1
A nume ical s udy on noise p edic ion and CIS de e mina ion using CFD
Byeong-U You1, Kwang-Jun Paik1,
*
Ho-Won Lee1, Jun-Hwan Kim1
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 . Recen ly, he issue o unde wa e adia ed noise (URN) has been ac i ely discussed by in e na ional
o ganiza ions such as he In e na ional Ma i ime O ganiza ion (IMO) due o i s po en ial impac on ma ine
ecosys ems. Among he a ious sou ces o unde wa e noise, ex e nal h us e s ha e been iden i ied as
signi ican con ibu o s. The noise gene a ed by h us e s is pa icula ly s ong when ca i a ion occu s, as
ca i a ion complica es he noise cha ac e is ics and becomes a p ima y sou ce o unde wa e noise. Fo
subma ines, s eal h is di ec ly ela ed o su i al, making noise educ ion a c i ical conce n.This s udy ocuses
on p edic ing p opelle noise unde ca i a ing condi ions. Compu a ional Fluid Dynamics (CFD) analysis was
conduc ed o p edic he occu ence o Tip Vo ex Ca i a ion (TVC) in he p opelle and de e mine he
Ca i a ion Incep ion Speed (CIS). Nume ical simula ions we e pe o med o he i s ime using he NACA
16-020 wing sec ion in STAR-CCM+ e sion 18.06, applying Reynolds-A e aged Na ie -S okes (RANS),
La ge Eddy Simula ion (LES), and De ached Eddy Simula ion (DES) u bulence models. Addi ionally, noise
p edic ions we e ca ied ou using he F owcs Williams-Hawkings (FW-H) equa ion and compa ed wi h
expe imen al esul s om a ca i a ion unnel. Based on he simula ion esul s, he ca i a ion shape and
associa ed noise cha ac e is ics we e nume ically analyzed, and he eliabili y o he CFD p edic ions was
imp o ed. Fu he mo e, a p ocedu al app oach o de e mining CIS was es ablished. This s udy is expec ed o
p o ide undamen al insigh s o imp o ing he accu acy o unde wa e noise p edic ion using CFD and o
se e as a basis o u u e esea ch on he analysis and op imal design o ca i a ion-induced noise cha ac e is ics
o ma ine p opulso s.
Keywo ds: Compu a ional luid dynamics, Ca i a ion, TVC, CIS, Hyd oacous ic, NACA 16-020.
1 In oduc ion
Ca i a ion is a phenomenon in which local p essu e in a liquid apidly d ops below he apo p essu e, leading
o he o ma ion o mic oscopic apo ca i ies. This phenomenon ypically occu s a ound high-speed o a ing
equipmen such as p opelle s, pumps, and u bines, and he collapse o hese ca i ies gene a es s ong shock wa es
and high- equency noise. Ca i a ion induced by p opelle o a ion leads o e osion, ib a ion, and noise, esul ing
no only in pe o mance deg ada ion o p opulsion and u bine sys ems bu also in signi ican h ea s o ma ine
ecosys ems.
In ecen yea s, g owing global in e es in ma ine li e p o ec ion and ocean en i onmen conse a ion has led
o ac i e esea ch and egula o y e o s aimed a mi iga ing Unde wa e Radia ed Noise (URN) om ships. Majo
in e na ional o ganiza ions, including he In e na ional Ma i ime O ganiza ion (IMO), he Ma ine En i onmen
P o ec ion Commi ee (MEPC), he Ma ine S a egy F amewo k Di ec i e (MSFD), and NORSOK (No wegian
Indus y S anda ds), ha e p oposed guidelines and ecommenda ions o educing unde wa e noise om ships. In
pa icula , he MEPC has iden i ied ca i a ion as a majo sou ce o URN and issued ecommenda ions o noise
educ ion unde MEPC.1/Ci c.906 [1]
Agains his backd op, ex ensi e esea ch has been conduc ed o unde s and ca i a ion and URN cha ac e is ics.
Maines and A nd [2] sys ema ically in es iga ed he o ma ion and de elopmen mechanisms o ca i a ing ip
o ices. While A nd e al. [3] quan i a i ely in es iga ed he occu ence condi ions and o ex co e cha ac e is ics
o Tip Vo ex Ca i a ion (TVC) h ough classical s udies. Shin e al. [4] conduc ed model es s on NACA 16-020
and NACA 66(2)-415 hyd o oils o examine he noise cha ac e is ics associa ed wi h TVC, and Peng e al. [5]
in es iga ed he low cha ac e is ics o ip o ex ca i a ion and bubble cloud o ma ion mechanisms wi h and
wi hou ca i a ion using expe imen s on ellip ic hyd o oils.
In nume ical s udies, Pa k e al. [6] analyzed he o ma ion mechanisms and low cha ac e is ics o TVC on
NACA sec ions using CFD, while Ku e al. [7] nume ically p edic ed TVC and URN cha ac e is ics on NACA
*
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
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sec ions by combining CFD wi h a Bubble Dynamics model. Jeong e al. [8] p oposed a me hod o p edic ing
ca i a ion and Ca i a ion Incep ion Speed (CIS) o subma ine p opelle s using a bubble dynamics-based model.
Fu he mo e, Ku e al. [9] demons a ed he capabili y o CFD-based analysis o e ec i ely p edic TVC and URN
o subma ines. Recen ly, Asnaghi e al. [10] conduc ed high- esolu ion simula ions o ca i a ing ip o ex lows
and bubble dynamics using CFD wi h La ge Eddy Simula ion (LES). While Pa k e al. [11] nume ically p edic ed
hyd o oil TVC noise by coupling he Dissipa ion Vo ex Model wi h bubble heo y.
Howe e , mos exis ing s udies ha e been conduc ed unde limi ed u bulence models and g id esolu ions,
which has hinde ed he accu a e ep oduc ion o de ailed ca i a ion s uc u es and hei ime-pe iodic
cha ac e is ics. Di e ences in co e o ex s uc u e o ma ion and bounda y laye de elopmen depending on
u bulence models ha e been epo ed o signi ican ly a ec he accu acy o ca i a ion shape and unde wa e noise
p edic ions. The e o e, his s udy aims o o e come he limi a ions o p e ious esea ch by comp ehensi ely
compa ing and analyzing ca i a ion shapes and gene a ion cha ac e is ics o he NACA 16-020 hyd o oil unde
a ious u bulence models and g id densi ies.
In his s udy, he F owcs Williams–Hawkings (FW-H) equa ion was applied o p edic he sound p essu e le el
(SPL) gene a ed by ca i a ion. By sys ema ically analyzing SPL a ia ions wi h changes in he ca i a ion numbe ,
a quan i a i e co ela ion be ween ca i a ion phenomena and URN was es ablished. The pe o mance o a ious
u bulence models—including LES, Reynolds S ess Model (RSM), and De ached Eddy Simula ion (DES)—was
compa ed o e alua ing hei p edic i e capabili y. The in luence o u bulence models and g id esolu ion on he
accu acy o ca i a ion-induced URN p edic ion was assessed. No ably, high- esolu ion LES calcula ions exhibi ed
ends mo e consis en wi h expe imen al esul s han con en ional URANS and DES app oaches unde bo h
ca i a ing and non-ca i a ing condi ions. These indings p o ide a ounda ion o u u e s udies on he acous ic
cha ac e is ics o ship p opelle s unde ca i a ion and o he de elopmen o op imal design s a egies.
Fu he mo e, hey o e po en ial as a baseline da ase o e alua ing ca i a ion incep ion speed (CIS).
2 Nume ical se -up
2.1 Go e ning Equa ions
In his s udy, nume ical analysis was pe o med based on he incomp essible Na ie -S okes (NS) equa ions.
The go e ning equa ion o incomp essible low can be exp essed as:
𝜕𝑢𝑖
𝜕𝑡+𝑢𝑗𝜕𝑢𝑖
𝜕𝑥𝑗=−1
𝜌𝜕𝑝
𝜕𝑥𝑖+𝜐 𝜕𝑢𝑖
𝜕𝑥𝑗𝜕𝑥𝑗
(1)
whe e 𝑢𝑖is he a e aged eloci y, 𝑝 is he a e aged p essu e, 𝜌 is he luid densi y, 𝝊 is he kinema ic iscosi y.
The equa ion consis s o uns eady accele a ion, con ec i e e ms, p essu e g adien , and iscous di usion e ms.
To ep oduce a ious u bulen low cha ac e is ics, he ollowing ep esen a i e u bulence models we e
applied:
2.1.1 RSM
The Reynolds S ess Model di ec ly sol es Reynolds s ess e ms o p o ide high accu acy in p edic ing
u bulence aniso opy and second-momen e ec s, o e ing imp o ed p edic ion pe o mance o e s anda d wo-
equa ion RANS models, especially in lows wi h s ong cu a u e o o a ion.
2.1.2 DES
The De ached Eddy Simula ion model combines he ad an ages o RANS and LES by applying RANS in he
bounda y laye egion o educe compu a ional cos and LES in he ee-s eam egion o esol e la ge-scale eddies
and u bulen s uc u es.
2.1.3 LES
The La ge Eddy Simula ion model esol es la ge-scale u bulen s uc u es di ec ly, while smalle eddies a e
modeled using a Sub-G id Scale (SGS) model. LES p o ides high- esolu ion u bulence p edic ion in bo h space
and ime.
3
2.2 FW-H Equa ion
The F owcs Williams-Hawkings (FW-H) equa ion, de eloped by F owcs Williams and Hawkings, ex ends
Ligh hill's acous ic analogy by including bounda y and su ace e ec s, making i applicable o complex uns eady
low ields. The equa ion accoun s o monopole, dipole, and quad upole acous ic sou ce e ms o p edic he sound
emi ed in o he a - ield.
The gene al o m o he FW-H equa ion is as ollows.
1
𝑐02𝜕2𝑝′
𝜕𝑡2−𝛻2𝑝′=𝑢𝑗𝜕
𝜕𝑡[𝜌0𝑈𝑛𝑖𝛿(𝑓)]−𝜕
𝜕𝑥𝑖[𝑃𝑖𝑗𝑛𝑗𝛿(𝑓)]
+𝜕
𝜕𝑥𝑖𝑥𝑗[𝑇𝑖𝑗𝐻(𝑓)
(2)
2.3 Flow Condi ions and Mesh Gene a ion
The NACA 16-020 hyd o oil model was used wi h a cho d leng h C=80 mm and span leng h S=60 mm,
co esponding o an aspec a io o 1.5. The angle o a ack was se o 15°. The dis ance om he inle o he
hyd o oil was 375 mm, and he gap o he ank side walls was se a 100 mm. The o al ank leng h was 1400 mm.
Slip condi ions we e applied o he op, bo om, and side bounda ies, and eloci y inle and ou le condi ions we e
applied a he inle and ou le .
Figu e 1. NACA 16-020
Figu e 2. Domain and bounda y condi ions
2.4 Nume ical Me hod
Uns eady simula ions we e conduc ed o analyze he ansien low ield using STAR-CCM+ e . 18.06R8. A
second-o de empo al disc e iza ion scheme was used o imp o e ime accu acy. The Semi-Implici Me hod o
P essu e-Linked Equa ions (SIMPLE) algo i hm was applied o couple eloci y and p essu e ields, p o iding
obus nume ical s abili y.
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To simula e ca i a ion phenomena, a Volume o Fluid (VOF) model was used o cap u e he ee su ace, and
he Schne -Saue ca i a ion model [12] was adop ed. Acous ic p essu e da a we e ex ac ed and inpu o he FW-
H model o p edic ime- a ying SPL a moni o ing poin s. Fas Fou ie T ans o m (FFT) was applied o analyze
he SPL equency spec a.
Th ee u bulence models we e applied: RSM, DES, and LES. Fo DES, a hyb id app oach combining SST k−ω
o RANS egions and LES in sepa a ed egions was used. Fo LES, he Wall-Adap ing Local Eddy- iscosi y
(WALE) model was applied o imp o e he subg id-scale esolu ion.
3 Nume ical Valida ion
3.1 G id Sensi i i y and Con e gence Tes
3.1.1 Con e gence es
To e i y he eliabili y o he nume ical simula ion, a g id con e gence analysis was pe o med using
di e en mesh densi ies. The LES model was selec ed o he g id sensi i i y s udy. The simula ion condi ions
we e se o ma ch hose o he expe imen s conduc ed a Chungnam Na ional Uni e si y: ca i a ion numbe σ =
2.29, in low eloci y o 10.12 m/s, inle p essu e o 120.04 kPa, and wa e empe a u e o 25.9°C (co esponding
o a apo p essu e o 3336 Pa).
The G id Con e gence Index (GCI) me hod was employed o quan i a i ely assess mesh sensi i i y and
solu ion s abili y. The ime s ep was se o 1.0 × 10⁻⁵ s, based on he maximum equency obse ed in he
expe imen s. Mesh gene a ion was ca ied ou in STAR-CCM+ using an uns uc u ed o hogonal mesh app oach.
Nea -wall mesh e inemen was applied o ensu e a non-dimensional wall dis ance o y⁺ ≤ 1.
Fou mesh le els we e de ined: coa se (9.1 million cells), medium (20.0 million cells), ine (3 million
cells), and e y ine (71.2 million cells). GCI analysis showed ha he unce ain y in he li coe icien (𝐶𝐿) was
0.689%, con i ming good con e gence beha io . The g id e inemen a io was se o = 1.414, and he GCI was
calcula ed using he ollowing equa ion: This is based on Celik's me hod.[13]
𝐺𝐶𝐼𝑓𝑖𝑛𝑒
21 =1.25|𝑄1−𝑄2
𝑄1|
𝑟21
𝑝−1
𝑤ℎ𝑒𝑟𝑒,𝑝= 1
𝑙𝑛 (𝑟21)|𝑙𝑛|∈32
∈21||,∈𝑖𝑗=𝑄𝑖−𝑄𝑗
(3)
An R alue o 0.112 was ob ained o he li coe icien , which indica es mono onic con e gence. This was
ecommended by ITTC [14]. The con e gence beha io was classi ied as ollows:
𝑅=∈32
∈21{0<𝑅<1∶𝑚𝑜𝑛𝑜𝑡𝑜𝑛𝑖𝑐 𝑐𝑜𝑛𝑣𝑒𝑟𝑔𝑒𝑛𝑐𝑒
−1<𝑅<0∶𝑜𝑠𝑐𝑖𝑙𝑙𝑎𝑡𝑜𝑟𝑦 𝑐𝑜𝑛𝑣𝑒𝑟𝑔𝑒𝑛𝑐𝑒
|𝑅|≥1∶𝑑𝑖𝑣𝑒𝑟𝑔𝑒𝑛𝑐𝑒
(4)
Table 1. Calcula ions o disc e iza ion e o
3.1.2 Compa ison wi h Expe imen al Resul s
Fig. 3 compa es he ca i a ion pa e ns ob ained om nume ical simula ions wi h hose obse ed in
expe imen s conduc ed a Chungnam Na ional Uni e si y unde a ca i a ion numbe o σ = 2.29 and a a VOF
alue o 0.5, o a ious mesh densi ies. The nume ical esul s showed good ag eemen wi h he expe imen ally
𝝈
CASE
Base
size
Num
O
G id[M]
𝑪𝑳
𝑹𝑮
GCI (%)
2.29
Coa se
0.11
9.1
0.591
0.112
0.689
Medium
0.078
20.0
0.614
Fine
0.055
33.0
0.642
Ve y Fine
0.039
71.2
0.645
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obse ed ca i a ion pa e ns, and a clea end o imp o ed p edic ion accu acy was obse ed as he mesh densi y
inc eased.
Fig. 3 also p esen s a de ailed analysis o he changes in ca i a ion pa e ns wi h inc easing mesh esolu ion. In
pa icula , he de elopmen o TVC was cap u ed based on he c i e ion o VOF = 0.5. The LES model success ully
ep oduced he gene a ion and dissipa ion o la ge-scale eddies, closely eplica ing he ca i a ion s uc u es
obse ed in he expe imen s.
Fu he mo e, as he mesh esolu ion inc eased, he TVC s uc u es g adually con e ged owa d he
expe imen al esul s. This demons a es ha he combina ion o he LES model and high- esolu ion mesh is highly
e ec i e o he accu a e nume ical p edic ion o ca i a ion and TVC phenomena.
(a) Expe imen al Resul s om Chungnam Na ional Uni e si y (σ = 2.29)
(b) Coa se
(c) Medium
(d) Fine
(e) Ve y Fine
Figu e 3. Ca i a ion Pa e ns a Di e en Mesh Densi ies (VOF = 0.5)
Addi ionally, he analysis o Fig. 4 e ealed ha z-di ec ion o ici y ends o in ensi y wi h inc easing mesh
esolu ion, depending on he ca i a ion s uc u e. As he su ace mesh densi y inc eased, he o ex s eng h nea
he su ace became mo e p onounced. S ong o ex s uc u es and sepa a ion low we e obse ed nea he ailing
edge o he NACA p o ile.
In Fig. 5, he s eamline dis ibu ion was u he analyzed o in es iga e he low cha ac e is ics. I was
con i med ha egions o high- eloci y low de eloped along he ca i a ion s uc u es. A ela i ely high low
eloci y was obse ed nea he leading edge, while a low- eloci y egion, caused by low sepa a ion, was iden i ied
nea he ailing edge. These low cha ac e is ics signi ican ly in luence he loca ion o ca i a ion incep ion and
he o ma ion o o ex s uc u es.
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(a) Coa se
(b) Medium
(c) Fine
(d) Ve y Fine
Figu e 4. Z-Di ec ion Vo ici y and Ca i a ion a Di e en Mesh Densi ies a LES
(a) Coa se
(b) Medium
(c) Fine
(d) Ve y Fine
Figu e 5. S eamline and Ca i a ion a Di e en Mesh Densi ies a LES
Fig. 6 p esen s he eloci y dis ibu ion in he z-di ec ion a he posi ion o x/c = 0.5. This ep esen s he adial
eloci y componen ela i e o he NACA p o ile. I was obse ed ha , wi h inc easing mesh densi y, he bounda y
be ween high- and low- eloci y egions became mo e sha ply de ined. In he high- esolu ion mesh, he eloci y
g adien was dis inc ly cap u ed, allowing o a mo e p ecise ep oduc ion o he de ailed low s uc u es.
Addi ionally, Fig. 7 shows he o ici y dis ibu ion a he same posi ion as x/c = 0.5. In all mesh condi ions,
epea ed gene a ion and dissipa ion o o ici y we e obse ed. As he mesh esolu ion inc eased, he size and
in ensi y o he o ici y s uc u es became mo e p onounced. These esul s u he demons a e ha he
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combina ion o high- esolu ion mesh and he LES model is pa icula ly e ec i e o he accu a e p edic ion o
o ex s uc u es and u bulen mo ions.
(a) Coa se
(b) Medium
(c) Fine
(d) Ve y Fine
Figu e 6. Z-Di ec ion Veloci y a x/c = 0.5 o Di e en Mesh Densi ies a LES
(a) Coa se
(b) Medium
(c) Fine
(d) Ve y Fine
Figu e 7. Vo ici y Dis ibu ion a x/c = 0.5 o Di e en Mesh Densi ies a LES
Fig. 8 p esen s he p edic ed SPL esul s unde a ious mesh condi ions and compa es hem wi h expe imen al
da a (EFD, Expe imen al Fluid Dynamics). The analysis showed ha , as he mesh densi y inc eased, he p edic ed
ends o maximum sound p essu e (dB) and equency a ia ion g adually app oached he expe imen al esul s.
No ably, in he high- esolu ion mesh, he p ima y peak alues and equency anges o he SPL spec um exhibi ed
good ag eemen wi h he expe imen al da a.
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In his s udy, conside ing he SPL p edic ion esul s in conjunc ion wi h he GCI analysis and low pa e n
compa isons, he ine g id condi ion was ul ima ely selec ed as he inal compu a ional mesh o he analysis.
(a) Expe imen al Resul s om Chungnam Na ional Uni e si y (σ = 2.29)
(b) Coa se
(c) Medium
(d) Fine
(e) Ve y Fine
Figu e 8. Valida ion o Sound P essu e Le el (SPL) a Di e en Mesh Densi ies Using LES
Figu e 9 shows he compu a ion ime o each mesh esolu ion. Because compu a ion ime a ies depending
on he numbe o co es and he compu e speci ica ions, all alues we e no malized wi h espec o he compu a ion
ime o he Ve y Fine mesh. Consequen ly, he compu a ion imes o he Coa se, Medium, Fine, and Ve y Fine
meshes co esponded o app oxima ely 14%, 28%, 42%, and 100% o he Ve y Fine mesh ime, espec i ely.
9
Figu e 9. Rela i e Compu a ion Time o Di e en Mesh Densi ies
3.2 Valida ion Acco ding o Tu bulence Models
The p edic i e pe o mance o ca i a ion pa e ns was e alua ed o di e en u bulence models. Nume ical
simula ions we e conduc ed unde iden ical low condi ions using h ee u bulence models: LES, DES, and RSM.
The analysis condi ions we e se o ma ch he expe imen al condi ions o Chungnam Na ional Uni e si y:
ca i a ion numbe σ = 2.29, low eloci y o 10.12 m/s, inle p essu e o 120.04 kPa, and luid empe a u e o
25.9°C (co esponding o a sa u a ed apo p essu e o 3336 Pa).
Fig. 9 p esen s a compa ison o he ca i a ion s uc u es p edic ed by each u bulence model. The LES model
mos closely ep oduced he ca i a ion pa e ns obse ed in he expe imen s, indica ing i s supe io capabili y o
accu a ely cap u e u bulen s uc u es and he gene a ion and dissipa ion o eddies. In con as , he RSM and DES
models exhibi ed ela i ely s able and smoo he ca i a ion s uc u es, bu wi h less de ailed a iabili y compa ed
o he LES esul s.
(a) Expe imen al Resul s om Chungnam Na ional Uni e si y (σ = 2.29)
(b) RSM
(c) DES
(d) LES
Figu e 10. Ca i a ion Pa e ns by Tu bulence Model (VOF = 0.1)
The z-di ec ion o ici y dis ibu ions o each u bulence model, oge he wi h he co esponding ca i a ion
pa e ns, a e compa ed in Fig. 10. In he RANS-based RSM model, o ici y nea he su ace was ela i ely low,
and no dis inc eddy s uc u es indica i e o o ex o ma ion we e obse ed. In he DES model, he SST k–ω
model was applied in he bounda y laye egion, while he low ansi ioned o an LES model in he ee-s eam
egion. As a esul , pa ial eddy s uc u es we e obse ed nea he in e ace be ween he wo models. In con as ,
he LES model con inuously cap u ed s ong eddy gene a ion and dissipa ion in bo h he sepa a ion-induced
o ices om he NACA su ace and he ca i a ion egions.
Fig. 11 p esen s he compa ison o s eamline dis ibu ions among he u bulence models. The RSM model
exhibi ed an o e all uni o m eloci y dis ibu ion, whe eas he DES model showed a endency o low- eloci y
