Influence o he u bulence ep esen a ion a he inle on he
downs eam flow pa e n in LES o backwa d- acing s ep
Ja osla VOLAVY*, Ma ej FORMAN**, Mi osla JICHA***
Abs ac : The impac o he choice o inle bounda y condi ion ea men on he fluid
flow is s udied in his wo k. The co ec ep esen a ion o he u bulence a he inle
o he domain is essen ial o he accu acy o La ge Eddy Simula ion. The inapp o-
p ia e specifica ion o he inle eloci y has significan e ec on he downs eam flow
pa e n. The case o backwa d- acing s ep was used as a es case. Th ee di e en
app oaches o he inle bounda y condi ions we e s udied: uni o m eloci y p ofile,
mean eloci y p ofile o he ully de eloped channel flow and eloci y ob ained om
mapping eloci y om plane posi ioned behind he inle back o he inle . The esul s
o he simula ions we e compa ed wi h expe imen al esul s. I has shown, ha using
uni o m eloci y p ofile on inle and e en p esc ibing u bulen mean eloci y p ofile
wi hou p ope ep esen a ion o u bulence fluc ua ions leads o un ealis ic esul s.
1INTRODUCTION
In he simula ion o u bulen flow, he mos impo an ac o seems o be p ope choice o u bulence
model ha will p o ide good ep esen a ion o he flow. Ano he issue o g ea impo ance is specifica ion
o bounda y condi ions, especially inle bounda y condi ion. The eloci y and ano he inflow da a linked
wi h u bulence p esc ibed by bounda y condi ion should be consis en wi h chosen u bulen model.
Desc ip ion o mean eloci y p ofile and o he u bulence a iables ( u bulen kine ic ene gy, ...) ob ained
om analy ical solu ion o om expe imen s can be ega ded as su ficien o he RANS simula ions.
This app oach was jus ified in [1]. I was shown ha RANS model each uni e sal asymp o ic beha io
i espec i e o he ini ial condi ions. Fo La ge Eddy Simula ion, whe e he field on he inle is u bulen ,
he si ua ion is mo e p oblema ic. Desc ip ion o he flow is usually limi ed by knowledge o s a is ical
quan i ies such as mean eloci y p ofiles and mass fluxes. In LES, he da a gene a ed by inle bound-
a y condi ion should include an uns eady u bulen eloci y signal ep esen ing u bulence a he inle .
Ideally, he simula ion o ups eam flow en e ing he compu a ional domain will p o ide a good flow ep-
esen a ion. Howe e , unlimi ed ex ension in he ups eam di ec ion is no possible because o high
compu a ional cos . The e o e app oxima e inle condi ions mus be specified.
A lo o me hods we e de eloped in he pas . Kal enbach e al. [2] used ecycling me hod. Tu bulen
fluc ua ions a e specified by unning p ecu so simula ion, whose only ole is o p o ide main simula ion
wi h accu a e bounda y da a. Ano he app oach is o add syn he ic u bulence a he inle . Lund e
al. [3] modified inle eloci y field by adding a andom e m o all eloci y componen s. Klein e al. [4]
p oposed digi al signal p ocessing p ocedu e o emedy lack o la ge- scale dominance in he inflow da a
gene a ed by he andom me hod.
*Ja osla Vola y, Facul y o Mechanical Enginee ing, B no Uni e si y o Technology, Technická 2896/2, 616 69 B no, Czech
Republic, ja osla . [email p o ec ed]
**Ma ej Fo man, Facul y o Mechanical Enginee ing, B no Uni e si y o Technology, Technická 2896/2, 616 69 B no, Czech Re-
public, o man@ me. u b .cz
***Mi osla Jicha, Facul y o Mechanical Enginee ing, B no Uni e si y o Technology, Technická 2896/2, 616 69 B no, Czech
Republic, [email p o ec ed].cz
EPJ Web o Con e ences , 010 (2012)
DOI: 10.1051/epjcon /201225010
© Owned by he au ho s, published by EDP Sciences, 2012
This is an Open Access a icle dis ibu ed unde he e ms o he C ea i e Commons A ibu ion License 2.0, which
pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal wo k is p ope ly ci ed.
A icle a ailable a h p://www.epj-con e ences.o g o h p://dx.doi.o g/10.1051/epjcon /20122501099
2GOVERNING EQUATIONS
Fo he solu ion o he fluid flow in his a icle was chosen La ge Eddy Simula ion. The main idea o
La ge Eddy Simula ion is o sepa a e la ge scales (g id-scales) om small scales (subg id-scales) o
lowe compu a ional cos . The subg id scales a e modelled using subg id model. The scale sepa a ion
is done by applying fil e ope a o on Na ie -S okes equa ion. I we apply he fil e ope a o on Na ie -
S okes equa ions we ob ain fil e ed Na ie -S okes equa ions:
∂¯ui
∂ +∂
∂xj
(¯ui¯uj)=−1
ρ
∂¯p
∂xi
+ν∂2¯ui
∂xk∂xk
−∂τij
∂xj
.(1)
Fo e alua ion o subg id s ess enso τij is used Smago insky model:
τij −1
3δijτkk =−2ν ¯
Sij,ν
=(CSΔ)2|¯
S|(2)
¯
Sij =1
2∂¯ui
∂xj
+∂¯uj
∂xi(3)
whe e |¯
S|=|2¯
Sij ¯
Sij|1/2.
3DESCRIPTION OF THE TEST CASE
Fo es ing o di e en app oaches o he inle bounda y condi ion was chosen backwa d- acing s ep
flow. This case o flow is good benchma k o alida ing a ious models because i con ains massi e
sepa a ion and consequen e-a achmen . Sepa a ion bubble on he wall opposi e o he s ep could
appea o some geome ical and flow pa ame e s.
The geome y and flow p ope ies was chosen acco ding o he expe imen al s udy done by [6]. The
Reynolds numbe o he inle channel flow was 13 800, based on he bulk eloci y o 10 m/s and he
channel hal -wid h o 20 mm. The expansion a io was 5/3. The flow pa ame e s o he inle channel and
backwa d acing s ep flow a e in able 1.
Table 1: Flow pa ame e s
Channel flow Backwa d- acing s ep flow
Channel hal -wid h, h20 mm S ep heigh , H26.7 mm
Channel bulk eloci y, U010 m/s Expansion a io 5:3
Reh=U0h
ν13 800 ReH=U0H
ν18 400
uτ, ic ion eloci y 0.5 m/s τ , la ge eddy ime scale, 5H/U012.7 ms
Viscous leng h scale 31 μm
Kolmogo o leng h scale, η170 μm
The compu a ional mesh consis s o 2.1 million hexahed al cells. The mesh is block-s uc u ed and
becomes fine owa ds he wall in o de o sa is y condi ion o y+≈1. The de ail o he mesh nea he
ailing edge is in he Figu e 1.
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Figu e 1: The de ail o he mesh nea he ailing edge.
4INLET BOUNDARY CONDITION
Fo he gene a ion o he eloci y on he inle o he domain we e used h ee di e en app oaches. Le
hem deno e as Case A, B and C. All cases ha e bulk eloci y o 10 m/s.
Case A: Uni o m eloci y p ofile is p esc ibed a he inle o he compu a ional domain. No eloci y
fluc ua ions a e p esen .
Case B: Mean eloci y p ofile o ully u bulen channel flow is p esc ibed on he inle . No eloci y
fluc ua ions a e p esen .
Case C: Fo he gene a ion o he eloci y on he inle o he domain was used di ec mapping app oach
[2]. The eloci y on he inle is ob ained by di ec mapping o he eloci y om he plane wi h 3h(60
mm) o se om he inle plane. The schema ic pic u e o he mapping is shown in he Figu e 2 ( he
placemen o he mapping plane in his figu e is only schema ic). Fo he flow ini ializa ion was used
ollowing p ocedu e: Fi s was done simula ion o inle channel only using pe iodic bounda y condi ion.
Fo as e ansi ion o he ully de eloped u bulen flow was used o cing scheme based on O ns ein-
Uhlenbeck p ocess p oposed by [7]. When he ully u bulen egime was eached hen he esul s o
his p e-simula ion was mapped o he inle channel o he backwa d- acing s ep geome y.
Figu e 2: Scheme o inle da a mapping.
5RESULTS
In his sec ion a e desc ibed esul s ob ained by a ious app oaches o he inle bounda y condi ion.
The simula ions we e s a ed om ze o eloci y ini ial condi ion o cases A and B. The ini ial condi ion
o case C could be seen in he Figu e 2. The simula ions an o 0.5 s in o de o allow de elopmen
o u bulen s uc u es in he domain. Then a e aging was u ned on and he simula ions con inued o
ano he 1 s. This ime was long enough o each s a is ical s eady s a e. The cen e o he coo dina e
sys em is posi ioned in he middle o he ailing edge.
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In he figu e 3 is ins an aneous eloci y magni ude o uni o m eloci y p ofile a he inle (Case A). F om
his pic u e is e iden ha he eloci y fluc ua ions a e gene a ed a e he sepa a ion o he s eam
(behind he ailing edge). The lack o hese fluc ua ions leads o he o ma ion o he sepa a ion bubble
on he op o he domain. The o he consequence o he missing fluc ua ions is di e en shape o he
eci cula ion egion. Fo he mean eloci y p ofile o ully u bulen channel flow desc ibed a he inle
(Case B) is si ua ion simila . The ins an aneous eloci y magni ude o ully de eloped u bulen flow a
he inle (Case C) is in he pic u e 4. The flow pa e n is much di e en om he p e ious one. The e is
no sepa a ion bubble on he op and he ea achmen poin is much u he om he s ep.
Figu e 3: Ins a eneous eloci y o uni o m in-
le p ofile (Case A)
Figu e 4: Ins a eneous eloci y o ully u bu-
len flow a inle (Case C)
In he figu e 5 a e eloci y p ofiles in sho dis ance om he s ep. I could be no iced ha he uni o m
inle eloci y gi es non ealis ic esul s. F om he fla ness o he p ofile abo e he s ep could be s a ed
ha he leng h o he inle channel is no long enough in o de o de elop u bulen eloci y p ofile.
Veloci y p ofiles u he om he s ep (x/H = 5) a e in he figu e 6 . Nega i e alues o eloci y a he
op o he domain p edic ed in cases A and B indica es ha sepa a ion bubble has been o med in his
egion. I is because o lack o wall-no mal eloci y fluc ua ion, which leads o absence o u bulen
mixing mechanism and he main s eam is bend down due he s ong ad e se p essu e g adien . Case
A also ails in p edic ion o e-a achmen o he flow behind he s ep.
−0.2 0 0.2 0.4 0.6 0.8 1 1.2
−1
−0.5
0
0.5
1
1.5
y/H
u/U0
x/H=2
Case A
Case B
Case C
Expe imen
Figu e 5: Veloci y p ofile a posi ion x/H=2
−0.2 0 0.2 0.4 0.6 0.8 1 1.2
−1
−0.5
0
0.5
1
1.5
y/H
u/U0
x/H=5
Case A
Case B
Case C
Expe imen
Figu e 6: Veloci y p ofile a posi ion x/H=5
Figu es 7 and 8 show si ua ion a behind he s ep. Case B also ails in p edic ion o e-a achmen . On
he o he side, case C p edic s e-a achmen poin qui e well. Re-a achmen poin p edic ed by case C
is a posi ion x/H = 9.2 (expe imen p edic s his poin a posi ion x/H=8.4).
6CONCLUSIONS
The La ge Eddy Simula ion o backwa d- acing s ep was done. The simula ions we e done o h ee
di e en ep esen a ion o inle bounda y condi ion: uni o m eloci y p ofile, u bulen eloci y p ofile and
di ec mapping o eloci y om plane behind he inle . Only he las case gi es ealis ic esul s because
is capable ep esen also u bulence eloci y fluc ua ion. This has shown c i ical o he accu acy o he
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−0.2 0 0.2 0.4 0.6 0.8 1 1.2
−1
−0.5
0
0.5
1
1.5
y/H
u/U0
x/H=7
Case A
Case B
Case C
Expe imen
Figu e 7: Veloci y p ofile a posi ion x/H=7
−0.2 0 0.2 0.4 0.6 0.8 1 1.2
−1
−0.5
0
0.5
1
1.5
y/H
u/U0
x/H=9
Case A
Case B
Case C
Expe imen
Figu e 8: Veloci y p ofile a posi ion x/H=9
simula ion. The fi s wo cases we e no able o p edic hese fluc ua ions wha esul ed in he inclina ion
o he incoming s eam downwa ds and o ming a sepa a ion bubble a he op o he domain. This is
no in acco dance wi h eal expe imen al s udy. The inclina ion o he s eam also a ec ed he posi ion
o he e-a achmen o he s eam behind he s ep, he s eam is e-a ached oo ea ly.
The only p ope way o ep esen a ion o he inle da a p esen ed in his wo k is unning p ecu so
simula ion o he inle channel using u bulence o cing and hen mapping esul ing fields o he main
domain and di ec mapping o eloci y o he inle . This is mos complica ed case bu gi es accu a e
esul s close o he expe imen . The p edic ion o he e-a achmen poin could be imp o ed by using
mo e ad anced subg id model, o example some a ian o localized Smago insky model [7].
ACKNOWLEDGMENT
The suppo o g an s GA CR 101/08/0096 as well as he p ojec FSI-S-11-6 is g a e ully acknowledged.
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