2D and 3D nume ical modelling o in e nal low o P essu e-swi l
a omize
Milan Maly1, Ja osla Slama2, Ma cel Sapik1 and Jan Jedelsky1
1B no Uni e si y o Technology, Technicka 2, 616 69 B no, Czech Republic
2P o yko s. .o, Vina ska 3a, 603 00 B no, Czech Republic
Abs ac . This pape compa es 2D axisymme ic and 3D nume ical models used o p edic he in e nal low
o a p essu e-swi l a omize using a comme cial so wa e Ansys Fluen 18.1. The compu ed esul s a e
compa ed wi h expe imen al da a in e ms o sp ay cone angle (SCA), discha ge coe icien (CD), in e nal ai -
co e dimensions and swi l eloci y p o ile. The swi l eloci y was expe imen ally s udied using a Lase
Dopple Anemome y in a scaled anspa en model o he a omize . The in e nal ai -co e was isualized a
high empo al and spa ial esolu ion by a high-speed came a wi h backli illumina ion. The in e nal low was
nume ically ea ed as ansien wo-phase low. The gas-liquid in e ace was cap u ed wi h Volume o Fluid
scheme. The nume ical sol e used bo h lamina and u bulen app oach. Tu bulence was modelled using k-
ε, k-ω, Reynolds S ess model (RSM) and coa se La ge Eddy Simula ion (LES). The lamina sol e was
capable o p edic all he pa ame e s wi h an e o less han 5% compa ed wi h he expe imen al esul s in
bo h 2D and 3D simula ion. Howe e , i o e p edic ed he eloci y o he discha ged liquid shee . The LES
model pe o med simila ly o he lamina sol e , bu he liquid shee eloci y was 10% lowe . The wo-
equa ion models k-ε and k-ω o e p edic ed he u bulence iscosi y and he in e nal ai -co e was no p edic ed.
1 In oduc ion
The P essu e swi l a omize s (PS) ha e an i eplaceable
ole in many indus ial applica ions including
combus ion, sp ay cooling, sp ay d ying e c. In a ypical
PS a omize , he pumped liquid is ed ia angen ial po s
in o a swi l chambe whe e i gains high angula eloci y
and c ea es a low-p essu e zone along a cen e line o he
swi l chambe . Subsequen ly, he ai is pulled inside he
low-p essu e zone, so an ai -co e is o med. The swi ling
liquid is discha ged om he exi o i ice in a o m o a
conical liquid shee a a ce ain sp ay cone angle (SCA)
and consequen ly disin eg a es due o ae odynamical
o ces in o ilamen s and ligamen s. Veloci y and
hickness o he liquid shee , as well as he SCA, a ec he
size o esul ing d ople s.
Despi e he simple geome y, he in e nal low
beha iou is complex, mainly due o he dominan
swi ling eloci y componen and he induced in e nal ai -
co e which blocks a po ion o he exi o i ice. The
in e nal o ex beha es as a Rankine o ex as he swi l
eloci y has i s maximum loca ed a he ai -co e su ace
[1]. Seconda y low e ec as Gö le o ices could be
also p esen ed in a bounda y laye inside he swi l
chambe [2, 3].
In open li e a u e, many co ela ions a e a ailable ( o
a gene al o e iew see [4]), which allows us o es ima e
he a omize pe o mance such as d ople sizes, SCA,
liquid shee hickness, discha ge coe icien , e c.
Howe e , he mos o hose co ela ions we e made by
i ing he expe imen al esul s and hey we e de eloped
o limi ed geome y a ia ions and ope a ing condi ions.
To be e unde s and he link be ween he a omize
pe o mance and design, he in e nal low mus be
examined. Some au ho s s udied he in e nal low
analy ically. Simple non- iscous ea men , e iewed in
[5, 6], can be used o a basic insigh in o he low
beha iou , bu i is no accu a e enough o p edic he
discha ge pa ame e s. The be e ag eemen can be
achie ed when he iscous low is assumed [7, 8], bu
some aspec s like a empo al s abili y o seconda y low
e ec s a e unable o be esol ed.
The numbe o pape s ela ed o he nume ical
simula ion o he PS a omize s had a isen in ecen yea s
due o an inc ease in a compu a ional pe o mance. One
o he i s nume ical s udies o he PS a omize was
conduc ed in 1997 by Yule and Chinn [9]. They used a 2D
axisymme ic model wi h he lamina sol e and epo ed
a de ia ion om he expe imen al da a o be less han 3%.
Simila nume ical se up was used by Amini [7] and
showed be e ag eemen wi h he expe imen al da a han
he analy ical iscous models. He compa ed hose models
a Reynolds numbe inside he inle po s in a ange o
Rep = 11,000–122,000. The di e ence be ween 2D and
3D compu a ional models was examined by Sume e al
[10]. They used he lamina sol e and ound ha he ai -
co e diame e was abou 5% smalle in he case o he 3D
model. Howe e , he equency o wa es on he ai -co e
su ace was p edic ed by bo h models closely and wi h
good ag eemen o he expe imen al da a. A compa ison
© The Au ho s, published by EDP Sciences. 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 4.0
(h p://c ea i ecommons.o g/licenses/by/4.0/).
EPJ Web o Con e ences 213, 02055 (2019) h ps://doi.o g/10.1051/epjcon /201921302055
EFM 2018
o La ge Eddy Simula ion (LES) and he lamina models
was pe o med by Madsen e al. [11]. They used a scaled
a omize and ope a ed i in ange o Rep = 12,000–41,000.
A hose ope a ing egimes, he lamina model had a
sligh ly be e ag eemen o he expe imen al da a han
LES. The au ho s also examined simple u bulence
models ep esen ed by he RNG and ealizable k-ε
models. Howe e , hese models we e unable o p edic he
in e nal ai -co e. Galbia i e al. [12] compa ed he LES
simula ion wi h RNG k-ε and RSM models. They ound
ha he a ia ion among used models was insigni ican
when compa ed o de ia ion in esul s om he empi ical
co ela ions. They also no ed ha he low ield was
consis en o he LES and k-ε model, while RSM had
some disc epancies. Baha anchi e al. [13] examined
se e al schemes o cap u e he liquid-ai in e ace using a
2D simula ion wi h he RNG k-ε u bulence model. A geo-
econs uc scheme was ound o be he mos sui able o
cap u ing he ai -co e. They also discussed i i is
necessa y o model a su ace ension and ound ha he
su ace ension had e ec only i he Webe numbe is
smalle han 204. F om a p ac ical poin o iew, i had a
negligible e ec on he de eloped low.
In his pape , 2D and 3D nume ical models o he PS
a omize a e compa ed. The nume ical sol e used bo h
lamina and u bulen app oach. The nume ical esul s a e
also compa ed wi h expe imen al da a om [1].
2 Expe imen al se up
The expe imen s we e pe o med on a cold es bench a
he B no Uni e si y o Technology.
2.1. The A omize
A small-sized Simplex a omize used in a combus ion
chambe o a u boje ai c a engine was in es iga ed.
Due o small p opo ions, see he dimension in Fig. 1, he
op ical measu emen inside he a omize would be
di icul . To o e come his issue he anspa en scaled
model was manu ac u ed. The scaled model was 10 imes
la ge han he o iginal a omize and i was made om
cas PMMA. To main ain he same low beha iou ,
dimensionless numbe s such as Reynolds numbe , Swi l
numbe , Webe numbe and F oude numbe mus be kep
he same.
Reynolds numbe ela ed o he inle po s is de ined:
=
,
(1)
whe e dp is he hyd aulic diame e o he inle po , wp is
he mean eloci y inside he po and  is he liquid
kinema ic iscosi y.
The swi l numbe S0 is he a io o swi l momen um
o he axial momen um, and o he Simplex a omize s i
can be de ined as [14]:
=
,
(2)
whe e o = do/2, do and s a e in Fig. 1 and Ai is he o al
a ea o he inle po s. The S0 is iden ical o bo h he
o iginal and he scaled a omize .
Fig. 1. A ske ch o he o iginal a omize wi h he main
dimensions in mm. The anspa en a omize had all
dimensions 10 imes la ge .
F oude numbe , F , compa es he e ec o g a i y wi h
he ene gy o he bulk low and can be calcula ed as:
 =2(−
)

(3)
whe e oa is he adius o ai -co e in he exi o i ice, Q is
he olume low a e. To minimalize he e ec o g a i y,
i is necessa y o keep F >> 1.
Webe numbe , We, is de ined as he a io o ine ia
and he su ace ension o ce. The su ace ension o ce
usually has negligible e ec inside he swi l chambe .
Acco ding o [13] and [14], ma ching he Webe numbe
can be sa ely igno ed. Simila ly, no e ec o su ace
ension was obse ed in ou ini ial CFD simula ions.
Bo h he o iginal and scaled a omize s we e ope a ed
a oom empe a u e o 23 °C using JET A1 wi h physical
p ope ies: σ = 0.029 kg/s2, μl = 0.0016 kg/(m·s) and
ρl = 795 kg/m3.
The o iginal a omize was ope a ed a he inle
p essu e Δpi = 1 MPa, he inle mass low a e was
 = 7.3 kg/h. The mean eloci y inside he inle po s
was wi = 5.16 m/s, which esul ed in Rep = 1021. The
scaled a omize was ope a ed a he same Rep hus he inle
p essu e had o be educed o 10 kPa. The F o o iginal
a omize was 293 bu i dec eased o 9.3 o he scaled
a omize .
2.2. Expe imen al se up
The high-speed came a Pho on SA-Z was used o
documen he spa ial and empo al beha iou o he ai -
co e inside he scaled anspa en model o he a omize .
The came a was se o 4,000 ames pe second wi h a
ame esolu ion o 1024×1024 px. The came a was used
a backli illumina ion wi h backg ound LED panel. The
ypical esul is shown in Fig. 2.
2
EPJ Web o Con e ences 213, 02055 (2019) h ps://doi.o g/10.1051/epjcon /201921302055
EFM 2018
Fig. 2. High-speed isualiza ion wi h LDA measu emen axis.
The Lase Dopple Anemome e (LDA), a 2D
FlowExplo e made by Dan ec Dynamics A/S was used o
measu e he swi l eloci y p o ile. The measu emen s
we e pe o med in he h ee axial dis ances o 2.5, 8 and
13 mm om he op o he swi l chambe . Howe e , only
he esul s om 8 mm axis a e p esen ed he e. The
loca ion o he measu emen axis is shown in Fig. 2. The
esul s we e co ec ed acco ding o Zhang [15] due o he
di e en e ac i e index o he liquid and a omize body.
Fo de ailed desc ip ion o he expe imen al se up see [1].
3 Nume ical se ups
The ansien CFD simula ions we e made using
comme cial so wa e Ansys Fluen 18.1. A 2D
axisymme ic model wi h a swi l, shown in Fig. 3, and a
h ee-dimensional 3D model wi h pe iodic bounda y
condi ions, as shown in Fig. 4, we e used. As he a omize
had h ee inle po s, a 120° sec ion was modelled.
P essu e- eloci y coupling was done using PISO scheme.
The liquid-ai in e ac ion was cap u ed by a Volume o
Fluid model wi h a geo- econs uc scheme o
Comp essi e scheme was used in he case o LES. The
inle bounda y was se o he eloci y inle wi h
wi = 5.16 m/s. In he case o he 2D model, i was se o
conse e he mass low a e in he adial di ec ion and
conse e he angula momen um in he angen ial
di ec ion. The p essu e ou le was se o he ou e
bounda ies. The no-slip condi ion was used on he in e nal
wall bounda ies. The ai was ea ed as bo h wi h cons an
densi y and as an ideal gas wi h ene gy equa ion.
Va iable ime s epping was used wi h a Cou an
numbe 0.5. A ypical ime s ep size was app oxima ely
2×10-8 s. As he low was ea ed as ansien , a e
eaching a quasi-s a ic solu ion, ime a e aging was
applied.
Se e al u bulence models based on a Reynolds-
a e aged Na ie -S okes (RANS) equa ion, LES and
lamina sol e we e used and compa ed o achie e esul s
compa able wi h he expe imen . De ailed ma hema ical
desc ip ion o he used models can be ound in [16].
Simple wo-equa ion models ep esen ed by k-ε and k-
ω we e chosen o hei good accu acy o indus ial
applica ions. Those models de e mine a u bulen leng h
scale and a ime scale by sol ing wo sepa a e anspo
equa ions. The k-ε model is based on a anspo equa ion
o kine ic ene gy k and dissipa ion a e ε. In his pape ,
he RNG k-ε model o swi l dominan lows was used as
i designed o swi ling lows. The k-ω SST model wi h
low-Re co ec ion was chosen as he second wo-equa ion
model. This model combines he s anda d k-ω model o
nea wall ea men and he k-ε model in he ee s eam
low.
Reynolds S ess model (RSM) is he mos ad anced
RANS model o he swi l dominan lows as i sol es all
he anspo equa ions o he Reynolds s esses. This
model was used wi h a low-Re and shea low co ec ion.
La ge Eddy Simula ion (LES) was ep esen ed by
Wall-Adap ing Local Eddy Viscosi y model (WALE).
Howe e , i was pe o med on he same mesh as he
RANS models, hus i is e e ed he e as a Coa se LES.
The e we e se no pe u ba ions in he eloci y inle .
3.1. Mesh independence es
The all quad/hex s uc u al meshes we e c ea ed in Ansys
Meshing o bo h 2D and 3D models. The 3D mesh used
ma ch con ol on he pe iodic bounda ies. An a e age
skewness o 2D mesh was 0.058 and an a e age aspec
a io o 1.18. The mesh independency es was made o
he 2D model. The inle p essu e was ound o be he mos
sensi i e pa ame e o he numbe o cells. As he in e nal
ai -co e blocks pa o he exi o i ice, i is necessa y o
cap u e he ai -co e bounda y wi h high accu acy. Thus,
he mesh needed o be ine nea he in e ace. The e ec
o mesh esolu ion h ough he adius o he exi o i ice is
shown in Fig. 5. The e o in he p edic ion o he inle
p essu e is apidly inc easing i he numbe o cells is
lowe han 20. Fo he 3D simula ion, a comp omise
be ween calcula ion speed and accu acy was chosen as he
mesh wi h a esolu ion o 25 cells h ough he adius o
he exi o i ice was used. This 3D mesh had a o al o
459,591 cells while he inal 2D mesh con ained 30 cells
h ough he adius o he exi o i ice wi h a o al o 46,645
cells.
Fig. 3. 2D mesh wi h bounda y condi ions.
3
EPJ Web o Con e ences 213, 02055 (2019) h ps://doi.o g/10.1051/epjcon /201921302055
EFM 2018
Fig. 4. 3D mesh wi h bounda y condi ions.
Fig. 5. Mesh independency s udy.
4 Resul s and discussion
In his chap e , he CFD simula ions a e compa ed wi h
he expe imen al da a in e ms o he discha ge pa ame e s
such as he discha ge coe icien CD, SCA and a omize
e iciency , he ai -co e dimensions and he eloci y
p o iles inside he swi l chambe . In he inle po , he
lamina low can be assumed as Rep = 1021. Howe e , i
may change o ansien o e en u bulen low inside he
exi o i ice as he eloci y inc eases. Ne e heless, Chinn
[14] o e old he lamina low e en o e y high Rep as
he swi l dominan low ends o lamina ise he low i sel
and he a omize is oo small o de elop a ully u bulen
low.
Ini ial CFD simula ions we e pe o med o bo h, he
o iginal and scaled a omize . The dimensionless ai -co e
diame e s, dimensionless eloci y p o iles, SCA and CD
we e iden ical o bo h a omize s, he e o e in his pape ,
he esul s a e shown he e in a dimensionless o m and
hey a e based on he CFD simula ions o he o iginally
sized a omize .
The di e ence be ween incomp essible and
comp essible gas phase was also in es iga ed bu no
e iden e ec was ound. This is in ag eemen wi h [17],
whe e Mach numbe smalle han 0.3 ensu es ha he ai
phase can be sa ely handled as incomp essible.
Conside ing he maximal ai eloci y in ou simula ions,
Mach numbe was much smalle han 0.1; hus, in his
pape , he simula ions a e done wi h he cons an ai
densi y.
4.1. Discha ge pa ame e s
An accu a e p edic ion o he ai -co e dimensions is he
c ucial aspec as i signi ican ly a ec s he discha ge
pa ame e s. The discha ge coe icien CD is an impo an
discha ge pa ame e de ined as a a io o he inle mass
low o he heo e ical mass low a e:
=
2Δ,
(4)
whe e Ao is he c oss-sec ional a ea o he exi o i ice. Fo
he PS a omize s, he CD is ela i ely low as a po ion o
he exi o i ice c oss sec ion is occupied by he ai -co e.
The e iciency o con e sion o he inle p essu e
ene gy in o kine ic ene gy a he a omize exi is called he
a omize e iciency, and i is de ined as:
=

2Δ,
(5)
whe e o is he eloci y o he liquid shee a he a omize
discha ge. I was no possible o measu e o di ec ly, hus
he liquid shee eloci y had o be es ima ed om he
high-speed eco ds and i is measu ed app oxima ely
1 mm downs eam om he a omize exi o i ice. PIVlab
so wa e was used o es ima e he eloci y o he liquid
shee as i is shown in Fig. 6. The o was ob ained om
he simula ions in he same downs eam dis ance as in he
expe imen . The swi l eloci y componen was neglec ed
in bo h cases, only he axial and adial eloci y
componen s we e conside ed.
Fig. 6. Veloci y ec o s om PIVlab so wa e.
0.80
0.85
0.90
0.95
1.00
1.05
1.10
0 10 20 30 40 50
Inle p essu e [MPa]
Cell coun [–]
4
EPJ Web o Con e ences 213, 02055 (2019) h ps://doi.o g/10.1051/epjcon /201921302055
EFM 2018
Table 1. The discha ge pa ame e s and ai -co e dimensions.
Δpi CD das/do dao/do SCA o ηn
[MPa] [-] [-] [-] [deg] [m/s] [%]
Expe imen al da a 1.00 0.37 0.47 0.71 72 36 0.51
LES 3D 1.03 0.36 0.31 0.67 75 41 0.63
RSM 3D 0.91 0.38 0.31 0.65 72 41 0.73
Lamina 3D 1.00 0.37 0.32 0.67 73 42 0.71
RSM 2D 0.82 0.41 0.23 0.65 72 40 0.77
Lamina 2D 1.01 0.37 0.37 0.7 74 46 0.83
k-ω SST 2D 0.39 0.59 – – – 17 0.29
RNG k-ε 2D 0.28 0.70 – – – 25 0.91
Fig. 7. Phases, ed = ai , blue = liquid. Top: 2D k-ω model,
bo om: 2D lamina model
In he expe imen , he in e nal ai -co e had an almos
cons an diame e along he swi l chambe and ex ends in
diame e in he exi o i ice.
The wo-equa ion u bulence models k-ε and k-ω we e
unable o p edic he ai -co e inside he swi l chambe .
The ypical low pa e n om hose models is shown in
Fig. 7. As he ai -co e is no p esen ed, all he discha ge
pa ame e s a e p edic ed wi h eno mous e o – see
able 1. These models p obably o e p edic ed he
u bulen eddy iscosi y which esul s in a dec ease in he
swi l eloci y and consequen ly he ai -co e decayed. We
exclude hose models om u he e alua ions.
The RSM model was able o cap u e he ai -co e shape
co ec ly. Howe e , i unde es ima es i s dimension. The
smalle ai -co e leads o he highe CD as he smalle ai -
co e block a smalle po ion o he exi o i ice. In he case
o 2D RSM simula ion, he ai -co e diame e was
unde es ima ed by 20% and by 10% in he case o he 3D
model.
Bo h 2D and 3D lamina models and LES model we e
able o p edic he inle p essu e, CD and he ai -co e
dimensions closely. Howe e , he 2D lamina model
signi ican ly o e p edic ed he eloci y o he discha ged
liquid shee o and he a omize e iciency. The LES
p edic ed he a omize e iciency mos closely bu i was
s ill o e p edic ed abou 20%. The eason may be ha he
CFD model neglec ed he su ace oughness o he eal
a omize .
4.2. Veloci y p o iles
The swi l eloci y p o iles a e shown in Fig. 8. The wo-
equa ion models a e excluded. The swi l eloci y eaches
i s maximum a he ai -co e su ace, which is ypical o a
Rankine o ex. In he expe imen , i was six imes g ea e
han he mean eloci y inside he inle po . All he
nume ical models we e able o p edic he posi ion o
eloci y maximum. Ne e heless, he 2D models we e
unable o cap u e he magni ude o he eloci y peak
accu a ely as he lamina 2D model o e p edic ed he
swi l eloci y maximum o abou 15% while he 2D RSM
unde p edic ed i abou 15%. This co ela es well wi h he
dimension o he ai -co e om Table 1 whe e he 2D
lamina model showed he la ges dimensions o he
in e nal ai -co e, while he 2D RSM pe o med opposi e.
Only small a ia ions in he swi l eloci y p o iles we e
ound a di e en axial dis ances om he op o he swi l
chambe as i was shown in [1].
The adial and axial eloci y p o iles a e shown in Fig
8 and Fig 9 espec i ely. The adial eloci y is e y low
compa ed o he o he eloci y componen s. The 3D RMS
and 3D lamina models p edic ed a posi i e local
maximum inside he ai -co e while o he models no . The
2D RSM, on he o he hand, showed a nega i e local
maximum in he posi ion o / s = 0.2.
The axial eloci y was almos ze o up o he posi ion
o / s = 0.2 whe e i s a s apidly g ow and eaches a
maximum o 4×wi a / s = 0.05. Simila ly, as in he case
o swi l eloci y, he 2D lamina model o e p edic ed he
axial eloci y magni ude while 2D RSM unde p edic ed i
compa ed o 3D models.
5
EPJ Web o Con e ences 213, 02055 (2019) h ps://doi.o g/10.1051/epjcon /201921302055
EFM 2018

Fig. 8. Swi l eloci y.
Fig. 9. Radial eloci y.
Fig. 10. Axial eloci y.
5 Conclusions
The a omize discha ge pa ame e s and he eloci y
p o iles we e p edic ed using a ious CFD models and he
esul s we e compa ed wi h he expe imen al da a.
The su ace ension and gas comp essibili y we e
neglec ed as hey ha e no p ac ical impac on he esul s.
The simple wo-equa ion models k-ε and k-ω we e
unable o p edic he ai -co e and he esul s a e wo hless.
The 2D lamina model was able o closely p edic CD
and SCA bu o e es ima ed swi l eloci y, liquid shee
eloci y o and ηn.
The bes esul s we e ob ained using he 3D lamina
and 3D LES model, which gi e he same CD and SCA, bu
he LES model had a be e p edic ion o ηn in compa ison
wi h he expe imen .
Fu he wo k will be ela ed o he alida ion o ime-
dependen a iables as ai -co e ins abili ies and su ace
wa es and also ull 3D simula ion will be included as he
pe iodic bounda y condi ions assume ha he cen e o he
ai -co e is ixed along he cen eline o he swi l chambe .
This wo k has been suppo ed by he p ojec No. GA18-15839S
unded by he Czech Science Founda ion, he p ojec “Compu e
Simula ions o E ec i e Low-Emission Ene gy” unded as
p ojec No. CZ.02.1.01/0.0/0.0/16_026/0008392 by Ope a ional
P og amme Resea ch, De elopmen and Educa ion, P io i y
axis 1: S eng hening capaci y o high-quali y esea ch and
p ojec No. RV9080000313 ounded by Facul y o Mechanical
Enginee ing, B no Uni e si y o Technology.
Re e ences
1. M. Maly, J. Jedelsky, J. Slama, L. Janacko a, M.
Sapik, G. Wigley, and M. Jicha, 123, 10, (2018)
2. D. Coope , A. Yule, and J. J. Chinn, ILASS, (1999)
3. W. Qian, X. Hui, C. Zhang, Q. Xu, Y. Lin, and C.
J.Sung, CFaE, 074A, (2017)
4. A. H. Le eb e and V. G. McDonell, A omiza ion and
sp ays, (2017)
5. J. J. Chinn., AaS, 19(3), (pa 1), (2009)
6. J. J. Chinn., AaS, 19(3), (pa 2), (2009)
7. G. Amini., 2016, " 79, 11 (2016)
8. E. Wimme , and G. B enn, IJMF, (2013)
9. A. Yule, and J. J. Chinn, ILASS, (1997)
10. B. Sume , N.E kan, O. Uzol, and I. Tunce , ICLASS,
(2012)
11. J. Madsen, B. H. Hje age , and T. Solbe g, ILASS,
6, (2004)
12. C. Galbia i, S. Tonini, P. Con i, and G. E. Cossali,
JPP, 6 (2016)
13. A. Abbasi Baha anchi, A. No din Da us, Ansa i, M.,
and E. Abbasi Baha anchi, IMECE, 12 (2012)
14. J. J. Chinn, ILASS, (2008)
15. Z. Zhang, LDA Applica ion Me hods: Lase Dopple
Anemome y o Fluid Dynamics, (2010)
16. Ansys®, Fluen Theo y Guide, Release 18.2. (2017)
17. J. D. Ande son, Fundamen als o Ae odynamics,
(2001)
0
1
2
3
4
5
6
7
8
0 0.2 0.4 0.6 0.8 1
w/wi[–]
/
s
[–]
3D Lamina
3D LES
3D RSM
2D lamina
2D RSM
expe imen
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.2 0.4 0.6 0.8 1
/wi[–]
/ s[–]
3D Lamina
3D LES
3D RSM
2D lamina
2D RSM
-8
-6
-4
-2
0
2
4
6
0 0.2 0.4 0.6 0.8 1
u/wi[–]
/
s
[–]
3D Lamina 3D LES
3D RSM 2D lamina
2D RSM
6
EPJ Web o Con e ences 213, 02055 (2019) h ps://doi.o g/10.1051/epjcon /201921302055
EFM 2018