eq. (7)ᨱ᭥ᨱᕽᱶ᮹⦽ᮁᗮᇥ⡍ෝ⡍⧉⦹Ł, ᯕෝ݅᜽Eq.

(6b)ᨱݡ᯦⦹ᩍ▱ᕽ⩶ᇥᔑ᮲ಆᮥĥᔑ⦹໕݅ᮭŝzᮡᖒᇥᮝ

(5)

(a) Primary Flow Function

(b) Secondary Flow Function

Fig. 3. De Vriend’s Primary and Secondary Flow Functions

ಽǍᖒࡽ݅. ℌჩṙᇥᔑ᮲ಆ⧎(

S xx

)ᮡ

^x−

ႊ⨆ᮁᗮ᮹⠪Ɂsŝ

ᄡ࠺s᮹ ₉᮹ Œᨱ ᮹⧕ ݅ᮭŝ zᯕ ĥᔑࡽ݅.

¬ _ƖƖ e ćƆ Î

õ

_¡ ^¡âƆ ^Þ ^Ɠ ^Î ^{ÞƘß àƓ} ^Î ^ß ^Ï ^{ƂƘ á}

õ

_× ^Î ^Þ ^Ɠ ^Î ^{Þļß àƓ} ^Î ^ß ^Ï ^Ƃļ

á Ɠ _Î ^Ï Þ ^ć

^ö

^ŀ ^ćƅ ß ^Ï ^{à ÏƆƓ} ^Î ^® ^Î ^ć

^ö

^ŀ ^ć ^ƅ ^Î ^âƆ ^Ï ^® ^Î ^Ï ^Ï

⁽¹¹⁾

ᩍʑᕽ

Î á

õ

_× ^Î ^{ÞÎ âļß Ƅ} ^Ƒ ^ÞļßƂļ ^Ï ^á

õ

_× ^Î ^Ƅ ^Ƒ ^Ï ^ÞļßƂļ

⁽¹²⁾

ࢱჩṙᖒᇥ(Sxy)ᮡ x−ႊ⨆ŝ

^{y −}

ႊ⨆ᮁᗮ᮹₉ᨱ᮹⧕ၽᔾ

⦹໑ ݅ᮭŝ zᯕ ĥᔑࡽ݅.

¬ ƖƗ e

õ

_× ^Î ^Þ ^Ɠ ^Î ^{Þļß à Ɠ} ^Î ^ß ^ÞƓ ^Ï ^{Þļß àƓ} ^Ï ^ßƂļ

⁽¹³⁾

á Ɠ _Î Ɠ Ï Þ ^ć

^ö

^ŀ ^ćƅ ß ^Ï ^{à ƆÞƓ} ^Î ^® ^Î ^âƓ ^Ï ^® ^Ï ^ßć

^ö

^ŀ ^ćƅ ^Î ^âƆ ^Ï ^® ^Î ^® ^Ï ^Ï

ษḡสᖒᇥ(^S^yy)ᮡ

^{y −}

ႊ⨆ᮁᗮ᮹₉᮹Œᨱ᮹⧕ᔾᖒࡹ໑

ᦥ௹᪡ z݅.

¬ ƗƗ e

õ

_× ^Î ^Þ ^Ɠ ^Ï ^{Þļß àƓ} ^Ï ^ß ^Ï ^Ƃļ

á Ɠ _Ï ^Ï Þ ^ć

^ö

^ŀ ^ć ^ƅ ß ^Ï ^{à ÏƆƓ} ^Ï ^® ^Ï ^ć

^ö

^ŀ ^ćƅ ^Î ^âƆ ^Ï ^® ^Ï ^Ï ^Ï

⁽¹⁴⁾

Eq. (10)ŝEq. (12)ᨱ⡍⧉ࡽᱢᇥᮡᔍ݅ญΕȽ⊺ᨱ᮹⧕

ĥᔑ⧁ ᙹ ᯩ݅.

4. ᙹ⊹༉᮹

ᅙᩑǍᨱᕽ۵ᯕ₉ඹ᮹ᩢ⨆ᮥᇥᔑ᮲ಆᮥᯕᬊ⦹ᩍၹᩢ⦽

Song॒(2012)᮹⃽ᙹ⮱෥⧕ᕾᙹ⊹༉⩶ᮥ30

^o

, 90

^o

ၰ270

^o

᮹

อłᇡෝ⡍⧉⦹۵ᙹಽᨱᱢᬊ⦹ᩍᇥᔑ᮲ಆ⧎᮹ ᮁྕᨱ঑ෙ

łᖁᙹಽᨱᕽ᮹⮱෥✚ᖒᮥᇥᕾ⦹ᩡ݅. ᙹ⊹ʑჶᮝಽ۵ᮁᗮŝ

⩶ᔢ⧉ᙹ⠙ၙᇥ᮹ԕᱢᨱ᮹⧕ᔢ⨆aᵲࡽᖎ࠺⧉ᙹaᮁℕ᮹

⮱෥ႊ⨆ᮝಽ᯲ᬊ⦹íࡹᨕ, ⃽ᙹႊᱶ᜾᮹እᖁ⩶ᯕᘂ⧎᮹ᇩᦩ ᱶᖒᮥqᗭ᜽┅۵SU/PG ʑჶ(Hughes᪡Brooks, 1979; Songŝ

Seo, 2012)ᮥ ᱢᬊ⦹ᩡ݅.

4.1 30ܑմট৤ߦ

Fig.4(a)᪡zᯕ⊂ᄞĞᔍ1V:2H᮹ᔍ݅ญΕ݉໕ᮥaḡŁ

30

^o

᮹อłᇡෝ⡍⧉⦹۵łᖁᙹಽᨱᕽᇥᔑ᮲ಆ⧎᮹ᮁྕᨱ঑ෙ

ᮁᗮᇥ⡍ෝ እƱ⦹ᩡ݅. 220}(᳦ႊ⨆ 22} x ⬂ႊ⨆ 10})᪡

880}(᳦ႊ⨆44}x ⬂ႊ⨆20})᮹2aḡĊᯱ⧕ᔢࠥᨱ঑ෙ

Sec.1ᨱᕽ᮹⬂ႊ⨆ᮁᗮsᮥMaynord(1996)᮹ᝅ⨹ᯱഭ᪡እƱ

⦹ᩍFig. 4(b)ᨱࠥ᜽⦹ᩡ݅. 220}᮹ᔍb฾ᨱ᮹⦽đŝ۵Sec.1 ᨱᕽ᮹ᮁᗮsᮥŝݡᔑᱶ⦹အಽ, ᙹ⊹༉᮹ᨱᯕᬊ⦽ᱩᱱᙹ᪡

(6)

(a) Finite Element and Flow Conditions (b) Comparison of Velocities at Sec.1 According to mesh Resolutions

Fig. 4. Geometry, Finite Elements, Flow Conditions and mesh Dependency for 30 Degree Curved Channel

Table 1. Simulation Conditions for Curved Channels

Element info. Boundary conditions Parameters

Bend Number of element Number of node Q (cms) h (m) n h/R c F r

30 ^o 880 945 0.5660 0.300 0.021 0.0437 0.518

90 ^o 1,728 1,885 0.0985 0.115 0.010 0.0135 0.345

270 ^o 4,312 4,531 0.0235 0.064 0.010 0.0179 0.507

Fig. 5. Velocity Vector and Influence of Dispersion Stresses in Region a for 30 Degree Curved Channel

᫵ᗭ ᙹ۵ Table 1 ၰ Fig. 4(a)ᨱ ᱽ᜽ࡽ Ċᯱ฾ŝ zᯕ bb

945}ၰ880}ಽđᱶ⦹ᩡ݅. 30

^o

ᙹಽ᮹ᙹ⊹༉᮹ᨱᕽ۵ᄞ໕Ğĥ

᳑Õᮥྕ⪽(no-slip) ᳑Õᮝಽᇡᩍ⦹ᩍMaynord(1996)᮹ ᝅ⊂ᯱ

ഭ᪡ Bernard᪡ Schneider(1992)ᨱ ᱽ᜽ࡽ STREMR ༉⩶᮹

༉᮹᳑Õᨱᅕ݅ɝᔍ⦹ࠥಾ⦹ᩡ݅. ᔢඹ݉ᮁప᳑Õᮡ0.566 cms, ⦹ඹ݉ᙹᝍĞĥ᳑Õᮡ0.3 mಽ᯦ಆ⦹ᩡᮝ໑ᯕĞᬑFr ᙹ۵0.518ᯕ݅. Maynord(1996)᮹ᙹญᝅ⨹᳑Õᮥၵ┶ᮝಽ⦹

ᩍ ᳑ࠥĥᙹ۵ 0.021ಽ ᖅᱶ⦹ᩡ݅.

Fig. 5ᨱ ᮁᗮ ᄂ░ࠥ᪡ 30

^o

อłᇡ ᇡɝᨱᕽ᮹ ॒ᮁᗮࠥෝ

ࠥ᜽⦹ᩡ݅. ྕ⪽᳑Õᮥ᯦ಆ⦹ᩡʑভྙᨱᔢඹ݉Ğĥ໕ᨱᇡᩍ

ࡽ Ɂᯝ⦽ᮁᗮᇥ⡍a ᱱ₉ ⡍ྜྷᖁ⩶ᮝಽܩ┡ӹ۵ äᮥ ᦭ᙹ

ᯩ݅. A ᩢᩎ᮹॒ᮁᗮࠥෝ⪶ݡ⦽əฝᨱᕽᇥᔑ᮲ಆᮥ⡍⧉⦽

Ğᬑ, 1.0 m/s᮹↽ݡᮁᗮᖁᯕอłᇡ᫙⊂ᮝಽᅕ݅⠙⨆ࡹᨕ

ӹ┡ԍ݅. ᯕ۵Sec. 1ŝSec. 2ᨱᕽ᳭ᦩᮝಽᇡ░ᬑᦩႊ⨆ᮝಽ᮹

⬂ႊ⨆Ñญ(y)ෝᙹಽ⡎(W)ᮝಽӹ٥ᨕྕ₉ᬱ⪵(y/W)⦹Ł⬂ႊ

⨆ᮁᗮᇥ⡍ෝࠥ᜽⦽Fig. 6ᨱᕽᅕ݅໦⪶⦹í⪶ᯙ⧁ᙹᯩ݅.

Fig. 6(a)᮹ Sec. 1ᨱᕽ ᱱᖁᮝಽ ⢽᜽⦽ ᇥᔑ᮲ಆᮥ ⡍⧉⦹ḡ

ᦫᮡ Ğᬑᨱ እ⧕ ᝅᖁᮝಽ ⢽᜽⦽ ᇥᔑ᮲ಆᮥ ⡍⧉⦽ Ğᬑ᮹

ᮁᗮᇥ⡍aᅕ݅อłᇡ᫙⊂ᮝಽᯕ࠺⦹ᩍáᮡᱱᮝಽ⢽᜽⦽

Maynord(1996)᮹ ᙹญᝅ⨹ đŝ᪡ ᯹ ᯝ⊹⦹ᩡ݅. ᯕ᪡ zᮡ

⩥ᔢᮡอłᇡෝ☖ŝ⦽⬥Ḣᖁᇡᨱ⧕ݚ⦹۵Sec. 2ᨱᕽࠥ࠺ᯝ⦹

í ӹ┡ԍ݅(Fig. 6(b)). 30ࠥ ᙹಽ ༉᮹ᨱᕽ۵ Bernard᪡

Schneider(1992)ᨱ ᱽ᜽ࡽ STREMR ༉⩶᮹ ᙹ⊹༉᮹ đŝෝ

ᯕᬊ⦹ᩍ⬂ႊ⨆ᮁᗮᇥ⡍ෝእƱ⦹ᩡ݅. STREMR ༉⩶ᮡᯕ₉ඹ

(7)

Fig. 6. Velocity Comparisons Along the Transverse Sections of 30 Degree Curved Channel

(a) Finite Elements and Flow Conditions (b) Comparison of Velocities at Sec.7 According to Mesh Resolutions

Fig. 7. Geometry, Finite Elements and Flow Conditions for 90 Degree Curved Channel

᮹ᩢ⨆ᮥ݉ᙽ⯩ᮁᖁႊ⨆᪡ࠥᨱš⦽Ğ⨹ᯕᘂ᜾ᨱ᮹⧕ĥᔑ⦹

ᩍ, ᇥᔑ᮲ಆᮥ⡍⧉⦽ᅙ༉⩶ᨱእ⧕อłᇡᨱᕽ⮱෥ᯕ᫙⊂ᮝಽ

⠙⨆ࡹ۵ᮁᗮǍ᳑ෝ᪍ၵ෕íၹᩢ⦹ḡ༜⦹ᩡᮝ໑, ᙹಽ᮹᳭ᦩ ŝᵲᦺᇡɝᨱᕽᇥᔑ᮲ಆᮥ⡍⧉⦹ḡᦫᮡᅙᩑǍ᮹༉᮹đŝ᪡

ᮁᔍ⦽ ᮁᗮsᮥ ᅕᩡ݅.

4.2 90ܑմট৤ߦ

ᱽᦩࡽ༉⩶᮹ࢱჩṙᱢᬊᔍಡಽFig. 7(a)᪡zᯕ⡎2.34 m᮹ Ḣᔍb⩶ ݉໕ᮥ aḡŁ ࢱ }᮹ 90

^o

อłᇡෝ ⡍⧉⦹۵

ᙹಽᨱᕽ᮹ᙹ⊹༉᮹đŝෝᙹญᝅ⨹đŝၰ┡༉⩶༉᮹đŝ᪡

እƱ⦹ᩡ݅. 432}(᳦ႊ⨆72}x ⬂ႊ⨆6})᪡1,728}(᳦ႊ⨆

144}x ⬂ႊ⨆12})᮹2aḡĊᯱ⧕ᔢࠥᨱ঑ෙSec.7ᨱᕽ᮹

⬂ႊ⨆ᮁᗮsᮥChang(1971)᮹ᝅ⨹ᯱഭ᪡እƱ⦹ᩍFig. 7(b)ᨱ

ࠥ᜽⦹ᩡ݅. 432}᮹ᔍb฾ᨱ᮹⦽đŝ۵Sec.7 ݉໕᮹ᵲᦺ

ၰ᫙⊂ᨱᕽᮁᗮsᮥŝݡᔑᱶ⦹Ł, ᖒɝĊᯱⓍʑᨱ᮹⧕ᇥᔑ᮲ ಆᨱ ᮹⦽ ⬂ႊ⨆ ᬕ࠺ప ᱥݍᮥ ᪍ၵ෕í ၹᩢ⦹ḡ ༜⦹အಽ, ᙹ⊹༉᮹ᨱᯕᬊ⦽ᱩᱱᙹ᪡᫵ᗭᙹ۵Table 1 ၰFig. 7(a)ᨱ

ᱽ᜽ࡽ 1,885} ၰ 1,728}ಽ đᱶ⦹ᩡ݅. ᔢඹ݉ ᮁప᳑Õᮡ

0.0985 cms, ⦹ඹ݉ ᙹᝍĞĥ᳑Õᮡ 0.115 mಽ ᯦ಆ⦹ᩡᮝ໑

ᯕĞᬑFr ᙹ۵0.345ᯕ݅. ᙹಽ᮹ᄞ໕ᨱ۵⪽࠺Ğĥ᳑Õᮥ

ᇡᩍ⦹ᩡᮝ໑, Chang(1971)᮹ᙹญᝅ⨹᳑Õᮥၵ┶ᮝಽ⦹ᩍ᳑

ࠥĥᙹ۵ 0.010ᮝಽ ᖅᱶ⦹ᩡ݅.

ࢱჩṙอłᇡᮁ᯦ḡᱱ᮹⊂ᖁ(Sec.5)ᮥ⡍⧉⦹ᩍ4}᮹⬂ႊ

⨆ ⊂ᖁᨱᕽ᮹ ᮁᗮᇥ⡍ෝ Fig. 8ᨱ ӹ┡ԩ݅. Chang(1971)᮹

ᙹญᝅ⨹đŝ᪡ᇥᔑ᮲ಆᮁྕᨱ᮹⦽ᅙᩑǍ᮹ᙹ⊹༉᮹đŝ, ᯕ₉ඹ᮹ᩢ⨆ᮥVAM ႊჶᮝಽၹᩢ⦽Ghamry᪡Steffler(2002) ᮹ đŝෝእƱ⦹ᩡ݅. ༉ुđŝᨱᕽŖ☖ᱢᮝಽࢱჩṙอłᇡ᮹

᜽ᱱ(Sec.5)ᇡ░อłᇡᱶᱱ(Sec.9)ʭḡ۵ᙹಽԕ⊂᮹ᮁᗮᯕ

዁෕íᇥ⡍⦹݅aSec.11ᇡ░۵ᱱ₉Ɂᯝ⦽ᮁᗮᮝಽᄡ⪵ࡹᨕ

a۵ äᮥ ᯕ əฝᨱᕽ ⪶ᯙ⧁ ᙹ ᯩ݅. ᇥᔑ᮲ಆ ᮁྕᨱ ঑ෙ

ᮁᗮᮥእƱ⧕ᅕ໕Sec.9ᯙอłᇡᱶᱱᨱᕽ۵ࢱđŝaᮁᔍ⦹í

ӹ┡ԍᮝӹ, อłᇡᮁ᯦ᇡᨱ⧕ݚ⦹۵Sec.5᪡Sec.7ᨱᕽ۵ᇥᔑ ᮲ಆᮥྕ᜽⦽Ğᬑᙹಽԕ⊂ᨱᕽ۵ᮁᗮᯕԏíӹ┡ӹŁ᫙⊂ᨱ ᕽ۵ ׳í ӹ┡ӹ ᇥᔑ᮲ಆᮥ ⡍⧉⦽ Ğᬑᨱ እ⧕ ᮁᗮ Ğᔍa

᪥อ⦹íᇥ⡍⦹ᩡ݅. ᇥᔑ᮲ಆᮥ⡍⧉⦽ᅙᩑǍ᮹༉⩶ŝGhamry

᪡ Steffler(2002)᮹༉᮹đŝෝእƱ⧕ᅕ໕Sec.5᪡Sec.7᮹

᳭ᦩŝSec.9᪡Sec.11᮹ᬑᦩᨱᕽ᮹ᮁᗮᯕᕽಽๅᬑᮁᔍ⦹í

(8)

Fig. 8. Velocity Comparisons Along the Transverse Sections of 90 Degree Curved Channel

(a) Finite Elements and Flow Conditions (b) Comparison of Velocities at Section 90 Degree Section According to mesh Resolutions Fig. 9. Geometry, Finite Elements and Flow Conditions for 270 Degree Curved Channel

ӹ┡ԍḡอ, Sec.7᮹ ᙹಽ ԕ⊂ŝ Sec.11᮹ ᵲᦺ ᇡᇥᨱᕽ ᅙ

ᩑǍᨱ᮹⦽༉⩶᮹༉᮹đŝaChang(1971)᮹ᙹญᝅ⨹đŝᨱ

ᅕ݅ɝᔍ⦹ᩡ݅. ੱ⦽Sec. 9᮹ᵲᦺᇡᇥᨱᕽᮁᗮᯕ׳íӹ┡ӹ ۵⩥ᔢᮥVAM ༉⩶ᨱእ⧕ᔢݡᱢᮝಽᱶ⪶⦹íᩩ⊂⦹ᩡ݅.

VAM ༉⩶ᮡᯕ₉ඹ᮹3₉ᬱᱢᮁᗮǍ᳑ෝၹᩢ⦹ʑ᭥⧕10}᮹

ႊᱶ᜾ᮥ⣡ᨕ᧝⦹۵ჩÑಽᬡᯕᯩŁĥᔑ᜽eࠥ᪅௹Ùญ۵

݉ᱱᯕ ᯩ݅.

4.3 270ܑմট৤ߦ

ᅙ ༉⩶᮹ ᖙ ჩṙ ᱢᬊᔍಡಽ Fig. 9(a)᪡ zᯕ ᫙⊂ ᄞ໕

Ğᔍ1V:2H᮹ᔍ݅ญΕ݉໕ᮥaḡŁ270

^o

᮹อłᇡෝ⡍⧉⦹۵

ᙹಽᨱᕽᇥᔑ᮲ಆ⧎᮹ᮁྕᨱ঑ෙᮁᗮᇥ⡍ෝእƱ⦹ᩡ݅. 1,078 }(᳦ႊ⨆98}x ⬂ႊ⨆11})᪡4,312}(᳦ႊ⨆196}x ⬂ႊ⨆

22})᮹2aḡĊᯱ⧕ᔢࠥᨱ঑ෙ90ࠥ݉໕ᨱᕽ᮹⬂ႊ⨆ᮁᗮs

ᮥHick ॒(1996)᮹ᝅ⨹ᯱഭ᪡እƱ⦹ᩍFig. 9(b)ᨱࠥ᜽⦹ᩡ݅.

(9)

(a) Without Dispersion (b) With Dispersion Fig. 10. Velocity Vector for 270 Degree Curved Channel

Fig. 11. Velocity Comparisons Along the Transverse Sections of 270 Degree Curved Channel

1,078}᮹ᔍb฾ᨱ᮹⦽༉᮹đŝ90ࠥ݉໕᮹ԕ⊂ၰᵲᦺᇡᨱ

ᕽ᮹ᮁᗮᮥŝᗭᔑᱶ⦹Ł᫙⊂ᨱᕽ۵ŝݡᔑᱶ⦹໑, ੱ⦽4,312 }Ċᯱ฾᮹Ğᬑᨱእ⧕ᇥᔑ᮲ಆᨱ᮹⦽⬂ႊ⨆ᬕ࠺ప᮹ᱥݍᯕ

ᱶ⪶⦹íၹᩢࡹḡ༜⦹အಽ, ᙹ⊹༉᮹ᨱᯕᬊ⦽ᱩᱱᙹ᪡᫵ᗭ

ᙹ۵Table 1 ၰFig. 9(a)ᨱᱽ᜽ࡽ4,531}ၰ4,312}ಽđᱶ⦹ᩡ

݅. ᔢඹ݉ᮁప᳑Õᮡ0.0235 cms, ⦹ඹ݉ᙹᝍĞĥ᳑Õᮡ0.064

(10)

mಽ᯦ಆ⦹ᩡ݅. ੱ⦽Hicks ॒(1990)᮹ᝅԕᙹญᝅ⨹᳑Õᮥ

ၵ┶ᮝಽ ᳑ࠥĥᙹ۵ 0.010ᮝಽ ᖅᱶ⦹ᩡ݅.

Fig. 10ᨱอłᇡᨱᕽ᮹ᮁᗮᄂ░ࠥෝࠥ᜽⦹ᩡ݅. ᇥᔑ᮲ಆᮥ

⡍⧉⦹ḡᦫᮡĞᬑอłᯕ᜽᯲ࡹ۵0

^o

ᇡ░ᙹಽԕ⊂᮹ᮁᗮᯕ

዁෕íᇥ⡍⦹ᩍอłᯕ᳦ഭࡹ۵270

^o

ʭḡᙹಽᬑ⊂᮹ᮁᗮᯕ

዁෕íӹ┡ԍŁ, łᖁᇡ᳦ഭᯕ⬥ᇡ░ᱱ₉Ɂᯝ⦽ᮁᗮᯕᇥ⡍⧉

ᮥ᦭ᙹᯩ݅. ၹ໕ᇥᔑ᮲ಆᮥ⡍⧉⦽Ğᬑᨱ۵อłᇡᮁ᯦ḡᱱᯙ

0

^o

ᯕ⬥ᙹಽԕ⊂᮹ᮁᗮᯕ዁෕íӹ┡ԍḡอ, 90

^o

ḡᱱᯕᱥᨱ

Ɂᯝ⦽ᮁᗮᯕၽᔾ⦹ᩡŁ, ᯕ⬥ᇡ░۵᪅⯩ಅᙹಽ᫙⊂᮹ᮁᗮᯕ

዁෕í ӹ┡ӹ ⦹ඹ݉ʭḡ ĥᗮ ᯕᨕᲭ݅. Fig. 11ᨱ۵ 270

^o

᮹

อłᇡෝ4॒ᇥ⦹۵⊂ᖁᯙ0

^o

, 90

^o

, 180

^o

ၰ270

^o

ᨱᕽ᮹⬂ႊ⨆

ᮁᗮᇥ⡍ෝᙹಾ⦹ᩡ݅. ᙹಽ᳭ᦩᮝಽᇡ░ԕ⊂ႊ⨆ᮝಽ᮹⬂ႊ

⨆ Ñญ(y)ෝ ᙹಽ ⡎(W)ᮝಽ ӹ٥ᨕ ྕ₉ᬱ⪵(y/W)⦽ ᄡᙹෝ

aಽ⇶ᨱ ᔍᬊ⦹ᩡŁ, ᖙಽ⇶ᮡ ݉໕⠪Ɂ ᮁᗮᮝಽ ྕ₉ᬱ⪵⦽

sᮥᯕᬊ⦹ᩡ݅. อłᯕ᜽᯲ࡹ۵0

^o

ᨱᕽ᮹⬂ႊ⨆ᮁᗮᇥ⡍ෝ

እƱ⦽Fig. 11(a)ᨱᕽ۵ᇥᔑ᮲ಆ᮹ᮁྕᨱšĥᨧᯕᙹಽԕ⊂᮹

ᮁᗮᯕ݅ᗭ׳íӹ┡ӹ۵ᮁᔍ⦽đŝෝᅕᩡ݅. ə్ӹᇥᔑ᮲ಆ

ᮥྕ᜽⦽Ğᬑᨱ۵90

^o

᪡180

^o

ᨱᕽࠥᩍᱥ⯩ᬑᦩ⊂(y/W=1)᮹

ᮁᗮᯕ׳íӹ┡ԍ݅. ၹ໕, ᇥᔑ᮲ಆᮥŁಅ⦽Ğᬑᨱ۵90

^o

ᨱᕽ

ᙹಽ⡎ᨱÙℱÑ᮹Ɂᯝ⦽ᮁᗮᯕၽᔾ⦹ᩍHicks ॒(1990)᮹

ᙹญᝅ⨹đŝ᪡ᅕ݅ɝᔍ⦹ᩡᮝ໑, 180

^o

ၰ270

^o

⊂ᖁᨱᕽࠥ0 ⴌ y/W ⴌ 0.2ᨱ ⧕ݚ⦹۵ ᙹಽ ᫙⊂᮹ ᮁᗮᯕ ዁෕í ӹ┡ӹ

ᇥᔑ᮲ಆᯕᨧ۵ᙹ⊹༉᮹đŝᨱእ⧕ᙹญᝅ⨹đŝ᪡᯹ɝᔍ⦹

ᩡ݅. ⦹ḡอࢱđŝ༉ࢱ90ࠥ݉໕ᯕ⬥ᇡ░ᙹಽᬑ⊂ᄞ໕

ɝ⃹ᨱᕽᙹญᝅ⨹đŝᨱእ⧕ᮁᗮᮥŝݡᔑᱶ⦹ᩡ݅. ᇥᔑ᮲ಆ

ᮥ⡍⧉⦽Ğᬑᨱࠥᬱᝍಆᨱ᮹⧕⮱෥ᯕaᗮࡹ۵ᇡᇥ᮹ᮁᗮᮡ

እƱᱢ ᯹ ᩩ⊂⦹ᩡḡอ ၹݡ⊂ ᄞ໕ ɝ⃹ᨱᕽ᮹ ᮁᗮᮥ ݅ᗭ

ŝݡᔑᱶ⦹ᩡ݅. ə్ӹᇥᔑ᮲ಆᮥ⡍⧉⦹ḡᦫᮡĞᬑᨱእ⧕

⬂ႊ⨆ ᬕ࠺ప ᇥ႑ ʑ᯲ᯕ ᯲ᬊ⦹ᩍ ᬑᦩᨱᕽ᮹ ᮁᗮᮥ ŝݡ

ᔑᱶ⦹۵ äᮥ ᵥᯝ ᙹ ᯩᨩ݅. ᄞ໕ Ğĥ᳑Õᮥ ྕ⪽᳑Õᮝಽ

ᇡᩍ⦹ᩍ ᙹ⊹༉᮹ෝ ᙹ⧪⦽ Ğᬑ ᯕ᪡ zᮡ ⩥ᔢᮡ ၽᔾ⦹ḡ

ᦫᦹḡอ, ᙹಽᵲᦺᇡᨱᕽᮁᗮᮥŝݡᔑᱶ⦹۵݉ᱱᯕᯩᨩ݅.

ᬕ࠺పႊᱶ᜾ᨱ ⡍⧉ࡽ ᇥᔑ᮲ಆ⧎ᮡ ᔾᖒ/ᗭ໙ŝ zᮡ ᩎ⧁ᮥ

⦹ᩍ, อł᮹ԕ⊂ᨱᕽ᫙⊂ᮝಽ⬂ႊ⨆ᬕ࠺పᮥᯕ࠺᜽┅íࡹအ ಽᇥᔑ᮲ಆᮥ⡍⧉⦹۵Ğᬑᅕ݅ᱶ⪶⦽ᙹ⊹༉᮹đŝෝ᨜ᮥ

ᙹ ᯩᨩ݅.

5. đು

ᅙᩑǍᨱᕽ۵3₉ᬱReynolds ႊᱶ᜾ᮥᙹᝍᱢᇥ⦹۵ŝᱶᨱ ᕽ Ɂᯝ⦽ ᮁᗮᇥ⡍ෝ aᱶ⦹ᩍ อłᇡᨱᕽ ᯕ₉ඹa ᵝ ⮱෥

ᮁᗮᨱၙ⊹۵ᯕᘂ᮹ᩢ⨆ᮥྕ᜽⦽ʑ᳕ݡᇡᇥ᮹ᩑǍၰ༉⩶ŝ

۵ݍญ᳦⬂ႊ⨆ᮁᗮ᮹ᩑḢᇥ⡍ෝ⠪Ɂsŝᯕಽᇡ░᮹ᄡ࠺ప ᮹⧊ᮝಽᱶ᮹⦹Ł, ᯕsॅᮥᬕ࠺పႊᱶ᜾ᨱݡ᯦⦹ᩍᔾᖒࡹ۵

⇵aᱢᯙ⧎ᯙᇥᔑ᮲ಆᮥ⡍⧉⦹۵ᙹ⊹༉⩶ᮥ}ၽ⦹ᩡ݅. ᮁᗮ ᇥ⡍ᨱ ݡ⦽ ᙹ⦺ᱢ ༉⩶ᮝಽ۵ ┥┥⦽ ᯕುᱢ ʑၹᮥ aḡŁ

ᯩᮝ໑, ၵ݆ᨱᕽ᮹ྕ⪽᳑Õᮥ᯹อ᳒᜽┅Ł, ʑ᳕᮹ᝅ⨹đŝ᪡

ࠥ᯹ᯝ⊹⦹۵ᰆᱱᯕᯩ۵de Vriend(1977)᮹ᱽᦩ᜾ᮥᯕᬊ⦹ᩡ

݅.

ᱽᦩࡽ༉⩶ᮥ30

^o

, 90

^o

, 270

^o

᮹łශᮥaḡ۵ᙹಽᨱᱢᬊ⦹ᩍ

༉᮹đŝෝᙹญᝅ⨹đŝၰ┡ᙹ⊹༉⩶༉᮹đŝ᪡እƱ⦹ᩡ݅.

30ࠥłᖁᙹಽ༉᮹đŝ, STREMR ༉⩶(Bernard᪡Schneider, 1992)᮹Ğᬑᯕ₉ඹ᮹ᩢ⨆ᮥ݉ᙽ⯩ᮁᖁႊ⨆᪡ࠥᨱš⦽Ğ⨹

ᯕᘂ᜾ᨱ᮹⧕ĥᔑ⦹ᩍᇥᔑ᮲ಆᮥ⡍⧉⦽ᅙ༉⩶ᨱእ⧕อłᇡ ᨱᕽ⮱෥ᯕ᫙⊂ᮝಽ⠙⨆ࡹ۵ᮁᗮǍ᳑ෝ ᪍ၵ෕íၹᩢ⦹ḡ

༜⦹ᩡᮝ໑, 90ࠥ łᖁᙹಽ ༉᮹ đŝ ᇥᔑ᮲ಆᮥ ྕ᜽⦽ Ğᬑ

ᙹಽԕ⊂ᨱᕽ۵ᮁᗮᯕԏíӹ┡ӹŁ᫙⊂ᨱᕽ۵׳íӹ┡ӹ

ᇥᔑ᮲ಆᮥ⡍⧉⦽Ğᬑᨱእ⧕ᮁᗮĞᔍa᪥อ⦹íᇥ⡍⦹ᩡ݅.

270ࠥłᖁᙹಽ༉᮹đŝᇥᔑ᮲ಆᮥ⡍⧉⦹ḡᦫᮡĞᬑอłᯕ

᜽᯲ࡹ۵0

^o

ᇡ░อłᯕ᳦ഭࡹ۵270

^o

ʭḡᙹಽԕ⊂᮹ᮁᗮᯕ

዁෕íӹ┡ԍŁ, łᖁᇡ᳦ഭᯕ⬥ᇡ░ᱱ₉Ɂᯝ⦽ᮁᗮᯕᇥ⡍⦹

ᩡᮝӹ, ᇥᔑ᮲ಆᮥ⡍⧉⦽Ğᬑᨱ۵อłᇡᮁ᯦ḡᱱᯙ0

^o

ᯕ⬥

ᙹಽԕ⊂᮹ᮁᗮᯕ዁෕íӹ┡ԍḡอ, 90

^o

ḡᱱᯕᱥᨱɁᯝ⦽

ᮁᗮᯕၽᔾ⦹ᩡŁ, ᯕ⬥ᇡ░۵᪅⯩ಅᙹಽ᫙⊂᮹ᮁᗮᯕ዁෕í

ӹ┡ӹ ⦹ඹ݉ʭḡ ĥᗮ ᯕᨕᲙᕽ ᙹญᝅ⨹đŝ᪡ ɝᔍ⦹ᩡ݅.

ᅙᩑǍ᮹ᙹ⊹༉᮹đŝ, ᬕ࠺పႊᱶ᜾ᨱ⡍⧉ࡽᇥᔑ᮲ಆ⧎ᮡ

ᔾᖒ/ᗭ໙ŝzᮡᩎ⧁ᮥ⦹۵äᮝಽ❱݉ࡹ໑, ᯕ۵อł᮹ԕ⊂ᨱ ᕽ᫙⊂ᮝಽ⬂ႊ⨆ᬕ࠺పᮥᯕ࠺᜽⍽ᕽ ᇥᔑ᮲ಆᮥ⡍⧉⦹ḡ

ᦫ۵Ğᬑᅕ݅ᱶ⪶⦽ᙹ⊹༉᮹đŝෝᱽŖ⦹۵äᮝಽᔍഭࡽ݅.

qᔍ᮹ɡ

ᅙᩑǍ۵ǎ☁Ʊ☖ᇡÕᖅƱ☖ʑᚁⅪḥᩑǍᔍᨦʑᚁᔍᨦ⪵

ŝᱽ᪡Õᖅʑᚁ⩢ᝁᔍᨦ(11ʑᚁ⩢ᝁC06)᮹ᩑǍእḡᬱᨱ᮹⧕

ᙹ⧪ࡹᨩ᜖ܩ݅. ᅙᩑǍ۵ᕽᬙݡ⦺ƱŖ⦺ᩑǍᗭၰÕᖅ⪹Ğ᳦

⧊ᩑǍᗭ᮹ ḡᬱᮝಽ ᙹ⧪ࡹᨩ᜖ܩ݅.

References

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Analysis of Shallow Water Flow in Curved Channel Using Dispersion Stresses Method

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0)

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৉ఢֽ ȵছଵ଀ ȵ׌೾଀ ȵੲ୨ָ

Song, Chang Geun*, Seo, Il Won**, Kim, Tae Won***, Ahn, Jungkyu****

Analysis of Shallow Water Flow in Curved Channel Using Dispersion Stresses Method

ABSTRACT

Key words : Curved channel, Secondary current, Velocity profile, Dispersion stresses method, Shallow water equations, Finite element model

Ⅹಾ

ᮡᩎ⧁ᮥ⦹ᩍ, อł᮹ԕ⊂ᨱᕽ᫙⊂ᮝಽ⬂ႊ⨆ᬕ࠺పᮥᯕ࠺᜽┅íࡹအಽᇥᔑ᮲ಆᮥ⡍⧉⦹ḡᦫ۵Ğᬑᅕ݅ᱶ⪶⦽ᙹ⊹༉᮹đŝෝᱽ

᜽⦹۵äᮝಽၾ⩡Ჭ݅.

áᔪᨕ łᖁᙹಽ, ᯕ₉ඹ, ᮁᗮᇥ⡍, ᇥᔑ᮲ಆჶ, ⃽ᙹႊᱶ᜾, ᮁ⦽᫵ᗭ༉⩶

1. ᕽು

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Fig. 1. Velocity Structure for Curved Open-Channel Flow (Song et al., 2012)

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2. ᯕುᱢᩑǍ

2.1 ଲఙࠑକুंඑ

2.2 ଲఙࠑઽේැজࢺ࣑

Fig. 2. Linear Vertical Distributions of Horizontal Velocities Used in Moment of Momentum Method

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ǤǤǤ

৉ఢֽȵছଵ଀ȵ׌೾଀ȵੲ୨ָ

Song, Chang Geun, Seo, Il Won, Kim, Tae Won, Ahn, Jungkyu****

áᔪᨕ łᖁᙹಽ, ᯕ₉ඹ, ᮁᗮᇥ⡍, ᇥᔑ᮲ಆჶ, ⃽ᙹႊᱶ᜾, ᮁ⦽᫵ᗭ༉⩶

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