Tes ing o e boa d hyd odynamic pe o mances in
wind unnel acili ies
Fe nando Mellibo skya,∗, Joana P a b, Emilio No ic, An onello Salac
aCas ellde els School o Telecom and Ae ospace Enginee ing, Uni e si a Poli `ecnica de
Ca alunya, Cas ellde els, 08860, Spain
bEPSEVG-SARTI, Uni e si a Poli `ecnica de Ca alunya, Dep . Ma em`a ica Aplicada 4,
Vilano a i la Gel ´u, 08800, Spain
cNa ional Resea ch Council (CNR), Ins i u e o Ma ine Sciences (ISMAR), 60125,
Ancona, I aly
Abs ac
The easibili y and po en ial ad an ages o wind unnel es ing o o e boa d
designs is assessed. T adi ional lume ank es s incu high ope a ional cos s
and p esen some limi a ions in e ms o lexibili y and accu acy. Mode n
lume anks, despi e mo e lexible and accu a e, a e s ill expensi e o ope a e
o hi e. Wind unnel acili ies a e widesp ead, wi h a po en ial o low bud-
ge es s, and allow o an accu a e con ol o eloci y, angle o a ack and
sideslip as well as p ecise measu emen o o ces and momen s in all h ee
axes. A comple e desc ip ion o o e boa d hyd odynamics is pa amoun o
op imising design and igging and o he design o ac i e con ol s a egies
ha allow o s able awling a a a ge speed and dep h. We desc ibe in
de ail he me hodology o wind unnel es s applied o gene al o e boa d
designs, exempli y i wi h a comme cial pelagic o e boa d and p o ide a
compa ison wi h exis ing lume ank esul s o he same design.
Keywo ds: wind unnel, o e boa d, hyd odynamics, awl gea
1. In oduc ion
O e boa ds o awl doo s a e key componen s o awl gea s o hei
e ec i e and e icien use [30, 24]. Thei main ole consis s in keeping he ne
open a he equi ed wing-end sp ead -and dep h in pelagic awling- while
∗Co esponding au ho . email: [email p o ec ed]
P ep in submi ed o Ocean Enginee ing Janua y 24, 2015
p oducing he minimum possible impac in e ms o awle uel consump ion
[38, 5, 25] and, in he case o bo om o e boa ds, sea bo om dis up ion.
O e boa ds mus also ensu e s able shoo ing and handling o he gea [10].
T awl doo s ul il hei ne -opening pa h ough he gene a ion o an
hyd odynamic li o ce a he cos o in oducing a d ag o ce ha adds o
he o al esis ance he awle mus o e come. As a esul , a low li o d ag
a io o he o e boa d esul s in high awle consump ion. The awl doo
li is mainly used in keeping he ne open and, when ishing in shallow wa-
e s, also in o e coming i s own weigh . In deep wa e s, he wa p akes mos
o he eponsibili y o balancing he o e boa d weigh . D ag can be mainly
asc ibed o h ee sou ces: ic ion, wake and wing ip o ices. F ic ion d ag
is chie ly dependen on he lamina o u bulen na u e o he bounda y laye .
Wake d ag, also known as p essu e o o m d ag, is a consequence o bound-
a y laye sepa a ion due o ad e se p essu e g adien s on he ou e su ace
ecomp ession a ea when gene a ing li . I is hus also c i ically dependen
on he lamina o u bulen na u e o he bounda y laye , which condi ions
sepa a ion, and inc eases wi h he squa e o li . Finally, wing ip o ices a e
esponsible o he so-called li -induced d ag, which is also p opo ional o
li squa ed and in e sely p opo ional o he aspec - a io o he o e boa d.
I is he e o e clea ha d ag can be educed bo h h ough diminishing li
equi emen s o by inc easing he hyd odynamic e iciency h ough inc easing
he aspec - a io. In shallow wa e ishing, minimising li equi es ligh o e
boa ds, while in deep wa e hea y o e boa ds a e p e e ed o en o ce dep h
upon he ne . The aspec - a io is no only limi ed by p ac ical and echnical
issues, bu also because ic ion is nega i ely in luenced by slende ness. All
in all d ag minimisa ion o he equi ed li is hen achie ed h ough ca e ul
hyd odynamic design and op imal igging. While classic o e boa ds used
o wo k wi h he ou e su ace in comple e s all o ensu e s abili y [31, 32],
mode n o e boa ds end o ea u e slo ed cambe ed ai oil shapes deployed
in high aspec - a io wings o s ably ope a e in condi ions close o ha o
op imal e iciency. In pelagic sys ems, o e boa ds may also se e a awl
gea pilo /con ol ask [29, 35], which ende s accu a e modelling essen ial
o an icipa e s abili y issues unde ealis ic condi ions. O he p ocesses such
as seabed impac o cap u e a ge ing a e s ongly a ec ed by he dynamic
in e ac ions o essel, igging, o e boa d and ne in e ac ions, wi h he o e
boa ds ha ing a i s o de e ec .
T awl ne opening and dep h con ol, sys em s abili y o manoeu ing,
awl gea esponse o ex e nal pe u ba ions such as cu en s o unde wa e
2
gus s, e c, ely on a deep unde s anding o he dynamics o he sys em as
a whole and a ealis ic model o he o e boa ds mus necessa ily include
an accu a e desc ip ion o hei hyd odynamic beha iou [41]. Mo ing pa s
aside, as may be de ised o con ol pu poses, his ansla es in o he p ecise
knowledge o how o ces and momen s in all h ee axes depend on he wo
ele an hyd odynamic angles: he angle o a ack and he sideslip angle.
Mos expe imen al e o s ha e been de o ed o analysing ne hyd ody-
namics bo h by means o sea ials [47, 37, 12, 13, 9, 4, 21] and lume ank
expe imen s o scaled ne models [26, 11, 16]. The e also exis s udies ha
compa e lume ank esul s wi h ull-scale sea ial da a o bo h isola ed
ne s and ull gea [50, 13, 18]. In addi ion, a numbe o nume ical models
o simula e ne dynamics ha e been de eloped [3, 23, 27, 49, 34, 44, 20],
and also some models o comple e gea s, including a c ude [19] o somewha
ai [14, 33] desc ip ion o awl doo beha iou , ha e been de ised. A ca e-
ul li e a u e sea ch shows ha he i s and only ull awl gea simula ion
embodying ho ough modelling o he o e boa ds was unde aken by [35].
T adi ionally, he s udy o o e boa d hyd odynamics has been limi ed
o he me e de e mina ion o he d ag and li coe icien s as a sole unc-
ion o he angle o a ack [1, 43]. These coe icien s a e usually ob ained
ia educed-scale es s in lume ank acili ies [28, 15, 39]. The adi ional
igging in lume anks, wi h he o e boa d held in place by cables, esul s
in low posi ioning accu acy and o ce measu emen s lack in p ecision. Mod-
e n lume ank acili ies ha e imp o ed on adi ional echniques (SINTEF
Fishe ies, Hi shals) by plunging he o e boa d in a p ecise o ien a ion and
measu ing o ces and momen s wi h a six componen balance. The downside
is hei ope a ion cos and he inabili y o eaching wa e speeds ha ensu e
dynamical simila i y wi h eal condi ions. Wind unnel es ing has seldom
been used in analysing awl doo hyd odynamics [6, 42, 32, 36, 22], despi e
a numbe o e iden ad an ages. The use o wind unnel acili ies is a na u al
s ep ha ollows he analysis o awl doo s in he amewo k o unde wa e
ligh mechanics [6, 41, 29, 31]
To achie e dynamic simila i y wi h a gi en o e boa d model, he bal-
ance in a lume ank has o endu e o ces six imes hose in a wind unnel.
Al hough he powe equi ed o d i e he wa e h ough he lume ank is
abou hal ha equi ed in a wind unnel o equal c oss-sec ion, he ac is
ha lume anks a e in a iably much la ge in o de o be able o accomoda e
es s o o he ma ine equipmen , such as ishing ne s, making hem o e sized
o o e boa d es ing, which en ails un easonably la ge powe consump ion.
3
O e boa d hyd odynamics a sea a e ex emely di icul o es and e y
ew s udies ha e a emp ed a measu ing o ces in eal ope a ion [39]. Nume -
ical modelling wi h CFD is a powe ul al e na i e o p oduce hyd odynamic
coe icien s, bu is compu a ionally e y cos ly and s ill needs expe imen al
alida ion [48, 17, 45].
In his pape we explo e he po en ial bene i s o exploi ing wind un-
nel acili ies in analysing awl doo hyd odynamics, aking ad an age o he
abili y o accu a ely se wind eloci y and o e boa d o ien a ion and o
measu e o ces and momen s in all h ee axes. We se up a me hodology
ha can be exploi ed gene ally and exempli y i wi h a p oduc ion pelagic
o e boa d ha we es a he wind unnel acili y o Ma iKom in Ros ock,
Ge many. The pape is hen s uc u ed as ollows: The me hodology o
wind unnel ope a ion and da a ob en ion is desc ibed in §2.1, oge he wi h
e e ence ame de ini ions and simila i y conside a ions o expe imen al a-
lidi y. §2.2 is de o ed o da a p ocessing and hyd odynamic pe o mance
pa ame e s ex ac ion. Tes esul s o a p oduc ion o e boa d a e p e-
sen ed in §3 and compa ed wi h lume ank esul s a ailable in he li e a u e.
Finally, in §4 we summa ise he p os and cons o wind unnel exploi a ion
and p o ide some ecommenda ions o u u e de elopmen .
2. Ma e ial & Me hods
2.1. Wind unnel es ing me hodology
Analysing o e boa d designs ia wind unnel es ing equi es ca e ul
planning. Geome ical da a o he awl doo model ha will be es ed
se s he basis o deciding on how he wind unnel is o be ope a ed. This
da a, along wi h wind unnel and balance specs mus be used o exploi
expe imen al da a in a meaning ul way.
In his sec ion we p o ide he model and wind unnel da a ha is ele-
an o such es s, along wi h some simila i y conside a ions ha mus be
aken in o accoun o gua an ee he alidi y o he expe imen s. The analysis
p ocedu e is desc ibed in de ail.
While mos o he me hodology discussed is gene ic o any wind unnel
es o an o e boa d, some de ails a e speci ic o he pa icula wind un-
nel se up. In ou case, he expe imen s we e pe o med in he Ma iKom
(h p://www.ma ikom.uni- os ock.de/en/) wind unnel acili ies, loca ed a
he Ros ock Uni e si y campus in Ge many. The wind unnel is o he
G¨o ingen cons uc ion ype (also known as P and l ype o closed e u n
4
wind unnel) and p o ides a h ee-axes posi ioning sys em and a six-componen
balance o o ce and momen measu emen .
2.1.1. T awl doo model da a
The model is a scaled ai h ul e sion o he ull-size awl doo . A num-
be o geome ical pa ame e s o he model need be conside ed o da a p o-
cessing. These pa ame e s a e summa ised in Table 1 and shown in Fig-
u e 1a. Ou es s will be demons a ed on a Thybo øn 15 pelagic awl
doo (h p://www. hybo on- awldoo .dk/), whose speci ic dimensions will
be duly in oduced in §3.
The span line (b) is de ined as he s aigh line connec ing bo h lap ips
a hei espec i e ailing edges. The pseudo-symme y plane is hen he
plane o hogonal o he span line ha con ains he in e sec ion o he laps.
The cho d line (l) is he s aigh line connec ing leading and ailing edge on
he pseudo-symme y plane.
2.1.2. Re e ence ames and wind unnel es da a
Th ee di e en ames o e e ence a e equi ed o p ope ly analyse awl
doo hyd odynamic beha iou and wind unnel esul s. The Ea h o , in ou
case, wind unnel e e ence ame is de ined as E={E;xe,ye,ze}, wi h he
o igin Eon he balance a achmen poin and, o cons uc he o hono -
mal basis, xe ollows he s eamwise di ec ion o he wind unnel, poin ing
o wa d, ye ollows he ho izon al spanwise wind unnel di ec ion, poin ing
igh wa ds, and zeis he e ical axis poin ing downwa ds in he di ec ion o
g a i y.
The body e e ence ame, a ached o he awl doo model, is de ined
as B={O;xb,yb,zb}≡{O;x,y,z}, wi h he o igin Oplaced on he cho d
line a i s ailing edge, x ollowing he cho d line in he o wa d di ec ion, y
o hogonal o xand on he pseudo-symme y plane, poin ing ou wa ds, and
zcomple ing he o hono mal basis (spanwise, poin ing owa ds he bo om
lap).
Ae odynamic o ces and momen s depend on ai densi y, on he model
size and shape, and on i s eloci y wi h espec o he su ounding luid
( he so called ae odynamic eloci y, Va). The ae odynamic eloci y ec o
is used o de ine a hi d e e ence ame dubbed he ae odynamic ame
A={O;xa,ya,za}wi h xain he di ec ion o Va, poin ing o wa d, ya
o hogonal o xa, on he pseudo-symme y plane, poin ing ou wa ds and za
5
comple ing he o hono mal basis. In a wind unnel es wi h expe imen al
eloci y V,kVak=Vand xa≡xe.
Th ee angles a e equi ed o desc ibe he o ien a ion o he o e boa d
wi h espec o he ea h e e ence ame. The choice he e will be he usual
Tai -B yan angles (some imes mis akenly called Eule angles) yaw (ψ), pi ch
(θ) and oll (φ). Figu e 2a shows he h ee o a ions ha ake ec o s om
wind unnel axes o body axes. The ans o ma ion ma ix om B o E akes
he o m
R(ψ, θ, φ) =
cθcψsφsθcψ−cφsψcφsθcψ+sφsψ
cθsψsφsθsψ+cφcψcφsθsψ−sφcψ
−sθsφcθcφcθ
,(1)
whe e cxand sxdeno e cosine and sine, espec i ely, o he angle indica ed
by he subsc ip x.
As shown in Figu e 2b only wo angles a e equi ed o de ine he o i-
en a ion o he doo wi h espec o he ae odynamic ame, namely he
angle o a ack (α) and he sideslip angle (β). Ro a ions ha p ese e he
ae odynamic angles (i.e o a ions a ound xa) esul in a me e o a ion o
he ae odynamic o ces and momen s, hei p ojec ion on ae odynamic axes
emaining unal e ed. The ans o ma ion ma ix om A o Bis
S(α, β) =
cβcαsα−sβcα
−cβsαcαsβsα
sβ0cβ
.(2)
The awl doo model was es ed in he wind unnel s anding on i s lowe
shoe (see Figu e 1b). The ins alla ion oll angle o he model has a alue φe
ha is gene ally non ze o. This angle, which s ays cons an h oughou he
expe imen , oge he wi h he wo addi ional angles he wind unnel allows
o sweep (yaw and pi ch angles), con o m he se o Eule angles ha allow
p ojec ion o measu ed o ces and momen s in body axes.
Gene ally speaking, he Eand A e e ence ames a e linked h ough he
di ec ion o he wind, he awl doo g ound eloci y ec o and he awl
doo o ien a ion. In he case o a wind unnel es , he ela ion simpli ies
g ea ly, as he doo is quiescen and he wind is s ic ly in he di ec ion o
he wind unnel axis. Unde hese condi ions he e exis s a di ec ela ion
be ween he o ien a ion angles (ψ, θ, φ) and he ae odynamic angles (α, β)
6
ha is gi en by he ollowing simple exp ession:
α= a an2 (−R12,R11),
β= a an2 (R13,R11 cos α−R12 sin α),(3)
whe e a an2 is he 4-quad an in e se angen , and he subsc ip s indica e
he o a ion ma ix elemen o be conside ed.
The model mus be held in he wind unnel es sec ion om an a ach-
men poin (A), as shown in Figu e 1. In ou es s, we can choose o i an
adap e ha holds he model a a ce ain dis ance om he g ound, and ha
connec s i o he balance o igin (E) whe e all o ces and momen s a e e-
e ed. The adap e , shown in Figu e 3 is mean o bo h sepa a e he model
om he wind unnel walls and o allow changing he model o ien a ion
s aigh o wa dly.
The posi ion ec o o A ela i e o O( see Figu e 3b) is he key o
p ope ly ansla ing wind unnel measu emen s in o awl doo pe o mance
esul s. In ou case i can be exp essed, in body coo dina es (indica ed by
he supe sc ip ), as:
b
OA =ξxi+ [(bb+ξz) sin Λb−ξycos Λb]j+ [(bb+ξz) cos Λb+ξysin Λb]k.
(4)
The wind unnel balance p o ides o ces and momen s in he wind unnel
e e ence ame as applied o i s o igin, E. The awl doo may be moun ed
s anding di ec ly on op o his poin , in which case only he yaw angle can
be se a will and ae odynamic g ound e ec s will play hei pa . This is
desi able in he case o bo om o e boa ds, whose ac ual ope a ion akes
place in di ec con ac wi h he g ound hus p ecluding he occu ence o wing
ip o ices. Ne e heless, he e ec o he g ound is only pa ially accoun ed
o , since only ip low blockage is conside ed and no he g ound-doo ela i e
eloci y e ec s ha in oduce bounda y laye s in he wind unnel ha a e
no p esen in eal condi ions. In he case o pelagic o semipelagic lying
awl doo s, g ound e ec s a e u e ly undesi able and i becomes manda o y
o sepa a e he model om he g ound ia he a o emen ioned adap e . The
adap e has he u he ad an age o allowing o a second deg ee o eedom
which co esponds o se ing he pi ch angle. The combina ion o yaw and
pi ch a ia ion g an s he oppo uni y o s udy he model in all possible
wo king condi ions om an hyd odynamic s andpoin .
Figu e 3a shows he adap e , which is an a icula ed elbow whose bo om
a m o leng h abcoincides wi h he zeaxis and ha can o a e abou i
7
in oducing yaw, ψ. This o a ion is au oma ically pilo ed om he wind
unnel con ol cabin. The op a m, which is bound o he awl doo h ough
he a achmen poin , has leng h a and can be il ed wi h espec o he
bo om a m. I he awl doo oo is con enien ly aligned as in Figu e 3b
he il di ec ly in oduces pi ch, θ. The pi ch mus be in oduced manually,
hus equi ing a hal o he wind unnel e e y ime i is o be modi ied. The
oll angle, which is ixed as discussed in Figu e 1b, is φe. Then, he iad
(ψ, θ, φe) a e he o ien a ion angles o he model du ing he wind unnel es .
Using he o ien a ion angles o he o e boa d he posi ion ec o o
he a achmen poin A ela i e o Eis s aigh o wa dly exp essed (see
Figu e 3b). In wind unnel coo dina es i eads
e
EA =−a sθcψi−a sθsψj−(a cθ+ab)k.(5)
whe e a = 0.06 m and ab= 0.109 m a e he a ms leng h o he adap e we
ha e employed in he expe imen s.
2.1.3. Simila i y conside a ions
A numbe o cons ain s in se ing expe imen al pa ame e s mus be ob-
se ed in o de o ob ain wind unnel esul s ha can be ex apola ed o
he hyd odynamic beha iou o ac ual awl doo s. This is called simila i y,
and equi es ha a se o ep esen a i e nondimensional pa ame e s be kep
cons an o nondimensional g oupings esul ing om dimensional analysis
o be p ese ed om expe imen o eali y.
The i s ob ious cons ain is geome ical simila i y, which equi es ha
he shape o he model ma ches exac ly he ull-scale o e boa d and ha
he a i ude (ae odynamic o ien a ion) o he doo in he es s mimics he
eal condi ions we wan o emula e.
The ele an physics o awl doo ligh in wa e in ol e con ec i e and
iscous anspo o momen um. The nondimensional numbe compa ing
hei ela i e impo ance is he Reynolds numbe :
Re =V l
ν,(6)
whe e Vis he ela i e eloci y o o e boa d and luid, lis a cha ac e is ic
leng h o he o e boa d (e.g. he cho d) and ν=µ/ρ is he kinema ic
iscosi y o he luid, wi h µand ρ he dynamic iscosi y and he mass
densi y, espec i ely. Models will be smalle han ull-size o e boa ds and
8
ai iscosi y is abou 15 imes highe han wa e . All in all, he wind unnel
mus be un a speeds highe han he ac ual eloci y o awl doo s in wa e .
Tempe a u e e ec s (hea conduc ion and con ec ion wi hin he luid)
can be dismissed so ha he ene gy equa ion plays no impo an ole and
he P and l numbe can be igno ed.
Also comp essibili y can be igno ed, since wa e is incomp essible and
p ac ical wind unnel eloci ies a e well wi hin he incomp essible ai low
egime. Comp essibili y e ec s ac as a lowe limi o he model dimensions
ela i e o ull-scale. Mach simila i y can be conside ed ul illed as long as
he wind unnel is un below Mach 0.3, which se s an uppe limi o ai speed
and, consequen ly, a lowe bound on model scale i Reynolds simila i y is o
be p ese ed.
Ca i a ion can be disca ded as long as he p essu e on he o e boa ds
and in he wake does no all below wa e apo isa ion condi ions, which is
a ely he case in usual awling condi ions.
Finally, F oude simila i y becomes c ucial whene e ex e nal olume o ces
such as he g a i y o ce a e impo an , as would be he case o pa ially
subme ged mo ing bodies due o wa e phenomena associa ed o he ee su -
ace. T awl doo s a e ully subme ged so ha F oude simila i y plays no
impo an ole.
Fo a ho ough discussion on simila i y we e e he eade o [2]. Ap-
plica ion o he ield o luid dynamics can be ound in any classical luid
dynamics book such as [40].
2.1.4. Wind unnel es ou pu da a
The aw da ase is loaded om a ile and sepa a ed in o h ee se s o
measu emen s depending on he nominal wind unnel ai eloci y a which
hey we e aken. Thus, he da a is spli in o measu emen s a ze o eloci y,
a he expe imen eloci y and, possibly, a one o mo e di e en eloci ies
o Reynolds simila i y alida ion.
E e y expe imen al poin , de ined by a iad (V, ψ, θ), has a co esponding
ze o-wind eloci y measu emen a (0, ψ, θ). This is equi ed o sub ac he
o ces and momen s caused by he weigh o he model.
The da a acquisi ion p ocess would be ex emely slow i he wind unnel
was o be un and hen s opped o each pai (ψ, θ). The al e na i e app oach
o sweeping all angles wi h he wind unnel on and hen again wi h he wind
unnel o has he d awback o in oducing some a iabili y in he ac ual
alues o he angles om expe imen o e e ence. An accu a e ea men o
9
and CL= 2.3711 is a ained o α= 40◦and β=−5◦.Czis low o
β= 0◦and i s dis ibu ion is non symme ic due o he sligh asymme y o
he uppe and bo om laps wi h espec o xy-plane. The same goes o he
pi ching momen (CMy). The oll momen (CMx) akes mode a e alues while
he la ges e ec is obse ed on he yaw momen (CMz), as expec ed. The
la ges αbecomes, he la ges he yaw momen ha will need compensa ion
by he ac ion o he wa p.
Con ou maps o ae odynamic e iciency (η=CL/CD) a e shown in
igu e 5a. As a ma e o ac , he highes CLdoes no co espond o he
maximum η, which is ac ually ai ly low. This is a classical esul o wing
heo y, which is a di ec consequence o he ac ha d ag deg ades as
wi h he squa e o li . Mo e modes angles o a ack a e p e e able o high
ae odynamic e iciency, he maximum η= 3.57 being ob ained o (α, β)≈
(15,−5)◦. This would be he op imal wo king poin o a neu ally buoyan
doo as i would p o ide he awl gea wi h he necessa y ne opening o ce
a he minimum d ag cos . η emains high o a wide ange o αand βa ound
he maximum, which ensu es ai ly low d ag o subop imal owing.
The loca ion o he cen e o p essu e has been ound using equa ion (20)
and ep esen ed on a side iew ske ch o he o e boa d in igu e 5b. The
dependence on he angle o a ack has been colou -coded, while he sizing
ep esen s a ia ion in sideslip angle, he la ges ci cle always co esponding
o β= 0◦. Table 3 quan i ies his α-dependence o he posi ion o he cen e
o p essu e as measu ed in uni s o cho d om he body ame o igin a he
mid-span ailing edge. The la ges e ec is ha o α h ough CMz, he o he
wo coe icien s ha ing li le o no e ec as e iden om he nea ly cen ed
z-loca ion o he cen e o p essu e. Inc easing αb ings he cen e o p essu e
o wa d owa d he leading edge and sligh ly down on he bo om lap, wi h a
endency o se le sligh ly o wa d (∼40% o he he cho d) om mid-cho d
and below he mid-span line. The e ec s o a ying βa e mode a e a low
αand negligible a high α. The p ecise loca ion o he cen e o p essu e,
combined wi h he mass dis ibu ion o he awl doo p o ide he means o
an icipa e he op imal igging o ha e he o e boa d wo king as desi ed in
eal condi ions.
In gene al, o e boa ds a e designed o wo k wi h li le o no sideslip
o op imal e iciency. While i emains use ul o analyse hei beha iou
when subjec o sideslip, as o e boa ds will ansien ly adop non negligi-
ble sideslip while manoeu ing o in non-s anda d sea condi ions, i makes
comple e sense o epo hei pe o mances a β= 0◦. Figu e 6ashows a
16
cu a β= 0◦ h ough he CL,CD,Czand ηcon ou maps. CL apidly g ows
wi h α, ini ially linea ly bu wi h a endency o sa u a e ha indica es ha
s all is no a beyond α= 40◦.CDalso g ows wi h αin he pa abolic ypical
ashion o li -p oducing objec s (d ag pola ). Czwould be nil o a pe ec ly
up-down symme ic o e boa d. I s inc easing ye mode a e alues a e a
consequence o asymme y and he ac ha hey a e posi i e indica es ha
hyd odynamics ends o add on weigh . As a ma e o ac , he awl doo
needs o sligh ly pi ch nose up o cancel his e ec . The as es g ow h o
CDwhen compa ed wi h CLis esponsible o he exis ence o a maximum
o η. Fo his o e boa d, he maximum o no sideslip angle is η≈3.5 o
α≈15◦.
3.1. Compa ison wi h lume ank es s and dynamic simila i y
To allow compa ison wi h lume ank esul s, wind unnel esul s mus be
in e pola ed on ac ual hyd odynamic angles and o ce coe icien s p ojec ed
on o he lume ank e e ence ame. The e is a s anda d in lume ank es s
o use o e boa d o ien a ion angles (ψ,θand φin ou no a ion) and call
hem a ack angle (e oneously), pi ch and heel (o oll), espec i ely. While
d ag is co ec ly de ined as he o ce in he di ec ion o low (CD=−C
x),
li is w ongly aken as he ho izon al p ojec ion o he low no mal o ce
(C
yin ou no a ion, wi h he supe sc ip deno ing p ojec ion on he lume
ank ame). To allow compa ison, we ha e ansla ed wind unnel esul s
in o he s anda d lume ank amewo k and plo ed hem oge he wi h
publicly a ailable lume ank esul s (h p://www. hybo on- awldoo .dk/)
o he same geome y in igu e 6b. The lume ank es s we e conduc ed wi h
φ≈0◦,θ≈2◦and ψ={27.6,30.0,33.6,36.8,39.2}◦(K. Hansen, SINTEF,
p i a e communica ion).
While he ends a e clea ly coinciden o a wide ange o α, he e seems
o be a sys ema ic o se in bo h C
yand C
x om lume ank o wind
unnel. Flume ank p oduces highe li and lowe d ag han wind unnel o
he whole ange explo ed. The de ia ion o lume ank wi h espec o wind
unnel ops a 20% o he lowes αand educes o unde 10% a he highes
α. No ably, lume ank es s pinpoin he ini ia ion o s all a α≈37◦,
while wind unnel es s do no e lec de achmen o α≤40◦. Con iden
as we a e o he p eciseness o he wind unnel esul s, he e is a high le el
o unce ain y ega ding lume ank es s. In he lume ank, he angle o
a ack (ac ually yaw ψ) is he angle o lume ank wa e low wi h he shoe o
he o e boa d [43]. Fo he 15 one would hink his choice is equi alen
17
o ou de ini ion wi h he cho d line, bu since he shoe is no ec angula ,
his would need some cla i ica ion ha is missing in he es s. Howe e , his
would accoun o a me e αshi ha would pa ially explain ei he CLo CD
disc epancies bu no bo h, as he cu es a e shi ed in opposi e di ec ions.
The bigges sou ce o unce ain y is he ac ual a i ude o he awl doo
du ing lume ank es s. Pelagic o e boa ds a e es ed a nea ly ze o heel
and pi ch, bu how accu a ely his is accomplished is no known. Allegedly,
he pi ch angle may be o up o 2◦and he ze o heel ha would co espond
o a pe ec ly ho izon al pseudo-symme y plane is only app oxima ely se o
ze o. Also he p ojec ion o o ces in he lume ank ame o e e ence is
somewha in ol ed and in oduces e o om se e al sou ces, such as cable
o ce measu emen s and angles. Taking all his in o conside a ion, we claim
ha he accu acy o o ces measu emen and p ojec ion in he wind unnel
is un i aled by classic lume anks. Mode n lume anks esol e his issue by
inco po a ing 3-componen balances, he ad an age o wind unnels being
hen me ely educed o hei lowe ope a ing cos .
The e exis s an addi ional sou ce o disc epancy ha needs be aken
in o conside a ion ha conce ns dynamic simila i y. As a gued in §2.1.3
esul s a e ep esen a i e o eal o e boa d beha iou i Reynolds simila i y
is ma ched. The Reynolds numbe co esponding o he wind unnel and
lume ank es s a e:
Rew =Vw lw
νai ≈4.6×105, Re =V l
νwa e ≈2.9×105,(21)
whe e Vw = 20 m/s, lw = 0.32 m/s, V = 0.7 m/s, l = 0.49 m/s, νwa e ≈
1.2×10−6m2/s and νai ≈1.4×10−5m2/s. The wind unnel es s wi h
Vw = 15 m/s co espond o Rew ≈3.4×105, close bu s ill abo e lume
ank condi ions. Anyhow, and as al eady men ioned, his second da ase a a
lowe eloci y only accoun s o unde a 2.5% dics epancy in he coe icien s,
no su icien o explain wind unnel and lume ank di e ences.
The Reynolds numbe a eal sea condi ions akes a minimum alue Re >
7.9×105 o he slowes owing speed V≈1.5 m/s and smalles p oduc ion
o e boa d wi h l= 0.63 m/s. Usual alues will be in he o de o Re =
O(106) eaching up o 5 ×106 o he la ges e sion o he o e boa d
(A= 20 m2) and he maximum owing speed (V= 2 m/s).
In his espec , wind unnel expe imen s, al hough s ill sho o achie -
ing ealis ic Reynolds numbe s, a e much close han usual lume ank es s
18
a e. Some acili ies allow o la ge eloci y and could po en ially accomo-
da e la ge models, hus inc easing lume ank Re. This also holds o wind
unnels, wi h cos clea ly a ou ing he la e . In gene al, hyd odynamic
coe icien s a e only ma ginally dependen on Re o su icien ly small Re-
anges, which jus i ies p o iding a unique se o coe icien s o a whole amily
o o e boa ds ega dless o size and owing speed. None heless, his may no
longe be he case i he Re- ange sweeps ac oss he so called c i ical Reynolds
numbe ha cha ac e ises indis inc ly bulky objec s and s eamlined objec s
a high angles o a ack. Supe c i icali y conce ns he u bulen ansi ion o
he bounda y laye p io o de achmen . Since u bulen bounda y laye s ex-
hibi highe momen um in he immedia e icini y o he wall due o u bulen
mixing, hey esis be e han lamina bounda y laye s he ad e se p essu e
g adien s he low usually unde goes in he ecomp ession egion owa ds he
ailing edge. This esul s in highe ic ion (due o he u bulen na u e o
he bounda y laye ) bu also in a much hinne wake and consequen lowe
o m o wake d ag, which is dominan in hese si ua ions. Fo low aspec
a io li ing objec s such as o e boa ds, his e ec is also measu able in
he li and side o ce coe icien s. Addi ional es s o a ying Re would be
equi ed o p ope ly iden i y c i icali y. In any case, he pos ponemen o
s all in he wind unnel wi h espec o lume ank, sugges s ha he c i ical
Reynolds numbe may lie in be ween.
Su p isingly, lume ank specs ea u e wa e speeds highe han ac ually
used in o e boa d es ing, which would esul in be e Reynolds simila i y.
We belie e his migh s em om a misconcep ion o he ele an physics
in ol ed in o e boa d and ne ing hyd odynamics. Flume ank acili ies
ha e ex ensi ely been used in awl ne ing es s, which basically ely on
simple modeling ules [46], empi ical obse a ion [11] o F oude’s law [8]
o dynamic simila i y o be accomplished. Bulk Reynolds numbe e ec s
can be dis ega ded as negligible and a me e co ec ion based on a Reynolds
numbe de ined wi h he ne wine diame e can la gely imp o e model o
ull-scale esul s ex apola ion [16]. F oude numbe simila i y equi es ha
he eloci y scales like he squa e oo o he leng h scale, esul ing in lowe
lume ank eloci ies han ull-scale owing eloci ies. While his emains
ole able o awl ne s in e ms o Reynolds simila i y, i becomes c i ical
o o e boa ds, as Reynolds numbe can ge as low as o ha e an impac on
he hyd odynamics. Un o una ely his has been sys ema ically dis ega ded
in lume ank o e boa d es ing [1, sec ion 3-7], whe e F oude simila i y has
been gi en p io i y esul ing o en in wo yingly low Reynolds numbe s ha
19
may comple ely in alida e he ob ained o ce coe icien s.
The e is ne e heless an impo an aspec ha was no conside ed in de-
signing he wind unnel es s and ha would p obably p o ide esul s close
o eal sea condi ions. F ee-s eam u bulence le els in wind unnels a e usu-
ally e y low a <1%, while in lume anks usually ange in he 4 o 5%.
This a ou s a u bulen bounda y laye om ou se , which esis s sepa a-
ion be e en ailing lowe wake d ag and a he same ime leads o be e
cu en quali y, allowing o inc eased li . La ge o e boa ds in eal sea
condi ions a e mo e likely o ace hese noisy condi ions han hose in he
i ually u bulence- ee ai s eam o wind unnels. This can be s aigh -
o wa dly sol ed in u u e wind unnel es ing o o e boa ds h ough a i-
icially inc easing p e u bulence le els. This is done by using an adequa e
u bulence-gene a ing g id a he en ance o he es chambe . We belie e
ha his alone will ge wind unnel es ing close o lume ank esul s and,
wha is mo e impo an , p o ide be e es ima es o o e boa d pe o mances
a sea, and all his a a low cos and wi h good accu acy.
4. Conclusions
We ha e p o ided a de ailed desc ip ion o a p ocedu e o unde ake
o e boa d es ing in wind unnel acili ies and exempli ied he me hod o
a p oduc ion awl doo o which lume ank esul s a e a ailable in he
li e a u e. While compa ible o some ex en , non negligible disc epancies a e
obse ed be ween lume ank and wind unnel expe imen s ha we esol e
in a ou o he la e . The di e ences we asc ibe o he inhe en unce ain y
o he lume ank me hodology and, mo e p ominen ly, o Reynolds numbe
e ec s.
The g ea ad an age o wind unnel expe imen s is hei e sa ili y, which
allows o s aigh o wa d measu emen o o ces and momen s in all h ee
axes and a all possible hyd odynamic a i udes (as gi en by he wo hyd o-
dynamic angles). This is no only essen ial o p oducing use ul in o ma ion
such as he loca ion o he cen e o p essu e, which comes e y handy in
deciding he igging, bu also o a su icien ly accu a e desc ip ion o he
hyd odynamics ha can be buil in o a ull awl gea simula ion o pe o -
mance p edic ion, s abili y analysis o con ol loop design.
Fu he mo e, we belie e ha by impo ing concep s and de ini ions om
ae onau ics and ligh mechanics, he awl ishing communi y could po en-
ially bene i om a be e unde s anding o he hyd odynamics o o e
20
boa ds, esul ing in mo e e icien designs and mo e e ec i e use. Using he
ac ual hyd odynamic angles (a ack and sideslip) ins ead o me e o ien a ion
angles and measu ing all o ces and momen s and no jus d ag and sp eading
o ce is a c ucial s ep owa ds ully comp ehending o e boa d beha iou and
po en ial o imp o emen . This is bo h possible in lume anks duly gea ed
wi h he igh equipmen o in wind unnels, as demons a ed he e. Ne e -
heless, he ope a ing cos o mode n lume ank acili ies exceeds by a ac o
o ou o six imes he cos o wind unnel ope a ion o a compa able es
comp ising he same numbe o models in an equi alen numbe o possible
con igu a ions.
One o he undamen al aspec s o es ing is dynamic simila i y. While
ou es s could only app oach he lowe Re-end o eal condi ions, which is
al eady be e han wha lume anks expe imen s ha e achie ed o he o e
boa d es ed, he e is a po en ial o imp o emen in his espec . A majo ,
ye e y simple imp o emen o be implemen ed in wind unnel es ing is he
use o a u bulence-gene a ion g id in he en ance o he es chambe . This
can imp o e dynamic simila i y wi h sea condi ions, despi e he Reynolds
numbe disc epancy, h ough ensu ing he u bulen na u e o he bounda y
laye s de eloping on he o e boa d su ace igh om onse . Sligh ly smalle
models made o polyme o composi e ma e ials such as glass o ca bon ib e
o educe weigh , and moun ed ho izon ally on he balance would help achie e
highe speeds wi hou o e loading he load cells o he balance. Building a
s onge balance, and/o using wind unnels wi h la ge es sec ions can
help inc ease he Reynolds numbe o be e ma ching simila i y.
To accoun o g ound p oximi y e ec s, which a e i ele an o pelagic
and semipelagic awl doo s bu can be impo an o bo om o e boa ds,
he models can be moun ed wi h he shoe e y close o he wind unnel
g ound. This would p e en bo om lap ip o ices bu would no p ope ly
emula e he ela i e mo ion o awl doo and sea bo om. Some wind unnel
acili ies o e he op ion o using a mo ing bel o accu a ely cap u e g ound
e ec .
Tes s o he same awl doo in a mode n lume ank acili y equipped
wi h he la es measu ing echniques, and in eal sea ials, is cu en ly un-
de way and will help alida e wind unnel es ing u he . Also nume ical
simula ion is o be implemen ed in he nea u u e o assess i s po en ials.
All in all, wind unnel acili ies, used ollowing he me hodology p e-
sen ed in his pape , p o ide a lexible, accu a e means o es ing o e boa d
hyd odynamic pe o mance.
21
5. Acknowledgemen s
We kindly hank Ma hias Paschen, Sebas ian Sch eie and Ch is ian Sem-
low (Ma iKom GmbH) o hei help in se ing up and ca ying ou he wind
unnel expe imen s a hei acili ies in Uni e si ¨a Ros ock.
We would also like o hank Jan Bundgaa d (Thybo on, DK) o le ing
us demons a e he me hod on one o hei comme cial o e boa ds and Ku
Hansen o p o iding de ailed in o ma ion on p e ious lume ank esul s o
he same o e boa d.
This wo k was pa ially unded by he EC Commission h ough he Se -
en h F amewo k P og amme wi h he Resea ch p ojec BENTHIS (Ben hic
ecosys em ishe ies impac s udy, KBBE 2012.1.2-09, G an Ag eemen N .
312088) and he Flagship P ojec RITMARE ”The I alian Resea ch o he
Sea”, coo dina ed by he I alian Na ional Resea ch Council and unded by
he I alian Minis y o Educa ion.
The esea ch o Fe nando Mellibo sky and Joana P a was also sup-
po ed by he Spanish Minis y o Economy and Compe i i i y unde g an
CGL201128682C0202.
22
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25
(a) (b)
b/2
z
−b/2
0x l
α=0◦
α=5◦
α=10◦
α=15◦
α=20◦
α=25◦
α=30◦
α=35◦
α=40◦
Figu e 5: (a) Con ou map o he e iciency (η=CL/CD) o Thybo øn 15 model as a
unc ion o he ae odynamic angles. (b) Loca ion o he cen e o p essu e on he awl
doo plane as a unc ion o angle o a ack (colou coding, as shown in he legend) and
sideslip angle (sizing, he la ges co esponding o α= 0◦).
(a) (b)
Figu e 6: (a) Fo ce coe icien s (CL,CDand Cz) and e iciency (η) as a unc ion o angle o
a ack o no sideslip angle. (b) Fo ce coe icien s compa ison o wind unnel ( ull symbols,
WT) and lume ank (emp y symbols, FT) esul s o he Thybo øn 15 model.
32
