Co esponding au ho : Pape Tamsi Ndiaye
Copy igh © 2025 Au ho (s) e ain he copy igh o his a icle. This a icle is published unde he e ms o he C ea i e Commons A ibu ion Liscense 4.0.
Compu a ional luid dynamics (CFD) o a h ee-inle -Y-junc ion duc connec ed o a
U-bend: In luence o inle eloci ies on ai and wa e lows subjec ed o cold on s
and u bulence
Pape Tamsi Ndiaye 1, *, Goumbo Ndiaye 2, Oma Ngo Thiam 1, 3, Moma h Ndiaye 1, 4 and Ouma D ame 1, 3
1 Fluid Mechanics and T ans e Labo a o y, Depa men o Physics, Sciences and Technologies Facul y, Cheikh An a DIOP
Uni e si y, Daka -Fann, Senegal.
2 The Wa e , Ene gy, En i onmen and Indus ial P ocesses Labo a o y o he Poly ech Highe School, Cheikh An a Diop
Uni e si y, Daka , Senegal.
3 Resea ch G oup on Sola Ene gy and T ans e s (GREST), Sciences and Technologies Facul y, Cheikh An a DIOP Uni e si y,
Daka -Fann, Senegal.
4 Depa men o he U Hyd aulics, Ru al Enginee ing, Machine y and Renewable Ene gy,Uni e si y o Sine Saloum Elhadji
Ib ahima NIASS, Kaolack, Senegal.
Wo ld Jou nal o Ad anced Resea ch and Re iews, 2025, 27(02), 680-692
Publica ion his o y: Recei ed on 30 June 2025; e ised on 09 Augus 2025; accep ed on 11 Augus 2025
A icle DOI: h ps://doi.o g/10.30574/wja .2025.27.2.2838
Abs ac
This s udy p esen s he mo emen o ai and wa e lowing in a Y-junc ion duc wi h h ee connec ed inle s o a U-bend
wi h a en ion o he impac o cold on s. Analyses we e ca ied ou o obse e he beha io o he luids (ai and
wa e ) a he duc axis, a e he mixing zone (a 70 mm), jus ups eam o he bend and downs eam, a he ou le . The
ealizable k-ε iscous u bulence model coupled wi h he ene gy equa ion we e sol ed nume ically using Ansys Fluen
2024R2. Th ee cases o cold on o ma ion we e s udied acco ding o he inle eloci ies. An ex ended cold on
appea s when he cold luid en e s slowly om inle s 2 and 3, while a high eloci y a inle 1 (case II) can ex end he
on o ou le CS3. The U-bend ac s as a u bulence ampli ie , bu he esponse o he luid in ques ion (ai and wa e )
depends bo h on hei physical p ope ies (densi y, kinema ic iscosi y, and ine ia) and hei physicochemical
cha ac e is ics. The complex dynamics o hese lows a e explained no only by mechanical phenomena bu also by
in e molecula in e ac ions: wa e (a pola molecule), capable o o ming hyd ogen bonds and suscep ible o cold on s,
eac s di e en ly om ai , a mix u e o non-pola gases wi h weak in e molecula in e ac ions.
Keywo ds: Ansys Fluen ; Ai and wa e mo emen ; CFD; Hea and mass ans e ; ealizable k-ε u bulence model; T-
Junc ion; U-bend
1. In oduc ion
Essen ial o achie ing op imal he mal com o and accep able indoo ai quali y, he mixing o ai a di e en
empe a u es is an impo an issue. In hea ing, en ila ion, and ai condi ioning (HVAC), ai quali y con ol conside s
he mas e y o he mo emen o ho and cold ai essen ial. Also, he mixing o wa e a di e en empe a u es is
conside ed du ing he cons uc ion o was ewa e ea men plan s, wa e ea men , and hyd aulic enginee ing. The
shape o duc s, ubes, channels, condui s, channels, and en s plays a majo ole in ai and wa e dynamics o achie ing
accep able indoo ai o wa e quali y, ho ai con ol, was ewa e managemen , plan cons uc ion, wa e ea men ,
and hyd aulic enginee ing. Whene e i is necessa y o di ide o combine lows, join s (T, Y, e c.) a e used in he main
piping sys ems.
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681
Along wi h join s, many o he obs acles such as al es, u bines, pumps, elbows, elbow-junc ions, con ac ions,
expansions, me e s may be p esen . They a ec he o e all e iciency by causing majo and mino losses in he pipes. A
lo o wo k on junc ions o expe imen al and nume ical CFD se ups wi h ools such as ANSYS FLUENT, OPENFOAM a e
used o his pu pose [1-16].
A hulya A. Sa e al. [1] p esen ed a mul iphase low model h ough he T-junc ion and he phase edis ibu ion
phenomenon a he junc ion using ANSYS FLUENT so wa e. Based on hei s udy, he ollowing conclusions we e
d awn: i can be seen ha a la ge amoun o ai pocke is o med in he lowe pa o he bypass a m, phase sepa a ion
is negligible in he bypass a m due o he e ec o g a i y and by analyzing he mul iphase low, hey saw ha
conside ing he luid alone, phase sepa a ion is g ea e a he ou le han a he junc ion.
Nimadge M .G.B. e al. [2] se he goal o s udy he s eady and incomp essible low o a luid h ough a T-junc ion and o
ge amilia wi h CFD by ocusing on losses in piping sys ems, as he wo king luid h ough pipes plays an impo an
ole in he ope a ion o indus ies such as chemical indus ies, pe oleum indus ies, e c. They p epa ed an expe imen al
se up o ob ain he e e ence da a when he luid passes h ough he T-junc ion o he pipe, he same da a is used o
CFD analysis using so wa e such as ANSYS FLUENT.
Khan Wasim e al. [3] nume ically s udied he plug o ma ion mechanism du ing gas-liquid wo-phase low in a T-
junc ion mic ochannel by de eloping a wo-dimensional (2D) model o he mic ochannel using ANSYS Academic
Resea ch CFD 18.2 so wa e and adop ing he olume o luid (VOF) me hod o sol e i . Thei ob ained esul s ag ee
well wi h he expe imen al esul s. The plug leng h, p essu e d op, and eloci y a ia ions inside he plugs we e
measu ed unde di e en ope a ing condi ions. The e ec s o con ac angle (0°–155°), luid iscosi y, and su ace
ension on he wo-phase low in e ac ion pa ame e s, as well as he e ec o gas and liquid supe icial eloci ies, we e
examined in de ail. They ound ha he liquid ilm o med a low capilla y coun (Ca) was e y hin and was obse ed
only o ine meshes nea he channel wall.
DOROSHENKO Ya osla e al. [4] ca ied ou 3D modeling o he elbow and T-junc ion in he linea pa o he gas
pipeline, especially a he places whe e a complex mo emen o mul iphase lows occu s and changes i s di ec ion. Based
on he Lag angian app oach (Disc e e Phase Model - DPM), nume ical modeling me hods we e de eloped o simula e
he mul iphase low mo emen in he elbow and T-junc ion o he linea pa o he gas pipeline using he ANSYS Fluen
R17.0 Academic so wa e package. The ma hema ical model is based on sol ing he Na ie -S okes equa ions and closed
disc e e phase con inui y and mo ion equa ions wi h he Launde -Sha ma wo-pa ame e u bulence model (k-e) wi h
app op ia e ini ial and bounda y condi ions. These esul s p o ide he oppo uni y o a comp ehensi e and in-dep h
s udy o he e osi e wea o he elbow and T-junc ion o he linea pa o he gas pipeline and adjacen pipeline sec ions,
as well as an assessmen o hei s eng h and esidual li e. The eloci y o liquid and solid pa icles, he impac angles,
he diame e s o condensed d ople s and solid pa icles a he collision si e we e de e mined. Such s udies open he
p ospec o a comp ehensi e and in-dep h esea ch on he e osi e wea o elbows and T-junc ions in he linea sec ion
o gas pipelines.
RAID AHMED MAHMOOD [5] p esen ed a CFD simula ion s udy o p edic and isualize he sepa a ion o wo-phase
lows in he e ical T-junc ion and a compa ison be ween he CFD esul s and he associa ed expe imen al esul s o
alida e hei CFD esul s. Using ANSYS 17.1 o pe o m he simula ion, he geome y o he T-junc ion was gene a ed
by ANSYS modula design based on he dimensions o he expe imen al es sec ion and hen passed o he ANSYS mesh
o gene a e a sui able mesh.
A nume ical s udy in a h ee-inle Y-junc ion mic ochannel was ca ied ou wi h wo di e en nume ical codes: ANSYS
Fluen and Open-FOAM by Chi iac Eugen e al. [6]. Using he same inle and bounda y condi ions, h ee main pa ame e s
a e s udied: eloci y ampli ude, p essu e and o ici y ampli ude. The mic ochannel was ab ica ed using PDMS
(Polydime hylsiloxane) so li og aphy and we e used o he alida ion o nume ical simula ions. The simula ion
esul s we e analyzed and a compa ison be ween he nume ical codes was ca ied ou wi h he aim o es ing he
capabili ies o he wo nume ical codes in a simula ion o low mixing in a mic ochannel.
Maka em M. A. [7] p oposed a CFD simula ion o CO2 cap u e in a mic ochannel by aqueous mix u es o MEA and
[Bmim] BF4 modi ied wi h TiO2 nanopa icles as chemical addi i es. The low hyd odynamics, mass ans e
cha ac e is ics and CO₂ abso p ion pe o mance o he p oposed sol en we e in es iga ed in a T-shaped mic ochannel
s uc u e by s eady-s a e compu a ional luid dynamics echnique. To p esen a de ailed model, he Na ie -S okes and
con inui y equa ions a e combined wi h a wo-phase lamina low module accoun ing o mass ans e be ween
he e ogeneous phases. The e ec s o [Bmim]BF₄ and TiO₂ mass ac ions on CO₂ loading, bubble o ma ion, and eloci y
p o ile we e hen s udied a di e en gas and liquid holdups, wi h an ionic liquid ac ion anging om 0% o 10% and
Wo ld Jou nal o Ad anced Resea ch and Re iews, 2025, 27(02), 680-692
682
a nanopa icle ac ion anging om 0% o 0.1%. Acco ding o hei simula ion esul s, he sol en con aining 10%
[Bmim]BF4, 3% MEA, and 0.04% TiO2 exhibi ed he maximum pu i ica ion ac ion o 79.62%.
Taha Enas Salman e al. [8] examined he in luence o u bulen pa ame e s on he cha ac e is ic cen e line o a luid
low h ough a T-junc ion connec ed o a Ven u i ube ia a pipe. The con inui y equa ion, momen um equa ion and
ene gy equa ion o wa e a e modeled and sol ed using ANSYS FLUENT 2020R1 so wa e while o u bulence, he
s anda d ype u bulen model (k-ε) is used. The model is ob ained on he eloci y dis ibu ion, p essu e d op
dis ibu ion, u bulen kine ic ene gy and u bulen dissipa ion a e. The esul s showed a di e gence in he alues o
he e ec o he T-junc ion on he Ven u i me e ega ding he eloci y dis ibu ion and p essu e d op, while hey
showed a simila beha io o he u bulence pa ame e s.
A h ee-dimensional (3D) nume ical simula ion o a liquid/liquid wo-phase low was ca ied ou in a ec angula
mic ochannel wi h a T-junc ion by SAID Mohammed e al. [9]. They used he olume o luid (VOF) me hod wi h ANSYS
Fluen o cap u e he in e ace be ween he wo phases and he dynamic mesh adap a ion echnique along wi h he
assump ion o a symme y plane helped hem educe he compu a ional cos . Thei s udy ocused on he low pa e ns
and hyd odynamics o plugs and hei esul s e ealed six dis inc low pa e ns by dispe sing wa e in a con inuous
silicone oil phase. By dec easing he low a e a io as well as he iscosi y a io, he liquid ilm hickness inc eases in
he co ne s and side planes. In u n, his has a signi ican impac on he liquid ilm eloci y and he plug eloci y.
Bush a Kha oon e al. [10] conduc ed nume ical and expe imen al s udies o he analysis o hyd odynamics and
olume ic mass ans e coe icien in a c oss-T junc ion mic ochannel o a wo-phase gas-liquid low sys em. Ini ially,
he CO2-wa e hyd odynamic simula ion was pe o med using ANSYS-FLUENT 2021 R2 wi h he luid olume
echnique. The compu a ional luid dynamics model was alida ed by compa ing he esul s wi h expe imen al da a.
The esul s ob ained in nume ical simula ion and expe imen al wo k show ha he o al olume ic mass ans e
coe icien (ma gin 0.1–0.8 1/s) inc eases wi h inc easing gas eloci y, bu i dec eases wi h inc easing ilm hickness
(0.01–0.05 mm) and empe a u e (T = 298.15 K and 303.15 K). I was obse ed ha wi h inc easing bubble eloci ies,
he o al mass ans e coe icien also inc eases, and wi h inc easing ilm hickness, i shows he opposi e e ec due o
he dominan pa ame e s in he mic ochannel, i.e., su ace ension.
Wang Fuzhang e al. [11] p esen ed a pape on he dynamics o uns eady ai and wa e h ough a h ee-inle T-shaped
duc , ocusing on he p oblem o cold on s. They pe o med simula ions o no ice he na u e o hese luids some
dis ances a e mixing (70 mm), be o e u ning he duc and a e u ning he duc . They sol ed he easible k-ε iscous
model and ene gy equa ion nume ically using Ansys Fluen 2022R1. The examina ion o esidual independence and
meshing was aken in o accoun o check he con e gence o he esul s. Conside ing he a ia ion o inle eloci y, hey
examined h ee cases o cold on o ma ion. When he inle eloci ies o cold ai /wa e and wa m ai /wa e a e he
same, he o ma ion o he cold on is in isible a he ea ly s age despi e he ac ha ai lows as e han wa e . They
ound ha he op imal a e age o ex kine ic ene gy pe uni mass o med nea he T-junc ion, no due o p e iously
o med cold on s, bu due o he p essu e eci cula ion a he bend a ec ing he eloci y o he cold luid subs ance
coming om he wo adjacen inle s (i.e., Inle 2 and Inle 3).
Howe e , like Wang Fuzhang e al. [11], we p opose a CFD s udy and a compa a i e analysis be ween he dynamics o
ai and wa e h ough a Y-junc ion duc (no T-junc ion unlike Wang Fuzhang e al. [11]) ollowed by a h ee-inle U-
bend whe e mixing and cold on s s a a 70 mm om he h ee inle s. We will s udy he e ec s o he a ia ion o he
h ee inle eloci ies o he luids (ai and wa e ) cold o ho on he low and he o e all dynamics ( eloci y ield,
p essu e a ia ions, empe a u e and u bulence) and how hey a y in he duc a a dis ance a e mixing, be o e he
bend and a e he bend and a ec he o ma ion and e olu ion o cold on s. We will also emphasize he di e ence
be ween ai and wa e .
2. Ma hema ical Fo mula ion
2.1. Desc ip ion o he physical model and simpli ying assump ions:
In his wo k, we conside ed wo ci cula aluminum duc s o 40 mm diame e , whe e i was assumed ha ai and wa e
ci cula e sepa a ely in each o he duc s in a Y-junc ion shape wi h h ee inle s ollowed by a U-bend. As shown in Figu e
1, he mixing zone is loca ed 70 mm om inle s 1, 2 and 3 in each o hese duc s. The geome ic s uc u e in 3D mode,
p esen s a ci cula su ace (CS1) loca ed 30 mm om he mixing domain, ano he ci cula su ace loca ed 100 mm om
he mixing domain (CS2) and an ou le loca ed 20 mm om he duc bend (CS3). The ho luid (ai o wa e ) en e s he
domain h ough inle 1 wi h a eloci y InV1 and a empe a u e o 30 °C, while he cold luid inle s a e loca ed h ough
inle s 2 and 3 wi h eloci ies InV2 and InV3 a 5 °C, espec i ely. The physical p ope ies o luids a e lis ed in Table 1.
Wo ld Jou nal o Ad anced Resea ch and Re iews, 2025, 27(02), 680-692
683
Figu e 1 Illus a ion o he geome ic model ( h ee-way Y-junc ion ollowed by a U-bend)
Table 1 The physical p ope ies o he luid conside ed : ai and liquid wa e
Ai
liquid wa e
Densi y ρ : [Kg/m3]
1.225
998.2
Viscosi y µ : [Kg/(m.s)]
1.7894-× 10-5
1.003× 10-3
The mal Conduc i i y k : [W/(m.K)]
0.0242
0.6
Speci ic Hea Cp : [J/(Kg.K]
1006.43
4182
To ca y ou his wo k, we admi some simpli ying hypo heses such as: he luids (wa e and ai ) a e incomp essible
and New onian, he physical p ope ies a e quasi-cons an , he e is no phase change and he low is ully u bulen and
pe manen .
2.2. Go e ning equa ions
Al hough Reynolds A e aged Na ie -S okes (RANS) models ha e some limi a ions bu dese e o be ecognized as he
mos eliable o cha ac e izing eloci y ields o u bulen lows due o nea -wall modeling, u bulence modeling (i.e.,
in ol ing a e aging he equa ions go e ning luid mo ion o e ime o space o ob ain an a e age low ield and
addi ional e ms ep esen ing u bulence e ec s), eliable o highe Reynolds numbe s, inhe en ly assumes ha
u bulen luc ua ions can be decomposed in o an a e age and luc ua ing componen , wi h he luc ua ions decaying
apidly owa d ze o. Mo eo e , RANS p o ides easonable esul s when in e ac ions, sepa a ion, and eci cula ion a e
simple [12-13]. In his s udy, he easible k-ε iscous model o RANS by Shih e al. [14] conside ed he eddy iscosi y no
as a cons an , bu as a unc ion depending on he angula o a ional eloci y o he sys em, he a e age de o ma ion and
o a ional eloci ies, as well as he u bulence p ope ies (k and ε).
The con inui y (1.a) and momen um (1.b) equa ions o a e aged Na ie -S okes called RANS a e as ollows:
Wo ld Jou nal o Ad anced Resea ch and Re iews, 2025, 27(02), 680-692
684
( ) ( )
0
i
i
i i j ij
i i j
i i j
u
x
p
u u u u u
x x x
=
+ = − + −
………(1)
Since he e a e mo e unknowns han equa ions, a s a egy o “close” he sys em a is equi ed. The easible k-ε closu e
model is accu a e o s udying he eloci y dis ibu ion o u bulen low h ough a cu ed channel, acco ding o
Shaheed e al. [15]. I cap u es o a ion, o ices, s ong cu a u e o he s eamline, and he unknown dissipa ion ε ha
inco po a es he mean squa e luc ua ion o he o ici y.
I is es ima ed by wo equa ions (2) and (3):
• The u bulen kine ic ene gy anspo equa ion (k): :
( )
( )
j k b M
j j k j
k
k ku P P Y
x x x
+ = + + + − −
……… (2)
Whe e he physical quan i ies a e: densi y (
), mean eloci y componen (
j
u
), molecula dynamic iscosi y (
),
u bulen iscosi y (
), u bulen P and l numbe o k (
k
), p oduc ion o k due o shea (
k
P
), p oduc ion o k
due o buoyancy (
b
P
), dissipa ion a e o k (), con ibu ion o expansion in comp essible lows (
M
Y
).
• The dissipa ion a e anspo equa ion (Ꜫ) :
( )
( )
2
1 2 1 3
jb
j j j
u C S C C C P
x x x k
k
+ = + + − +
+
(3)
Whe e he physical quan i ies a e: Tu bulen P and l numbe o ε (
), s ain a e modulus S,
2ij ij
S S S=
a ec
1
2
j
i
ij
ji
u
u
Sxx
=+
e
=
• Closu e: u bulen iscosi y
✓ The u bulen iscosi y is gi en by :
2
C
=
✓
1max 0.43, 3
C
=
+
,
k
S
=
,
22
3
ij ij ij
kS
= − +
✓
C
depends on he low, i is no cons an :
0
1
S
Ck
A A s
=
+
✓ Wi h
04.04A=
e
6cos
S
A
=
, which depends on he local s uc u e o he low
1
3
1cos 6
3
ij jk ki
S S S
S
−
=
;
ij ij
S S S=
;
0.09C
=
;
11.44C
=
;
21.9C
=
;
1.0
k
=
;
1.2
=
• The ene gy conse a ion equa ion can be exp essed as ollows::
Wo ld Jou nal o Ad anced Resea ch and Re iews, 2025, 27(02), 680-692
685
( )
je
j j j
TT
Tu
x x x
+=
(4)
In Eq. (4):
✓ T ep esen s he empe a u e,
✓ λe is an e ec i e coe icien ha includes he con ibu ion o u bulen mixing in addi ion o molecula conduc ion
and can be exp essed as:
P
e
Cp
=+
, whe e k and Cp a e he he mal conduc i i y and speci ic hea a
cons an luid p essu e and µ is he u bulen iscosi y.
✓ P is a u bulen P and l numbe , we will ake: P = 0.85.
3. Nume ical Modeling and Valida ion:
Since i is i ually impossible o ob ain an exac analy ical solu ion o he equa ions o ou p oblem, we will eso o a
nume ical solu ion. The ini e olume me hod was used [16]. I is mo e economical in e ms o olume and compu a ion
ime while ensu ing high compu a ional s abili y and is mo e e icien han classical ini e di e ence me hods o
complex geome y p oblems. We op ed o he QUICK scheme o disc e ize he con ec i e e ms. I minimizes nume ical
di usion e ec s and is enowned o i s accu acy in ep esen ing g adien s, and is pa icula ly e ec i e o u bulen
lows and high g adien s. Fo he p essu e- eloci y coupling, we chose he coupled scheme [16]. Nume ical es s a e
pe o med wi h con e gence h eshold esiduals o he con inui y, mo ion, k-epsilon, and ene gy equa ions equal o
10-6 in o de o add ess bo h speed, accu acy, and be e con e gence o he calcula ions. Mesh independence was
in es iga ed and ound o be sa is ac o y. We pe o med he nume ical solu ion using Ansys Fluen 2024R2.
Thanks o a sa is ac o y compa ison wi h esul s o Wang Fuzhang e al. [11] and we alida ed ou wo k.
4. Analysis and discussion o esul s
Each inle , whe he ho o cold, has i s own cha ac e is ics (sec ion, empe a u e and speed, e c.), which implies dis inc
physical p ope ies depending on he cases s udied: case I (InV1= InV2= InV3 = 3), case II (InV1 =10; InV2 = InV3 =3) and
case III (InV1 =3; InV2 = InV3 =10). These di e ences a e e lec ed in pa icula by po en ial a ia ions in he mass low
a e and he o al hea ans e a e o each inle , which di ec ly in luences he low dynamics and he hea ans e
phenomena in he duc . Tables 2 and 3 p esen he mass low a e and he o al hea ans e a e o each inle o each
case o ai and wa e .
Table 2 Mass low a e [kg/s]
Case (Inle Veloci ies [m/s])
Inle 1 [kg/s]
Inle 2 [kg/s]
Inle 3[kg/s]
Mo ion o ai
Case I
InV1 = InV2 = InV3 = 3
0.00461814120078
0.00461814120078
0.00461814120078
Mo ion o wa e
3.763125344176
3.763125344176
3.763125344176
Mo ion o ai
Case II
InV1=10; InV2 = InV3 =3
0.01539380400259
0.00461814120078
0.00461814120078
Mo ion o wa e
12.5437511472533
3.763125344176
3.763125344176
Mo ion o ai
Case III
InV1=3; InV2 = InV3 = 10
0.00461814120078
0.01539380400259
0.01539380400259
Mo ion o wa e
3.763125344176
12.5437511472533
12.5437511472533
The mee ing o he je s om he h ee inle s o he addi ion o hei physical quan i ies c ea es shocks o collisions in
he mixing zone o he junc ion which will gene a e s ong hyd odynamic and he mal in e ac ions, dis u bances and
u bulence in he condui . To e alua e and s udy i s e ec s, he eloci y, empe a u e dis ibu ion and u bulen kine ic
ene gy p o iles in he plane (x,y,z=0) and a sec ions CS1 (i.e., he ci cula su ace 30 mm a e mixing), CS2 (i.e., ano he
ci cula su ace 100 mm om he mixing domain) and CS3 (i.e., he ci cula ou le su ace, loca ed 20 mm a e he duc
bend) wi h h ee cases: case I (InV1= InV2= InV3 = 3), case II (InV1 =10 ; InV2 = InV3 =3) and case III (InV1 =3 ; InV2 = InV3
=10) a e p esen ed acco ding o he con ou s (Figu e 2-19).
Wo ld Jou nal o Ad anced Resea ch and Re iews, 2025, 27(02), 680-692
686
Table 3 To al hea ans e a e a he inle s [W]:
CaseInle Veloci ies [m/s]
Inle 1 [W]
Inle 2[W]
Inle 3[W]
Mo ion o ai
Case I
InV1 = InV2 = InV3 = 3
23.23917924349
-92.9567169739598
-92.9567169739598
Mo ion o wa e
78,686.9509467201
-314,747.80378688
-314,747.80378688
Mo ion o ai
Case II
InV1=10; InV2 = InV3 =3
77.4639308116332
-92.9567169739598
-92.9567169739598
Mo ion o wa e
262,289.836489067
-314,747.80378688
-314,747.80378688
Mo ion o ai
Case III
InV1=3; InV2 = InV3 = 10
23.23917924349
-309.855723246533
-309.855723246533
Mo ion o wa e
78,686.9509467201
-
1,049,159.34595627
-
1,049,159.34595627
The luid eloci y appea s o inc ease along he adial di ec ion, wi h he maximum eloci y occu ing a he pipe axis
(Figu e 2-7). A he in e sec ion, he ho izon al je is dis u bed by he wo inclined je s om he wo inle s (inle 2 and
inle 3). This causes eloci y g adien s (inc eased local eloci y, in ense mixing wi h high u bulence) and o ices in
he mixing zone a he cen e o he junc ion. Flow accele a ion is obse ed a e he junc ion (mixing zone) and be o e
he bend. A he bend, i s cen i ugal e ec causes he peak eloci y o be de lec ed owa d he ou e wall o he bend
and decele a ed owa d he inne wall. When a luid mo es om a s aigh pa h owa d a cu ed pipe (180° bend), he
low appea s o be subjec o a cen i ugal o ce ha pulls he luid ou wa d. This is compounded by a adial p essu e
a ia ion ha a emp s o compensa e o his cen i ugal o ce. I c ea es ans e se ins abili y and gene a es
seconda y lows, in addi ion o he main low. These seconda y lows o m wo coun e - o a ing o ices called Dean
o ices. Hence, he inc ease o maximiza ion o eloci y a he inne wall o he bend is due o he seconda y mo emen
(Dean o ex). The opposi e e ec occu s when he luid lea es he bend owa ds he s aigh pipe. A he ou e wall,
he a ea wi h he la ges adius, ic ion is g ea e , which can also lead o a slowdown.
The u bulen low speed o ai and wa e h ough sec ions CS1 and CS2 appea s o be almos iden ical o cases 1 (Figs.
2 and 3). They show an inc easingly homogeneous dis ibu ion o eloci y, highe in he cen e . In CS2, he e ec o he
bend begins o be el wi h he dec ease in eloci y a he bo om. In CS3, a e he bend he minimum eloci y is ejec ed
owa ds he inne wall (blue spo a he bo om which enla ges), he maximum eloci y is ejec ed owa ds he ou e
wall, which is due o he eci cula ion o he luid in he bend (Dean o ex e ec ). Fo Case II (InV1 = 10; InV2 = InV3 =
3), he mass low a e o inle 1 is highe han ha o inle s 2 and 3. The collision o he la e wo wi h he i s is no
s ong enough o dis u b i , hence he mixing zone o he junc ion is less agi a ed (Figu e 4,5). The eloci ies in CS1 and
CS2 a e highe han hose in Case I because i s mass low a e om inle 1 is g ea e and mo e imposing. The e ec o
he U-bend will be el in CS3. Fo Case III (InV1 = 3; InV2 = InV3 = 10), he cumula i e mass low a es o he h ee inle s
a e g ea e han hose in Cases II and I, leading o much s onge collisions and much s eepe eloci y g adien s,
esul ing in inc eased u bulence (Figu e 6,7). The eloci ies in CS1 and CS2 a e mo e signi ican han hose in Cases I
and II. The e ec s o he seconda y low o he Dean o ex a e mo e p onounced in case III, ollowed by case II and case
I. We ha e a be e hyd odynamic mixing espec i ely o case III, case II, and case I. The blue spo a he bo om (slow
luid) on CS3 is much mo e signi ican o ai han o wa e and much mo e pe sis en espec i ely o cases I, ollowed
by case II and case III (hyd odynamic mixing). This is due o he ac ha hyd ogen bonds a e mo e p esen in wa e
han in ai ( he dynamic iscosi y o wa e is g ea e han ha o ai ).
Wo ld Jou nal o Ad anced Resea ch and Re iews, 2025, 27(02), 680-692
687
Figu e 2 Veloci y dis ibu ion ac oss he domain o ai
dynamics - Case I (InV1= InV2= InV3 = 3).
Figu e 3 Veloci y dis ibu ion ac oss he domain o
wa e dynamics - Case I(InV1= InV2= InV3 = 3).
Figu e 4 Veloci y dis ibu ion ac oss he domain o ai
dynamics - Case II (InV1 =10 ; InV2 = InV3 =3).
Figu e 5 Veloci y dis ibu ion ac oss he domain o
wa e dynamics - Case II (InV1 =10 ; InV2 = InV3 =3).
Figu e 6 Veloci y dis ibu ion ac oss he domain o ai
dynamics - Case III (InV1 =3 ; InV2 = InV3 =10).
Figu e 7 Veloci y dis ibu ion ac oss he domain o
wa e dynamics - Case III (InV1 =3 ; InV2 = InV3 =10).
Figu e 8-13 shows he ho low inle 1 and he o he wo inle s (inle 2 and inle 3) which ca y cold luid. Wi h he
mee ing o he cold lows on he ho low, a clea he mal ansi ion zone called cold on s a e o med and eme ge om
he mixing zone o he junc ion along he axis o he duc in he h ee cases (Case I, Case II and Case III). This o ma ion
o isible cold on s is e y impo an in he mixing domain. This is due o he signi ican changes obse ed in he
empe a u e dis ibu ion wi h he eloci ies o each inle .
Wo ld Jou nal o Ad anced Resea ch and Re iews, 2025, 27(02), 680-692
688
Figu e 8 Tempe a u e dis ibu ion ac oss he domain o
ai dynamics - Case I (InV1= InV2= InV3 = 3)..
Figu e 9 Tempe a u e dis ibu ion ac oss he domain o
wa e dynamics - Case I (InV1= InV2= InV3 = 3).
Figu e 10 Tempe a u e dis ibu ion ac oss he domain
o ai dynamics - Case II (InV1 =10 ; InV2 = InV3 =3).
Figu e 11 Tempe a u e dis ibu ion ac oss he domain
o wa e dynamics - Case II (InV1 =10 ; InV2 = InV3 =3).
Figu e 12 Tempe a u e dis ibu ion ac oss he domain
o ai dynamics - Case III (InV1 =3 ; InV2 = InV3 =10).
Figu e 13 Tempe a u e dis ibu ion ac oss he domain
o wa e dynamics - Case III (InV1 =3 ; InV2 = InV3 =10).
Fo Case I (InV1= InV2= InV3 = 3), he eloci ies o he cold lows a e equal o hose o he ho ones, we ha e a mo e
mode a e and con olled collision (Figu e 8,9). Fo Figu e 10, 11 (Case II (InV1 =10; InV2 = InV3 =3)), he hea o he
ho low om inle 1 is mo e imposing, so he empe a u e is li le dis u bed a ound he axis o he duc e en a e he
collision a he mixing zone. The e is a dominance o he ho in he cen al zone, on he axis o he duc and a p og essi e
cooling in he la e al zones. Fo Figu e 12, 13 (Case III (InV1 =3; InV2 = InV3 =10)), he ho low om inle 1 is weak
compa ed o he wo cold lows, so hinne o weakened a ound he axis o he duc .
