NUMERICAL MODELLING OF WAVES INTERACTING WITH THE
BREAKWATERS OF LEIXÕES HARBOUR, PORTUGAL
MARINE 2011
Ma ia G. Ne es*, Ma ia T. Reis
*
, Jo ge F. Gadelho*, Ja ie L. La a
†
, F ancisco T. Pin o!,
Hugo G. Lopes!, José P. Cab al!
*
Labo a ó io Nacional de Engenha ia Ci il (LNEC)
A . do B asil, 101, 1700-066 Lisboa, Po ugal
e-mail: gne [email protected] , [email protected] , [email protected] , web page: h p://www.lnec.p
†
Ins i u o de Hid áulica Ambien al
Uni e sidad de Can ab ia
A da. Los Cas os s/n San ande , España
e-mail: ja [email protected], web page: h p://www.ihcan ab ia.unican.es/WebIH/en/
! Faculdade de Engenha ia da Uni e sidade do Po o, (FEUP)
Rua D . Robe o F ias, 4200-465Po o. Po ugal
e-mail: pin o@ e.up.p , hg[email p o ec ed], cab al@ e.up.p , web page: h p://www. e.up.p
Key wo ds: nume ical modelling, wa e-s uc u e in e ac ion, po ous low, physical
modelling, ideo image y echniques
Summa y. Two nume ical models – AMAZON, based on he non-linea shallow-wa e
(NLSW) equa ions, and IH-2VOF, based on he Reynolds a e aged Na ie –S okes (RANS)
equa ions – a e planned o be used o model he hyd odynamic p ocesses a ound he Leixões
ha bou b eakwa e s ( he exis ing and he subme ged b eakwa e ). In pa icula , he eloci y
ield be ween he wo b eakwa e s and he wa e o e opping o e he exis ing b eakwa e will
be analyzed. This pape p esen s he me hodology ha has been used o analyze he sensi i i y
o he IH-2VOF esul s o he po ous media pa ame e s ha should be calib a ed. Fi s esul s
ob ained in his s udy a e also p esen ed in o de o illus a e his me hodology.
1 INTRODUCTION
The No h b eakwa e o Leixões Ha bou , loca ed a he No h pa o he Wes coas o
Po ugal, p o ec s an oil e minal and i is subjec ed o o e opping and ansmission o wa e
and sedimen s h ough he po ous s uc u e. In o de o mi iga e he ela ed p oblems, a
subme ged b eakwa e has been s udied o cons uc ion in on o he exis ing b eakwa e .
De ining he dimensions and cha ac e is ics o he subme ged s uc u e, as well as i s posi ion
in ela ion o he exis ing s uc u e, a e some o he design di icul ies. The e may be also, in
some cases, en i onmen al es ic ions and economic limi a ions.
To da e, he design o he subme ged b eakwa e has been suppo ed mainly by empi ical
knowledge and, o some speci ic wa e/wa e -le el condi ions, by physical modelling.
The e o e, wi hin he scope o he esea ch p ojec en i led “DESTAQ – De elopmen o
eloci y measu emen s ad anced echniques o he In e ac ion analysis be ween de ached
In e na ional Con e ence on Compu a ional Me hods in Ma ine Enginee ing
MARINE 2011
L.Eça, E. Oña e, J. Ga cía, T. K amsdal and P. Be gan (Eds)
Nume ical Modelling o Wa es In e ac ing wi h he B eakwa e s o Leixões Ha bou , Po ugal
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2
b eakwa e and ha bou s uc u e”
1
, nume ical models a e also being applied o imp o e he
knowledge abou he hyd odynamic p ocesses in he icini y o he s uc u es and o op imize
i s design. Once p ope ly calib a ed, he models can be applied and ex ended o si ua ions no
es ed du ing he expe imen al s udy.
Two nume ical models – AMAZON and IH-2VOF – a e being used o desc ibe he
hyd odynamic p ocesses a ound he Leixões ha bou b eakwa e s, in pa icula he eloci y
ield be ween he wo b eakwa e s and he wa e o e opping o e he exis ing b eakwa e .
AMAZON
2
is based on he non-linea shallow-wa e (NLSW) equa ions and i desc ibes
wa e mo ions in e ms o he ins an aneous o al wa e dep h and he dep h-a e aged eloci y
o egula o i egula wa es. The o iginal e sion o AMAZON did no explici ly accoun
o po ous low. The de elopmen o he po ous low model was ca ied ou ecen ly
3
and i
includes he addi ion o one po ous laye o he o iginal model design and he conside a ion o
a cons an po osi y o he whole po ous elemen . In his s udy, AMAZON will be used o
e alua e he wa e o e opping o e he No h b eakwa e , compa ing he esul s wi h he da a
measu ed in he physical model and wi h he esul s ob ained wi h IH-2VOF. Once he po ous
media cha ac e is ics a e calib a ed wi h he physical model da a, AMAZON will allow a as
analysis o he s uc u e’s beha iou o di e en geome ies and wa e condi ions. IH-2VOF
4
is based on he Reynolds-a e aged Na ie -S okes (RANS) equa ions and i desc ibes he low
inside and ou side ma i ime s uc u es including pe meable laye s. I has al eady been
ex ensi ely alida ed o low-c es ed s uc u es and wa e b eaking on pe meable slopes. The
model will be used o calcula e he eloci y ield esul ing om he in e ac ion o he
subme ged b eakwa e wi h he exis ing ubble-mound b eakwa e and he wa e o e opping
o e his b eakwa e . Once calib a ed, i will allow he e alua ion o e ical and ho izon al
eloci ies in all he mesh poin s and hei compa ison wi h he labo a o y esul s.
This pape p esen s he me hodology ha has been used o analyze he sensi i i y o he
IH-2VOF esul s o he calib a ed po ous media pa ame e s. The analysis is mainly ocused
on he ee su ace ele a ion be o e he subme ged b eakwa e and be ween he subme ged
and he exis ing b eakwa e s. Fi s esul s ob ained in his s udy a e also p esen ed in o de o
illus a e he me hodology.
2 CASE STUDY
2.1. Leixões No h B eakwa e
The No h b eakwa e o Leixões ha bou is an unusual s uc u e, whose geome y su e ed
se e al changes since he i s layou , back in 1892. The s uc u e was ini ially a subme ged
b eakwa e ha due o ha bou expansion was aised in he la e 60’s o he c es le el o
+15.0 m(ZH). In he 80’s a subme ged b eakwa e was buil on he head o he No h
b eakwa e o imp o e i s s abili y, de ining he cu en con igu a ion (Figu e 1).
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3
Figu e 1: C oss sec ion o he No h b eakwa e o Leixões ha bou .
2.2. Physical Model S udy
The physical model es s o he No h b eakwa e o Leixões ha bou a e being pe o med
a he wa e ank o he Hyd aulics Labo a o y o he Uni e si y o Po o (Figu e 2). The wa e
ank is 28.0 m long, 12.0 m wide and 1.2 m deep. A 0.75 m lume was buil inside he wa e
ank o pe o m he 2D model es s. The model was buil a a 1:60 geome ical scale and i e
p obes we e placed on he seaside o he main s uc u e, o con ol he wa e ac ion and o
de e mine he e lec ion o he s uc u e and he ansmission be ween he wo s uc u es. The
es p og amme includes h ee di e en ide le els (0.0 m, +2.0 m and +4.0 m(ZH)), egula
and i egula wa es (JONSWAP spec um) and ou di e en wa e pe iods (T o Tp – 13 s,
16 s, 20 s and 24 s, whe e T is he egula wa e pe iod and Tp is he peak o he JONSWAP
spec um). The egula wa e heigh s (H) ange om 2.0 m o 14.0 m, while he signi ican
wa e heigh s (Hs) ange om 1.0 m o 7.0 m (all alues in p o o ype).
Two GigE E he ne came as we e used (UI 5220 and UI 5480 µeye – 0.8MPX wi h up o
90 ps; 5MPx wi h up o 14 ps, espec i ely) o analyze he low du ing he es s and o
eco d pa icle mo emen s o PIV (Pa icle Image Velocime y) applica ion and eloci y
ield cha ac e iza ion.
Figu e 2: Model se -up.
The eco ds we e made in wo di e en a eas o he lume, in he icini y o he subme ged
b eakwa e and in be ween he wo b eakwa e s, so ha all pe o mance issues could be
add essed. The high esolu ion came a (UI5480) was also used o cap u e small s e ches in
de ail o esolu ion analysis compa ison.
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4
On adi ional PIV and PTV (Pa icle T acking Velocime y) echniques a lase ligh
sou ce is used o illumina e he a ea o in e es . In hese es s a new app oach is applied, using
only whi e ligh (halogen ocus - 2x300W). The use o whi e ligh ollows he idea o de ining
an economic and low equi emen s solu ion ha could be applied o open lume es s wi h
wa e b eaking. The use o lase ligh sou ce in his case was no ecommended due o he
p esence o b eaking wa es and, he e o e, mul iphase low.
This s udy is s ill ongoing and eloci y ields a e also being analyzed using Video Image y
echniques, namely PIV adi ional me hods. A mul i-pa ame ic p obe will also be used o
analyze low cha ac e is ics.
3. NUMERICAL MODELS
3.1. AMAZON
AMAZON was o iginally de eloped a Manches e Me opoli an Uni e si y
2
, i is w i en
in C++ and i comes as bo h a one-dimensional model, applied he e, and as a wo-dimensional
plan model. I is based on sol ing he NLSW equa ions, which a e a simpli ica ion o he
Reynolds equa ions by dep h in eg a ion. I simula es andom wa es and wa e b eaking is
app oxima ed by s eep on s ep esen ed by bo es. AMAZON uses a “non- e lec i e wa e
inle bounda y condi ion", which is able o emo e a he seawa d bounda y mo e han 98% o
he ene gy o any wa es e lec ed om he modelled s uc u es. As a consequence, he
seawa d bounda y can be se close o he s uc u e o a oid deep wa e condi ions, whe e
AMAZON has limi a ions. I is capable o gene a ing g id cells wi h any shape and a ying
dimensions. The ou pu de ines he ee su ace, dep h-a e aged eloci ies and, based on hese
alues, discha ge ime-se ies, mean discha ge and peak discha ge a any loca ion on he
s uc u e.
AMAZON has been alida ed o a a ie y o ep esen a i e es p oblems
2
in ol ing
s eady and uns eady, in iscid and iscous, and subc i ical and supe c i ical lows. I has also
been alida ed and ex ensi ely used o s udy he wa e o e opping o impe meable dikes.
Howe e , AMAZON has no been sys ema ically alida ed o s udy he o e opping o po ous
s uc u es ye , since i s o iginal e sion did no explici ly accoun o po ous low. The
de elopmen and ini ial alida ion o he po ous low model has been ca ied ou only
ecen ly
3,5,6,7
. To go e n he wa e exchange be ween he po ous cells, bo h he Da cy and he
Fo chheime equa ions a e implemen ed.
In spi e o AMAZON limi a ions, mainly ela ing o he shallow wa e assump ions, i is
al eady being used o he pu poses o design and lood o ecas ing, since wa e ains o
se e al housand andom wa es a e simula ed apidly.
A de ailed desc ip ion o AMAZON can be ound in Hu
2
and in Reis e al.
5,6
.
In his s udy, AMAZON will be applied o calcula e he su ace ele a ion and he mean
wa e o e opping discha ge o e he No h b eakwa e o Leixões Ha bou .
3.2. IH-2VOF
By aking he olume-a e age o RANS (VARANS) equa ions, Lin and Liu
8
p esen ed a
wo-dimensional nume ical model, nicknamed COBRAS, o desc ibe he low inside and
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5
ou side ma i ime s uc u es including pe meable laye s. Hsu e al.
9
ex ended he p elimina y
model by including a se o olume-a e aged k-ε u bulence balance equa ions. The
mo emen o he ee su ace is acked by he Volume o Fluid (VOF) me hod. In he
VARANS equa ions, he in e acial o ces be ween he luids and he solids ha e been
modelled by he ex ended Fo chheime ela ionship, in which bo h linea and nonlinea d ag
o ces a e included.
IH-2VOF is a new e sion o he model de eloped a he Uni e si y o Can ab ia o
o e come some o he ini ial limi a ions and especially o con e i in o a ool o p ac ical
applica ion. Mos o hese modi ica ions ha e been based on he ex ensi e alida ion wo k
ca ied ou wi h he model o low-c es ed s uc u es and o wa e b eaking on pe meable
slopes
10,11
. The imp o emen s co e he wa e gene a ion p ocess and code upda ing;
op imiza ion and imp o emen o he main sub ou ines; imp o emen o inpu and ou pu da a
de ini ion; and he de elopmen o a g aphical use in e ace and ou pu da a p ocessing
p og ams.
In his s udy, IH-2VOF will be used o calcula e he su ace ele a ion, he eloci y ield
esul ing om he in e ac ion o he wo b eakwa e s and he wa e o e opping o e he No h
b eakwa e .
4. MODEL CALIBRATION
To simula e he low in a po ous medium in IH-2VOF some pa ame e s equi e calib a ion:
he linea , α, and he nonlinea , β, coe icien s ela ed o he linea and nonlinea d ag o ces,
espec i ely. The po osi y, n, and he ock diame e , D
50
, a e usually inpu pa ame e s
ob ained om he physical model.
In his case (see sec ion 2.2), he s uc u e was ep oduced in he physical model by ou
di e en po ous media (PM): h ee composed by a i icial blocks (PM1, PM2, PM3) and one
by small ocks (PM4). The a i icial blocks a e: cubes, in wo di e en sec ions (PM1 and
PM2), wi h di e en weigh s and sligh ly di e en geome ies, and e apods (PM3), as can be
seen in Figu e 3. The main cha ac e is ics o he media a e p esen ed in Table 1.
Figu e 3: Expe imen al s uc u e: a) op iew o he physical model wi h he di e en a i icial blocks used in he
es s; b) schema ic ep esen a ion o he s uc u e, wi h di e en po ous media.
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n (%) D
50
(mm) ρ
ρρρ (kN/m
3
)
PM1 - Cubes 35 - 45 56 24
PM2 - Cubes 35 - 45 56 24
PM3 - Te apods 45 - 55 43 24
PM4 - Rock 20 - 35 19 - 25 18
Table 1: Main cha ac e is ics o he ma e ials in he po ous laye s.
Fo he po ous medium composed by small ock, he po osi y and he diame e a e easily
de e mined in he physical model and a e almos cons an h oughou he es s. Fo hose
speci ic cha ac e is ics o he po ous medium he e a e some sugges ed alues o α and β in
he li e a u e
10
. The ecommended alues o α ange om 200 o 1000 and o β be ween 0.8
and 1.1.
Fo a i icial blocks, he po osi y depends on he block a angemen and, i he blocks
mo e o ock du ing he es s, he po osi y may change. Consequen ly, i should be calib a ed
as well. The diame e is calcula ed as he nominal diame e , based on he weigh o he blocks.
Howe e , he same nominal diame e wi h a di e en shape o he block can lead o a e y
di e en po ous low. Mo eo e , he e is no indica ion in he li e a u e on he bes alues o
α and β o be used in he case o laye s composed by a i icial blocks.
All hese cons ain s, as well as he ac ha he e ec s o one po ous medium a e di icul
o isola e om he o he s, made calib a ion especially di icul o his case s udy.
Addi ionally, he calib a ion should gi e an indica ion on he ela i e impo ance o each
po ous medium pa ame e in wa e o e opping. This in o ma ion is e y impo an o decide
on he pa ame e s o he single po ous medium ha will be used in AMAZON o compu e he
o e opping, since he di e en po ous media will be simula ed by jus one single
homogenous medium in his model. Consequen ly, especial ca e has been aken in o de o
de ine which po ous medium in luences he mos he global low when o e opping occu s.
The me hodology ha has been used o analyze he sensi i i y o he IH-2VOF esul s o
each po ous medium s a ed wi h he de ini ion o se e al base alues o he po ous
pa ame e s. A e ha , o selec ed cases, he sensi i i y uns consis ed on changing, o each
po ous medium a a ime, he alue o each pa ame e one by one, main aining he o he
alues wi h a cons an base alue, o make i easie o analyze he in luence o each pa ame e
and o each po ous medium on he esul s. The selec ed cases we e hose whe e he in luence
o one po ous medium was expec ed o be la ge han he o he s, making i possible o analyze
he in luence o each po ous medium sepa a ely. Di e en cases we e p ima ily selec ed:
i s ly, wo cases we e chosen whe e no o e opping occu s and he wa e e lec ion on PM3
( o he highes wa e le el) and PM2 ( o he lowes wa e le el) is expec ed o be he main
phenomenon, making PM3 and PM2, espec i ely, he expec ed key in luence; secondly, a
case was analyzed whe e b eaking occu s a he subme ged s uc u e, wi h no o e opping,
making PM1 he expec ed key in luence.
In o de o illus a e he abo e me hodology, he i s simula ion case ca ied ou wi h
IH-2VOF is p esen ed he e.
Fo he simula ion, he loca ion, dimensions and geome y o he expe imen al s uc u e
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(see sec ion 2.2) we e ep oduced in he compu a ional domain, which was 8 m long and
0.8 m high. I ep oduced he main dimensions o he expe imen al lume, wi h he paddle
loca ed sligh ly close o he s uc u e han he paddle in he lume.
In o de o educe he compu a ional ime whils assu ing he equi ed accu acy, he i s
se o calib a ion es s was un wi h a ela i ely coa se mesh. The g id was uni o m bo h in he
x and in he y di ec ions, wi h a cell wid h, dx, o 0.01 m and a cell heigh , dy, o 0.005 m in
he whole domain. The o al numbe o cells was 161x851. Figu e 4 shows an aspec o he
compu a ional g id close o he s uc u e wi h he ou po ous media geome y and he
(impe meable) c own wall.
Figu e 4: Aspec o he compu a ional g id close o he s uc u e wi h he ou po ous media geome y (in ed),
he impe meable c own wall (in yellow) and he sea wa e le el.
Eigh sec ions we e conside ed in he nume ical lume: i e we e loca ed a he same
posi ions as he wa e gauges in he physical model ( ou be ween he paddle and he
subme ge b eakwa e - G3, G5, G11 and G12 - and ano he be ween b eakwa e s – G4); one
was placed close o he paddle, in o de o con ol he wa e gene a ion; and ano he wo we e
posi ioned on op o he s uc u e o compu e he o e opping discha ge. Each calib a ion es
has un o 100 s in he IH-2VOF.
Se e al alues o he po ous pa ame e s we e es ed in he sensi i i y s udy. Fi s o all,
some alues o he pa ame e s α, β and n we e de ined as base alues (Table 2). Fo he
a i icial blocks, he nominal diame e was calcula ed based on he weigh o he blocks and
o he ock medium, he mean alue was adop ed based on he measu ed ange o alues. Fo
he po osi y, a mean alue o he measu ed ange was adop ed. The alues o α and β we e
de ined based on alues used in p e ious simula ions epo ed in he li e a u e.
n (-) α (-) β (-) D
50
(mm)
PM1 0.25 200 1.1 22
PM2 0.40 200 0.8 56
PM3 0.40 200 0.8 56
PM4 0.30 200 1.0 43
Table 2 : Values o po ous media pa ame e s adop ed as base alues.
A e ha , he alue o each pa ame e in each po ous medium was changed, one a a ime,
main aining he o he alues cons an , equal o he alues p esen ed in Table 2. The aim o
his me hodology is o analyze he in luence o each pa ame e and o each po ous medium on
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he esul s. Table 3 shows he alues used in he calib a ion es s o each pa ame e in each
po ous medium. E en hough some o he alues a e in he limi o he ecommended alues,
i was decided o use a wide ange o alues in o de o analyze hei in luence on he esul s.
n (-) α (-) β (-)
PM1 0.25, 0.35, 0.45, 0.55 100, 200, 1000 0.5, 0.8, 1.1
PM2 0.25, 0.35, 0.45, 0.55 100, 200, 1000 0.5, 0.8, 1.1
PM3 0.4, 0.50, 0.60 100, 200, 1000 0.5, 0.8, 1.1
Table 3 Values o po ous media pa ame e s used in calib a ion es s.
Ha ing all he e e ed cons ain s in mind, he sensi i i y analysis s a ed o es s wi h he
highes wa e le el (+4.0 m(ZH)), since o he lowes one (ZH), no o e opping was measu ed
du ing he physical model es s. The i s simula ed condi ion is cha ac e ised by an inciden
wa e heigh H=3.5 cm and a wa e pe iod T=1.68 s, wi h a wa e dep h a he paddle h=0.35 m.
The ee su ace ele a ions compu ed by IH-2VOF o he di e en alues o each po ous
pa ame e we e compa ed wi h each o he in o de o analyze he in luence o he pa ame e s
on he wa e shape. The ee su ace ele a ions we e also compa ed wi h hose measu ed in
he physical model es s a gauges G3, G4, G5, G11 and G12 in o de o es ablish he
op imum alues o he calib a ion pa ame e s. Since he wa e signals o gauges G3, G5, G11
and G12 a e almos sinusoidal, wi h almos no ene gy in he highe ha monics, he signals a e
well ep esen ed by he wa e heigh , H, and he wa e pe iod, T. This sinusoidal wa e shape is
clea ly seen in Figu e 5, which shows he ime se ies o su ace ele a ion, η, measu ed by
gauges G3, G5, G11 and G12 a he physical model be ween =60 s and =70 s. In gauge G4,
loca ed be ween he subme ged and he exis ing b eakwa e s, he ans e ence o ene gy o
highe ha monics is e y clea . In his case, he signi ican wa e heigh , Hs, and he peak
pe iod, Tp, a e analyzed oge he wi h he ene gy in each o he i s i e ha monics.
-0.025
-0.015
-0.005
0.005
0.015
0.025
60 62 64 66 68 70
(s)
η
η
η
η (m)
G3 G5 G11 G12 G4
Figu e 5: Time se ies o su ace ele a ion measu ed by gauges G3, G4, G5, G11 and G12 a he physical model
o H=3.5 cm, T=1.68 s and h=0.35 m.
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Figu e 6 shows he a io o he alues o H (o Hs) calcula ed wi h IH-2VOF (H
IH-2VOF
) and
H (o Hs) measu ed in he physical model (H
PM
) and he a io o he ene gy calcula ed wi h
IH-2VOF (S
IH-2VOF
) and measu ed in he physical model (S
PM
) o each ha monic, o all
gauges (G3, G4, G5, G11 and G12) and o he di e en pa ame e s. In o de o illus a e he
esul s, he g aphics wi h he in luence o he pa ame e s α, β, and n on H and on S a e
p esen ed o PM1, PM2 and PM3, espec i ely. The wa e pe iod was well ep oduced in he
model in each one o he gauges loca ed be o e he subme ged b eakwa e , as well as he peak
pe iod a gauge G4.
PM1
0.85
0.90
0.95
1.00
1.05
1.10
1.15
G4 G3 G5 G11 G12
Gauges
Hs
IH-2VOF
/ Hs
PM
α = 100 α = 200 α = 1000
PM1
0.00
0.25
0.50
0.75
1.00
1.25
1.50
0.00.61.21.82.43.03.64.2
(Hz)
S
IH-2VOF
/ S
PM
α = 100 α = 200 α = 1000
PM2
0.85
0.90
0.95
1.00
1.05
1.10
1.15
G4 G3 G5 G11 G12
Gauges
Hs
IH-2VOF
/ Hs
PM
β = 0.5 β = 0.8 β = 1.1
PM2
0.00
0.25
0.50
0.75
1.00
1.25
1.50
0.00.61.21.82.43.03.64.2
(Hz)
S
IH-2VOF
/ S
PM
β = 0.5 β = 0.8 β = 1.1
PM3
0.85
0.90
0.95
1.00
1.05
1.10
1.15
G4 G3 G5 G11 G12
Gauges
Hs
IH-2VOF
/ Hs
PM
n = 0.40 n = 0.50 n = 0.60
PM3
0.00
0.25
0.50
0.75
1.00
1.25
1.50
0.0 0.6 1.2 1.8 2.4 3.0 3.6 4.2
(Hz)
S
IH-2VOF
/ S
PM
n = 0.40 n = 0.50 n = 0.60
Figu e 6: In luence o he po ous pa ame e s on he alues o H (le ) and o S ( ig h) ob ained in each gauge:
a) α o PM1, b) β o PM2 and c) n o PM3.
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