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 Fluids Dynamics o ai and wa e lows subjec ed o u bulence and
con on ed wi h cold on s in a h ee-inle -T-junc ion duc ollowed by wo 90-
deg ee elbows connec ed by a s aigh sec ion o adjus able leng h (C-shaped elbow)
Pape Tamsi Ndiaye 1, *, Goumbo Ndiaye 2, Moma h Ndiaye 1, 3, Ouma D ame 1, 4 and Oma Ngo Thiam 1, 4
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 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.
4 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.
Wo ld Jou nal o Ad anced Resea ch and Re iews, 2025, 27(02), 693-705
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 .2025.27.2.2839
Abs ac
This s udy examines ai and wa e lows in a h ee-inle T-junc ion duc ollowed by wo 90° elbows connec ed by a
s aigh sec ion o adjus able leng h (C-shaped elbow), wi h a pa icula ocus on he impac o he s aigh sec ion
leng h be ween he wo 90° elbows. The analysis ocuses on he beha io o he luids (ai and wa e ) along he duc
axis (x, y, z=0), a e he mixing zone (a 70 mm), ups eam o he i s elbow, and a he duc ou le . The nume ical
solu ion is based on he ealizable k-Ꜫ iscous u bulence model coupled wi h he ene gy equa ion, implemen ed in
Ansys Fluen 2024R2. Th ee s aigh sec ion leng h cases we e s udied: Case I (L= 20 mm), Case II (L=50 mm), and Case
III (L=100 mm). Acco ding o he esul s ob ained, he c-bend, consis ing o wo 90° elbows connec ed by he s aigh
sec ion, in ensi ies he u bulence wi hin he low, wi h e ec s depending on he he mophysical cha ac e is ics o he
luid (densi y, he mal conduc i i y, kinema ic iscosi y, e c.). The s aigh sec ion connec ing he wo 90° elbows
mode a es he combined dynamic and he mal dis u bances o he successi e elbows. I i is oo sho , i agg a a es he
dis u bances; i p ope ly dimensioned, i ac s as a s abilizing bu e zone, imp o ing he he mal and hyd aulic e iciency
o he duc .
Keywo ds: Ansys Fluen ; Ai and wa e mo emen ; C-elbow; CFD; Hea and mass ans e ; ealizable k-ε u bulence
model; S aigh sec ion; T-Junc ion;
1. In oduc ion
Mixing ai a di e en empe a u es is essen ial o ensu e op imal he mal com o and sa is ac o y indoo ai quali y.
In he ields o hea ing, en ila ion, and ai condi ioning (HVAC), con olling he mo emen and in e ac ions be ween
ho and cold ai lows is essen ial. Simila ly, mixing wa e a di e en empe a u es is impo an in he design o
was ewa e ea men plan s, wa e ea men sys ems, sani a ion ne wo ks, and hyd aulic enginee ing. The geome y
o duc s ( ubes, channels, condui s, channels, and en s, e c.) s ongly in luences he low dynamics o bo h ai and wa e
o achie e accep able quali y. In piping ne wo ks, T- o Y- ype junc ions a e commonly used o dis ibu e o collec
lows. These junc ions, along wi h o he elemen s such as al es, u bines, pumps, elbows, elbow-junc ions,
con ac ions, expansions, me e s in oduce majo as well as mino p essu e losses, a ec ing he o e all e iciency o he
Wo ld Jou nal o Ad anced Resea ch and Re iews, 2025, 27(02), 693-705
694
sys ems. Many expe imen al and nume ical esea ch wo ks wi h ools such as Ansys Fluen , OpenFOAM ha e been
ca ied ou o be e unde s and his phenomenon [1-16].
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 was p esen ed by A hulya A. Sa e al. [1]. The ollowing conclusions we e d awn based on hei s udy:
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 ound ha conside ing he luid alone, he
phase sepa a ion is g ea e a he ou le han a he junc ion.
Nimadge M .G.B. e al. [2] aimed 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 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 s a ed wi h an expe imen al
se up o ob ain e e ence da a as he luid passes h ough he pipe T-junc ion, and hen he same da a we e used o
CFD analysis using so wa e such as ANSYS FLUENT.
Khan Wasim e al. [3] conduc ed a nume ical s udy on he mechanism o plug o ma ion du ing wo-phase gas-liquid
low in a T-junc ion mic ochannel. They de eloped a wo-dimensional (2D) model o he mic ochannel using ANSYS
Academic Resea ch CFD 18.2 so wa e and he olume o luid (VOF) me hod o sol e i . Thei esul s showed good
ag eemen wi h he expe imen al da a. They measu ed he plug leng h, p essu e d op, and eloci y a ia ions inside he
plugs o di e en ope a ing condi ions. The s udy also in es iga ed he in luence 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. They ound ha a low capilla y numbe (Ca), he liquid ilm o med was e y hin, obse able
only wi h ine meshes nea he channel walls.
DOROSHENKO Ya osla e al. [4] pe o med 3D modeling o he elbow and T-junc ion loca ed in he linea pa o a gas
pipeline, especially in a eas whe e he mul iphase low adop s complex ajec o ies and changes di ec ion. Based on he
Lag angian app oach (Disc e e Phase Model - DPM), hey de eloped nume ical modeling me hods o model he beha io
o mul iphase low in hese s uc u es, using ANSYS FLUENT R17.0 Academic so wa e. The ma hema ical model is
based on he solu ion o he Na ie -S okes equa ions and he disc e e phase con inui y and mo ion equa ions, coupled
wi h he Launde -Sha ma k-Ꜫ u bulence model, wi h sui able ini ial and bounda y condi ions. The esul s ob ained
allow a ho ough and comp ehensi e analysis o he e osi e wea o he elbow and T-junc ion o he linea pa o he
gas pipeline and adjacen sec ions o he pipeline, as well as an assessmen o hei s eng h and esidual se ice li e.
The eloci ies o liquid and solid pa icles, impac angles, diame e s o condensed d ople s and solid pa icles a he
collision si e we e de e mined. This wo k pa es he way o a be e unde s anding o e osi e wea phenomena in gas
pipelines.
RAID AHMED MAHMOOD [5] conduc ed a CFD simula ion o p edic and isualize he sepa a ion o wo-phase lows in
he e ical T-junc ion. A compa ison be ween he CFD esul s and he associa ed expe imen al da a was ca ied ou o
alida e he simula ions. Fo his pu pose ANSYS 17.1 was used o he nume ical simula ion, wi h a geome y o he T-
junc ion designed ia he ANSYS design module, based on he dimensions o he expe imen al sec ion, hen meshed
using ANSYS Meshing o ob ain a sui able mesh. Fu he mo e Chi iac Eugen e al. [6] conduc ed a nume ical s udy o a
h ee-inle Y-junc ion mic ochannel, using wo sepa a e so wa e ANSYS Fluen and Open-FOAM, unde iden ical inle
and bounda y condi ions. Th 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 by so li og aphy in PDMS (Polydime hylsiloxane) and was used o he alida ion o
nume ical simula ions. The mic ochannel was ab ica ed using PDMS (Polydime hylsiloxane) so li og aphy and used
o alida e nume ical simula ions. A compa ison o he simula ion esul s allowed e alua ing he espec i e
pe o mances o he wo nume ical codes in modeling low mixing in a mic ochannel.
Maka em M. A. [7] pe o med a CFD simula ion o s udy 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. Thei wo k ocuses on he hyd odynamic
analysis o low, mass ans e and CO₂ abso p ion pe o mance in a T-shaped mic ochannel geome y, in a s eady s a e
o he compu a ional luid dynamics echnique. Thei models a e based on he Na ie -S okes and con inui y equa ions
coupled wi h a lamina model wi h mass ans e be ween he e ogeneous phases. They examined he in luence o mass
ac ions o [Bmim] BF₄ (up o 10%) and TiO₂ (up o 0.1%) on CO₂ loading, bubble o ma ion and eloci y dis ibu ion
unde a ious gas-liquid e en ions. Thei esul s indica e ha he op imal composi ion (10% [Bmim] BF₄, 3% MEA,
0.04% TiO₂) allowed o achie e a maximum pu i ica ion a e o 79.62%.
Taha Enas Salman e al. [8] explo ed he impac 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. Using ANSYS FLUENT 2020R1 and he s anda d k-ε
Wo ld Jou nal o Ad anced Resea ch and Re iews, 2025, 27(02), 693-705
695
u bulence model, hey sol ed he con inui y, momen um, and ene gy equa ions. They analyzed he eloci y dis ibu ion
and p essu e d ops, u bulen kine ic ene gy, and dissipa ion. The esul s e ealed a ma ked di e gence in eloci y and
p essu e d ops, while hey showed simila beha io o he u bulence pa ame e s.
SAID Mohammed e al. [9] conduc ed a 3D nume ical simula ion o liquid/liquid wo-phase low in a ec angula
mic ochannel wi h a T-junc ion, using he olume o luid (VOF) me hod wi h ANSYS Fluen , combined wi h adap i e
meshing and a symme y assump ion o op imize he calcula ion. They iden i ied six dis inc low pa e ns by dispe sing
wa e in a con inuous silicone oil phase. Reducing he low a e a ios as well as he iscosi y leads o an inc ease in he
liquid ilm hickness in he co ne s and side planes, which signi ican ly a ec s he ilm and plug eloci ies.
Bush a Kha oon e al. [10] p oposed a nume ical simula ion and expe imen o analyze he hyd odynamics and mass
ans e in a c ossed T-junc ion mic ochannel subjec ed o a gas-liquid low sys em. The CO2-wa e hyd odynamic
simula ion ia ANSYS-FLUENT 2021 R2 wi h he luid olume echnique was alida ed by expe imen al da a. They
obse ed ha he o al olume ic mass ans e coe icien (ma gin 0.1–0.8 1/s) inc eases wi h gas eloci y, bu
dec eases wi h ilm hickness (0.01–0.05 mm) and empe a u e (T = 298.15 K and 303.15 K). An inc ease in bubble
eloci y also inc eases his coe icien , unlike ilm hickening, due o he dominan e ec o su ace ension.
Wang Fuzhang e al. [11] s udied he dynamics o uns eady ai and wa e in a h ee-inle T-shaped duc , ocusing on he
o ma ion o cold on s. Using he k-ε iscous model de eloped unde Ansys Fluen 2022R1, hey examined he low
e olu ion be o e and a e he bend. Th ee inle eloci y con igu a ions we e es ed. Ve i ica ion o he con e gence o
he esul s was ensu ed by pe o ming esidual and mesh independence analysis. Th ee cold on o ma ion
con igu a ions we e s udied acco ding o he a ia ions o he inle eloci y. When he inle eloci ies o cold ai /wa e
and ho ai /wa e we e equal, no cold on was no iceable a he ea ly s ages, al hough he ai eloci y emained highe
han ha o he wa e . The au ho s obse ed ha he maximum a e age kine ic ene gy o he o ices pe uni mass
de eloped mainly nea he T-junc ion, no as a di ec esul o he p e iously o med cold on s, bu due o he
eci cula ion o he p essu e gene a ed a he elbow, in luencing he eloci y o he cold lows coming om he wo
e ical inle s (inle 2 and inle 3).
Howe e , simila ly o Wang Fuzhang e al. [11], we p opose a CFD nume ical s udy and a compa a i e s udy be ween
he dynamics o ai and wa e h ough a h ee-inle T-junc ion duc ollowed by wo 90° elbows connec ed by a s aigh
sec ion o adjus able leng h (C-shaped elbow). We will s udy he in luence o he a ia ion o he leng h o he s aigh
sec ion connec ing he wo 90° elbows on he low and he o e all dynamics, in pa icula he eloci y ield, p essu e
and empe a u e a ia ions and u bulence, as well as how hey a y in he duc a a dis ance a e mixing, be o e he
elbows and a e he elbows. We will also s udy he impac o hese pa ame e s on he o ma ion and beha io o cold
on s, highligh ing he di e ences in beha io 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:
Wo ld Jou nal o Ad anced Resea ch and Re iews, 2025, 27(02), 693-705
696
Figu e 1 Illus a ion o he geome ic model (a h ee-inle -T-junc ion duc ollowed by wo 90-deg ee elbows
connec ed by a s aigh sec ion o adjus able leng h (C-shaped elbow))
In his s udy, we conside wo ci cula aluminum duc s o 40 mm diame e , whe e i is assumed ha ai and wa e low
sepa a ely in each o he duc s in he o m o a T-junc ion wi h h ee inle s ollowed by wo 90° elbows connec ed by a
s aigh sec ion o adjus able leng h (C-shaped elbow). 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 con igu a ion in 3D mode includes a i s ci cula su ace (CS1)
loca ed 30 mm om he mixing zone, a second ci cula su ace (CS2) loca ed 100 mm om he same zone, jus be o e
he i s elbow and an ou le su ace loca ed 20 mm om he second elbow o he duc (CS3). The ho luid (ai o wa e )
en e s he domain h ough inle 1 wi h a speed InV1 = 10 m/s and a empe a u e o 30 °C, on he o he hand he cold
luid inle s a e ound h ough inle s 2 and 3 wi h espec i ely speeds InV2 = InV3 = 3 m/s a 5 °C, which will a o cold
on s acco ding o Wang Fuzhang e al. [11], The low speed o he cold luid (ai and wa e ) a inle s 2 and 3 and a high
speed a inle 1 gene a es an ex ended cold on . The physical p ope ies o he luids a e summa ized in Table 1.
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 well, we conside ce ain simpli ying assump ions such as: luids (wa e and ai ) a e conside ed
incomp essible and New onian, quasi-cons an physical p ope ies, no phase change and ully u bulen and pe manen
low.
Wo ld Jou nal o Ad anced Resea ch and Re iews, 2025, 27(02), 693-705
697
2.2. Go e ning equa ions:
Gi en ha Reynolds A e aged Na ie -S okes (RANS) models ha e ce ain limi a ions, hey dese e o be ecognized as
among he mos eliable o cha ac e izing he eloci y ields o u bulen lows due o hei nea -wall modeling.
Tu bulence modeling (i.e., in ol ing he a e aging o he equa ions go e ning luid mo ion o e ime o space o ob ain
a mean 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 a mean and luc ua ing componen , wi h he
luc ua ions decaying apidly owa d ze o. Mo eo e , he RANS equa ions p o ide easonable esul s when in e ac ions,
sepa a ion, and eci cula ion a e simple.
The con inui y (1.a) and momen um (1.b) equa ions o he RANS a e aged Na ie -S okes a e as ollows:
( ) ( )
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 [12-13]. 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. [14]. 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
which inco po a es he mean squa e luc ua ion o he o ici y. In his easible k-ε iscous model, Shih e al. [15]
conside ed he eddy iscosi y no as a cons an , bu as a unc ion depending on he sys em o a ional angula eloci y,
he mean s ain and o a ion a es, and he u bulence p ope ies (ε and k).
The easible k-ε closu e model is es ima ed by wo equa ions (2) and (3):
L’équa ion de anspo de l’éne gie ciné ique u bulen e (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
=
Wo ld Jou nal o Ad anced Resea ch and Re iews, 2025, 27(02), 693-705
698
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: :
( )
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:
Gi en he nea impossibili y o ob aining an exac analy ical solu ion o he equa ions go e ning ou p oblem, a
nume ical app oach was a o ed. We used he ini e olume me hod, enowned o i s e iciency in e ms o memo y,
compu a ion ime, and nume ical s abili y, pa icula ly when dealing wi h complex geome ies [16]. Fo he
disc e iza ion o con ec i e e ms, we selec ed he QUICK scheme, known o limi ing nume ical di usion e ec s and
o e ing high accu acy in cap u ing g adien s [16]. This is pa icula ly ad an ageous o u bulen lows o hose wi h
s ong g adien s. The p essu e- eloci y coupling was ensu ed using he coupled scheme. Nume ical es s we e
conduc ed wi h igo ous con e gence c i e ia se a 10-6 o he con inui y, momen um, k-k, and ene gy equa ions o
ensu e accu acy, speed, and s abili y o he esul s. The mesh independence s udy was pe o med and ound
sa is ac o y. The nume ical solu ion was pe o med using Ansys Fluen 2024R2 so wa e.
Ou esul s we e alida ed h ough a sa is ac o y compa ison wi h hose o Wang Fuzhang e al. [11].
4. Analysis and discussion o esul s
Whe he ho o cold, each inle has i s own cha ac e is ics (sec ion, empe a u e and eloci y, e c.), which implies
dis inc physical p ope ies o each o he h ee inle s. These di e ences a e e lec ed in pa icula by po en ial
a ia ions in quan i ies such as 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 in each case o ai and wa e .
Wo ld Jou nal o Ad anced Resea ch and Re iews, 2025, 27(02), 693-705
699
Table 2 Mass low a e [kg/s]
Inle 1 [kg/s]
Inle 2 [kg/s]
Inle 3[kg/s]
Mo ion o ai
0.01539380400259
0.00461814120078
0.00461814120078
Mo ion o wa e
12.5437511472533
3.763125344176
3.763125344176
Table 3 To al hea ans e a e a he inle s [W]
Inle 1 [W]
Inle 2[W]
Inle 3[W]
Mo ion o ai
77.4639308116332
-92.9567169739598
-92.9567169739598
Mo ion o wa e
78,686.9509467201
-1,049,159.34595627
-1,049,159.34595627
The mee ing o he je s o he h ee inle s o addi ion o hei physical quan i ies (mass low a e o o al hea ans e
a e o momen um, e c. o each inle ) c ea es shocks o collisions a he mixing zone o he junc ion which will cause
s ong hyd odynamic and he mal in e ac ions, dis u bances and u bulence in he condui . To es ablish and s udy i s
consequences, he eloci y, empe a u e dis ibu ion and u bulen kine ic ene gy p o iles in he (x,y,z=0) plane 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, be o e he i s bend) and CS3 (i.e., he ci cula ou le su ace, loca ed 20 mm a e he second bend o he duc )
o di e en alues o he leng h o he s aigh sec ion connec ing he wo 90° elbowswi h h ee cases: case I (L= 20
mm), case II (L=50 mm) and case III (L=100 mm) a e p esen ed acco ding o he con ou s (Fig. 2-19).
We no e ha he mass low a e o inle 1 is g ea e han hose o inle s 2 and 3. Despi e his, a he in e sec ion, he
ho izon al je is dis u bed by he wo pe pendicula je s om he wo inle s (inle s 2 and 3). This causes a mixing zone,
eloci y g adien s, and an inc ease in local eloci y a he cen e o he junc ion. Flow accele a ion is also obse ed a e
he junc ion (mixing zone) and be o e he i s bend, ollowing he adial di ec ion, wi h he maximum eloci y
appea ing a he duc axis (Fig. 2-7).
Figu e 2 Veloci y dis ibu ion ac oss he domain o ai
dynamics - - Case I (L= 20 mm)
Figu e 3 Veloci y dis ibu ion ac oss he domain o
wa e dynamics - Case I (L= 20 mm)
Wo ld Jou nal o Ad anced Resea ch and Re iews, 2025, 27(02), 693-705
700
Figu e 4 Veloci y dis ibu ion ac oss he domain o ai
dynamics - Case II (L= 50 mm)
Figu e 5 Veloci y dis ibu ion ac oss he domain o
wa e dynamics - Case II (L= 50 mm)
Figu e 6 Veloci y dis ibu ion ac oss he domain o ai
dynamics - Case III (L= 100 mm)
Figu e 7 Veloci y dis ibu ion ac oss he domain o
wa e dynamics - Case III (L= 100 mm
A he bends (in 'C', he wo 90° elbows and he s aigh sec ion), hei cen i ugal e ec s and seconda y mo ions (Dean
o ices) cause he peak eloci y o be de lec ed owa d he inne wall o he wo bends. We obse e ha as he leng h
o he s aigh sec ion be ween he wo bends inc eases, he eloci y becomes mo e uni o m in his zone, and i s peak
inc eases up o L = 50 mm and dec eases he ea e . Fo example, o case I (L=20 mm), he speed can each 22.0 m/s
o ai and 22.1 m/s o wa e ; o case II (L=50 mm), he speed can each 22.3 m/s o ai and 23.2 m/s o wa e and
inally o case III (L=100 mm), hey all and he maximum speed is 21.8 m/s o ai and 21.9 m/s o wa e .
A su icien s aigh sec ion leng h allows o a es uc u ing o he eloci y p o ile be o e he second bend (in he egion
be ween he wo bends); ex ending his leng h is equi alen o so ening he g adien . I he sec ion is oo sho , he
u bulen s uc u es gene a ed by he i s bend can in e ac di ec ly wi h he second bend, ampli ying ins abili ies, and
he e ogeneous eloci y zones a e obse ed.
The leng h o he s aigh sec ion ac s as a bu e space o low s abiliza ion. I helps con ol he combined e ec s o
successi e bends on eloci y. I i is oo sho , i agg a a es dis u bances; i p ope ly dimensioned, i imp o es sys em
pe o mance.
Wa e eloci ies a e highe han hose o ai due o i s physical p ope ies. The u bulen low eloci ies o ai and wa e
h ough sec ions CS1 and CS2 appea o be nea ly iden ical o Cases I (Fig. 2, 3), Case II (Fig. 4, 5), and Case III (Fig. 6,
7). In CS2 he e ec o he i s bend begins o be el . In CS3, a e he wo bends he minimum eloci y is ejec ed
Wo ld Jou nal o Ad anced Resea ch and Re iews, 2025, 27(02), 693-705
701
owa ds he inne wall (blue spo a he bo om), a consequence o he supe imposed eci cula ions o he luid in he
wo bends (Dean o ex e ec ).
Figu e 8 Tempe a u e dis ibu ion ac oss he domain o
ai dynamics - Case I (L= 20 mm).
Figu e 9 Tempe a u e dis ibu ion ac oss he domain o
wa e dynamics - Case I (L= 20 mm).
Figu e 10 Tempe a u e dis ibu ion ac oss he domain
o ai dynamics - Case II (L=50 mm).
Figu e 11 Tempe a u e dis ibu ion ac oss he domain
o wa e dynamics - Case II (L=50 mm).
Figu e 12 Tempe a u e dis ibu ion ac oss he domain
o ai dynamics - Case III (L=100 mm).
Figu e 13 Tempe a u e dis ibu ion ac oss he domain
o wa e dynamics - Case III (L=100 mm)
