In e nal low and ai co e dynamics in Simplex
and Spill- e u n p essu e-swi l a omize s
MALÝ, M.; JEDELSKÝ, J.; SLÁMA, J.; JANÁČKOVÁ, L.; SAPÍK, M.; WIGLEY, G.; JÍCHA, M.
In e na ional jou nal o hea and mass ans e
2018, ol. 123, Augus 2018, pp. 805-814
ISSN: 0017-9310
DOI: h ps://doi.o g/10.1016/j.ijhea mass ans e .2018.02.090
Accep ed manusc ip
© 2018. This manusc ip e sion is made a ailable unde he CC-BY-NC-ND 4.0 license
(h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/), doi: h ps://doi.o g/ 10.1016/j. uel.2013.03.053
Final e sion a ailable om h ps://www.sciencedi ec .com/science/a icle/pii/S0017931017356879
dspace. u b .cz
In e nal low and ai co e dynamics in Simplex and Spill- e u n p essu e-
swi l a omize s
Milan Malý*1, Jan Jedelský1, Ja osla Sláma2, Lada Janáčko á1, Ma cel Sapík1, G aham Wigley3,
Mi osla Jícha1
1 Facul y o Mechanical Enginee ing, B no Uni e si y o Technology, Czech Republic
2 P o yko s. .o, Czech Republic
3 Loughbo ough Uni e si y, Uni ed Kingdom
*Co esponding au ho : milan.maly@ u b .cz
Abs ac
Spill- e u n (SR) a omize s enhance he cons uc ion o Simplex a omize s by addi ion o a passage in
he ea wall o he swi l chambe h ough which he liquid can be spilled away. I allows o discha ge
he liquid always a a high p essu e and o sp ay well o e a wide low a e ange. The sp ay
cha ac e is ics o p essu e-swi l a omize s a e s ongly linked o he in e nal low, and he ai -co e
dynamics a ec he sp ay s abili y. The SR a omize s a e a ely s udied and hei in e nal low is no
s udied a all. The e o e, in his pape , he Simplex and SR a omize s wi h a cen al SR o i ice we e
examined compa a i ely.
T anspa en polyme hyl me hac yla e (PMMA) models o bo h a omize s scaled 10:1 we e
manu ac u ed o he isualiza ion and eloci y measu emen s o he low inside he swi l chambe . The
a omize s we e examined by means o high-speed imaging, lase -Dopple anemome y and
compu a ional luid dynamics ools. The expe imen al and nume ical esul s we e analysed and
compa ed in e ms o he sp ay cone angle (SCA), discha ge coe icien (CD), and he mo phology and
empo al s abili y o he ai co e. The in e nal low cha ac e is ics be ween he o iginal and he model
we e ma ched using he Reynolds, Swi l and F oude numbe s. The es condi ions we e limi ed o inle
Reynolds numbe s om 750 o 1750.
The esul s show ha he addi ion o he spill passage s ongly a ec s he in e nal low e en i he spill-
line is closed. The ai co e in he Simplex a omize is ully de eloped and s able o all low egimes.
The SR a omize beha ed di e en ly; wi h closed spill-line (spill- o- eed a io, SFR=0), he ai co e
does no o m a all; he e o e he sp ay is uns able. The eason is ha he liquid, con ained in he spill-
line, is d ained back in o he swi l chambe due o a eci cula ion zone ound inside he spill-line.
Inc easing he SFR s abilizes he in e nal low, and he sp ay becomes s able i SFR > 0.15. The ai co e
begins o o m o SFR > 0.4. The esul s sugges ha he axially posi ioned spill o i ice is inapp op ia e
and i s placing o -axis would imp o e he sp ay s abili y. The esul s o he 2D nume ical simula ion
ma ched closely wi h he expe imen s in e ms o SCA, CD, eloci y p o iles, and ai co e mo phology
which p o ed i s p edic ion capabili ies.
Keywo ds
In e nal low dynamics, P essu e-swi l, anspa en nozzle, CFD
1 In oduc ion
P essu e-swi l (PS) a omize s a e used in many applica ions whe e a la ge su ace a ea o d ople s
is needed, o a su ace mus be coa ed wi h a liquid, e.g. combus ion, i e suspension o ai condi ioning.
PS a omize s a e easy o manu ac u e, eliable and p o ide good a omiza ion quali y. They con e he
p essu e ene gy o he pumped liquid in o kine ic and su ace ene gy o he esul ing d ople s. The liquid
is injec ed ia angen ial po s in o a swi l chambe whe e i gains a swi l mo ion unde which i lea es
he exi o i ice as a conical liquid shee . The cen i ugal mo ion o he swi ling liquid c ea es a low-
p essu e zone in he cen e o he swi l chambe and gene a es an ai co e along he cen eline. The low
inside he a omize is a he complex; i is wo-phase wi h seconda y low e ec s. The e is a s ong link
be ween in e nal low condi ions and he esul ing sp ay cha ac e is ics. Howe e , no all aspec s o he
in e nal low a e well unde s ood. A d awback o he Simplex a omize is ha he d ople size depends
on he inle p essu e, hence on he liquid low a e. The low a e a ies as he squa e oo o he injec ion
p essu e. Thus, doubling he flow a e demands a ou old inc ease in injec ion p essu e, which means
ha he ange o applicable low a es is limi ed and hus he u n-down a io (de ined as a io o
2
maximum liquid flow a e o minimum liquid flow a e which ul ils he equi emen o a omiza ion
quali y) is usually low [1]. This disad an age can be elimina ed using a SR a omize which is basically
a Simplex ype wi h a passage added in he ea wall o he swi l chambe , see Figu e 1. When he spill-
line is closed, he a omize ope a es as a s anda d Simplex ype. When a low injec ion low a e is
equi ed, he liquid is spilled away h ough he spill o i ice while he inle p essu e and he swi l
momen um emain high, and he a omiza ion quali y emains. Howe e , inc easing spilled low a e
causes educ ion in he axial momen um o discha ged liquid which consequen ly leads o change in he
sp ay cone angle (SCA), as he SCA is de e mined by he a io o he swi l momen um o he axial
momen um. Ano he d awback is he equi emen o inc eased pump powe and complica ed o low
me e ing. Fo hese easons, he in e es in SR a omize s o ai c a combus o s declined, howe e , i
he a oma ic con en o gas u bine uels ises, gum o ma ion in he small sized a omize s could pose
se ious p oblems o he a omize blockage [2, 3]. The SR a omize s a e i ually ee o his de ec as
hey ha e no small passages. Beside he ai c a combus o s, he SR a omize we e used in s a iona y
gas u bines [4] and indus ial bu ne s [5]. Howe e , he abo e-men ioned ad an ages o SR a omize s
a e c ucial in special applica ions ha equi e a ine sp ay a e y low low a e, e.g. decon amina ion
de ices [6], o o a omiza ion o was e uels and liquids con aining impu i ies whe e la ge dimensions
o low c oss-sec ions a e necessa y o p e en he a omize om clogging, o in applica ions whe e
pneuma ic a omize s a e no allowed bu he wide egula ion ange is equi ed. The s udied spill- e u n
a omize is o iginally used in a combus ion chambe o small u boje ai c a engine manu ac u ed by
PBS Velká Bí eš, a.s., Czech Republic.
Be o e he ad en o compu a ional luid dynamics, a numbe o au ho s a emp ed o desc ibe
he in e nal low o Simplex a omize by ela i ely simple analy ical app oaches. One o he i s was
p esen ed by Taylo [7] who ocused on an in iscid analysis using Be noulli’s equa ion and he p inciple
o maximal low. Taylo de i ed an equa ion o he discha ge coe icien (CD) and he sp ay cone angle
(SCA) solely dependen on he a omize cons an k = 2·Ap/(π·do·ds), whe e Ap is he o al a ea o he
inle po s, do, and ds a e de ined in Figu e 1. Simila esul s we e ound independen ly by o he au ho s,
and hese wo ks ha e been compa ed and e iewed by Chinn [8, 9]. Resul s ob ained by he in iscid
heo y a e no gene ally in good ag eemen wi h expe imen s. Howe e , indings om he in iscid
heo y may be used as a basis o design imp o emen s.
The expe imen al co ela ions o CD we e ound o be mo e complex han he in iscid heo y
p edic ed. Rizk and Le eb e [10] de i ed a semi-empi ical co ela ion whe e, besides he cons an k,
he a io ds/do had a s ong in luence. Jones [11] ound a weak dependence o CD on he leng h o he
swi l chambe and exi o i ice, and liquid iscosi y. Balles e [12] added a dependence on he inle
p essu e. Benjamin [13] ollowed he wo k o Jones [11] and ound in e se ends o some pa ame e s.
Wimme and B enn [14] heo e ically unco e ed a ela i ely s ong e ec o he liquid iscosi y on CD,
which was la e expe imen ally con i med by Maly e al. [15].
The in e nal low cha ac e is ics, especially he ai co e s abili y, we e in es iga ed by a ew
au ho s. Halde [16] in es iga ed he ai co e shape in 21 di e en anspa en a omize s a a ious inle
mass low a es o wa e . Two limi ing alues o Reynolds numbe (Re) we e conduc ed o he incep ion
o he ai co e o each a omize . Below he lowe limi , he ai co e was no o med a all, while abo e
he uppe limi , i was always ound o be s able. He obse ed ha he limi ing Re dec eases wi h an
inc ease in do/ds and a dec ease in Ap/ds. The s able ai co e had a cylind ical shape, and o la ge Re
alues, i was almos cons an in diame e . Fo Re alues close o he limi ing alue, he diame e o he
ai co e inc eased sha ply wi h inc easing Re. A simila concep o limi ing alues o Re was in oduced
by Lee e al. [17]. In his expe imen al wo k, a anspa en a omize wi h diesel and ke osene used o e
a ange o inle p essu es and empe a u es. They deduced ha he ai co e s abili y was a unc ion o Re
ela ed o he exi o i ice, Reo. I was s able o Re > 3300; a lowe alues i became uns able un il o
Reo below 2400, whe e he e was no ai co e a all due o insu icien cen i ugal o ces, and he sp ay
luc ua ed s ongly. Kim e al. [18] in es iga ed he in luence o diame e and leng h o he swi l chambe
on he ai co e s abili y. A omize s wi h a a io o swi l chambe heigh o i s diame e hs/ds highe han
1.27 demons a ed an uns able ai co e. The au ho s [18] desc ibed he uns able ai co e as ha ing a
o a ing and double helical s uc u e. Moon [19] ound a limi ing alue o he swi l numbe S0 = 0.6,
which ensu ed a s able ai co e. The same limi ing alue o S0 was also p oposed by Pa k [20] o swi ling
je s. SR a omize s ha e a ely been s udied, and hei in e nal low has no been documen ed so a o
he bes o ou knowledge. Especially he e ec o he spill o i ice a angemen on he in e nal low is
3
no a all clea . The liquid spill can be ealized by a single axial o i ice, by se e al o -axis o i ices, o
by an annula slo [21]. The simples designs use a single, axially placed spill o i ice bu he p oblems
wi h sp ay s abili y we e epo ed [21-23], especially unde ope a ing egimes wi h a closed spill-line.
The o me app oaches o s udy he in e nal low we e mos ly expe imen al [24, 25] and analy ical
[8, 9, 26]. The applica ion o CFD has g ea ly simpli ied design p ocess o he a omize due o inc ease
in compu ing pe o mance in ecen yea s. In 1997, Yule and Chinn [27] conduc ed one o he i s
nume ical s udies using a 2D simula ion. They assumed a lamina low e en o Re = 50,000; an in e nal
ai -co e was cap u ed by he Volume o Fluid (VOF) me hod. They epo ed he di e ence be ween
nume ical calcula ions and he expe imen o be less han 3%. Simila ly a 2D lamina se up was used by
Amini [28] and Mandal [29]; bo h au ho s epo ed a close ma ch wi h expe imen al da a. Summe [30]
compa ed 2D and 3D simula ions wi h a lamina solu ion and ound only a small di e ences be ween
hem. Madsen [31] es ed lamina and u bulen k-ε models oge he wi h a La ge Eddy Simula ion
(LES). The u bulen model o e es ima ed he u bulen iscosi y; he ai -co e was no o med a all.
The lamina model was compa able o he LES p edic ions. Va ious models o cap u e he liquid–ai
in e ace we e in es iga ed by Baha anchi [32]. A geome ical econs uc ion scheme was ound o be
an op imal me hod o cap u ing he ai co e. While he e a e some pape s p o iding CFD simula ions
o Simplex a omize s, no nume ical simula ion o SR a omize we e ound.
Due o he lack o published esul s on SR a omiza ion, he p esen s udy in es iga ed
expe imen ally and nume ically he in e nal low o SR a omize . Fi s ly he wo k examines he
possibili y o p edic he a omize cha ac e is ics such as CD and SCA, and he eloci y ield in he swi l
chambe , using a ela i ely simple 2D simula ion. The main ocus is o elucida e on he sp ay
luc ua ions, epo ed in ou p e ious wo ks [22, 33], and o de e mine hei sou ce. Fu he mo e, he
in e nal low cha ac e is ics a e o be compa ed wi h a Simplex a omize .
2 A omize geome ies and liquid p ope ies
The expe imen s we e pe o med using bo h Simplex and SR a omize designs. In o de o
examine he in e nal low, he a omize s we e manu ac u ed as anspa en copies. Due o he small
dimensions o he o iginal a omize s (see Figu e 1), i was impossible o manu ac u e hem and o
examine hei lows di ec ly. To sol e his issue, he anspa en e sions we e designed as en imes
scaled copies. The scaled a omize s ha e a modula cons uc ion (Figu e 2, igh ). The assembly consis s
o h ee pa s, each made om PMMA. The bo om pa con ains he swi l chambe wi h he exi o i ice,
he cen al one o ms he angen ial inle po s, while he op pa is a plain wall, in he case o Simplex
a omize o , con ains he spill o i ice in he case o he SR a omize . This modula cons uc ion allows
o each pa o be eplaced by ano he one o a di e en geome y o shape. The su aces o each pa
we e g ound and polished o achie e he anspa ency su icien o op ical access.
Figu e 1. A ske ch o he o iginal SR a omize wi h he main dimensions in millime es. The Simplex a omize
has he same geome y and size, bu he spill-line o i ice is missing. The anspa en a omize has he same
shape, and all dimensions a e 10 imes la ge .
4
Due o he en imes model scale i is necessa y o ma ch he low o he o iginal and scaled
a omize s so he ele an dimensionless numbe s mus be conside ed. Re is de ined as he a io o ine ial
o ce o he iscous o ce. In he case o he swi l a omize , he mos common de ini ion o Re is ela ed
o he inle po s [34] as:
ν
p
d
p
wRe =
(1)
whe e wp is he mean eloci y in he inle po s, calcula ed as a olume ic low a e di ided by he o al
c oss-sec ion o inle po s,
ν
is he liquid kinema ic iscosi y, and dp is he hyd aulic diame e o he
inle po s:
)
p
b
p
h(
p
b
p
h
p
d+= 2
(2)
, o dimensions, see igu e 1. The Re alues o he scaled model mus ma ch hose o he o iginal o
keep he same in e nal low cha ac e . The Swi l numbe S0 is use ul in de e mining he a io o he
angula momen um o he axial momen um. I can be calcula ed as a unc ion o he in e nal geome y
[34]:
0
S R A
op
π
=
(3)
whe e R is a adius o low en y o he swi l chambe and Ap is he o al c oss-sec ion o he inle po s.
I is ob ious ha he swi l numbe s o he o iginal and scaled a omize s a e iden ical. The F oude
numbe (F ) shows he e ec o g a i y in compa ison wi h he ene gy o he bulk low and is calcula ed
as:
22
2( )
Q
F g
o oa o
π
=
−
(4)
whe e Q is he olume low a e and oa is he adius o he ai co e in he exi o i ice. To minimize he
e ec o g a i y, i is necessa y o keep F >> 1, as in he o iginal a omize case. The F oude numbe
o he lowes p essu e used was 6.9 hus he e ec o he g a i y was small. Sp ay ela ed dimensionless
numbe s, such as Webe numbe and Ohneso ge numbe di e be ween he o iginal and scaled
a omize s by an o de o magni ude hus he sp ay pa ame e s we e no in es iga ed excep o he sp ay
cone angle, SCA, close o he exi o i ice.
Table 1 lis s he expe imen al low egimes wi h hei dimensionless numbe s. The ope a ing
egimes we e de i ed om hose used in p e ious s udy [22]. The main con ol pa ame e was he inle
p essu e o he o iginal a omize s and consequen ly i s mass low a e, om which he Re was calcula ed.
The SR a omize was e alua ed wi h bo h he closed spill-line o simula e he maximum injec ion a e
and a ious spill- o- eed (SFR) egimes. Ke osene- ype Je A-1 ep esen ing he commonly used uel
was used in bo h he o iginal and modelled a omize . Howe e , he e ac i e index o ke osene di e s
om he e ac i e index o he PMMA by abou 0.05 a 660 nm wa eleng h a 25 °C which dis u bs
he op ical measu emen close o he in e nal su aces o he anspa en model. A liquid wi h a e ac i e
index e y close o he PMMA should be used o educe he op ical dis o ions. Fo his pu pose, se e al
di e en liquids and mix u es we e e alua ed o de e mine he mos sui able. Pa acymene (p-cymene o
1-Me hyl-4-(p opan-2-yl)benzene) was chosen. I is a colou less, anspa en o ganic compound wi h a
e ac i e index di e en om Plexiglas by less han 0.001 a 660 nm wa eleng h and a 25 °C. I also
has a ela i ely low agg essi eness o PMMA; howe e , a e a ew hou s o measu emen , i did cause
c acks in hose pa s whe e inc eased in e nal s esses may be an icipa ed, i.e. in he icini y o bol s and
h eads; hus, i was only used o high-speed imaging. The physical p ope ies o Je A-1 a e
σ = 0.029 kg/s2, μl = 0.0016 kg/(m·s), ρl = 795 kg/m3 and p-cymene: σ = 0.028 kg/s2, μl = 8×10-
4 kg/(m·s), ρl = 850 kg/m3.
Simila ly designed es benches we e used o es ing o bo h he o iginal and scaled a omize s,
see Figu e 2. The es liquids we e supplied o he a omize (8) om a uel ank (1) ia a il e (2) by a
gea pump o a cen i ugal pump (3) o he o iginal and he scaled a omize espec i ely. The mass low
was egula ed by a ying he pump speed. The uel lowing h ough he inle line was me e ed by he
Co iolis mass low me e Mass 2100 Di3 i ed wi h he Mass 6000 ansmi e (Siemens AG, GE) (4)

5
wi h an accu acy ±0.1% o he ac ual low a e. S a ic inle o e -p essu e was measu ed by a piezo-
esis i e p essu e senso DMP 331i (BD SENSORS s. .o., CZ) (7). The unce ain y in he p essu e
sensing was 0.05 kPa and 2 kPa o he scaled and he o iginal a omize espec i ely as di e en senso s
we e used in each case. The inle line was also equipped wi h a empe a u e senso PR-13 made by
OMEGA Enginee ing, INC., USA wi h an e o o 0.2 °C. The spill-line had a piezo- esis i e p essu e
senso DMP 331i (BD SENSORS s. .o., CZ) (9), a ball al e (11) and a posi i e displacemen low
me e KOBOLD DOM-S05 wi h accu acy ±1% o he ac ual low a e (KOBOLD Mess ing GmbH,
GE) (10). The calcula ed unce ain y o CD a Re = 1021was 0.14 % and 0.25 % o o iginal and scaled
Simplex a omize espec i ely. The a omized liquid was cap u ed by a collec ion chambe and ou ed
back in o he uel ank. Fuel mis and apou s we e en ila ed by a an. The a omize was moun ed o a
CNC posi ioning sys em wi h a posi ional e o less han 0.1 mm.
Figu e 2 Le : Schema ic layou o liquid supply. Righ : A Schema ic o he scaled anspa en a omize
Table 1 Ope a ing low egimes, ke osene, S0 = 3.87
O iginal a omize
Scaled a omize
Re
Δp
ml
CD
F
Δp
ml
CD
F
[–]
[MPa]
[kg/h]
[–]
[–]
[kPa]
[kg/h]
[–]
[–]
Simplex
755
0.5
5.41
0.387
137
5
53.8
0.378
6.9
Simplex
1021
1
7.31
0.369
293
10
73.1
0.366
9.3
Simplex
1252
1.5
8.97
0.365
359
15
88.2
0.362
11.4
SR
1075
0.5
7.7
0.542
308
5
69.4
0.483
9.8
SR
1431
1
10.25
0.519
411
10
93.4
0.466
13.0
SR
1731
1.5
12.4
0.510
497
15
110.0
0.454
15.7
SR, SFR 0.4
1676
1
12.0
0.378
481
10
103
0.3
15
(2) (3)
(7)
(5)
(6)
(1)
(8)
(4)
(11)
(9)
(10) (12)
6
Figu e 3. High-speed isualiza ion, p-cymene, 1 MPa, Simplex, c oss-sec ion a, b and c placed 2.5, 8 and 13
mm om he op o he swi l chambe
3 Expe imen al and nume ical se ups
Following subchap e s documen he se ups o he expe imen al app oach using a high-speed
came a and lase -Dopple anemome y (LDA) and he CFD simula ions.
3.1 Expe imen al se up
The expe imen s we e pe o med on he cold es bench a oom empe a u e. A Pho on SA-Z
high-speed came a was used o documen he spa ial and empo al beha iou o he ai co e. The
a omize was illumina ed by a backg ound ligh using an LED panel. Th ee eco ds we e acqui ed a
each ope a ing egime; he i s was a gene al image showing he whole a omize while he o he wo
obse ed he exi o i ice and he op o he swi l chambe in close up, see Figu e 3. The came a ame
a e was 4,000 and 20,000 ps o he gene al image; he esolu ion was 1024 × 1024 px, and he shu e
speed was se o 20 μs. The close-up eco ds used a ame a e o 28,000 ps, esolu ion 768 × 904 px,
and a shu e ime o 10 μs. Mean and RMS images we e calcula ed o each egime. The ai co e
dimensions we e cap u ed by MATLAB code based on he Canny edge de ec o . The ai co e
luc ua ions we e analysed using he Fas Fou ie T ans o m (FFT) in he c oss-sec ion b. The FFT was
applied o he ime- esol ed ai co e su ace cap u ed by he Canny edge de ec o . Ano he FFT was
used on he a e age pixel in ensi ies o e a ec angle 3 × 3 px placed nea he ai co e bounda y o e i y
he p e ious FFT app oach. The ai co e dimensions we e measu ed a h ee c oss-sec ions (a, b and c)
o e he swi l chambe and one c oss-sec ion a he ip o he exi o i ice.
The LDA, a FlowExplo e (Dan ec Dynamics A/S), was employed o he poin -wise
measu emen o he eloci y o indi idual pa icles inside he anspa en a omize . The swi l eloci y
componen was measu ed in h ee c oss-sec ions ac oss he swi l chambe (see Figu e 3 igh ). The axial
dis ances om he op o he swi l chambe we e 2.5, 8 and 13 mm o c oss-sec ions a, b and c
espec i ely, and 50, 38 and 25 measu emen poin s we e aken on each c oss-sec ion. The dis ance
be ween wo su ounding poin s was 0.25 mm. The LDA was con igu ed in he backsca e mode. A
buil -in, diode-pumped solid-s a e lase gene a ed a beam wi h 660 nm wa eleng h. The beam was spli
in o wo pa allel beams wi h he powe o 30 mW each. One o he beams was shi ed by 80 MHz. A
con e ging ansmi ing/ ecei ing lens wi h 150 mm ocal leng h was used o o m an ellipsoidal
measu emen olume wi h he size o app. 0.1 × 0.1 × 0.8 mm. Dan ec BSA P80 signal p ocesso was
used o p ocess he measu ed signal. BSA low so wa e 5.20 was used o con ol he da a acquisi ion
and he ollowing se ing was used: Pho omul iplie sensi i i y 700 V, signal gain 20 dB, eloci y cen e
2.4 m/s, eloci y span 4.8 m/s. The measu emen was limi ed o 10,000 samples acqui ed o a 10-second
acquisi ion du a ion a each measu ed poin . A epea abili y e o based on h ee consequen
measu emen s was less han 4%. The measu ing olume posi ion ela i e o he LDA posi ioning sys em
had o be co ec ed due o he di e en e ac i e index o he a omize body and he liquid as [35]:
)
1
11
(
2
1
1
2
−+
=
Sn
R
n
n
R
S
,
(5)
7
whe e S1 is he i ual dis ance o measu emen olume om he a omize wall, S2 is he eal
dis ance o measu emen olume, R is he diame e o he swi l chambe a measu emen plane, n1 and
n2 a e he e ac i e indexes o PMMA and ke osene espec i ely. The measu ed eloci y was mul iplied
by co ec ion coe icien k el based on he simpli ied app oach om [35] as:
R
S
n
n
el
k2
)1(1
2
1−+=
. (6)
The co ec ion ac o eached he maximum o 1.04 o ke osene a he a omize axis. In posi ions
close o he ai -co e, he aw eloci y da a we e il e ed since he s ong noise was gene a ed by he
e lec ion om he ai co e su ace. The il a ion p ocess seeks o he Gaussian dis ibu ion in he
eloci y his og am, and he mean eloci y was calcula ed only om he da a which sa is ied he Gaussian
dis ibu ion.
The low ace pa icles we e SL75 e-sphe es wi h a mean diame e o 45 μm. Thei S okes
numbe , based on he swi l eloci y and diame e o he swi l chambe , was less han 0.01 o each
egime, which ensu ed a su icien ly small low aceabili y e o .
3.2 Nume ical se up
Conse a ion o mass (con inui y) and conse a ion o momen um (Na ie –S okes) equa ions
we e sol ed nume ically using Ansys Fluen 17.2. The low simula ion was conduc ed as a ansien 2D
axisymme ic model. A Volume o Fluid (VOF) model wi h he geo- econs uc scheme was used o
cap u e he bounda y o he ai co e. The 3D inle bounda y condi ion was se o conse e he mass low
a e in he adial di ec ion and ensu e he same angula momen um in he angen ial di ec ion. The
p essu e ou le bounda y condi ion was applied on he ou e bounda ies wi h no-slip condi ions applied
on he wall bounda ies. A lamina low was assumed due o he low Re alues inside he inle po s, and
also because inside he swi l chambe , he adial o ces o he swi l end o lamina ise he low [34]. The
simula ions we e pe o med o bo h he o iginal and scaled a omize s. The SR a omize was simula ed
including a 4-mm long pa o he spill-line geome y (see Figu e 10 in sec ion 4.3). The spill low in
he egime wi h SFR = 0.4 was se as a nega i e liquid sou ce ac oss he en i e spill-line. I was no
possible o se he p essu e bounda y condi ion o he spill-line wall as he solu ion was e y uns able.
The all quad s uc u ed mesh wi h an a e age skewness o 0.058 and an a e age aspec a io o
1.18 was c ea ed (Figu e 4), and he mesh independence es was ca ied ou o ou di e en elemen
base sizes in e ms o CD, SCA and he ai co e diame e (da) a he end o he exi o i ice (do) in a
dimensionless o m as da/do (see Table 2). The e was a signi ican di e ence be ween he meshes o
11,684 and 22,669 elemen s. This di e ence dec eased wi h u he inc ease in he numbe o elemen s,
and he mesh wi h 46,765 elemen s was chosen as a good comp omise be ween he accu acy and he
calcula ion speed. Two sizes o an ou low a ea, which is an a i icial a ea downs eam o he a omize
ou le , we e also es ed. A calcula ion o ou imes la ge ou low a ea e ealed he same esul s as he
o iginal one, see esul s o meshes wi h 68,610 and 46,765 elemen s.
Table 2. Mesh independence es
Numbe o elemen s
CD [–]
da/do [–]
SCA [deg]
11,684
0.392
0.655
58
22,669
0.365
0.707
58
46,765
0.358
0.710
57
68,610*
0.359
0.710
57
90,684
0.356
0.711
56
*The base size o he elemen s was he same as in he case o 46,765 elemen s. The ou low a ea was
ou imes la ge .
8
Figu e 4. Le : Nume ical domain and i s mesh. Righ : Typical esul s ob ained wi h he wa y su ace o he ai
co e, phase dis ibu ion: 1 = ai , 0 = liquid.
4 Resul s and discussion
The ai co e shape and s abili y play a key ole in he o ma ion o he liquid shee a he discha ge
o i ice. A desc ip ion o he ai co e dynamics is based on high-speed image eco ds and nume ical
simula ions. The discha ge pa ame e s a e discussed in e ms o CD and SCA. The measu ed swi l
eloci y p o iles se ed o consequen alida ion o he nume ical simula ions.
4.1 Ai co e shape and sp ay cone angle
In a compa a i e manne , he high-speed eco ds wi h bo h ke osene and p-cymene as he wo king
liquid a e shown in Figu e 5. Fo he ke osene image, he e a e da ke egions owa ds he edge o he
swi l chambe . This is caused by ligh e ac ion a he swi l chambe wall. I is no e iden in he
a omize cen e due o he small ela i e cu a u e. This is sol ed using he liquid wi h he same
e ac i e index as he a omize body which can be seen o he esul s o p-cymene.
The ai co e was ully de eloped in he case o all he Simplex a omize s. I was cylind ically
shaped and inc eased in i s diame e inside he exi o i ice; such beha iou was also desc ibed by o he
au ho s [16, 17, 28]. The dimensionless diame e o he ai co e in he exi o i ice was da/do = 0.72 ± 0.02
o all he inle p essu es and bo h liquids wi h no e iden co ela ions o Re. Inside he swi l chambe ,
da/do = 0.47 ± 0.03 and i was also almos independen o Re. Bo h indings a e in acco dance wi h o he
au ho s [16, 36, 37] who epo ed he independen ai co e size o high Re egimes, while Halde and
Som [16] ound a sligh ly inc easing ai co e diame e wi h Re. Ins abili ies, in he o m o ai co e
luc ua ions, bo h in he axial and adial di ec ion (Figu e 6), we e obse ed a he op o he swi l
chambe . These luc ua ions a e linked wi h he wa y s uc u e on he ai co e su ace. The equency
o he su ace wa es = 32 ± 4 Hz was es ima ed using he FFT analysis o images o he Simplex
a omize wi h p-cymene a Re = 1021. A simila analysis was epo ed by Sume e al. [30] who used a
simila ly sized a omize , bu wi h he eloci y in he inle po s app oxima ely en imes highe ; hey
ound wa e equencies o = 273 Hz. Chinn e al. in [38] s udied he su ace wa es on he ai co e and
desc ibed h ee dis inc i e ypes o su ace wa es: helical s ia ions, s a iona y wa es and andom
ipples. They no ed ha he s a iona y wa es we e esponsible o changes in he liquid shee hickness.
The same phenomenon was also e iden in ou eco ds. The helical s ia ions, which a e caused by ini e
numbe o he inle po s, we e no obse ed he e.