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Empi ical co ela ion o sp ay hal cone angle in plain-je ai blas a omize s
And ás U bán
a
, Bálin Ka ona
a
, Milan Malý
b
, Jan Jedelský
b
, Vik o Józsa
a,⁎
a
Budapes Uni e si y o Technology and Economics, Facul y o Mechanical Enginee ing, Depa men o Ene gy Enginee ing, 1111, Budapes , Műegye em kp. 3., Hunga y
b
Facul y o Mechanical Enginee ing, B no Uni e si y o Technology, Technicka 2896/2, 616 69 B no, Czech Republic
ARTICLE INFO
Keywo ds:
Ai blas
Rapeseed oil
Sp ay cone angle
Image p ocessing
Th eshold
A omiza ion
ABSTRACT
Plain-je ai blas a omize s a e widely used in indus ial applica ions. The li e a u e con ains nume ous pape s
on Sau e mean diame e , howe e , he e is no es ima ion me hod a ailable o sp ay cone angle, SCA, which
de i a ion is he p ima y goal o his s udy. Fou dis inc , p ac ical model liquids we e analyzed: dis illed wa e ,
diesel oil, ligh hea ing oil, and c ude apeseed oil. The a omizing p essu e and liquid p ehea ing empe a u e
we e a ied in he ange o 0.3–2.4 ba and 25–85 °C, espec i ely. This la e pa ame e enabled a wide and
con inuous liquid kinema ic iscosi y in es iga ion ange o 0.33–44.2 mm
2
/s. The esul ing sp ays we e imaged
a a ious shu e speeds o p ope edge de ec ion. An adap i e h esholding algo i hm was de eloped in Ma lab
so wa e en i onmen o calcula e SCA. The me hodology is discussed in de ail o acili a e he e-im-
plemen a ion o his echnique since he e is no gene ally accep ed me hod o SCA measu emen . SCA in e sely
a ied wi h liquid densi y and ollowed a powe law wi h he ai - o-liquid mass low a io; howe e , he de i ed
exp ession also pe o med well by eplacing ai - o-liquid mass low a io by ei he Mach numbe o momen um
lux a io. A simple empi ical equa ion was de i ed, which allows he es ima ion o SCA o ai blas a omiza ion
in a wide pa ame e ange wi hin a 3.5% de ia ion. The measu ed esul s we e e alua ed in he ligh o high-
speed came a images in he icini y o he nozzle; i was ound ha inc eased liquid je b eakup leng h dec eases
SCA while in ense ligamen o ma ion inc eases i .
1. In oduc ion
The mos impo an pa ame e o a liquid sp ay is i s mean d ople
size, which de e mines he a e age e apo a ion/solidi ica ion ime,
impingemen , and he gene al in e ac ion wi h he su ounding gas
low. The second highligh ed pa ame e is he Sp ay Cone Angle, SCA,
which cha ac e izes sp ay sp eading. I bea s an emphasized ole in
nume ous applica ions, including cooling [1], me allu gy [2], and
combus ion sys ems [3]. While he e a e a ew in e na ionally accep ed
and used mean d ople diame e de ini ions – depending on he appli-
ca ion and ocus –, he e is no gene al de ini ion o SCA [4]. A eason
o i is he wide a ie y o exis ing a omize geome ies and ope a ing
condi ions. P ac ical a omize s wo k in a u bulen low ield ha
couples wi h he d ople mo emen [5].SCA de e mina ion o swi l
a omize s shows a high sensi i i y on he a omize cons an [6], and
analy ical app oxima ions a e a ailable o in iscid low [7]. The li -
e a u e is signi ican ly hinne o o he a omize ypes in which SCA is
de e mined by he esul ing sp ay ins ead o a well-localized liquid
shee . Hence, he d ople - u bulence in e ac ion makes sp ay edge de-
ec ion a non i ial ask [8]. Upon de ining he edges, SCA can be easily
es ima ed.
A gene al ecommenda ion o SCA measu emen o gasoline uel
injec o s was made by Hung e al. [9], including sp ay edge de e mi-
na ion. They ha e highligh ed ha he sp ay can be cu ed, hence a
well-de ined dis ance om he nozzle should be se . Ne e heless, hei
esul s canno be gene alized o ai blas a omize s, which is he subjec
o his pape due o he well-es ablished geome y anges and speci i-
ca ions in ecip oca ing engine applica ions. As a consequence, 60 imes
he liquid o i ice diame e was chosen o he p esen analysis ha is
used o p essu e a omize s [4] and lies in he sel -simila egion o
annula je s [10]. The sp ay edge de ec ion can be pe o med by ei he
imaging [11] o non-imaging op ical echniques [12]. The image e-
solu ion o cu en comme cial came as is high enough o pe o m ac-
cu a e measu emen s, also used in he cu en s udy. Ma ínez-Gal án
e al. [1] and Bizjan e al. [13] simila ly aced he blu y sp ay edge
p oblem and used a h esholding echnique. Thei idea was imp o ed in
he p esen s udy, i.e., by using an adap i e app oach, discussed in
Subsec ion 2.2. A simila algo i hm was success ully applied in pa icle
de ec ion in mic oscopy [14] and X- ay image p ocessing [15]. Since a
sp ay image is an ins an aneous map o d ople s, a e aging is necessa y
o elimina e his a ia ion. I can be done by a e aging a ce ain
numbe o images [1] o using a p ope exposu e ime. In he p esen
h ps://doi.o g/10.1016/j. uel.2020.118197
Recei ed 29 Feb ua y 2020; Recei ed in e ised o m 14 Ap il 2020; Accep ed 22 May 2020
⁎
Co esponding au ho .
E-mail add ess: [email p o ec ed] (V. Józsa).
Fuel 277 (2020) 118197
A ailable online 31 May 2020
0016-2361/ © 2020 The Au ho (s). Published by Else ie L d. This is an open access a icle unde he CC BY license
(h p://c ea i ecommons.o g/licenses/BY/4.0/).
T
pape , his la e me hod was used, wi h an ex ension o e alua ing he
SCA a ia ion wi h he shu e speed.
Ai blas a omize s we e de eloped o eplace p essu e swi l a omi-
ze s, which ha e low lexibili y in he liquid low a e [16]. Tu ndown
a io o 50:1 was made a ailable h ough go e ning he a omiza ion
p ocess by he high- eloci y ai low; he liquid is injec ed a a ew m/s
wi hou lowe limi a ion. This a omize ype belongs o he win- luid
amily and elies on he a ailable high-p essu e gas, which blows o e
he liquid su ace, leading o ligamen hen d ople o ma ion; he
go e ning physics was e iewed by Lashe as and Hop inge [17]. The
p esen ly in es iga ed plain-je ai blas a omize has a simple pipe-in-
pipe design ha makes i s manu ac u ing and main enance easy. Sp ay
cha ac e is ics o ai blas a omiza ion we e in es iga ed by Ma e al.
[18] and Gad e al. [19]; ne e heless, hey did no aim o de i e an
empi ical co ela ion be ween he ope a ing pa ame e s and SCA which
is he p ima y goal o his s udy. Ta eq e al. [20] in es iga ed he SCA
o a p e ilming ai blas a omize , and, simila ly, hey did no de i e any
co ela ion o his pa ame e .
The liquid b eakup p ocess go e ns SCA, hence, he liquid disin-
eg a ion in he icini y o he nozzle g ea ly a ec s he inal esul .
Wa anawanyoo e al. [21] in es iga ed a win- luid a omize in a si-
mila ai - o-liquid pa ame e ange, which is analyzed p esen ly, de-
ailed in Subsec ion 2.1. They iden i ied a ious b eakup modes and
es ima ed only he d ople size dis ibu ion 100 mm downs eam o he
nozzle wi hou SCA e alua ion. Cha alampous e al. [22] analyzed he
liquid je b eakup leng h by h ee di e en echniques, concluding ha
e en a simple elec ical connec i i y echnique can lead o signi ican
esul s; howe e , i equi es an in usi e p obe. The liquid je b eakup
leng h a ec s he sp ay sp eading since he high- eloci y ai je quickly
decays as i in e ac s wi h he low- eloci y liquid je . Hence, g ea e
liquid je b eakup leng h leads so smalle SCA. A no el, dual-angle
pa icle acking elocime y echnique o sp ay and d ople b eakup
measu emen was p oposed by Pham e al. [23], which enables highly
de ailed acking o he d ople b eakup p ocess.
I nume ous pa ame e s in luence a quan i y, he use o he
Buckingham π heo em helps in inding he p ope co ela ion h ough
de i ing non-dimensional quan i ies [24]. The absence o such an in-
es iga ion o SCA o ai blas a omize s s a s wi h he analysis o he
possible pa ame e s a ec ing a omiza ion, which a e discussed in de ail
o , e.g., de e mining he Sau e Mean Diame e , SMD [25]. An ea ly
wo k by Ab amo ich [26] on p essu e a omiza ion concluded ha SCA
depends on he densi y a io o ai and liquid. Ul ima ely, i was ound
ha Ohneso ge and Webe numbe s de e mine he a omiza ion mode,
hence SCA is also a ec ed by hem [4]. This pape is a successo o ou
p e ious wo k in which he SMD o he sp ay was deeply in es iga ed
[27]. The p esen ly in es iga ed liquids a e he same o consis ency:
dis illed wa e (W), s anda d diesel oil (D, EN 590), ligh hea ing oil
(LHO), and c ude apeseed oil (RO).
The no el y o he p esen pape is p incipally illing a scien i ic gap
by de i ing an empi ical co ela ion o SCA o a plain-je ai blas
a omize . Since he d ople o ma ion is la gely depending on he nea -
nozzle egime o he sp ay, he liquid s uc u es o he p ima y b eakup
a e isually e alua ed. The hi d goal is o p o ide a gene al SCA de-
e mining amewo k o make his p ocedu e anspa en and easy o
implemen o p ac ical applica ions whe e measu emen echniques
beyond a comme cial digi al came a a e seldom a ailable.
2. Ma e ials and me hods
Fi s ly, he expe imen al se up is de ailed, along wi h he discussion
o he measu emen unce ain ies. Then he image p ocessing me ho-
dology is desc ibed o p o ide a gene al amewo k o SCA analysis o
a possible e-implemen a ion o his echnique. Las ly, he de i a ion o
he non-dimensional quan i ies and he empi ical co ela ion o SCA
a e de ailed.
2.1. Expe imen al se up
The schema ic d awing o he a omiza ion es ig shown in Fig. 1a,
ea u ing he nozzle ip. The liquid je was in oduced o he plain-je
ai blas a omize ia a cen al pipe wi h 0.4 mm inne diame e while
inne and ou e diame e s o he annula a omizing ai o i ice we e
0.8 mm and 1.6 mm, espec i ely. The gauge p essu e o he a omizing
ai , p
g
, was se by a egula o al e in he ange o 0.3 and 2.4 ba in 5
s eps wi h 1 kPa accu acy. The ai was also used o p essu ize he liquid
ank o main ain a low ye smoo h liquid low a e which was 0.35 g/s
o all he ou liquids: D, LHO, RO, and W. The liquid olume low a e
was measu ed by an Omega FPD3202 low me e which has < 2.7%
Nomencla u e
La in le e s
A[deg] cons an in he SCA co ela ion
a[m/s] speed o sound
=ALR m m/
A L
[–] ai - o-liquid mass low a io
B[–] cons an in he SCA co ela ion
d
0
[mm] liquid pipe inne diame e o he a omize
m
[kg/s] mass low a e
=w aMa /
[–] Mach numbe
=MFR w w· / ·
AALL
2 2
[–] momen um lux a io
N
1
,N
2
[–] non-dimensional numbe s
=Oh We /Re
[–] Ohneso ge numbe
p[ba ] p essu e
R[J/(kg·K)] speci ic gas cons an
R
2
[–] coe icien o de e mina ion
=w dRe · /
R0
[–] Reynolds numbe
S
,A
[–] ela i e s anda d de ia ion o Acons an
SCA [deg] sp ay cone angle
SMD [μm] Sau e mean diame e
T[°C] empe a u e
w[m/s] eloci y
=w dWe · · /
R
2
0
[–] Webe numbe
G eek le e s
κ[–] speci ic hea a io
μ[kg/(m·s)] dynamic iscosi y
ν[m
2
/s] kinema ic iscosi y
ρ[kg/m
3
] densi y
σ[N/m] su ace ension
0 ambien
25 °C a 25 °C
Aa omizing ai
ga omizing ai gauge
Lliquid
R ela i e
Abb e ia ions
D diesel oil
LHO ligh hea ing oil
RO c ude apeseed oil
SSE sum o squa ed es ima e o e o s
W dis illed wa e
. Tilde deno es non-dimensional numbe s de i ed om a
single physical quan i y.
A. U bán, e al. Fuel 277 (2020) 118197
2
unce ain y a 95% le el o signi icance. The calib a ion was pe o med
a six poin s a ound he desi ed low a e, using he se up p esen ed in
Fig. 1. An elec ic hea e was ins alled o he liquid line o se he
p ehea ing empe a u e, T
L
, be ween 25 and 85 °C in i e 15 °C s eps.
The liquid empe a u e was con olled by a PID con olle , using a B
class P 100 esis ance he mome e wi h an accu acy o < 0.8 °C. The
condi ions lis ed abo e esul ed in 100 di e en condi ions in o al wi h
a wide pa ame e ange in su ace ension (20.7–32.1 and 62.3–72.1
mN/m), kinema ic iscosi y (0.33–44.2 mm
2
/s), and liquid densi y
(808–997 kg/m
3
), which a e cha ac e is ic o liquid uels in combus-
ion. No e ha he gap in su ace ension is p esen due o he sig-
ni ican ly highe alues o wa e han o he hyd oca bon liquids.
Ne e heless, he p incipal aim in selec ing he liquids was o ensu e a
con inuous ange in iscosi y. The measu ed ma e ial p ope ies, along
wi h hei co esponding unce ain ies, a e discussed in ou p e ious
wo k [27]. A an was used o emo e he mis o enable he acquisi ion
o clea images wi hou a ec ing he SCA. I did no wo k lawlessly a
high p
g
when e y ine sp ay was gene a ed, discussed in Subsec ion
2.2. The ange o he key non-dimensional numbe s is summa ized in
Table 1 in Subsec ion 2.3.
The shu e speed was expec ed o a ec SCA as longe exposu e
ime allows mo e in o ma ion o be collec ed in he pe iphe al egime
whe e he d ople mass lux is low he e. Hence, 1/60 s, 1/80 s, and 1/
100 s shu e speeds we e used o ge ela i ely sha p images. Fi e
pic u es we e eco ded wi h all h ee se ings, which means 1500
images in o al o be p ocessed. The con e sion ac o in hese images
was 15.5 pixels/mm. The sp ay was imaged in on o a black pla e by
a Panasonic DMC-TZ80 comme cial digi al came a and illumina ed
om he on in a small angle by a comme cial 50 W LED spo ligh ,
shown in Fig. 1b. The image esolu ion was 18 MP, while he ocal a io
was se o 4.3. Since ai blas a omiza ion gene a es dilu e sp ay, he
posi ion o he LED ligh had no no able in luence on he calcula ed SCA
alues, which was ca e ully checked.
In o de o unde s and he d ople o ma ion and SCA a ia ion
be e , a high-speed came a, a FASTCAM SA-Z ype 2100 K-M−16 GB
(Pho on, Japan) wi h long-dis ance mic oscope 12X Zoom lens
(NAVITAR, USA) composed o 2X F-moun adap e ( ype 1–62922),
12 mm F.F zoom lens ( ype 1–50486) and a ached 0.25X lens ( ype
1–50011), was used o cap u e he b eakup o he liquid je in he i-
cini y o he a omize nozzle; he op ical se up is shown in Fig. 1c. The
sp ay was illumina ed om he backg ound by an HPLS-36DD18B
(Ligh speed Technologies, Inc., USA) pulsed LED ligh sou ce. The ligh
pulse du a ion was 100 ns. No e ha he eco ding o hese images was
pe o med ea lie , along wi h he Phase Dopple measu emen s in e
[27], using he same a omize and liquid p ehea e appa a us. The
di e ence was ha he maximum T
L
was highe han he p esen ly se
85 °C alue. Hence, T
L
was 90 °C o W and 100 °C o he h ee o he
liquids o high-speed imaging esul s. The shu e speed was 1/
630,000 s o 159 s, and he ame a e was 160,000 ames/second. The
image esolu ion was 256 × 256 pixels, which is equi alen o
3.2 × 3.2 mm physical size wi h a con e sion ac o o 80 pixels/mm.
The high ame a e was necessa y o cap u e he mo emen o he luid
packe s while he a omizing discha ge eloci y was in he ange o
208–420 m/s, acco ding o p
g
= 0.3–2.4 ba . Since he high-speed
came a was ocused on he icini y o he nozzle, SCA canno be de-
duced om hese esul s. Ne e heless, he d ople o ma ion and hei
mo ion due o u bulence allow a be e unde s anding o he a ia ion
o SCA.
2.2. Image p ocessing
To p ocess a la ge numbe o images wi hou he bias o manual
e alua ion, a Ma lab code was de eloped o his pu pose. I s low cha
is shown in Fig. 2. Since he elemen a y p ocesses a e simple manip-
ula ion algo i hms, he un ime is in he ange o one second.
The i s s ep is eading he image o be p ocessed. Then he image
has o be cu o a uni o m shape, which is c ucial o he e alua ion,
shown in Fig. 3a. P e-calib a ion is equi ed o c opping, i.e., he pixels
a e con e ed o physical dimensions. The ou le diame e o he liquid
je is 400 µm, being equal o he inne diame e o he uel pipe. I was
conside ed as a e e ence o image calib a ion, also suppo ed by he
high-speed images ocusing on he p ima y b eakup egion, discussed in
Subsec ion 3.2. Nex , he esul ing image was subjec ed o gamma
co ec ion and g ayscale con e sion, shown in Fig. 3b. Gamma be ween
0 and 1 makes he image ligh e while alues exceeding one shi s i
owa ds black. A cons an alue o 1.1 was used in he p esen s udy o
emo e a po ion o he isible ine mis and image noise, based on he
ollowing obse a ions. Gene ally, excessi e gamma alues a ec SCA,
Fig. 1. Schema ic o a) liquid and a omizing ai piping and hei ins umen a-
ion and op ical se up o b) SCA and c) p ima y b eakup measu emen .
Table 1
The main non-dimensional ange o he liquids.
D LHO RO W
p
g
[ba ] min. 0.3 0.3 0.3 0.3
max. 2.4 2.4 2.4 2.4
ALR [-] min. 0.78 0.78 0.78 0.78
max. 2.07 2.07 2.07 2.07
Re
A
[-] min. 9166 9173 9178 9192
max. 30,712 30,723 30,734 30,751
Re
L
/10
6
[-] min. 22.7 5.04 1.57 91.2
max. 115.4 51.8 21.0 380
We
A
[-] min. 824.7 711.4 659.2 294.4
max. 5582 5080 4375 1859
Oh
L
[-] min. 0.014 0.0309 0.072 0.00274
max. 0.0325 0.140 0.442 0.00528
Ma [-] min. 0.62 0.62 0.62 0.62
max. 1.45 1.45 1.45 1.45
MFR [-] min. 5.71 5.96 6.19 6.86
max. 30.73 32.05 32.31 36.9
A. U bán, e al. Fuel 277 (2020) 118197
3
which should be a oided. This e ec was obse ed a , e.g., p
g
= 2.4 ba
when ine sp ay was gene a ed and he mis became dense, making he
edge de ec ion cumbe some. Highe iscosi y cases also caused biased
esul s when excessi e gamma co ec ion was applied. Then he image
was subjec ed o bina y con e sion whe e 1 is he whi e an 0 is he
black. This p ocedu e was necessa y o p epa e he h esholding algo-
i hm o calcula e he bounda ies o he sp ay. Final smoo hing was
pe o med o ill he inne gaps, shown in Fig. 3c. By sea ching o he
i s and las whi e pixels in a ow, he sp ay bounda ies can be de-
e mined, esul ing in wo cu es. Fig. 3d shows he i ed lines o he
le and igh edge o he sp ay bounda y, which in e sec ion angle
gi es he SCA ul ima ely.
Besides he shu e speed selec ion, inapp op ia e h eshold alue
leads o biased esul s. Hence, sweeping wi h he h eshold le el was
pe o med i s , shown in Fig. 4, o adap i ely ind he app op ia e
h eshold. Ini ially, a small alue does no a ec he numbe o whi e
pixels. Abo e 0.8 he e, only black pixels emain since he e was no ully
whi e pixel. E en hough a black backg ound was used, he co e-
sponding pa o he image was da k g ey in he images. Hence, he
ini ial apid dec ease is due o he con e sion o he backg ound o
black. Then smalle , ligh e pa ches o he image u n o black ha
p ecedes he disappea ing o he subs an ial pa s o he sp ay, shown in
Fig. 4b, as a local minimum be o e he jump o ze o. To ind he sp ay
edges, his minimum was calcula ed, which adap i ely p o ided he
app op ia e h eshold alue o SCA de e mina ion. Hence, no single
h eshold alue was used in he p esen s udy, unlike in he case o
Gamma. E en hough he e was a di e ence in he shu e speeds, he
applied p ocedu e esul ed in highly simila esul s, and he discussed
SCA alue in Subsec ion 3.1 was he a e age o hem. No e ha he
a ia ion o he SCA alues was e y low, hence he a e aging ma -
ginally a ec ed he inal esul .
High p
g
esul ed in d ople s below 5 µm, which we e less p one o
lea e he es sec ion due o hei low ine ia, shown in Fig. 5. To a oid
biased SCA de e mina ion, excessi e mis suc ion should be a oided
ha ine i ably esul s in coa se image quali y. As a consequence, a
manual e iew o he il e ing p ocedu e was necessa y a a ew ope -
a ing poin s.
2.3. Empi ical equa ion o mula ion
By pe o ming he Buckingham π heo em on he ele an pa a-
me e s in he p esen measu emen se ies and, he ollowing non-di-
mensional numbe s we e de i ed. Fi s ly, he single physical quan i y
a ios – and also hei ecip ocals – can be conside ed:
= + +T T T
~( 273. 15)/( 273. 15)
A A L
(1)
=°
T T
~
25 C/
L L
(2)
=
~/
A A L
(3)
=°
~/
LLL
,25 C
(4)
=
~/
A A L
(5)
=°
~/
LLL
,25 C
(6)
= =µ µ µ
~/ · /( · )
AA L AALL
(7)
= =
° ° °
µ µ µ
~/ · /( · )
LL C LL L LL
,25 ,25 C ,25 C
(8)
=°
~/
25 C
(9)
Fig. 2. The image p ocessing low cha .
Fig. 3. The s eps o image p ocessing and SCA de e mina ion. The axes show
he numbe o pixels.
Fig. 4. Image h esholding. a) pe cen age o whi e pixels and b) de i a i e o
a).
A. U bán, e al. Fuel 277 (2020) 118197
4
=ALR m m/
A L
(10)
=w aMa /
A
(11)
whe e Tis he empe a u e, ρis he densi y, νis he kinema ic iscosi y,
μis he dynamic iscosi y, σis he su ace ension, ALR is he ai - o-
liquid mass low a io,
m
is he mass low a e, Ma is he Mach numbe ,
ais he local speed o sound, and w
A
is he ai eloci y a e adiaba ic
expansion [27]. Tilde deno es non-dimensional numbe s de i ed om a
single physical quan i y. Subsc ip 25 °C e e s o a 25 °C. a,w
A
, and ρ
A
a e calcula ed by Eqs. (12)–(14):
= +a R T· ·( 273. 15)
A
(12)
= +
+
w R T p
p p
2·
1· ·( 273. 15)· 1
A A A
A g
,0
1
(13)
=
+
+ +
p p
R T
p
p p·( 273. 15) ·
A
A g
A
A
A g
,0
1
(14)
whe e R= 287 J/(kg·K) is he speci ic gas cons an o ai , κ= 1.4 is he
Fig. 5. Raw images o D a omiza ion a T
L
= 25 °C and p
g
= a) 0.3 ba , b) 0.9 ba , c) 2.4 ba . No e he coa sening image quali y.
Fig. 6. SCA as a unc ion o T
L
a a ious p
g
o all liquids.
A. U bán, e al. Fuel 277 (2020) 118197
5

speci ic hea a io, p
A
is he ambien p essu e, which is also he a o-
mizing ai p essu e a e he adiaba ic expansion. T
A,0
is he a omizing
ai empe a u e be o e eaching he nozzle. Subsc ip A e e s o a o-
mizing ai – a e he expansion –, Ldeno es liquid, and T
A,0
is he
a omizing ai empe a u e be o e he nozzle. Equa ions (2),(4),(6), and
(8) we e in oduced o allow he isola ed inclusion o liquid empe a-
u e wi hou a ec ing he quan i ies which con ain he p ope ies o
a omizing ai . Besides he single quan i y a ios, h ee u he highly
ele an non-dimensional numbe s in sp ays we e also e alua ed,
shown by Eqs. (15)–(18):
=w dRe · /
R0
(15)
=w dWe · · /
R
2
0
(16)
= = µ dOh We /Re / · ·
0
(17)
=MFR w w· / ·
AALL
2 2
(18)
whe e Re is he Reynolds numbe , We is he Webe numbe , Oh is he
Ohneso ge numbe , and MFR is he momen um lux a io. w
R
=w
A
-w
L
is he ela i e eloci y be ween he wo s eams and σis he su ace
ension. Since bo h densi y and iscosi y can be unde s ood as he
Fig. 7. High-speed images in he icini y o he nozzle o all liquids and a ious p
g
and T
L
. No e ha he uppe limi o T
L
was 90 °C in he case o W ins ead o 100 °C.
The physical size o he images is 3.2 × 3.2 mm. The numbe s in he op igh co ne a e We
A
and Oh.
A. U bán, e al. Fuel 277 (2020) 118197
6
ma e ial p ope y o ei he he a omizing ai o he liquid, he i s h ee
o hese numbe s also ea u e Ao Lsubsc ip in he ollowing o
cla i ica ion. The main non-dimensional pa ame e s o he p esen in-
es iga ion a e lis ed in Table 1.p
g
,ALR, Re
A
, Ma, and MFR a e iden-
ical o simila o all liquids. Since he su ace ension o W is abou he
iple o ha o he o he liquids, leading o di e ences in We
A
. Re
L
and
Oh include he liquid iscosi y, which was ca e ully selec ed o allow
he in es iga ion o a con inuous ange. Hence, he ange o hese
p ope ies is unique o all liquids.
Based on all he non-dimensional numbe s, i is e iden ha keeping
all o hem simila is impossible. To o e come his issue and allow he
compa ison o a ious a omize s and liquid sp ays, Ohneso ge in-
oduced he Oh-Re
L
diag am [4] in which all o he poin s lie in he
‘a omiza ion’ ange. Fae h e al. [28] in es iga ed he b eakup egimes
o d ople s and in oduced a We
A
-Oh diag am o classi ica ion. P e-
sen ly, all he poin s all in o he ‘shea b eakup’ egime since
We
A
> 200 and Oh < 0.5. Consequen ly, i can be s a ed ha he
d ople o ma ion is go e ned by he same physical mechanisms in all
o he abo e cases, hence liquid b eakup and SCA o di e en liquids a
di e en condi ions can be compa ed.
3. Resul s and discussion
Fi s ly, he SCA measu emen esul s a e p esen ed, e alua ing he
e ec o all p
g
,T
L
, and liquids. Since he je b eakup has a signi ican
impac on SCA, he p ima y b eakup is analyzed nex a wo empe a-
u es and h ee p essu e o all liquids o be e unde s and he abo e
esul s. Las ly, he de i a ion o he empi ical co ela ion is de ailed,
using an op imiza ion algo i hm. Since he pa ame e i ing easily e-
sul s in high R
2
alues, he i ed coe icien s we e pe u bed by 1% o
see hei e ec on he sum o he squa ed es ima e o e o s, SSE, o ind
he esul s wi h low sensi i i y and hence po en ially applicable o SCA
es ima ion.
3.1. SCA measu emen esul s
The de e mined SCA as a unc ion o p
g
and T
L
o all liquids is
shown in Fig. 6. The esul s show a dec easing end p incipally wi h
inc easing p
g
in all he cases. I can be explained by he e ec o con-
inuously inc easing he axial momen um o he a omizing ai ha in-
ensi ies d ople con ec ion. Tu bulence acili a es he adial p opaga-
ion o d ople s and coun e ac s wi h his phenomenon, which is
becoming mo e in ense wi h he inc eased p
g
. Howe e , he o me
e ec is no ably s onge , leading o ul ima ely smalle SCA a highe
Table 2
Pe o mance o a ious non-dimensional numbe s a N
2
while
=N~
L
1
was used.
No e ha he conside ed da ase o W was limi ed o T
L
= 70 °C.
N
2
Liquid R
2
SSE S
,A
ALR D 0.920 8.24 0.0225
LHO 0.950 4.24 0.00760
RO 0.951 5.9 0.0198
W 0.881 7.46 0.0185
Ma D 0.912 8.08 0.0183
LHO 0.941 13.4 0.00378
RO 0.961 14.3 0.0117
W 0.864 13.5 0.0203
MFR D 0.912 9.06 0.0633
LHO 0.937 15.6 0.0309
RO 0.948 16.2 0.0779
W 0.848 12.7 0.0443
~
A
D 0.933 17.7 1.099
LHO 0.960 48.1 0.447
RO 0.937 68.1 0.958
W 0.895 52.4 0.553
We
L
D 0.899 11.9 0.155
LHO 0.926 11.2 0
RO 0.945 193 0.363
W 0.835 61.9 0.260
Re
A
D 0.930 9.47 0.228
LHO 0.951 4.29 0.0729
RO 0.949 8.33 0.151
W 0.862 37.3 0.231
Re
L
D 0.903 856 0
LHO 0.930 117 0.000134
RO 0.946 150 0
W 0.836 15.4 0
T
~
A
D 0.943 27.1 0.0492
LHO 0.960 221 0.0465
RO 0.937 180 0.0269
W 0.894 13.9 0.0339
Table 3
Poo ly pe o med combina ions in he case o D.
N
1
N
2
R
2
SSE S
,A
~
L
~
A
0.873 2.3 × 10
9
0.641
~
L
µ
~
A
0.570 214,415 1.86
~
L
We
A
0.915 1128 0.154
Oh
L
ALR 0.749 995 0.294
Oh
L
Ma 0.915 995 0.293
Oh
L
MFR 0.913 991 0.298
T
~
L
ALR 0.546 2598 0.521
T
~
L
Ma 0.556 2599 0.517
T
~
L
MFR 0.589 1980 0.540
~
L
ALR 0.922 1463 0.390
~
L
Ma 0.911 9017 0.0183
~
L
MFR 0.911 9695 0.0633
µ
~
L
ALR 0.922 8028 0.0225
µ
~
L
Ma 0.911 8067 0.0183
µ
~
L
MFR 0.911 8691 0.0633
~
ALR 0.922 71.7 0.092
~
Ma 0.911 191 0.0183
~
MFR 0.911 244 0.063
Table 4
Inc ease o SSE in pe cen age compa ed o he o iginal alue by pe u bing only
Aand Bby ± 1% while he o he cons an was unchanged.
N
2
Liquid A+ 1%/-1% B+ 1%/-1%
ALR D 15.1/8.80 0.635/0.469
ALR LHO 45.2/24.3 1.14/1.59
ALR RO 33.4/17.5 0.82/1.13
ALR W 9.70/40.8 0.079/0.09
Ma D 6.05/30.0 0.61/0.491
Ma LHO 29.4/50.5 0.618/0.707
Ma RO 35.7/55.7 0.654/0.732
Ma W 21.2/38.0 0.338/0.348
MFR D 38.5/16.3 6.47/8.60
MFR LHO 31.3/39.2 12.6/11.0
MFR RO 34.3/52.0 13.2/11.7
MFR W 18.1/36.2 2.87/2.63
T
~
A
D 37.9/30.1 4.59/4.77
T
~
A
LHO 19.0/17.3 1.49/1.50
T
~
A
RO 20.8/18.7 1.52/1.55
T
~
A
W 52.3/34.5 1.61/1.63
Table 5
Cons an o Eq. (20) o he in es iga ed liquids.
N
2
Cons . D LHO RO W
ALR A 20.7 25.0 25.1 24.3
B−0.20 −0.19 −0.18 −0.07
Ma A19.5 23.6 23.8 23.8
B−0.23 −0.22 −0.21 −0.08
MFR A 27.2 32.0 32.0 26.8
B−0.11 −0.11 −0.11 −0.04
A. U bán, e al. Fuel 277 (2020) 118197
7
p
g
. Inc eased T
L
ea u es sligh ly inc eased SCA o p incipally LHO and
RO. I s e ec on D and W is signi ican ly lowe , complying wi h he
limi ing iscosi y e m, de ined in ou p e ious wo k [27]. I is a ki-
nema ic iscosi y alue below which he liquid p ehea ing has no ad-
di ional physical e ec on he We-con aining e m o SMD es ima ion
beyond he empe a u e-dependen ma e ial p ope ies, and i was
ound o be 4.2 mm
2
/s ha was no eached by RO a any in es iga ed
T
L
and eached by LHO a T
L
= 55 °C.
The SCA esul s show ha he a ia ion in he in es iga ed anges is
ela i ely small. D and LHO showed 5.27° and 5.38°, espec i ely, while
i was 6.22° o RO, which is ela ed o he signi ican d op in i s
iscosi y wi h p ehea ing, discussed in Subsec ion 3.2. The a ia ion o
SCA o W was only 3.6°. The measu emen esul s o W a 85 °C show a
dec ease a all p
g,
which is agains he o he ends, and he ma e ial
p ope ies do no jus i y his phenomenon. Also, his T
L
is well below
he boiling empe a u e; hence, local s eam o ma ion in he p ehea ing
chambe can be excluded. Mo eo e , SCA a ied ma ginally wi h p
g
unlike in he case o he o he liquids and lowe T
L
o W a omiza ion.
Since his obse a ion equi es signi ican ly deepe , highly ocused
u he in es iga ions, he measu emen esul s o W we e e alua ed
only up o 70 °C.
3.2. P ima y je b eakup isualiza ion
The p ima y b eakup o liquid je s is shown in Fig. 7 a T
L
= 25 and
100 °C – excep o W whe e he uppe limi was 90 °C, and a p
g
= 0.3,
0.9, and 2.4 ba . The p omp ly expanding a omizing ai is esponsible
o he dispe sion o he d ople s in he adial di ec ion, which e ec is
g ea ly enhanced by he highly u bulen ai je ha b ings chao ic
mo ion ha also sp eads he d ople s in all di ec ions. The o al disin-
eg a ion leng h o D je is he g ea es a all condi ions, which is no
accompanied by no able ligamen o ma ion. This seems he mos sig-
ni ican di e ence be ween his and o he liquid ypes and being he
eason o smalle SCA, shown in Fig. 6. Since he icini y o he nozzle
has a lowe d ople popula ion, he iny d ople s a e less likely o sp ead
a a la ge angle. A p
g
= 2.4 ba and T
L
= 100 °C, D disin eg a ion is
apid, and he ansi ion be ween he liquid je co e and he ine d o-
ple s is no isible. The b eakup o liquid packe s is he ca as ophic
ype o all liquids unde hese condi ions.
Rega ding liquid iscosi y, densi y, and su ace ension, LHO lies
be ween D and RO. Mo e speci ically, i s ma e ial p ope ies a
T
L
= 100 °C closely ma ch ha o D a 25 °C, and LHO a 25 °C beha es
simila ly as RO a 100 °C [27] which is also obse able in he co e-
sponding images as he b eakup mode closely ma ches. The di e ence
in Oh o D a 25 °C and LHO a 100 °C is 5% while i is 12.5% in We
A
ha also sugges s a simila beha io . By compa ing LHO a 25 °C and
RO a 100 °C, Oh is hal ed and he 12.5% di e ence in We
A
emains.
This esul complies wi h he Oh-We
A
simila i y condi ion p oposed by
Fae h e al. [28], men ioned ea lie . By e alua ing LHO a iden ical
condi ions o D and RO, i is cha ac e ized by mode a e ligamen o -
ma ion, and he liquid je b eakup leng h also lies be ween he wo
liquids.
The ligamen o ma ion is mos spec acula in he case o RO a
p
g
= 0.3 ba and T
L
= 25 °C, whe e he liquid iscosi y is he highes .
This p ocess is also obse able a ele a ed p essu es. Ne e heless, a
T
L
= 100 °C, he ligamen s a e only isible a p
g
= 0.3 ba wi h sig-
ni ican ly smalle sizes. The liquid sp eading is high due o he in ense
ligamen o ma ion, leading o he highes SCA alues in he
Fig. 8. The ela i e de ia ion o Eq. (20) in pe cen age a each measu emen poin .
A. U bán, e al. Fuel 277 (2020) 118197
8
in es iga ed pa ame e ange. The high iscosi y o RO is clea ly isible
since all he o ming liquid ac ions a e signi ican ly la ge han in he
case o o he liquids.
The ca as ophic je b eakup p ocess is bes isualized in he case o
W, which also shows e y small ligamen s a all condi ions due o he
high su ace ension alue while iscosi y is low, also meaning low Oh.
The liquid packe s a e la ge in he wake o he liquid je , which un-
de goes u he b eakup downs eam. The wa e d ople s show mo e
in ense sp eading in he icini y o he nozzle, and he e ec o T
L
is
low, as i was shown in Fig. 6. E en hough We o W a ele a ed p
g
ma ches ha wi h he o he liquids, Oh is one magni ude lowe han
ha o D and wo magni udes lowe han ha o RO. This answe s why
i s p ima y b eakup signi ican ly di e s om ha o o he liquids.
SCA es ima ion based on he high-speed came a images is no pos-
sible since he sp eading o he sp ay is delayed a highe p
g
; only a
sligh ly dis u bed s aigh wo-phase je is isible. E en hough he
gene a ed iny d ople s a e isible, hei sp eading is only obse able a
a highe downs eam dis ance. The images show only 8 d
0
, while i was
concluded based on he global sp ay images ha 60 d
0
is a su icien
dis ance o ha e a ully de eloped SCA.
3.3. De i ing an empi ical co ela ion o SCA
Upon de e mining he ele an non-dimensional numbe s, discussed
in Subsec ion 2.3, he o mula ion o he empi ical co ela ion is he
nex ask. Since wo p incipal pa ame e s we e a ied, p
g
and T
L
, he
inal SCA o mula is abou o be de e mined in he o m o Eq. (19):
=SCA A N N· · B
12
(19)
whe e Aand Ba e cons an s, and N
1
and N
2
a e wildca d non-dimen-
sional numbe s. This o m was de i ed by analyzing he SCA co ela-
ions o o he a omize ypes [4] and conside ing he powe law e ec
o p
g
on SCA, which is ep esen ed by N
2
.N
1
s ands o he inclusion o
he e ec o liquid p ehea ing. Since he numbe o cons an s is equal o
he numbe o a ying pa ame e s, o he o mulae wi h mo e deg ee o
eedom would lead o o e i ing. This ex ension is only could be done
i he numbe o pa ame e s is inc easing, e.g., by adjus ing he a o-
mize geome y, liquid mass low a e, e c., which would lead o an
excessi e numbe o measu emen poin s. To o e come his issue, he
design o expe imen s me hod can be used, which was success ully
applied by Chen e al. [29] o SMD de e mina ion. Howe e , his
echnique only can wo k e icien ly i he shape o he equa ion is well-
es ablished; hence his pape only aims o p o ide an adequa ely
shaped o mula, and i s ex ension is he nex s ep in his esea ch.
Fi s ly, an R
2
analysis was pe o med, subs i u ing N
1
wi h
T
~
L
,
~
L
,
~
L
,
µ
~
L
,
~
, and Oh and N
2
wi h
T
~
A
,
~
A
,
~
A
,
µ
~
A
,ALR, Ma, Re, We, and
MFR. The Aand Bcoe icien s we e de e mined simul aneously by
using he GlobalSea ch algo i hm in Ma lab, based on he SCA–p
g
e-
sul s a a ious T
L
and liquids. Since
~
L
was he bes -pe o ming non-
dimensional numbe o N
1
, he candida es o N
2
a e p esen ed in
Table 2 by ixing N
1
a
~
L
. In addi ion o R
2
,SSE, and ela i e s anda d
de ia ion o he A cons an , S
,A
, a e also p esen ed. Since S
o B was
al eady low in all he cases, his pa ame e was omi ed om Table 2.
By conside ing only R
2
,
T
~
A
is he bes non-dimensional numbe can-
dida e o N
2
, closely ollowed by
~
A
. Howe e , bo h o hem a e
cha ac e ized by high SSE and S
,A
. Conside ing all he pa ame e s, ALR
is he bes choice, ollowed by Ma and MFR. The es o he non-di-
mensional numbe s showed high SSE o S
,A
, hence hey a e disca ded.
This la e pa ame e e e s o ha e en hough he i ing o Eq. (19)
can be pe o med by achie ing high R
2
alues, A a ies signi ican ly
wi h he ope a ing condi ion.
Table 3 summa izes some o he es combina ions which did no
wo k, p esen ing he esul s only o D.
=N~
L
1
was ixed in he i s
h ee cases, and hen he emaining non-dimensional pa ame e s o N
1
we e e alua ed wi h all ALR, Ma, and MFR, which we e pe o med
excellen ly o N
2
, shown in Table 2. E en hough high R
2
alues could
be achie ed in se e al cases, SSE and S
,A
show ha hese pai s a e
inapp op ia e o SCA es ima ion.
To e alua e he app op ia eness o he concluded N
1
and N
2
non-
dimensional numbe s in Eq. (19), bo h Aand B alues we e pe u bed
by 1% in bo h posi i e and nega i e di ec ions while he o he one was
ixed. The eason behind his was he ollowing. Equa ion (19), he
model, has wo a iables, while wo pa ame e s, T
L
and p
g
, we e a ied.
Hence, a wide ange o N
1
and N
2
can be used wi h an accep able i
quali y. Howe e , i is expec ed ha he p esen ly app oxima ed and
unknown equa ion o SCA de e mina ion should no a y much when
ei he Ao Bcons an is sligh ly al e ed due o, e.g., measu emen e o .
In o he wo ds, a good app oxima ion o SCA es ima ion should show
low sensi i i y o he model and measu emen unce ain ies. To quan-
i y his sensi i i y, he esul ing SSE is compa ed o he o iginal alue
in pe cen age, shown in Table 4. The less he inc ease, he mo e obus
he gi en o m o Eq. (19) is.
I can be concluded ha he a ia ion o Bhas a signi ican ly lowe
impac on he inal esul han A. Besides he excellen ly pe o ming
ALR, Ma, and MFR,
T
~
A
was also included since i s pe o mance app oach
ha o he o he h ee non-dimensional numbe s, e en hough i s o i-
ginal SSE was no ably highe , shown in Table 2.
Following he ul ima e goal o his pape , i.e., de e mining an em-
pi ical co ela ion ha adequa ely es ima es SCA o plain-je ai blas
a omiza ion in a wide ange o condi ions, he liquid densi y a io, and
ALR p o ided he bes i , shown by Eq. (20):
=SCA A ALR· ·
L
B
(20)
He e, ALR is p ima ily esponsible o desc ibing he a ia ion in p
g
.
~
L
inco po a es he e ec o liquid p ehea ing and is ee om he
e ec o he a omizing ai . The liquid-dependen cons an s in Eq. (20)
a e summa ized in Table 5 o bo h Ma and MFR besides ALR. These
o he wo non-dimensional numbe s can be used i a ellow esea che
would like o ex end he alidi y o Eq. (20) and ALR ails o pe o m
well. I Eq. (20) would be he pe ec model o SCA es ima ion, hen all
cons an s would ma ch. No e ha a uni ied model was es ed; howe e ,
i was omi ed due o he excessi e de ia ion exceeding 100%. The
ma ching o he cons an s is ul illed in he case o LHO and RO, which
o he wise showed simila beha io in all he p e ious in es iga ions.
Howe e , he exponen o W is la gely di e en , p obably due o he
e y low Oh numbe s, which we e no achie able by he o he liquids.
In ligh o his condi ion, i is an unexpec ed esul ha i s SCA a ied in
a simila ange han ha o LHO and RO. This migh change i , e.g., he
ambien p essu e a ies. The physical p ope ies o LHO a e close o
hose o D; howe e , he gene ally smalle SCA o D esul ed in 20%
lowe A alues while Bis close o ha o LHO and RO. Consequen ly,
he p esen physical model is no liquid-independen bu can be ex-
ended by u he sys ema ic s udies.
Fig. 8 shows he de ia ion be ween he measu ed and es ima ed SCA
o all liquids, using Eq. (20). The de e mined 3.5% maximum de ia ion
is an accep able esul , meaning 1° in SCA. The de ia ion in he ex-
pe imen s o Gi en and Mu aszew [30] o a p essu e-swi l a omize
was 5%, which is o en conside ed as a e e ence in he li e a u e o SCA
es ima ion. E en hough hese alues could be u he educed by using
ad anced measu emen and e alua ion echniques, conside ing he
manu ac u ing ole ances and he sligh ly a ying condi ions in p ac-
ical sys ems, his esul mee s he equi emen s o common indus ial
p ac ice.
4. Conclusions
Plain-je ai blas a omiza ion o wa e (W), diesel oil (D), ligh
hea ing oil (LHO), and c ude apeseed oil (RO) was in es iga ed in an
a mosphe ic es ig a a ious a omizing gauge p essu es, p
g
, and liquid
p ehea ing empe a u es, T
L
. The inal goal o his pape was o de i e
A. U bán, e al. Fuel 277 (2020) 118197
9