a Co esponding au ho : [email p o ec ed]
Flow s uc u e in on o he b oad-c es ed wei
Zbynk Zacho al1,a and Ladisla Rouša 2
1BUT, FCE, IWS, LWMR, 602 00 B no, Czech Republic
2BUT, FCE, IWS, 602 00 B no, Czech Republic
Abs ac . The pape deals wi h esea ch ocused on desc ip ion o low s uc u e in on o b oad-c es ed
wei . Based on expe imen al measu emen , he low s uc u e in on o he wei ( he eci cula ion zone o
low and o nado o ices) and low s uc u e on he wei c es has been desc ibed. The de e mined low
cha ac e has been simula ed using nume ical model and based on compa ing esul s he sui able model o
u bulence has been ecommended.
1 In oduc ion
Rec angula b oad-c es ed wei s a e equen ly used o
he de e mina ion o discha ge [1]. Wei s a e moun ed in
a p isma ic ec angula channel usually he same wid h B
as wid h o wei b o su icien ly inc ease wa e su ace,
ne e hless, do no in luence on maximum capaci y o
channel. The wei c es is ho izon al wi h he wei
hickness , he ups eam and downs eam aces a e
e ical, he wei su ace is smoo h, he ups eam and
downs eam wei edges a e sha p and he wei heigh is P
(Figu e 1). The e o o moun ing hem is o ensu e a
ee o e low in whole a ange o measu ing discha ges
[2].
Rec angula b oad-c es ed wei s o m h ee
eci cula ion zones o low [3]: ups eam [4], c es [5]
and downs eam eci cula ion zones [3] (Figu e 1). The
ups eam and c es eci cula ion zones ha e an in luence
on a wei capaci y, he downs eam eci cula ion zone
does no because he pa allel supe c i ical low is c ea ed
on he wei c es [6].
2 Flow s uc u e in on o he b oad-
c es ed wei
A di e en ela i e wei heigh s h/P, a di e en low
s uc u e o ms in on o ups eam ace [7]. In a case o
high wei s, he ups eam eci cula ion zone is no o med;
in medium-high wei s, only he ups eam eci cula ion
zone is o med; and in low wei s, he ups eam
eci cula ion zone is o med and is supplemen ed by
o nado o ices [8-11]. The c i e ia o he o ma ion o
indi idual low s uc u es ha e been de e mined by
Zacho al and Rouša [12].
Lu z
P
hu z ups eam
eci cula ion
zone
c es eci cula ion
zone
L
h
poin o low s agna ion
line o low s agna ion
ups eam
eci cula ion
zone
a ea o
low
s agna ion
line o
low
s agna ion
a ea o
de eloping
o eces
bed
s eamline
a e age posi ion o
o nado o ex axis
Lc z
hc z
c es
eci cula ion
zone
Figu e 1. Scheme o wei , low and no a ion o a iables.
3 Re iew o nume ical models o low
o e b oad-c es ed wei
The nume ical modelling o po en ial low o e b oad-
c es ed wei was in es iga ed by, e.g., Moos [13],
S ee ha an [14], Dias e al. [15]. Howe e , he po en ial
low does no desc ibe eci cula ion zones o low, hence
he esul s we e di e en . To achie e eliable esul s o
DOI: 10.1051/
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Owned by he au ho s, published by EDP Sciences, 2015
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021
201epjcon
EPJ Web o Con e ences ,
021
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(2015)
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7
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A icle a ailable a h p://www.epj-con e ences.o g o h p://dx.doi.o g/10.1051/epjcon /20159202117
ansi low, hey mus ha e been composed by special
ways [13].
The simula ion o o ical low o e ec angula wei
was s udied by Bomba deli e al. [16]. They used 2D
model o u bulen low o incomp essible iscous
liquid. The low was desc ibed by Reynolds-a e aged
Na ie –S okes equa ions (RANS). Tu bulence was
sol ed by Reno malized G oup (RNG) k-
ε
model [17].
They compa ed esul s wi h measu emen s Hage and
Schwal [18] and s a ed good ag eemen wi h a pa e n o
wa e su ace e en in ange o he c es eci cula ion
zone. Shake and Rhodes [19] simula ed wo phase low
in 3D desc ibed by RANS equa ions supplemen ed wi h
k-
ε
u bulence model [20] and wall unc ion. To
de e mine wa e su ace hey used Volume o luid
(VOF) me hod [21]. They ound good ag eemen wi h
low and wa e su ace le el, only hey no ed di e ences
in posi ion o he c es eci cula ion zone and in pos i ion
o a nappe. Ha gea es e al. [22] simula ed wo phase 2D
low (one case 3D) and es ed h ee di e en u bulence
models k-
ε
, RNG k-
ε
and Reynolds S ess Model (RSM)
[23]. RNG k-
ε
and RSM u bulence models simula ed
low mo e eliable han k-
ε
. They de e mined ha 3D
model does no p o ide in compa ison wi h 2D model a
imp o emen in pa e n o wa e su ace. The g ea es
di icul ies hey saw in simula ion o hyd aulic jump and
a ea ion o low. Hsu and Ozdemi [24] modeled he
same low as Ha g ea es and concen a ed on
compa ison wi h RNG k-
ε
and RSM u bulence models.
They s a ed ha model RSM yields be e esul s o
wa e su ace le el. Ki kgoz e al. [11] deal wi h 2D
modelling. They compa ed nume ically sol ed po en ial
low ield, nume ically sol ed low ield wi h he use o
RANS equa ions and k-
ω
[25] and k-
ε
ubulence models
wi h measu ed by me hod Pa icle Image Velocime y
(PIV) [26]. They ecommended RANS app oach wi h k-
ω
u bulence model. Adegbulugbe [27] ca ied ou a s udy o
he ela ed e i ica ion as Ha g ea es e al. [22]. He
claimed ha he mos accu a e esul s we e ob ained
using wi h RNG k-
ε
u bulence model.
4 Expe imen
Fo compa ing was chosen he wei desc ibed by
Zacho al e al. [29]. The wei was made o o ganic glass,
was moun ed in o a ec angula lume, wi h wei heigh
P = 0.250 m, wid h b = 1.003 m and hickness
= 0.500 m. The eloci y ield measu emen s was
conduc ed wi h a combina ion o Ul asonic Veloci y
P o ile (UVP) Moni o and PIV. The eloci y ield was
measu ed a inle channel by UVP Moni o [29] and in
on o he wei and on he wei c es by PIV [5]. The
shape o eci cula ion zones was isualiza ed by dye and
by pa icles added in o low. The ea e , he low
s uc u e was displayed by pa icles mo ing on he
bo om. The le el o wa e su ace was measu ed by a
poin gauge and he discha ge was de e mined by
calib a ed iangula sha p-c es ed wei .
5 Nume ical model
5.1 Selec ed app oach
The a ie y o app oaches may be used o sol ing low
s uc u e in on o he ec angula b oad-c es ed wei .
E e y app oach b ings wi h i a ce ain deg ee o
simpli ica ion and, he eby e o desc ip ion compa ed
wi h eali y. The equi emen s o he esul s de e mine
he choice o empo al and spa ial schema iza ion.
Fo sol ing s eady o e low om a mac oscopic iew
desc ibed by pa e n o wa e su ace and by ime-
a e aged eloci y ield he models we e used based on
RANS equa ions and La ge eddy simula ion (LES) model
wi h Smago insky subg id-scale (SGS) model. The
modelling o eci cula ion zones no a ec ed side walls
was pe o med by 2D and o nado o ex by 3D due o
hei spa ial cha ac e . Fo modelling u bulence wi h
RANS app oach he i s o de models we e selec ed
based on u bulence iscosi y: one laye models S anda d
k-
ε
, RNG k-
ε
, S anda d k-
ω
models and wo laye Shea
S ess T anspo (SST) model [28]. Fu he , he second
o de models we e used based on Reynolds s ess
anspo equa ion [23]: Baseline (BSL) Reynolds S ess
(RS) and Speziale-Sa ka -Ga ski (SSG) RS [30]. Fo
sol ing he so wa e we e used ANSYS-CFX (3D, 2D)
(Figu e 2) – wo phase low, ANSYS-Flo an (2D)
(Figu e 3) – one phase low and Flow-3D (2D) (Figu e 4)
– one phase low.
5.2 Calcula ion
Fluid domain geome y included he inle channel, he
wei and a pa o ou le channel wi h ee nappe. The
inle channel leng h was so long o de elop eloci y
p o ile.
A inle bounda y he hyd os a ic p essu e
dis ibu ion was se o a dep h es ablished om he
measu emen s and a cons an eloci y. A ou le bounda y
he ee ou low was se . The walls we e hyd aulically
smoo h. The hal domain was sol ed because longi udinal
symme y. The e e ence p essu e was ze o.
The numbe o elemen s depended on used so wa e
and dimension, o 2D model i was app oxima ely om
1·105 (Flow-3D, ANSYS-Flo an) o 5·105 (ANSYS-
CFX) and o 3D model 5·106. The calcula ions we e
pe o med in ange o discha ges 0.040 m3/s, 0.070 m3/s
and 0.130 m3/s. Ma e ial p ope ies o wa e we e:
densi y 998 kg/m3 and iscosi y 1·10-6 m2/s. All
coe icien s o u bulence models we e le unchanged.
The mesh was s uc u ed wi h ec angula elemen s.
5.3 E alua ed pa ame e s
The e alua ed pa ame e s we e he o e low head h a a
gi en discha ge, he leng h o c es eci cula ion zone
Lc z, he heigh o c es eci cula ion zone hc z, he leng h
o ups eam eci cula ion zone Lu z, he heigh o
ups eam eci cula ion zone hu z and he a e age posi ion
o o nado o ex axis L .
EPJ Web o Con e ences
02117-p.2
6 Resul s
The measu ed alues o e alua ed pa ame e s calcula ed
o he discha ge 0.070 m3/s a e shown in Table 1.
The esul s 2D calcula ions a e p esen ed in he o m
o eloci y ields o all e alua ed discha ges sol ed by
all so wa e.
Table 1. E alua ed pa ame e s [uni s in m], 2D, Q = 0.070 m3/s.
Model h Lc z h
c z L
u z h
u z
Measu ed 0.131 0.108 0.022 0.140 0.140
S anda d k-
ε
ANSYS-Flo an
ANSYS-CFX
Flow-3D
0.132
0.129
0.129
0.050
0.100
0.087
0.006
0.019
0.013
0.087
0.142
0.198
0.067
0.075
0.103
RNG k-
ε
ANSYS-Flo an
ANSYS-CFX
Flow-3D
0.130
0.130
0.127
0.068
0.130
0.081
0.008
0.020
0.012
0.072
0.148
0.144
0.060
0.106
0.084
S anda d k-
ω
ANSYS-Flo an
ANSYS-CFX
0.129
0.132
0.057
0.069
0.006
0.011
0.139
0.165
0.061
0.111
SST
ANSYS-Flo an
ANSYS-CFX
0.128
0.130
0.074
0.114
0.015
0.020
0.360
0.162
0.113
0.111
BSL RS
ANSYS-CFX 0.129 0.123 0.020 0.197 0.128
SSG RS
ANSYS-CFX 0.129 0.143 0.021 0.230 0.114
LES
(Smago insky SGS)
Flow-3D
0.128 0.092 0.015 0.317 0.116
Figu e 2. ANSYS-CFX, 2D, k-
ε
, 0.070 m3/s, eloci y ield.
Figu e 3. ANSYS-Flo an, 2D, k-
ε
, 0.040 m3/s, eloci y ield
Figu e 4. Flow-3D, 2D, k-
ε
, 0.130 m3/s, eloci y ield.
Figu e 5. To nado o ex.
Figu e 6. ANSYS-CFX, 2D, SST, 0.070 m3/s, s eamlines.
Figu e 7. ANSYS-CFX, 3D, SST, 0.070 m3/s.
EFM 2014
02117-p.3
.
7 Conclusions
F om he esul s in Table 1 is e iden ha alues o
e alua ed pa ame e s change wi h used so wa e and
u bulence model.
P ac ically, all one laye models based on u bulen
iscosi y unde es ima e a size o eci cula ion zones. The
mos eliable esul s o hem RNG k-
ε
u bulence model
p o ide. The models based on Reynolds s ess anspo
equa ion o e es ima e he leng h o eci cula ion zones in
di ec ion o low. Two laye s model SST p o ides he
mos eliable esul s om all used models (Figu e 6).
LES model o e es ima es he leng h o ups eam
eci cula ion zone. O e es ima ion o he leng h o
ups eam eci cula ion zone may be caused by a ac ha
he nume ical model due o small numbe o elemen s
does no simula e o ices a ising nea he bed in on o
he ups eam eci cula ion zone [12].
The alues o esul s in Table 1 a e signi ican ly
dependen on he elemen size which i is mainly
e lec ed a he heigh o c es eci cula ion zone. The
bes esul s a e achie ed wi h he la ges numbe o
elemen s which explains he di e ences in esul s wi h
used so wa e.
The sol ed o e low head was p ac ically o all
models sligh ly smalle han measu ed. E o o i s
de e mina ion is in all cases up o 3 %. The co ec
modelling o he heigh o he c es eci cula ion zone is
essen ial o de e mina e he o e low head. The e o e, i
is ecommended o use a leas 8 elemen s along i s
heigh . In he case o using a smalle numbe o elemen s
he modelled c es eci cula ion zone is smalle . In he
case o using a la ge numbe o elemen s ha ing no
signi ican e inemen i s heigh . The co ec modelling o
he ups eam eci cula ion zone has signi ican ly less an
in luence on he o e low head han he c es
eci cula ion zone.
To nado o ex (Figu e 5) was able o simula e
(Figu e 7), i s posi ion is in a ange o measu ed alues
[12]. The low in a ea o o nado o ex is de eloped
du ing he simula ion p ocess as he las . The e o e, he
su icien numbe o simula ion is necessa y o pe o m.
Fo de e mining o he o e low head has negligible
e ec .
Fo p ac ical use in de e mining o he o e low head
a known discha ge and ice e sa is possible due o he
ela i ely small demands on mesh and high accu acy
de e mina ion o low cha ac e o ecommend RANS
app oach and a wo laye SST u bulence model.
Acknowledgmen s
Acknowledgmen s a e due o p ojec s FAST-S-14-2203 -
Cha ac e is ics o subme gence o low ec angula b oad-
c es ed wei s and FAST-S-13-2010 T anspo o pa icles
o e he ec angula b oad-c es ed wei .
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