1
The bene i s o combined hull o m and p opelle op imisa ion
Joy Klinkenbe g
*
, John Huisman, B am S a ke and E e -Jan Foe h
Ma i ime Resea ch Ins i u e Ne he lands (MARIN), The Ne he lands
Abs ac . A new app oach is demons a ed o he combined pe o mance op imisa ion o bo h hull o m and p opelle .
The app oach is based on op imizing powe a he han minimising he esis ance. Consequen ly, he in e ac ion be ween
p opelle and hull o m is inco po a ed in he app oach, including op imisa ion o p opelle pa ame e s.
Calm-wa e hull- o m op imisa ion is pa o many design p ocesses o new-buil essels. Mos in es iga ions ocus on
educing he esis ance con ibu ions o bo h o ebody and a e body. Some imes, also he h us -deduc ion ac o is
s udied, o en using an ac ua o disk app oach. As a nex s ep, he p opelle is op imised a e he hull has been designed,
using he nominal wake and p opelle clea ance ob ained om he esis ance-based op imised hull. This me hod does no
accoun o he mu ual in e ac ion be ween he p opelle and he hull.
The p esen app oach has been de eloped o ind he bes combina ion o hull o m and p opelle , o achie e highe o al
e iciency. A es case o an a -ship op imised essel o esis ance only and in combina ion wi h an in eg a ed p opelle
op imisa ion is p esen ed o show i s po en ial. The op imisa ion is pe o med using a Su oga e Based Global
Op imisa ion wi h pa ame e s de ining he hull o m and he p opelle geome y. The s a ing poin in he p opelle
op imisa ion is an F-se ies p opelle and du ing he op imisa ion he p opelle design pi ch is adjus ed o main ain a ixed
o a ion a e. The p opelle op imisa ion ocuses on p opelle e iciency, ca i a ion olume and p opelle -induced
p essu e luc ua ions on he a body. Using he p opelle op imise P opA in combina ion wi h he iscous low sol e
ReFRESCO o he hull and he BEM code PROCAL o he p opelle , he balance is ound be ween p opelle h us and
hull esis ance.
The esul s show ha he combined op imisa ion esul s in di e en op imal hull o ms when op imising wi h he
p opelle .
Keywo ds: Op imisa ion, hull o m, p opelle , RaNS-BEM.
1 In oduc ion
In ship design, one aims o minimizing ship esis ance o equi ed engine powe . Howe e , due o e.g. ime
cons ain s and compu a ional cos s, he op imisa ion is o en spli be ween hull o m op imisa ion o esis ance
ollowed by a sepa a e p opelle op imisa ion. This can be ega ded as a easonable i s app oach as in gene al he
in luence o he hull on he p opelle is much la ge han he in luence o he p opelle on he hull. The in luence
o he p opelle on he hull o m can be accoun ed o wi h o ins ance an ac ua o disc app oach o al e na i ely a
bounda y elemen me hod when a basic p opelle design is a ailable, see o ins ance [1]. In many s udies he
p opelle geome y is hen ixed and does no espond o changes in he hull o m. In he cu en pape , he e ec o
he p opelle on he hull and udde is aken in o accoun in an op imisa ion. This pape in oduces a me hodology
whe e he hull o m and he p opelle geome y a e op imized simul aneously o achie e he bes combina ion
possible.
Fi s , he nume ical code and me hods a e in oduced and he coupling p ocedu e be ween he codes is discussed.
This p ocedu e is hen shown in an op imisa ion o a Gene al Ca go essel o esis ance and powe o show he
addi ional gain ha can be ob ained when p opelle -hull in e ac ion is included.
*
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
2 Nume ical Me hods
2.1 The iscous- low (RaNS) sol e o he hull
The RaNS sol e used o he iscous low a ound he hull is ReFRESCO [2]. I sol es he mul iphase uns eady
incomp essible RaNS equa ions, complemen ed wi h a u bulence model (k-ω-SST in he p esen pape ) and
olume ac ion anspo equa ions o di e en phases. The equa ions a e disc e ized using a ini e- olume
app oach wi h cell-cen e ed colloca ed a iables. The implemen a ion is ace-based, which pe mi s g ids wi h
elemen s consis ing o an a bi a y numbe o aces, and h- e inemen (hanging-nodes). The code is pa allelized
using MPI and sub-domain decomposi ion and uns on Linux wo ks a ions and HPC clus e s. The momen um and
p essu e equa ions can be sol ed in a seg ega ed o coupled app oach. The code is a ge ed a and op imized o
hyd odynamic applica ions. I has been applied, e i ied and alida ed o a ious lows, including ca i a ing lows
and p opelle s [2] [3].
2.2 The po en ial- low (BEM) sol e o he p opelle
Fo he analysis o he low passing he p opelle , a bounda y elemen me hod (BEM) is used ha sol es he
incomp essible po en ial low equa ions o li ing and non-li ing bodies. The me hod, designa ed PROCAL, is
being de eloped wi hin MARIN’S Coope a i e Resea ch Ships (CRS) o he uns eady analysis o ca i a ing
p opelle s ope a ing in a p esc ibed hull wake. I has been alida ed o open wa e cha ac e is ics, sha o ces,
shee ca i a ion incep ion and ex en and hull-p essu e luc ua ions.
2.3 The RANS-BEM coupling p ocedu e
The s eady RANS sol e and he uns eady bounda y elemen me hod a e coupled in he ollowing way [4] :
• A RANS compu a ion is made o he hull wi hou p opelle . This p o ides he ship esis ance and he
nominal wake ield a he p opelle plane.
• In his wake ield a i s p opelle compu a ion is made using he BEM, i e a i ely upda ing he p opelle
RPM o a p esc ibed h us coe icien . This p o ides a h us - and loading dis ibu ion. This uns eady
loading dis ibu ion, in a ship- ixed coo dina e sys em, is a e aged in ime o all blade posi ions o
p oduce a s eady, bu axially, ci cum e en ially and adially non-uni o m o ce dis ibu ion. This o ce
dis ibu ion is in e pola ed on o he RANS g id.
• Finally, he iscous- low compu a ion is es a ed om he p e ious solu ion, imposing he loading
dis ibu ion om he BEM as a o ce ield ac ing on he low. This yields a new o al wake ield, om
which we hen sub ac he induced eloci ies coming om he BEM o ob ain a i s es ima e o he
e ec i e wake ield. An i e a ion is pe o med be ween bo h me hods un il changes in he RPM and
o que coe icien s as well as he e ec i e in low o he p opelle ha e become negligibly small.
3
Figu e 1 Flow cha o he RANS/BEM coupling p ocedu e.
2.4 The op imize (P opA )
P opA is a oolbox de eloped by MARIN o day- o-day p opelle design wo k [5, 6]. Wi hin P opA , an
op imisa ion wo k low manage is p esen ha couples he p opelle geome y wi h PROCAL, along wi h hi d-
pa y op imisa ion oolboxes o he au oma ed design o p opelle s.
P opA ypically balances he p opelle e iciency by noise and ib a ion and ca i a ion e osion isk. I uses a
pa ame ic desc ip ion o he p opelle and ies o ind he mos op imal p opelle wi hin he gi en inpu and
se ings. Wi hin each op imisa ion ound, a se ies o PROCAL compu a ions is pe o med. The esul s om
PROCAL a e con e ed in o new objec i es and cons ain s o P opA . The esul o he op imisa ion s udy is a
Pa e o on .
The i e a ion owa ds sel -p opulsion can ei he be done by changing he RPM o he p opelle o , wi h a ixed
RPM, by changing he pi ch o he p opelle . The la e has he p e e ence because he ship’s engine and p opelle
a e a e known and ixed. Changing he RPM would unin en ionally also include he e ec o o a ion a e on he
op imisa ion esul s. The e o e, o he cu en wo k low, P opA is used o i e a i ely upda e he pi ch o he
p opelle owa ds sel -p opulsion a a p esc ibed o a ion a e.
Addi ional ad an ages o including he p opelle in he op imisa ion is ha many hings can be op imized o , apa
om esis ance and wake ield quan i ies only. Besides powe , also he ca i a ion olume ( a ia ions), he ip o ex
s eng h (ETV model), he in eg a ed luc ua ing o ce on he a ship and he ampli ude o he p essu e pulses on
he hull a e assessed.
PROPART
4
2.5 Op imisa ion p ocess
The op imisa ion in his pape is based on a Su oga e-Based Global Op imisa ion (SBGO) using a Design o
Expe imen s (DoE) and is ex ensi ely desc ibed in [7] and [8]. A schema ic o e iew o he se e al p ocessing
s eps is gi en below.
The op imisa ion p ocess s a s wi h he pa en , o ini ial, hull o m. Then se e al base a ian s o he pa en hull
o m a e de ined, based on he analysis o he CFD esul s on he pa en hull (e.g. p essu e dis ibu ion, wa e
making esis ance and wake ield). Each o hese base a ian s is expec ed o imp o e he esul s ei he indi idually,
o in combina ion wi h o he a ian s. In he s udy p esen ed in his pape we ha e six base a ian s, which ha e
been linea ly combined and sampled o o m he DoE, using La in Hype cube Sampling (LHS). All hull o ms
wi hin his DoE a e compu ed: i s a nominal compu a ion and he ea e a compu a ion including Ac ua o Disc
(AD) and a compu a ion including p opelle wi h RaNS-BEM. Fo he la e , he p opelle geome ies a e all based
on he Wageningen F-se ies
Each o hese h ee compu a ions esul in ce ain possible objec i es, lis ed inTable 1 and desc ibed below. All
objec i e da a is ga he ed oge he o pe o m he SBGO o one o mo e o hese objec i es. Fo his, he p og am
Dako a [9] is used, using K iging, see [7] and [8] o mo e de ails on he op imisa ion p ocess. A Pa e o on is
cons uc ed o which a ew hulls on he on a e hen also compu ed o e i y he p edic ions o he su oga e
model l. The inal hull o ms a e hen analyzed esul ing in he choice o he op imal hull o m.
The i s objec i es a e ob ained wi h nominal compu a ions: he esis ance and he nominal wake ield can be
ex ac ed. F om he wake ield we ob ain he wake ac ion w. Fu he mo e, we also would like an indica ion o he
wake ield quali y. Fo ha pu pose, he Wake Objec Func ion (WOF) can be used. The Wake Objec Func ion,
WOF, is a measu e o he non-uni o mi y in he wake ield, see e.g. [10], [11] and is de ined as ollows:
𝑊𝑂𝐹=∫ ∫ |𝜕𝛽
𝜕𝜃|𝑓(𝜃,𝑟)𝑑𝜃𝑟𝑑𝑟
𝜃
𝑅𝑃
𝑅𝐻
∫ ∫ 𝑓(𝜃,𝑟)𝑑𝜃𝑟𝑑𝑟
𝜃
𝑅𝑃
𝑅𝐻 (1)
In which β is he angle o a ack, as compu ed:
𝛽=𝑎𝑟𝑐𝑡𝑎𝑛( 𝑢
𝜔𝑟
𝑅𝑃−𝑣𝑡) (2)
Whe e u is he axial eloci y in he wake ield, Rp he p opelle adius, RH he adius o he hub, he angen ial
eloci y ield, ω he o a ion a e o he p opelle . (θ, ) is a weighing unc ion which could be used o pu mo e
emphasis on a ia ions o β in a speci ic pa o he p opelle plane, o example a ound he wake peak. In his
pape , his unc ion is se o (θ, ) = 1. The WOF can be used as an indica i e alue o imp o ing o wo sening he
wake ield quali y and can only be used ela i ely be ween wakes in an op imisa ion. A lowe alue o he WOF
would indica e a be e wake ield quali y wi h less a ia ion in he angle o a ack.
5
The second se o objec i es comes om compu a ions wi h an ac ua o disc (AD). The ac ua o disc mimics
he h us in axial di ec ion a he p opelle loca ion, whe e he ac ua o disc o ce balances wi h he esis ance.
The compu a ion wi h ac ua o disc esul s in he o al h us , bu also an es ima ion o he powe can be ex ac ed
[11]:
𝑃𝐷=∫ 𝑢1∆𝑝𝑑𝐴1 (3)
𝐴1
Wi h A1, he a ea o he ac ua o Disc, Δp he p essu e jump o e he ac ua o disc induced by he body o ces o
he ac ua o disc and u1 he local low eloci y in he ac ua o disc. This PD includes he hull e iciency and pa o
he open wa e e iciency: he ideal e iciency.
The las objec i es a e ob ained wi h he RaNS-BEM compu a ions: he o al deli e ed powe , including he open
wa e e iciency. Besides he powe , he ca i a ion olume and he in eg a ed hull p essu e luc ua ion a e
objec i es ha could be op imized o ; in his pape we use he hull p essu e luc ua ions as objec i e. Ins ead o
objec i es, hese could also be used as cons ain s, e.g he p essu e luc ua ion should no exceed a ce ain alue.
Addi ional cons ain s a e moni o ed such as ma gins agains e osi e ca i a ion and he gene al isk on ca i a ion
e osion as assessed based on he dynamic shape o he shee ca i a ion ollowing he EROCAV obse a ion
handbook [12]
Finally, hyd os a ic da a pe a ian in he DoE is collec ed o impose o example cons ain s on displacemen ,
LCB posi ion o KM- alue.
Table 1: Lis o possible objec i es o each o he h ee me hodologies. These a e explained in mo e de ail in Sec ion 2.5
Nominal Compu a ion
Ac ua o Disc Compu a ion
RaNS-BEM Compu a ion
Resis ance (R)
Resis ance (Th us deduc ion) (R)
Resis ance (Th us deduc ion) (R)
Wake ac ion (w)
Powe (P)
Powe (P)
Wake Objec Func ion (WOF)
Ca i a ion olume
Tip o ex s eng h
In eg a ed p essu e pulses
3 Gene al Ca go essel
One es case wi h a gene al ca go essel is shown he e o show he me hodology and i s po en ial in hull o m
op imisa ion. The hull o m is aken om he Leanships [13] EU p ojec , wi h he main pa icula s gi en in Table
2 and he p opelle in Table 3. Wi hin Leanships, one wo k package in es iga ed he in luence o p opelle diame e
on e iciency and powe . Fo he cu en s udy a subse o he hull o m base a ian s was chosen o which we
expec o ha e an in luence on hull p opelle in e ac ion. In Figu e 1, he Pa en hull lines a e gi en in blue, while
he base a ian s a e gi en in ed. Base a ian A emo es he unnel. Va ian B and Va ian C change he con ou
and hickness o he gondola, wi h he idea ha bo h a ec wake ac ion and h us deduc ion. Va ian D changes
he p opelle posi ion upwa ds, while Va ian E mo es he p opelle u he a . Finally, Va ian F changes he
bu ock lines.
Fo he compu a ions wi h p opelle , some ini ializa ion is equi ed o se he inpu o he compu a ions. In a
eal op imisa ion, hese inpu pa ame e s should be selec ed wi h ca e and migh also be di e en pe design
a ian . In he cu en simpli ied es case he diame e is cons an , and he o a ion a e is aken om he Leanships
p ojec and se a 120 pm.
Table 2: Main pa icula s o gene al ca go essel
Leng h be ween pe pendicula s
214.70
[m]
B ead h moulded
23.74
[m]
Design d augh moulded
8.00
[m]
Displacemen olume moulded
34318
[m3]
6
Table 3: Main pa icula s o he p opelle
P opelle diame e
6.0
[m]
Boss-diame e a io
0.2
[-]
Numbe o Blades
4
[-]
Ro a ion a e a Vs = 17.0kn
120
[ pm]
Blade a ea a io
0.548
[-]
Va ian A: Remo ing he unnel
Va ian B: Con ou Gondola
Va ian C: Gondola hickness
Va ian D: P opelle posi ion upwa ds
Va ian E: P opelle Fu he A
Va ian F: Bu ock lines
Figu e 2: The hull o m base a ian s as used in he es case. Blue: he Pa en hull o m, ed: he base a ian s.
F om hese base hull o ms, se en y linea combina ions a e made o he DoE ia La in Hype cube Sampling
me hod, chosen o be domain space- illing, as also discussed in [7] and [8].
7
4 Resul s
Se e al objec i es will be compa ed o in es iga e he in luence o di e en objec i es o he inal op imal hull
o m. The i s pa shows he esul s wi hou changing he p opelle posi ion and he powe as compu ed wi h bo h
Ac ua o Disc and wi h RaNS-BEM a e compa ed. This is ollowed by an op imiza ion whe e he p opelle posi ion
is shi ed, and we show he di e ences in he op imisa ion be ween esis ance and powe . The las sec ion show
he esul s when op imizing o powe and o p essu e pulses on he hull.
4.1 Fixed p opelle posi ion
The i s s ep is o analyze he da a ob ained om DoE whe e we do no change he p opelle posi ion. A
su oga e wi h K iging is cons uc ed, wi h he base a ian s D and E se o ze o as a iables in he SBGO. To
show di e ences be ween wo me hods, he powe ob ained h ough he Ac ua o Disc app oach and h ough
RaNS-BEM a e compa ed. The pa e o plo is p esen ed in Figu e 3 whe e he esul s a e p esen ed in ela i e
di e ence compa ed o he pa en hull o m o wo measu es o he deli e ed powe . I he ends o bo h powe s
a e equal, a linea co ela ion should exis , which is no ue o hese esul s. The pa e o on om he su oga e
is loca ed on he bo om le o he pa e o diag am. E en hough bo h me hods p edic powe , he gains ound wi h
he ac ua o disc a e la ge compa ed o hose wi h he RaNS-BEM me hod. Assuming ha he RaNS-BEM me hod
has a highe ideli y, he gains wi h he AD me hod a e o e p edic ed.
The di e ences be ween he pa e o on and he checkpoin s a e ela i ely la ge. This could ei he be due o
some inaccu acy o he Su oga e o oo ew poin s we e compu ed wi h he DoE. This is open o u he
in es iga ion.
Fo he en i e pa e o on , base a ian s B, C and F (see Figu e 2) a e a hei maximum alues which esul s
in a ship wi h a small gondola and some change o he bu ock lines. Table 4 shows he esul s o hulls (a) and (b):
The wake ac ion educes, he wake becomes less uni o m and consequen ly, also he ca i a ion olume and hull
p essu e luc ua ion le el inc eases. In e es ingly, he mos gain in powe wi h RaNS-BEM is in case he unnel is
emo ed, while he mos gain in powe wi h only an Ac ua o Disc is whe e he unnel is pa ially kep .
The esul s also show ha by using a s ock p opelle like he Wageningen F-se ies, he p essu e pulse is mo e
han wice as high as commonly accep ed. This indica es he need o a cus om op imized p opelle design o his
pa icula ship, especially due o he unnel shape. Ne e heless, by keeping he p opelle geome y consis en , he
in luence o he hull design on he ca i a ion p ope ies is made isible.
Figu e 3: Resul o he compu a ions wi h he Powe ob ained om he ac ua o disc on he ho izon al axis and he Powe
ob ained om he RaNS-BEM compu a ions whe e he p opelle posi ion is no allowed o change. The blue do s deno e he
compu ed Design o Expe imen s; he o ange squa es he pa e o diag am ob ained om he SBGO. The blue iangles show
he inal compu a ions on wo op ima ( he 2 ex emes) om he Pa e o plo s.
8
Table 4: Lis o esul s o he pa en hull o m and hull o ms (a) and (b) om Figu e 3. Bo h he di e ences in powe a e
gi en (on he wo igh mos columns) as well as some in o ma ion on he wake ield, ca i a ion and p essu e pulses.
P opelle
heigh [m]
w [-]
WOF [-]
Ca i a ion
Volume [m3]
P essu e Pulse [kPa]
1s ha monic
ΔP
RaNS-
BEM
ΔP
AD
Pa en
3.0
0.304
0.0765
0.069
12.4
Hull a
3.0
0.270
0.0843
0.083
14.4
-2.0
-3.2
Hull b
3.0
0.267
0.0822
0.083
14.3
-1.6
-3.4
4.2 Resis ance and powe
The nex s ep includes changing he p opelle posi ion. To show di e ences be ween he op imiza ion me hods,
he objec i es ha a e ini ially in es iga ed and op imized o , a e he nominal esis ance and he esul ing powe
ob ained om he RaNS-BEM compu a ions. The esul s a e shown in Figu e 4 and show some gains compa ed
o he pa en hull o m. The di e ences be ween he pa e o on and he checkpoin s a e much smalle compa ed
o he ones in he p e ious sec ion.
The igu e shows ha he op imisa ion o powe wi h RaNS-BEM esul s in a di e en op imum compa ed o
he op imized hull o m o esis ance. The op imal hull o m o esis ance only migh ac ually be wo se in powe
(hull a), o ha ing a smalle dec ease in powe (hull b) compa ed o he op imal hull o ms in powe (hull c) ha
shows a smalle gain in nominal esis ance. The lines plans o hese hull o ms a e gi en in Figu e 5. Fo powe ing,
a unnel is mo e bene icial, while also he gondola is la ge o ha e la ge wake ac ion.
Figu e 4: Resul o he compu a ions wi h he nominal esis ance on he ho izon al axis and he Powe ob ained om he
RaNS-BEM compu a ions. The blue ci cles deno e he compu ed Design o Expe imen s, he o ange squa es he pa e o
diag am ob ained om he SBGO. The blue iangles show he inal compu a ions on h ee op ima om he Pa e o plo s (2
ex emes and an in e media e esul )
9
Hull a
Hull b
Hull c
Figu e 5: Linesplan o he op imal hull o ms om Figu e 4. No isible, bu he p opelle heigh inc eases o hull o m a o
i s maximum alue, o (b) in he middle, and ha dly any change in (c). The p opelle is posi ioned somewha u he a o
all h ee cases.
So a , we ha e only in es iga ed compu ed powe and esis ance and no o he objec i es. I we ake he h ee
hull o ms [a, b and c] o u he in es iga ions, we can di e in o mo e de ail whe e he changes a e de i ed om.
Could we maybe al eady o esee he op imal hull o m o powe ing, solely based on a nominal compu a ion? I
ha is ue, i would be much cheape o pe o m. As men ioned ea lie , om he nominal compu a ion, also he
wake ac ion is ex ac ed om he compu a ions as well as he wake objec unc ion. These esul s, o he pa en
hull and he h ee hull a ian s, a e shown in Table 5 below. The wake ac ion dec eases om he pa en hull o m
o hull o ms (b) and (c); he WOF is simila , bu sligh ly smalle o hull o m (c). A smalle wake ac ion would
imply ha he hull e iciency is smalle and hus one could a i e a he conclusion ha hese hull o ms a e wo se.
Howe e , he opposi e is ue in his case: a smalle wake ac ion seems o imp o e he p edic ed powe . I could
also be expec ed ha he Wake Objec Func ion and Ca i a ion Volume ollow a simila end: when he wake ield
is smoo he , less ca i a ion and lowe p essu e pulses a e expec ed. Howe e , due o changes in p opelle ope a ing
poin , his does no always hold.
The wake ields hemsel es a e shown in Figu e 6 and di e qui e signi ican ly be ween he Pa en hull and
hull (a). The wake peak is deepe compa ed o ha o he pa en hull (Ux/Vs=0.362 s Ux/Vs=0.403) and also he
Wake Objec Func ion is signi ican ly la ge . The p opelle is loca ed highe ; he ca i a ion olume is la ge and
especially he p essu es pulses a e signi ican ly highe due o a smalle hull clea ance. Hull o m (b) also has a
deepe wake peak (Ux/Vs=0.373), bu hull (c) wi h a wake peak o Ux/Vs==0.390 has a smalle g adien , made clea
wi h he lowe WOF. Hull o m (c) is he e o e be e o ca i a ion olume and p essu e pulses, compa ed o hull
(b). Howe e , he pa en hull o m has he smalles p essu e pulses and ca i a ion olume, because he p opelle
posi ion has shi ed upwa ds in all o he cases, which appea s o be be e in e ms o powe . This implies ha he
new me hod is necessa y when he p opelle is shi ed owa ds he hull and when p essu e pulses a e o in e es in
he op imisa ion.
