1
Analysis o Wake Cha ac e is ics o Con a-Ro a ing P opelle s by CFD
Sua Jeong1, Kwang-Jun Paik1,
*
Seong-Jin Eom1
1 Depa men o Na al A chi ec u e and Ocean Enginee ing, Inha Uni e si y, Incheon, Sou h Ko ea
Abs ac . This s udy aims o e alua e he wake low cha ac e is ics o a Con a-Ro a ing P opelle (CRP)
sys em h ough high- esolu ion nume ical simula ions and analyze hei in luence on p opulsion pe o mance.
A CRP, consis ing o wo coaxial p opelle s o a ing in opposi e di ec ions, enhances p opulsion e iciency by
eco e ing esidual o a ional ene gy and a enua ing o ex in ensi y in he wake low. This con igu a ion
con ibu es o uel sa ings and g eenhouse gas educ ion, p o iding a p ac ical solu ion o mee ing
en i onmen al egula ions such as he In e na ional Ma i ime O ganiza ion (IMO)’s ne -ze o a ge o 2050.
In his s udy, he Reynolds-A e aged Na ie -S okes (RANS) and La ge Eddy Simula ion (LES) models we e
applied o simula e he low a ound a CRP sys em. Compa a i e analyses we e conduc ed o examine
di e ences in wake low s uc u es, h us and o que cha ac e is ics, and ip o ex o ma ion cap u ed by each
u bulence model. The o ex gene a ion, de elopmen , and dissipa ion p ocesses we e isualized using Q-
c i e ion and axial eloci y ields, enabling a mo e de ailed in e p e a ion o he wake dynamics. The LES model,
in pa icula , demons a ed supe io capabili y in esol ing ine-scale low s uc u es and cap u ing uns eady
low beha io , such as o a ional ene gy eco e y and o ex b eakdown, which a e di icul o p edic wi h
ime-a e aged models like RANS. All simula ions we e pe o med using STAR-CCM+ ( e sion 18.06), and
mesh con e gence was alida ed using he G id Con e gence Index (GCI) me hod o ensu e nume ical
eliabili y. The esul s con i m ha LES is an e ec i e ool o analyzing he complex hyd odynamic
in e ac ions inhe en in CRP sys ems and p o ides aluable insigh s in o wake low physics. The indings o
his s udy a e expec ed o se e as a ounda ion o he design and op imiza ion o CRP sys ems and con ibu e
o he ad ancemen o high-e iciency, eco- iendly ship p opulsion echnologies.
Keywo ds: Con a-Ro a ing P opelle (CRP), RANS (Reynolds-A e aged Na ie -S okes), LES (La ge Eddy
Simula ion), Ene gy E iciency, Tu bulen Flow Analysis, CFD
1 In oduc ion
1.1 S eng hening o IMO En i onmen al Regula ions and he Need o Eco-F iendly P opulsion
Sys ems
In esponse o he inc easing demand o en i onmen al sus ainabili y, he In e na ional Ma i ime O ganiza ion
(IMO) adop ed he IMO 2023 G eenhouse Gas S a egy, which es ablishes an ambi ious a ge o achie ing ne -
ze o g eenhouse gas (GHG) emissions om in e na ional shipping by 2050. Fu he mo e, du ing he 83 d session
o he Ma ine En i onmen P o ec ion Commi ee (MEPC) held in Ap il 2025, he IMO in oduced manda o y
egula ions equi ing essels o 5,000 g oss onnage and abo e o main ain hei annual G eenhouse Gas Fuel
In ensi y (GFI) below a speci ied h eshold [1].
GFI is a comp ehensi e me ic ha no only e lec s he ca bon cha ac e is ics o ma ine uels bu also
inco po a es he o e all ene gy consump ion associa ed wi h ship cons uc ion, p opulsion e iciency, and
ope a ional condi ions. Consequen ly, me e uel subs i u ion is inadequa e o ensu e compliance wi h he e ised
egula o y amewo k. Ins ead, echnological inno a ions ha enhance ship p opulsion sys em e iciency ha e
become impe a i e, he eby accele a ing global in e es in eco- iendly p opulsion echnologies.
Among such echnologies, he con a- o a ing p opelle (CRP) sys em has eme ged as a p omising solu ion o
imp o ing p opulsion e iciency. The CRP sys em employs wo coaxial p opelle s o a ing in opposi e di ec ions,
whe ein he a p opelle e ec i ely eco e s he o a ional ene gy impa ed by he o wa d p opelle , educing
o a ional losses and mi iga ing o ex s eng h [2]. This mechanism no only leads o subs an ial uel sa ings bu
also con ibu es o he educ ion o GHG emissions, posi ioning he CRP sys em as a iable and p ac ical
echnology o compliance wi h eme ging en i onmen al s anda ds.
*
Co espondence o: [email p o ec ed]
16 h In e na ional Symposium on P ac ical Design o Ships and O he Floa ing S uc u es PRADS 2025
Ann A bo , MI, USA, Oc obe 19 h – 23 d 2025
2
Howe e , he inhe en p oximi y o he wo coun e - o a ing p opelle s ine i ably esul s in complex o ex
s uc u es and p onounced blade- o-blade in e ac ions wi hin he wake ield. Consequen ly, accu a e pe o mance
p edic ions o CRP sys ems emain challenging when elying solely on con en ional simpli ied models o
expe imen al me hods. Acco dingly, he p esen s udy aims o quan i a i ely e alua e he imp o emen s in
p opulsion e iciency a o ded by CRP sys ems and assess hei po en ial o comply wi h he la es IMO and MEPC
en i onmen al egula ions.
1.2 Cha ac e is ics o Con a-Ro a ing P opelle s (CRP)
The CRP sys em has been widely ecognized as an e ec i e solu ion o enhancing p opulsion e iciency by
eco e ing o a ional ene gy losses and educing o ex s eng h h ough he coun e - o a ion o he a p opelle ,
which cancels he esidual swi l gene a ed by he o wa d p opelle . This mechanism con ibu es no only o uel
sa ings bu also signi ican ly educes GHG emissions, he eby es ablishing he CRP sys em as a p ac ical and
iable echnology o comme cial ship applica ions.
Ne e heless, he inhe en ly close con igu a ion o he wo opposi ely o a ing p opelle s induces complex
wake o ex s uc u es and signi ican hyd odynamic in e ac ions, p esen ing subs an ial challenges in accu a ely
p edic ing he pe o mance o CRP sys ems. As such, con en ional simpli ied models and expe imen al me hods
a e insu icien o p ecise pe o mance e alua ion.
Mo eo e , he CRP sys em allows o he adjus men o a ious geome ic and ope a ional pa ame e s,
including blade numbe , diame e a io, sha spacing, and o a ion speed a io, all o which ha e a di ec impac
on p opulsion e iciency and pe o mance cha ac e is ics. P e ious s udies ha e epo ed ha a ia ions in hese
pa ame e s can esul in e iciency de ia ions o up o 5–10%, and e en mino adjus men s can lead o subs an ial
changes in o e all pe o mance due o he s ong hyd odynamic coupling be ween he wo p opelle s [3].
Acco dingly, a de ailed analysis o he wake low s uc u es in CRP sys ems, capable o cap u ing sub le
a ia ions in e iciency, is essen ial o p ac ical op imiza ion and design e inemen o CRP sys ems.
1.3 Necessi y o CFD and Po en ial Flow Analysis
In his con ex , high- ideli y compu a ional me hods based on Compu a ional Fluid Dynamics (CFD) ha e been
ac i ely employed o o e come he limi a ions o con en ional app oaches. While analyses u ilizing he Reynolds-
A e aged Na ie -S okes (RANS) equa ions a e e ec i e o p edic ing o e all low s uc u es, ad anced
u bulence modeling app oaches such as De ached Eddy Simula ion (DES) and La ge Eddy Simula ion (LES) ha e
ecen ly been adop ed o cap u e de ailed low phenomena, including ip o ex dynamics, blade- o-blade
in e ac ions, and ene gy ans e mechanisms.
Se e al s udies ha e highligh ed he supe io i y o LES in esol ing ip o ices and u bulen s uc u es,
making i an indispensable ool o quan i a i e analysis o he complex wake lows cha ac e is ic o CRP sys ems.
LES inco po a es wall ea men models such as he Wall-Adap ing Local Eddy-Viscosi y (WALE) model o
accu a ely cap u e nea -wall bounda y laye lows, while di ec ly esol ing he ene gy cascade and o ex
b eakdown p ocesses in he wake egion, allowing LES o ep oduce much ine low s uc u es han hose
a ainable wi h RANS [4].
When applied o wake low analysis, LES enables he quan i a i e e alua ion o low ield cha ac e is ics using
a ious diagnos ic ools, including ene gy spec um analysis, Q-c i e ion-based o ex isualiza ion, ime-
a e aged eloci y ields, and u bulence in ensi y dis ibu ions, acili a ing he iden i ica ion o de ailed u bulen
s uc u es ha a e di icul o esol e using RANS o po en ial low me hods.
Al hough p e ious s udies ha e ex ensi ely in es iga ed he gene al pe o mance and low ield cha ac e is ics
o CRP sys ems, he p esen s udy speci ically ocuses on he p ecise analysis o changes in wake low s uc u es
esul ing om a ia ions in p opelle o a ional speed. In he case o elec ic p opulsion essels, which allow eal-
ime adjus men o p opelle RPM, such op imiza ion is c ucial o imp o ing p opulsion e iciency unde a ying
ope a ional condi ions and is also highly ele an in e ms o complying wi h en i onmen al egula ions.
Meanwhile, Paik e al. [5] conduc ed RANS-based simula ions coupled wi h SPIV measu emen s o in es iga e
he wake e olu ion and p ima y low cha ac e is ics o CRP sys ems, while Paik [6] also employed RANS me hods
o analyze wake s uc u es and pe o mance a ia ions. These s udies demons a ed ha while RANS me hods a e
e ec i e in e alua ing he gene al low cha ac e is ics, he inhe en limi a ions o he a e age go e ning equa ions
es ic hei capabili y in esol ing ine-scale o ex s uc u es and u bulen low phenomena, indica ing he
necessi y o complemen a y high- esolu ion analysis.
Howe e , due o he high compu a ional cos associa ed wi h LES, i s applica ion ac oss all o a ional speed
condi ions is imp ac ical. The e o e, his s udy adop s a complemen a y app oach combining RANS-based
simula ions and po en ial low me hods. High- ideli y wake low analyses a e conduc ed using LES a selec ed
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op imized o a ion speeds and p opelle con igu a ions, while b oade pa ame ic s udies a e pe o med using
po en ial low codes and RANS simula ions o iden i y op imal ope a ing condi ions.
Highe -o de Bounda y Elemen Me hod (BEM) app oaches, such as he one de eloped by Paik, Suh, and
Chun [7], ha e been widely applied o he pe o mance e alua ion o ma ine p opelle s unde s eady low
condi ions. Al hough such me hods ha e p o en e ec i e in gene al pe o mance p edic ion, hey emain limi ed
in esol ing he in ica e wake o ex in e ac ions p esen in CRP sys ems.
Acco dingly, his s udy employs mul iple u bulence models, including RANS, DES, and LES, o conduc a
de ailed in es iga ion o he wake low cha ac e is ics o CRP sys ems and o quan i a i ely analyze a ia ions in
low s uc u es and p opulsion pe o mance induced by changes in o a ional speed. The comme cial CFD sol e
STAR-CCM+ was u ilized o all simula ions, and he eliabili y o he esul s was ensu ed h ough g id
con e gence e i ica ion using he G id Con e gence Index (GCI) [8].
I is an icipa ed ha he ou comes o his s udy will p o ide aluable insigh s o he op imiza ion o CRP
designs h ough he quan i a i e analysis o complex wake lows, he eby con ibu ing o he de elopmen o eco-
iendly, high-e iciency ship p opulsion sys ems.
2 Me hodology
2.1 Nume ical Me hods
In his s udy, a combined app oach employing bo h Compu a ional Fluid Dynamics (CFD) and po en ial low
me hods was adop ed o accu a ely p edic he wake low cha ac e is ics o a con a- o a ing p opelle (CRP)
sys em unde a ying o a ional speeds. This complemen a y s a egy enabled he le e aging o he s eng hs o
each me hod while compensa ing o hei espec i e limi a ions.
The CFD analyses we e ca ied ou using he comme cial so wa e STAR-CCM+ (Ve sion 18.06), applying
wo u bulence modeling app oaches as desc ibed in he ollowing sec ions.
2.1.1 Nume ical Me hods : Po en ial
Fo he ini ial pe o mance p edic ion and wake low analysis o he CRP sys em, a po en ial low code
de eloped by Paik e al. [7] was u ilized. This me hod is based on he Vo ex La ice Me hod (VLM), which
assumes in iscid and incomp essible low condi ions, and sol es he Laplace equa ion, gi en as Equa ion (1), as
i s go e ning equa ion:
∇2𝜙 = 0
(1)
whe e 𝜙 is he eloci y po en ial. Sou ce dis ibu ions and o ex la ices we e placed on he blade su aces o
model he en i e low ield. The sou ce dis ibu ion was adjus ed o sa is y he Ku a condi ion a he blade ailing
edge, ensu ing smoo h low sepa a ion and enabling physically consis en modeling o he wake o ex s eng h.
Addi ionally, o inco po a e he in e ac ions cha ac e is ic o CRP sys ems in o he po en ial low model, he
low ield gene a ed by he o wa d p opelle was accoun ed o in he calcula ion o he a p opelle , he eby
enabling he simula ion o blade- o-blade in e ac ion phenomena inhe en o con a- o a ing sys ems. Unde his
con igu a ion, he a p opelle ecei ed he eloci y ield gene a ed by he o wa d p opelle as i s in low bounda y
condi ion, allowing he calcula ion o h us , o que, and e iciency while conside ing he in e e ence e ec s
be ween he wo p opelle s.
2.1.2 Nume ical Me hods : RANS
The Reynolds-A e aged Na ie -S okes (RANS) model p edic s he mean low ield by applying s a is ical
a e aging o he go e ning equa ions h ough Reynolds decomposi ion, whe ein he u bulen luc ua ion
componen s a e ep esen ed as a e aged e ms. While he RANS model exhibi s limi a ions in cap u ing complex
low phenomena such as bounda y laye sepa a ion and la ge-scale o ex s uc u es, i o e s he ad an ages o
high compu a ional e iciency and he capabili y o p edic he o e all low ield cha ac e is ics.
The go e ning equa ions o incomp essible New onian luids a e exp essed using Eins ein's index no a ion,
as shown in Equa ion (2):
𝜕𝑢𝑖
𝜕𝑡 + 𝑢𝑗
𝜕𝑢𝑖
𝜕𝑥𝑗= − 1
𝜌
𝜕𝑝
𝜕𝑥𝑗+ 𝑣 𝜕2𝑢𝑖
𝜕𝑥𝑗
2
(2)
4
whe e 𝑢𝑖 is he low eloci y, 𝜌is he luid densi y, 𝑝 is he p essu e, and 𝑣 is he kinema ic iscosi y. By applying
Reynolds decomposi ion o he eloci y componen s and pe o ming ime-a e aging, he go e ning equa ions can
be e o mula ed as he Reynolds-A e aged Na ie -S okes (RANS) equa ions, gi en as Equa ion (3):
𝜕𝑢𝑖
𝜕𝑡 + 𝑢𝑗
𝜕𝑢𝑖
𝜕𝑥𝑗= − 1
𝜌
𝜕𝑝
𝜕𝑥𝑖+ 𝑣 𝜕2𝑢𝑖
𝜕𝑥𝑗
2−𝜕𝑢𝑖
′𝑢𝑗
′
𝜕𝑥𝑗
(3)
In hese equa ions, he las e m on he igh -hand side ep esen s he Reynolds s ess enso , which mus be
modeled using an app op ia e u bulence model. In he p esen s udy, he Shea S ess T anspo (SST) 𝑘 −
𝜔 model was employed o p opelle low analysis. The 𝑆𝑆𝑇 𝑘 − 𝜔 model combines he s eng hs o he s anda d
𝑆𝑆𝑇 𝑘 − 𝜔 o mula ion in he nea wall egion wi h he 𝑆𝑆𝑇 𝑘 − 𝜀 model cha ac e is ics in he ee s eam egion,
enabling mo e accu a e p edic ions o low sepa a ion and o ex gene a ion compa ed o con en ional wo-
equa ion models.
Al hough he RANS app oach signi ican ly enhances compu a ional e iciency by a e aging he en i e low
ield, i s capabili y o esol e ine-scale o ices and u bulen s uc u es is inhe en ly limi ed by he u bulence
model applied.
2.1.3 Nume ical Me hods : LES
La ge Eddy Simula ion (LES) applies spa ial il e ing o he Na ie -S okes equa ions, enabling he di ec
esolu ion o la ge-scale u bulen eddies h ough nume ical me hods, while he e ec s o smalle subg id-scale
(SGS) eddies a e modeled using app op ia e subg id-scale models. The go e ning equa ions o LES a e he
il e ed Na ie -S okes equa ions, gi en as Equa ion (4):
𝜕𝑢𝑖
𝜕𝑡 + 𝑢𝑗
𝜕𝑢𝑖
𝜕𝑥𝑗= −1
𝜌
𝜕𝑝
𝜕𝑥𝑖+ 𝑣 𝜕2𝑢𝑖
𝜕𝑥𝑗
2−𝜕𝜏𝑖𝑗
𝜕𝑥𝑗
(4)
whe e 𝜏𝑖𝑗 deno es he subg id-scale (SGS) s ess enso , ep esen ing he e ec s o un esol ed smalle eddies on
he esol ed low ield.
In he p esen s udy, he Wall-Adap ing Local Eddy-Viscosi y (WALE) model was employed o compu e he
u bulen iscosi y, p o iding accu a e p edic ions e en wi hin nea -wall bounda y laye s. The WALE model
adjus s he u bulen iscosi y locally no only in egions o high shea s ess bu also in a eas domina ed by s ong
o a ional o ices, o e ing supe io accu acy in wall-bounded low egions compa ed o con en ional LES wall
ea men models. This capabili y enables he high- esolu ion simula ion o bounda y laye sepa a ion as well as
he gene a ion and dissipa ion o ip o ices, e en in highly complex low egions.
By in eg a ing CFD and po en ial low analyses, a complemen a y app oach was adop ed in his s udy, whe ein
he po en ial low me hod acili a ed apid pa ame ic s udies, while LES was applied o high- ideli y low ield
analysis. This combined app oach enabled comp ehensi e in es iga ions o wake low s uc u es unde a ious
p opelle o a ional speed condi ions, he eby suppo ing e icien and eliable pe o mance assessmen s o he
CRP sys em.
2.1.4 Nondimensionaliza ion o Single P opelle and CRP Sys em
Fo he analysis o he CRP sys em conduc ed in his s udy, he pe o mance coe icien s we e
nondimensionalized based on he o wa d p opelle , ollowing he me hodology p oposed by Van Manen [9].
The key nondimensional pe o mance pa ame e s ad ance coe icien (𝐽), h us coe icien (𝐾𝑇), and o que
coe icien (𝐾𝑄) a e de ined by Equa ions (5) – (7), espec i ely:
𝐴𝑑𝑣𝑎𝑛𝑐𝑒 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡(𝐽)= 𝑉
𝑎
𝑛𝑓𝐷𝑓
(5)
𝑇ℎ𝑟𝑢𝑠𝑡 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡(𝐾𝑇)= 𝑇𝑓+ 𝑇𝑎
𝜌𝑛𝑓
2𝐷𝑓
4
(6)
𝑇𝑜𝑟𝑞𝑢𝑒 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡(𝐾𝑄) = 𝑛𝑓𝑄𝑓+ 𝑛𝑎𝑄𝑎
𝜌𝑛𝑓
3𝐷𝑓
5
(7)
5
whe e 𝑉
𝑎 is he in low eloci y, 𝑛𝑓 and 𝑛𝑎 a e he o a ional speeds o he o wa d and a p opelle s, espec i ely,
𝐷𝑓 is he diame e o he o wa d p opelle , and 𝑇𝑓, 𝑇𝑎, 𝑄𝑓, and 𝑄𝑎 ep esen he h us and o que o he o wa d
and a p opelle s, espec i ely.
All nondimensionaliza ion was pe o med using he o a ional speed and diame e o he o wa d p opelle as he
e e ence pa ame e s. This app oach was adop ed o e alua e he o e all p opulsion pe o mance o he CRP
sys em based on he o wa d p opelle cha ac e is ics.
2.2 Ta ge Model
Fo his s udy, a con a- o a ing p opelle (CRP) sys em de eloped by Hyundai Hea y Indus ies was selec ed
as he e e ence model [10]. This CRP sys em was speci ically designed o ull-scale ship applica ions wi h he
objec i e o maximizing p opulsion e iciency and enhancing o a ional ene gy eco e y pe o mance. The
p incipal pa icula s o he analyzed CRP sys em a e de ailed in Table 1. Expe imen al luid dynamics (EFD) da a
o his CRP sys em we e ob ained om model es s conduc ed a a scale a io o 1/42.063 in he deep-wa e owing
ank o he Hyundai Ma i ime Resea ch Ins i u e (HMRI). These es s, including open-wa e and sel -p opulsion
expe imen s, ha e been epo ed in Min e al. [10] and p o ide he e e ence o he p esen CFD alida ion.
Table 1. P incipal pa icula s o he con a- o a ing p opelle sys em analyzed in his s udy
Fo wa d P opelle
A e P opelle
Diame e
9.1 m
7.9 m
Numbe o Blades
5
4
RPM
70.1 RPM
93.5 RPM
Th us Ra io
50
50
Sepa a ion Dis ance
2.06 m
In low eloci y
12.86 m/s
2.3 Compu a ional Se up
All CFD simula ions we e pe o med using he comme cial so wa e STAR-CCM+ (Ve sion 18.06). Fo he
RANS simula ions, he Shea S ess T anspo 𝑆𝑆𝑇 𝑘 − 𝜔 u bulence model was employed o esol e he ime-
a e aged low ield wi h pa icula emphasis on he accu a e p edic ion o nea wall bounda y laye beha io .
Th oughou he en i e blade su ace, he dimensionless wall dis ance Y+ was main ained below 1.5, as shown in
Figu e 1. Fo he LES simula ions, he Wall-Adap ing Local Eddy Viscosi y (WALE) model was adop ed o
explici ly esol e he majo u bulen s uc u es. The ime s ep size o bo h RANS and LES simula ions was
de e mined in acco dance wi h he In e na ional Towing Tank Con e ence (ITTC) ecommended guidelines [11]
o ensu e nume ical s abili y and esul accu acy. The compu a ional domain was disc e ized using an uns uc u ed
mesh app oach. Addi ional mesh e inemen was applied in he icini y o he p opelle blades and wi hin he
downs eam wake egion o adequa ely cap u e wake con ac ion phenomena, u bulen ene gy ans e , and he
o ma ion and decay o ip o ices.
Figu e 1. Compu a ional mesh opology a ound he CRP p opelle and downs eam wake egion used o CFD analysis.
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2.4 G id Con e gence Index
To ensu e he eliabili y o he CFD esul s, g id con e gence e i ica ion was pe o med ollowing he
p ocedu es ecommended by he In e na ional Towing Tank Con e ence (ITTC). The G id Con e gence Index
(GCI) me hod, as p oposed by Celik e al. [8], was employed o quan i a i ely assess disc e iza ion unce ain y.
Fo his pu pose, h ee le els o mesh esolu ion we e p epa ed, and he sensi i i y o he key pe o mance
pa ame e s speci ically, he h us coe icien (𝐾𝑇) and o que coe icien (𝐾𝑄) was e alua ed. The GCI me hod
p o ides an es ima e o he disc e iza ion e o associa ed wi h he ines mesh and enables he calcula ion o he
con e gence a io (𝑅𝐺), he eby acili a ing he assessmen o he g id independence o he nume ical solu ion.
In his s udy, he GCI analysis was conduc ed o he LES simula ions, and he coa se mesh con igu a ion
ob ained om he analysis was subsequen ly applied in he RANS simula ions. The esul s o he g id con e gence
s udies o he h us and o que coe icien s a e summa ized in Tables 2 and 3, espec i ely.
Table 2. G id con e gence s udy o h us coe icien (𝐾𝑇) using G id Con e gence Index (GCI) me hod
Num. o G id [M]
𝐾𝑇
𝑅𝐺
GCI
Coa se
64.2
0.7498
0.102
0.137 %
Medium
90.8
0.7571
Fine
128.4
0.7578
Table 3. G id con e gence s udy o o que coe icien (𝐾𝑄) using G id Con e gence Index (GCI) me hod
Num. o G id [M]
𝐾𝑄
𝑅𝐺
GCI
Coa se
64.2
0.1463
0.133
0.185 %
Medium
90.8
0.1478
Fine
128.4
0.1481
Figu e 2. G id con e gence end o h us coe icien (𝐾𝑇) and o que coe icien (𝐾𝑄) wi h espec o he numbe o g ids.
As shown in Figu e 2, he GCI alues o bo h he h us coe icien 𝐾𝑇 and o que coe icien 𝐾𝑄 we e
con i med o be wi hin app oxima ely 0.1%, he eby e i ying he g id con e gence o he nume ical simula ions.
Figu e 3 shows he compu a ional domain and bounda y condi ions used in his s udy. A cylind ical domain was
a anged along he p opelle axis, wi h an axial leng h o app oxima ely 8D, so ha he in low and he gene a ion
and dissipa ion o he wake could be adequa ely ep oduced. The in low was se as an inle , whe e a uni o m in low
eloci y and u bulence condi ions we e imposed, while he ou low plane was de ined as an ou le wi h a p essu e-
based bounda y condi ion. The ou e wall o he domain was assigned a slip bounda y condi ion. This condi ion
assumes ha he luid slides along he wall wi hou ic ion, modeling a s a e wi hou iscous esis ance, in which
he angen ial eloci y componen is allowed o low eely while he no mal eloci y componen is supp essed.
Th ough his se ing, he g ow h o iscous bounda y laye s and shea s esses nea he wall a e elimina ed,
ensu ing ha he ou e bounda y o he domain does no impose a i icial e ec s on he low. Figu e 4 p esen s he
ac ual mesh dis ibu ion a ound he p opelle blades and he wake egion. F om he on iew and he axial c oss-
7
sec ion, bounda y-laye esol ing p ism laye s a e a anged nea he blade su aces, wi h a g adual ansi ion in
g id size. To accu a ely cap u e he gene a ion, de elopmen , and ajec o y o he ip o ices shed om he blade
ips, local mesh e inemen was applied along he p edic ed o ex pa h. This inely e ined egion was designed
o ensu e ha he o ices o med in he wake a e s ably esol ed wi hou nume ical dissipa ion o a i icial
a enua ion, and he mesh was ex ended downs eam o encompass he en i e wake dissipa ion egion.
Figu e 3. Compu a ional domain and bounda y condi ions o p opelle CFD analysis
Figu e 4. Compu a ional mesh opology a ound he p opelle blade and wake egion
8
3 Resul s and Discussion
In his s udy, he wake low cha ac e is ics o a con a- o a ing p opelle (CRP) sys em we e in es iga ed
h ough compa a i e simula ions employing bo h RANS and LES app oaches. These me hods we e used o
calcula e he axial eloci y dis ibu ion and analyze he wake low s uc u es o he CRP sys em. In addi ion, he
LES model was applied o compa e he low cha ac e is ics be ween he single o wa d p opelle and he CRP
con igu a ion, wi h he objec i e o quan i a i ely demons a ing he e iciency bene i s o he CRP sys em.
3.1 Compa ison o Single P opelle Pe o mance: EFD, CFD, and Po en ial Flow Analysis
3.1.1 Compa ison o Single P opelle Pe o mance Resul s
Figu e 5. Compa ison o single o wa d p opelle pe o mance esul s om EFD, RANS and po en ial low analysis.
The pe o mance esul s o he single p opelle ob ained om expe imen al luid dynamics (EFD) es s
conduc ed by Hyundai Hea y Indus ies we e compa ed wi h hose de i ed om CFD simula ions and po en ial
low calcula ions. As shown in Figu e 4, all h ee me hods yielded closely aligned esul s and ends, wi h
disc epancies wi hin app oxima ely 5%. This close ag eemen among he EFD, CFD, and po en ial low esul s
con i ms he eliabili y o he nume ical me hods employed in his s udy.
3.1.2 Compa ison o CRP Sys em P opulsion Pe o mance (POW) Resul s
Figu e 6. Compa ison o CRP sys em p opulsion pe o mance (POW) esul s om EFD, CFD (RANS, LES), and po en ial
low analysis
9
As shown in Figu e 6, when compa ed wi h he EFD esul s, he nume ical analyses conduc ed using po en ial
low, RANS, and LES exhibi ed only mino disc epancies in he absolu e alues o h us coe icien (𝐾𝑇) o que
coe icien (𝐾𝑄), and e iciency (𝜂𝑂). Howe e , he di e ences emained app oxima ely 5%, and he o e all
ag eemen ac oss he en i e ange o ad ance a ios was e y good. Fu he mo e, he gene al ends ob ained om
each nume ical app oach we e almos iden ical o hose o he expe imen al esul s. These indings indica e ha
he nume ical me hods employed in his s udy p o ide eliable esul s, he eby ensu ing su icien alida ion o
subsequen analyses o he wake low ield and o ex s uc u e cha ac e is ics.
3.2 Compa ison o CRP Wake Flow S uc u es: RANS and LES
The wake low s uc u es o he CRP sys em we e analyzed and compa ed based on simula ions conduc ed
using bo h RANS and LES app oaches. In all cases, he low ields we e isualized using he nondimensional axial
eloci y componen (𝑢/𝑈) as he e e ence pa ame e .
(a) (b)
Figu e 7. Compa ison o CRP wake low s uc u es om RANS and LES analysis, isualized by axial eloci y 𝑢/𝑈 con ou s
As shown in Figu e 7, he compa ison o CRP wake low s uc u es isualized by axial eloci y (𝑢/𝑈) con ou s
e eals dis inc di e ences be ween he RANS and LES simula ions. Figu e 7(a) p esen s he esul s om he
RANS simula ion, whe e he wake low exhibi ed a smoo he and ela i ely simpli ied o ex s uc u e as i
p og essed downs eam. In con as , Figu e 7(b), which shows he LES simula ion esul s, e ealed mo e
p onounced u bulen ene gy dispe sion and ine o ex s uc u es, ep esen ing a low ield ha mo e closely
esembles ac ual low beha io .
These obse a ions indica e ha he highe spa ial and empo al esolu ion inhe en o he LES app oach
enables he accu a e cap u e o ine scale o ices wi hin he wake, he eby allowing o a mo e de ailed and
ealis ic analysis o he wake low s uc u es.
3.3 Compa ison o P opelle Flow and Wake S uc u es Using LES: Single P opelle s. CRP Sys em
Based on he LES simula ions, he wake low s uc u es o he single p opelle and he con a- o a ing p opelle
(CRP) sys em we e compa ed and analyzed.
