E ec o liquid p ehea ing on high- eloci y ai blas
a omiza ion: F om wa e o c ude apeseed oil
URBÁN, A.; MALÝ, M.; JÓZSA, V.; JEDELSKÝ, J.
Expe imen al The mal and Fluid Science
2019, ol. 102, Ap il 2019, pp. 137-151
ISSN: 0894-1777
DOI: h ps://doi.o g/10.1016/j.exp he m lusci.2018.11.006
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.exp he m lusci.2018.11.006
Final e sion a ailable om h ps://www.sciencedi ec .com/science/a icle/pii/S0894177718314377
dspace. u b .cz
E ec o liquid p ehea ing on high- eloci y ai blas a omiza ion: om
wa e o c ude apeseed oil
And ás U bána, Milan Malýb, Vik o Józsaa, Jan Jedelskýb
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
Abs ac
Ai blas a omiza ion is a sui able model pla o m o unde s and a omiza ion physics since
he a omize geome y has an insigni ican in luence on he sp ay o ma ion. Besides i s
heo e ical ele ance, his con igu a ion is used in se e al p ac ical applica ions anging
om heal hca e o combus ion. P esen ly, a plain-je ai blas a omize has been
in es iga ed expe imen ally unde a mosphe ic condi ions a a ious a omizing p essu es
and liquid p ehea ing empe a u es. To co e a wide ange o liquids by iscosi y and
su ace ension, wa e , diesel oil, ligh hea ing oil, and c ude apeseed oil we e a omized
o e alua e he d ople size- eloci y co ela ions when he sp ay is ully de eloped.
Inc easing he empe a u e o high- iscosi y liquids p io o a omiza ion imp o es he
sp ay cha ac e is ics un il hei kinema ic iscosi y dec eases o a ce ain alue ha is
newly in oduced as a limi ing iscosi y. Fu he p ehea ing has a ma ginal e ec on
d ople size- eloci y plo s, and he sp ay becomes mo e homogeneous. Se e al SMD-
es ima ing o mulae we e analyzed and imp o ed o conside he e ec o liquid
p ehea ing and o ex end hei ange o alidi y. When he kinema ic iscosi y exceeded
he limi ing iscosi y, he pa con aining he Webe numbe was co ec ed linea ly by he
p ehea ing empe a u e. The coe icien o he Ohneso ge numbe was co ec ed by he
in e se o he kinema ic iscosi y, wi hou conside ing he limi ing iscosi y. The abo e
esul s help o co ec he SMD o a mosphe ic measu emen s o ele a ed liquid
empe a u es and o con ibu e o ad anced a omiza ion models o nume ical so wa e.
Keywo ds: ai blas a omize ; SMD; PDA; apeseed oil; ligh hea ing oil; p ehea ing
Nomencla u e
La in le e s
a
Speed o sound, m/s
A, B, C, E, F, G, H, I, J, K, L, M
Expe imen al pa ame e s
ALR
Ai - o-liquid mass low a io, –
D
D ople diame e , µm
d, d0
Cha ac e is ic size, mm
EFR
Ene gy lux a e, –
ISMD
meas
Measu ed in eg al SMD, µm
l
Dimension o measu emen olume, mm
m
Mass low a e, kg/s
Ma
Mach numbe , –
MFR
Momen um lux a e, –
Oh
Ohneso ge numbe , –
p
g
A omiza ion gauge p essu e, ba
R2
Coe icien o de e mina ion, –
Re
Reynolds numbe , –
SMD
Sau e mean diame e , µm
SMD
calc
Calcula ed SMD, µm
p
P ehea ed liquid empe a u e, °C
Re e ence empe a u e, °C
u
Veloci y, m/s
We
Webe numbe , –
z
Axial dis ance, mm
G eek symbols
µ
Dynamic iscosi y, kg/(m∙s)
ρ
Densi y, kg/m
3
σ
Su ace ension, N/m
υ
Kinema ic iscosi y, mm2/s
υ
l,lim
Limi ing iscosi y o he liquid, mm2/s
Abb e ia ions
D
Diesel
GA
Gene ic algo i hm
LHO
Ligh hea ing oil
PDA
Phase Dopple Anemome y
RO
Rapeseed oil
ScS
Sca e Sea ch
W
Wa e
Subsc ip s
a
Ai
l
Liquid
Rela i e
x, y, z
p ojec ion in he XYZ coo dina e sys em
1. In oduc ion
Plain-je ai blas a omiza ion, in es iga ed in he p esen pape , is an excellen model
pla o m o be e unde s and he a omiza ion phenomena. Besides i s heo e ical ele ance, i is
widely used in nume ous ields om heal hca e [1] h ough hea ans e enhancemen [2] o
combus ion [3]. Ou mo i a ion comes om he las example since he e is a echnological push
o eplace ossil uels wi h enewable ones o achie e a sus ainable economy [4]. None o he
enewable-based uels has u ned o be dominan in he pas decades [5]; ne e heless, u ilizing
he locally a ailable ones is usually a easonable choice. Hence, liquid uel combus ion
in es iga ions wi h bo h long-chained hyd oca bons, like c ude apeseed oil [6] and ligh uels,
like aqueous e hanol [7], we e pe o med ea lie . The ci ed pape s use an a omize simila o he
cu en ly in es iga ed one. Du ing he e alua ion o c op-o igina ed uels, hei impac on ood
secu i y should i s ly be aken in o accoun [8]. Compa ing a ious enewable uels and
echnologies is c ucial o decision making o selec he bes candida e and u ilize i mos
e icien ly. Fo his pu pose, he e hanol equi alen is a easonable basis since he p oduc ion,
and hence he ene gy balance o e hanol is well-known [9].
A omiza ion was in ensi ely in es iga ed a ound he 1980s [10], p incipally in es iga ing
wa e , ke osene, diesel oil, and a ious oil sp ays a ambien empe a u e [11]. A ha ime, he
e ec s o a omizing ai empe a u e and ope a ing p essu e we e in ocus due o he ma ke pull
by he gas u bine indus y [12]. Due o he a ailable measu emen echnology a ha ime, he
semi-empi ical es ima ions o he a e age d ople size we e limi ed o 100 m/s ai discha ge
eloci y in he case o ai blas a omize s [13]. In combus ion applica ions, he d ople s ha e o
e apo a e p io o he lame on . Hence, he olume- o-su ace diame e (D32) o Sau e Mean
Diame e (SMD) is de e mined ins ead o o he a e age diame e ypes. This is de ined as
ollows:

𝑆𝑆𝑆𝑆𝑆𝑆=∑𝑆𝑆𝑖𝑖3
𝑖𝑖/∑𝑆𝑆𝑖𝑖2
𝑖𝑖, (1)
whe e Di is he diame e o a single d ople a a single measu emen poin . I was discussed in
ou p e ious wo k [14] ha he sugges ed o mula o Le eb e [10], de ailed a i s in Sec ion 2,
es ima ed he SMD mos accu a ely. Ne e heless, he in es iga ed ai discha ge eloci y ange
was 200–500 m/s in ou case, which a exceeds he o iginal alidi y ange o 10–120 m/s.
Injec ion o ligh uels a ambien empe a u e is usually adequa e o e icien
combus ion. Howe e , a ious long-chained oils – which ha e an eme ging ele ance as
enewable uels – need p ehea ing [15]. Wang and Le eb e [16] discussed he e ec o uel
p ehea ing, emphasizing ha i educes he SMD and i s e ec seems independen o he ambien
p essu e. The esea che s published plain measu emen esul s and pe o med no s a is ical
e alua ion o compa ison wi h he es ima ed SMD. Mo e ecen ly, Shah and Ganesh [17]
measu ed he ele an empe a u e-dependen p ope ies o ka anj oil, which is a s aigh
ege able oil ype. The esea che s di ec ly pu he measu emen da a in o an SMD-es ima ing
equa ion, bu he expe imen al alida ion o he esul s was no discussed. Hanna and Zoughaib
[18] expe ienced a empe a u e change o he a omized comp esso lub ican oil. Howe e , hey
did no con ol he injec ion empe a u e sys ema ically, and he measu emen s we e limi ed o
he ange o 11–27 °C. Fuel p ehea ing in in e nal combus ion engine was pe o med by Pa k e
al. [19], leading o a simila esul as ha o Wang and Le eb e. The p esen pape ocuses on
he a mosphe ic empe a u e-dependen sp ay cha ac e is ics o he ollowing model liquids o
co e a ela i ely wide ange o iscosi y, which is one o he no el ies o he p esen pape .
A omiza ion o dis illed wa e (W), s anda d diesel oil (D, EN 590:2014), ligh hea ing oil (LHO),
and c ude apeseed oil (RO) we e in es iga ed in he liquid p ehea ing empe a u e ange o 25–
100 °C which pa ially co e s, e.g., he he mal s abili y ange o he py olysis oils as well [20–
22]. These empe a u e limi s o he ou liquids allows he in es iga ion o a wide physical
pa ame e ange. I.e., o liquid iscosi y, i co e s mo e han wo magni udes. The co esponding
measu ed liquid p ope ies a e summa ized in Appendix A. A key issue in many o he empi ical
co ela ions published o da e is ha hey a e gene ally only es ed on simple uels o e a e y
na ow ange o physical p ope ies, he e o e making co ela ions o da e o limi ed use. Hence,
he esul ing wide non-dimensional space allows he e-assessmen o he exis ing empi ical
co ela ions, which is he p incipal goal o he p esen pape .
The scien i ic ele ance o a mosphe ic measu emen s is o en ques ioned by esea che s
since he ope a ing p essu e o e.g. gas u bines is se e al ens o ba s [23]. I was shown by
Zheng e al. [24] ha SMD a ies sligh ly up o 12 ba in a gas u bine combus ion chambe .
Chigie [3] highligh ed ha he engine s a up – when a omiza ion occu s a educed p essu e –
is he mos c i ical phase. Then, ope a ion cha ac e is ics, including lammabili y limi s and uel-
ai mix u e quali y a he lame on , s a o imp o e.
Nukiyama and Tanasawa [25], he i s sys ema ic in es iga o s o ai blas a omiza ion,
poin ed ou ha he mean d ople diame e depends on su ace ension, densi y, luid iscosi y,
olume low a es o ai and liquid, and he ela i e eloci y be ween he wo phases. The
go e ning dimensionless numbe s o ai blas a omiza ion a e Reynolds numbe (Re), Webe
numbe (We), Ohneso ge numbe (Oh), and ai - o-liquid mass low a io (ALR), de ined by Eqs.
(2)–(5):
𝑅𝑅𝑅𝑅=𝑢𝑢𝑟𝑟∙𝑑𝑑∙𝜌𝜌/𝜇𝜇, (2)
𝑊𝑊𝑅𝑅=𝑢𝑢𝑟𝑟2∙𝑑𝑑∙𝜌𝜌/𝜎𝜎, (3)
𝑂𝑂ℎ=𝑊𝑊𝑅𝑅0.5/𝑅𝑅𝑅𝑅=𝜇𝜇/(𝜎𝜎∙𝑑𝑑∙𝜌𝜌)0.5, (4)
𝐴𝐴𝐴𝐴𝑅𝑅=𝑚𝑚𝑎𝑎/𝑚𝑚𝑙𝑙, (5)
whe e u is he ela i e eloci y be ween he ai and he liquid, d is a cha ac e is ic size, ρ is he
densi y, µ is he dynamic iscosi y, σ is he su ace ension, and m is he mass low a e. a and l
subsc ip s e e o ai and liquid, espec i ely. La e on, i Re o We ecei e an A o L subsc ip ,
he equa ions e e o he luid used o he densi y and dynamic iscosi y calcula ion.
Non-in usi e sp ay measu emen s can be pe o med by bo h imaging and non-imaging
op ical echniques [11]. Fo size cha ac e iza ion, he Phase Dopple echnique is used mos
widely. In pa allel, high-speed imaging is usually applied o quali a i e analysis [26,27]. The
p esen s udy is p ima ily ocused on he esul s o Phase Dopple Anemome y (PDA)
measu emen s.
Full simula ion o a omiza ion in a p ac ical combus ion chambe is un easible a he
p esen ime since he con ol olume o one li e would equi e ~1020 cells. Such a de ailed mesh
is necessa y o acking liquid ac ions down o one µm by he Eule ian app oach. Howe e ,
he e a e spec acula esul s achie ed ecen ly by he PAMELA so wa e code [28] o p e ilming
ai blas a omize s; i s applica ion in enginee ing p ac ice equi es he addi ional e inemen and
de elopmen o be ex ended o o he a omize ypes. Ne e heless, he p ima y liquid b eakup
in h ee dimensions can be modeled wi h he p esen compu a ional capabili ies [29–31].
A omiza ion simula ion in a mixed Eule ian-Lag angian space is common in compu a ional luid
dynamics so wa e codes [32]. This app oach is cha ac e ized by se e al magni udes lowe
compu a ional ime as he mesh size can be signi ican ly smalle . Howe e , he co esponding
models s ongly ely on empi ical o mulae [32]. Hence, imp o ing hese models h ough
analyzing he esul s o sys ema ic measu emen s has a no able impo ance e en oday.
Consequen ly, he p esen pape p o ides he analysis o measu emen da a in a wide pa ame e
ange o enhance hese a omize models and p o ide a mo e ealis ic pe o mance in enginee ing
applica ions. I.e., he p esen esul s acili a e he a omiza ion modeling o e.g. ypical liquid uels
om c ude ege able oil o ligh uels.
Concluding om he abo e indings, he e ec o liquid p ehea ing on a omiza ion
cha ac e is ics has bo h heo e ical and p ac ical ele ance. The e o e, he p incipal aim o his
wo k is o analyze quan i a i ely he global and local sp ay cha ac e is ics o a ious liquids
a omized by an a mosphe ic plain-je ai blas a omize . The high ai discha ge eloci ies wi h he
p ehea ing empe a u e ange o 25–100 °C o ou liquids (W, D, LHO, and RO) inco po a e a
wide non-dimensional pa ame e ange, summa ized in a abula o m in he end o Sec ion 3.
The e o e, e-assessmen o he exis ing SMD-es ima ing o mulae – e iewed in Sec ion 2 – is
discussed wi h he inclusion o he e ec o liquid p ehea ing.
2. Re iew o SMD-es ima ing o mulae o ai blas a omiza ion
This sec ion e iews six di e en empi ical and semi-empi ical o mulae o es ima ing
SMD, which we e de i ed om op ical measu emen s. Each con ains a leas one empi ical
pa ame e o be de e mined by a i ing me hod, which is las ly discussed.
2.1. SMD-es ima ing o mulae
P e ious empi ical eg ession analyses lead o he conclusion ha SMD is p ima ily
go e ned by We, Oh, and ALR, o plain-je ai blas a omize s which we e discussed by se e al
esea che s [11,13,23]. Equa ion (6) shows he mos widely used equa ion o ai blas
a omiza ion, p incipally de i ed o he p e ilming ype [10]:
𝑆𝑆𝑆𝑆𝑆𝑆=𝑑𝑑0(1 + 1/𝐴𝐴𝐴𝐴𝑅𝑅)(𝐴𝐴∙𝑊𝑊𝑅𝑅𝑎𝑎𝐶𝐶+𝐵𝐵∙𝑂𝑂ℎ𝑙𝑙𝐸𝐸),(6Chyba! Záložka není
used wi h a lens o 112 mm diame e . The ocal leng h was 310 and 500 mm o he ansmi ing
and he ecei ing op ics, espec i ely. The hal -in e sec ion angle be ween he lase beams was
se o 6.92°. Dimensions o he measu emen olume we e lx = 0.60 mm, ly = 0.072 mm, lz =
0.073 mm, acco ding o he coo dina e sys em in Fig. 2. A spa ial il e wi h a sli size o 0.1 mm
was used o educe he lx dimension o he measu emen olume. The sca e ing angle was se o
B ews e ’s angle, 68° [53].
The measu ed signals we e p ocessed by he BSA P80 low and he pa icle p ocesso
and isualized by BSA Flow So wa e 5.2. The modula ins umen was con igu ed o he
measu emen in he dense sp ay con aining small d ople s. The d ople eloci ies no ably a ied
in space and we e sensi i e o he inle condi ions. Hence, he sys em pa ame e s we e se
indi idually o di e en inle p essu es and axial dis ances om he a omize nozzle.
The maximum d ople size o measu e was se o 64.1 μm wi h a size esolu ion o ±0.05
μm and unce ain y o ±0.5 μm. The pa icle e ac i e index was se o 1.45 o all oils and 1.33
o wa e . The axial and adial eloci y ange was se om 0–64 m/s o 0–144 m/s and 0–46 m/s
o 0–98 m/s, espec i ely, conside ing he e ec s o axial dis ance om he a omize nozzle and
he a omizing p essu e on he maximum d ople eloci y. Fo his eason, he eloci y span was
se om 128 m/s o 192 m/s. The eloci y esolu ion was 0.002%, and he unce ain y was less
han 1% o he selec ed ange. The PDA sys em was se o acqui e 40,000 indi idual pa icles o
measu e o 15 seconds in he low-densi y egions. Acco ding o he p elimina y esul s (no
shown he e), he sp ay was ound o be axisymme ic.
The expe imen al a mosphe ic es ig is shown in Fig. 3. The a omizing ai was aken
om he cen al comp essed ai sys em h ough a p essu e egula o ollowed by a mass low
me e owa ds he a omize . The ollowing a omizing gauge p essu es, pg, we e in es iga ed: 0.3,
0.6, 0.9, 1.2, 1.8, and 2.4 ba . The lowes alue was selec ed based on he c i e ia o s able

combus ion in he ho es cases – wi hou sp ay measu emen – [50,54]. A p essu ized ank was
used o eed he liquids in o he a omize wi hou luc ua ion. A con ol al e and a Co iolis mass
low me e Mass 2100 Di3 i ed wi h he Mass 6000 ansmi e (Siemens AG, GE) we e applied
o se a cons an 0.35 g/s liquid mass low a e wi h an accu acy o ±0.1% o he ac ual low a e.
A o ame e was also ins alled in o he eed pipe o isual checking. Bo h liquid and a omizing
ai lines we e equipped wi h piezo- esis i e p essu e ansduce s DMP 331i (BD SENSORS
s. .o., CZ) and B class P 100 esis ance he mome e s. The unce ain y was 2 kPa and 0.3 °C in
he p essu e and empe a u e sensing, espec i ely. The esul ing ALR ange o all measu emen s
was 0.78–2.07.
Fig. 3. Liquid and a omizing ai supply lines and hei ins umen a ion o he expe imen al es ig.
The liquid p ehea e was con olled by a PID uni made by HAGA K . using a
empe a u e con ol signal o a P 100 esis ance empe a u e de ec o . A o oidal ans o me was
used o se he hea ing powe o he PID con ol o a oid ou le empe a u e oscilla ions. The
ollowing p ehea ing empe a u es, p, we e in es iga ed o D, LHO, and RO: 25, 40, 55, 70 and
100 °C. W is an excep ion om his se ies since he maximum empe a u e was 90 °C o a oid
boiling, bu he lowe ps we e he same. The ele an physical p ope ies o he liquids and hei
measu emen me hods we e p esen ed in Appendix A.
The PDA measu emen s we e ca ied ou a h ee axial dis ances downs eam o he
nozzle, z = 20, 40 and 60 mm, wi h i een equally spaced adial poin s along X and Y axes a z =
60 mm, hi een a z = 40 mm and se en een a z = 20 mm. A z = 20 mm, he s ep was 1 mm
be ween he poin s and 2 mm a z = 40 and 60 mm. Based on he analysis o he p e ious
measu emen esul s, he z < 20 mm egime was la e ejec ed [14] as d ople eloci ies close o
he nozzle exceed he limi a ions o PDA (~300 m/s). Based on he esul s o ou p e ious s udies,
z = 60 mm was ound o be a su icien downs eam dis ance o ensu e a ully de eloped, s able
sp ay ha was sui able o ISMD calcula ion.
Besides he men ioned dimensionless numbe s, de ined by Eqs. (2) – (5), he momen um
lux a e, MFR, ene gy lux a e, EFR, and Mach numbe , Ma, a e also key pa ame e s o ai blas
a omiza ion. They a e de ined by Eqs. (13) – (15):
𝑆𝑆𝐹𝐹𝑅𝑅=𝜌𝜌𝑎𝑎∙𝑢𝑢𝑎𝑎
2/(𝜌𝜌𝑙𝑙∙𝑢𝑢𝑙𝑙2), (13)
𝐸𝐸𝐹𝐹𝑅𝑅=𝜌𝜌𝑎𝑎∙𝑢𝑢𝑎𝑎
3/(𝜌𝜌𝑙𝑙∙𝑢𝑢𝑙𝑙3), (14)
𝑆𝑆𝑀𝑀=𝑢𝑢𝑎𝑎/𝑀𝑀, (15)
whe e a is he speed o sound. All he men ioned dimensionless numbe s, including Re and We
o bo h ai and liquid phases a e summa ized in Table 3 o show he ange o in es iga ed cases.
Table 3. In e als o he in es iga ion anges o he liquids.
D
LHO
RO
W
pg [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
Rea [-]
min.
8969
8974
8979
8994
max.
30037
30047
30058
30075
Rel [-]
min.
22749452
5035776
1565911
91217176
max.
115408537
51798814
21023241
380150588
Wea [-]
min.
988.4
792.5
730.6
289.7
max.
9549
4640
5014
1982
Wea [-]
min.
655242
550332
531391
228328
max.
4638184
2346382
2626442
1157407
Oh [-]
min.
0.019
0.029
0.077
0.0028
max.
0.036
0.147
0.465
0.0052
Ma [-]
min.
0.62
0.62
0.62
0.62
max.
1.45
1.45
1.45
1.45
MFR [-]
min.
5.68
5.91
6.13
6.83
max.
31.7
33.23
34.8
37.7
EFR [-]
min.
342.2
370.9
398
494.7
max.
4011
4401
4828
5667
ISMD/d0 [-]
min.
0.0216
0.0218
0.0278
0.0244
max.
0.0652
0.0656
0.0671
0.0691
4. Resul s and discussion
Fi s ly, his sec ion ocuses on he d ople size- eloci y co ela ion a a ious pg and p o
e alua e single measu emen poin s o all ou liquids. Secondly, he empe a u e-dependen
cha ac e is ics o SMD es ima ing o mulae a e discussed and adjus ed o i he e ec s o
p ehea ing empe a u e. Hence, he go e ning pa ame e s we e iden i ied and included in he
expe imen ally de e mined cons an pa ame e s.
4.1. D ople size- eloci y co ela ions
The liquid je is dis up ed by he shea e ec o he lowing gas, and he newly c ea ed
liquid ac ions a e u he accele a ed, which leads o he o ma ion o ligamen s; hese hen
b eak up in o smalle d ople s. The la ge d ople s, accele a ed by he a omizing ai nea he
nozzle, ypically lose hei momen um slowe han he su ounding gas je . Hence, i leads o a
e e se momen um exchange be ween he gas and liquid phases downs eam, which is called
o e shoo ing [14,55].
Figu es 4–7 show ypical adial-axial eloci y sca e plo s a selec ed a omiza ion gauge
p essu es and liquid empe a u es o all ou liquids a he cen e , and z = 60 mm o he ully
de eloped sp ay. The esul s o he nea ield can be ound in ou p e ious wo k [14] and a e no
discussed he e since he esul s we e qui e simila . Now he ocus is on he e ec s o liquid
p ehea ing on he sp ay a only h ee p and pg. The es o he cases ollowed he same end.
No e ha he loga i hm o he d ople diame e gi es he base o colo ing o help dis inguishing
a ious sizes and hence cha ac e is ics.
A d ople eloci y has a dominan axial componen while he adial componen emains
ela i ely low wi h dec easing a omizing p essu e. The swi l componen was below 10 m/s e en
a high a omizing p essu es. Since he used PDA measu es wo pe pendicula eloci y
componen s simul aneously, he swi l eloci y was omi ed in he sys ema ic analysis. As o he
axial eloci y dis ibu ion, he esul s ollow a simila end; in gene al, he la ge d ople s ha e
a highe eloci y. Howe e , he adial componen s end o inc ease e enly wi h he a omizing
p essu e o all d ople s. A p = 100 °C and pg = 1.8 ba , he majo i y o d ople s in he sp ay a e
smalle han 20 µm, and he d ople size ange is na ow. As he sp ay de elops, he smalle
d ople s lose hei momen um as e , clea ly showing he phenomenon o o e shoo ing.
Fig. 4. Size- eloci y co ela ion a x = y = 0 mm and z = 60 mm in he case o diesel oil (D) a a ious p and pg.
Fig. 5. Size- eloci y co ela ion a x = y = 0 mm and z = 60 mm in he case o ligh hea ing oil (LHO) a a ious p
and pg.

Fig. 6. Size- eloci y co ela ion a x = y = 0 mm and z = 60 mm in he case o apeseed oil (RO) a a ious p and
pg.
Fig. 7. Size- eloci y co ela ion a x = y = 0 mm and z = 60 mm in he case o wa e (W) a a ious p and pg.
The d ople eloci y a ia ion, including bo h uz and uy componen s, is p incipally
go e ned by pg; liquid ype and p ha e a smalle e ec on i . Howe e , in he case o he high-
iscosi y LHO and RO, he plo s signi ican ly di e om D and W. This e ec is u he
suppo ed by he ac ha only small d ople s ea u e he same eloci y sca e as i is in he D
and W cases. The medium-sized d ople s a e concen a ed on he ho izon al axis while he la ge
d ople s a e cha ac e ized by a simila sca e compa ed o D and W. The sca e o LHO a
empe a u e o 100 °C becomes simila o ha o he low iscosi y liquids. Ne e heless, RO did
no achie e his s a e since i s iscosi y a 100 °C is 2.4 imes highe han ha o D a 25 °C.
Consequen ly, p ehea ing o LHO up o 70 °C and abo e, discussed in subsec ion 4.2., leads o
simila a omiza ion cha ac e is ics as D. The poo a omiza ion cha ac e is ics o RO we e
indi ec ly iden i ied du ing he combus ion es s [6]. The liquid om he same shipmen – which
was used o a omiza ion measu emen s – was equi ed o be p ehea ed up o 150 °C o elimina e
he p esence o he bu ning d ople s in he lame.
O e all, he inc easing liquid empe a u e sligh ly educes he SMDs, as shown in Fig. 8a.
The inc eased a omizing p essu e smoo hens he d ople size dis ibu ion and makes i mo e
monodispe se, as shown in Fig. 8b. I can be concluded om he wo plo s ha a omizing p essu e
has a g ea e e ec on he sp ay size dis ibu ion han he liquid p ehea ing, as ine ial o ces
go e n he sp ay o ma ion o e iscous o ces unde he p esen ly in es iga ed condi ions. No e
ha a ich s a is ical analysis o he p esen da a on he size dis ibu ion in he sp ay will be
published in a successo wo k.
Fig. 8. E ec o a) p and b) pg on d ople size dis ibu ion o W a pg = 2.4 ba and p = 25 °C, espec i ely. The
applied bin size was uni o mly 1 µm.
4.2. The empe a u e dependence o he SMD-es ima ing o mulae
Figu e 9 shows ISMD o he measu ed da a a p = 25 °C and z = 60 mm o D and RO.
While Fig. 9a sugges s ha all he o mulae p o ide a easonably good es ima ion o SMD, Fig.
9b shows ha he e ec o iscosi y is poo ly ea ed in Eqs. (8) and (11). These a e he wo
ex eme examples whe e he liquid iscosi y was low (D) and high (RO) while he es o he
measu emen pa ame e s we e ma ched. Ne e heless, his ou come was e iden only in he la e
case since Oh is absen in Eq. (11). Concluding om he esul s, i was a gene al obse a ion
ha , when he liquid iscosi y was below ~4.3 mm2/s, all he o mulae p o ided a ai es ima ion
o ISMD, e en Eq. (11), whe e he e m con aining Oh is missing. This inding and he mode n
PDA sys em p o ide he answe why Kulka ni and Deshmukh [56] achie ed he bes es ima ion
o SMD in he case o ai blas a omiza ion o wa e by using Eq. (11).
Fig. 9. Fi ed SMD-es ima ing o mulae a p = 25 °C and z = 60 mm in he case o a) D and b) RO. No e he log-
log scales.
To e alua e he i quali y quan i a i ely, R2 alues we e summa ized in Table 4.
Equa ions (6a) – (7) ep esen a single ype o SMD-es ima ing o mulae. The exponen s in Eq.
(6a) we e no limi ed. Howe e , hei ypical alues we e in he [-5, 5] ange. To achie e as e
con e gence and mo e accu a e esul s, he exponen s in Eq. (6b) we e limi ed o his ange. No e
ha he equa ions we e i ed o he six measu ed p essu e poin s o a gi en liquid and p. Hence,
4
8
16
32
64
0,25 0,5 124
SMD [µm]
p
g
[ba ]
a) Meas. [D] Eq. 6a
Eq. 6b Eq. 6c
Eq. 6d Eq. 7
Eq. 8 Eq. 9
Eq. 10 Eq. 11
4
8
16
32
64
0,25 0,5 124
SMD [µm]
p
g
[ba ]
b) Meas. [RO] Eq. 6a
Eq. 6b Eq. 6c
Eq. 6d Eq. 7
Eq. 8 Eq. 9
Eq. 10 Eq. 11
590:2014 s anda d allows o he iscosi y o D as υl = 2–4.5 mm2/s, implying ha e en D should
be p ehea ed i i has a sligh ly highe iscosi y bu wi hin he allowed ange. This ou come is
agains he p ac ice since no commonly used diesel engine con ains a uel p ehea e o achie e
be e a omiza ion. Thi dly, he es ima ion o I o RO ailed. Howe e , his equa ion was
o iginally de i ed o low- iscosi y liquids, and he es ima ions wo k nea ly ine o he
emaining h ee liquids. The pa ame e J could be excellen ly co ec ed by he iscosi y; hence,
Fig. 12b shows a sa is ying esul .
Fig. 13. Tempe a u e dependence o K and L pa ame e s o Eq. (10) o all liquids.
Equa ion (10) was de i ed o high- iscosi y liquids. The e o e, pa ame e K is es ima ed
excellen ly e en o RO as shown in Fig. 13a. υl,lim = 4.85 mm2/s, which is simila o ha o Eq.
0
0,002
0,004
0,006
0,008
0,01
0,012
20 40 60 80 100
K[m0.55]
p
[°C]
a)
DLHO
RO W
D es . LHO es .
RO es . W es .
0
0,001
0,002
0,003
0,004
0,005
0,006
0,007
20 40 60 80 100
L[m0.6]
p[°C]
b) DLHO
RO W
D es . LHO es .
RO es . W es .

(7) and sligh ly highe han ha o Eq. (6d). Figu e 13b shows a good es ima ion o D and W
while pa ame e L is unde es ima ed in he case o LHO and RO. I migh be add essed o he
sligh ly di e en exponen s o Eq. (10) compa ed o Eq. (6d). O e all, in he dynamic e m, Eq.
(10) p o ides excellen i s; howe e , he ma e ial p ope y e m is less accu a ely es ima ed.
As o a summa y, Eq. (6d) u ned ou o be he mos accu a e equa ion o SMD
es ima ion which is ollowed by Eqs. (7) and (10). E en hough he p esen analysis con ained
a ious o mulae, i seems ha he equa ion s uc u e, sugges ed by Le eb e in 1980 [10], seems
o be he bes one o da e. Namely, SMD is go e ned by wo e ms, which should be summa ized:
he i s depends on he ecip ocal o squa e oo We, while he o he on Oh.
5. Conclusions
The p esen pape discussed a high- eloci y a mosphe ic a omiza ion o ou liquids:
wa e (W), s anda d diesel oil (D), ligh hea ing oil (LHO), and c ude apeseed oil (RO) a a ious
liquid p ehea ing empe a u es. The sp ay o he plain-je ai blas a omize was non-in usi ely
in es iga ed by a wo-componen Phase Dopple Anemome e . The eloci y componen s, along
wi h d ople sizes, we e e alua ed a a downs eam dis ance, z = 60 mm om he a omize nozzle.
Then, nine empi ical o mulae we e i ed o he measu emen da a o es ima e he Sau e Mean
Diame e , SMD, o he sp ay wi h liquid p ehea ing. Since he e is no known analy ic way o
es ima e he SMD o he sp ay o an ai blas a omize in he p esen ly in es iga ed condi ions,
he gi en empi ical o mulae we e analyzed o be e unde s and he backg ound physics. Based
on he esul s, he ollowing conclusions we e de i ed:
1. The e is a limi ing iscosi y which signi ican ly a ec s sp ay cha ac e is ics. I is
suppo ed by bo h he d ople size- eloci y sca e plo s and he i ed empi ical
o mulae o es ima ing SMD. The iscosi y limi in he cu en se up is es ima ed as
υl,lim = 4.21 mm2/s based on Eq. (6d). Below his alue, u he p ehea ing has no
addi ional e ec on he sp ay quali y. This inding is in line wi h he ac s ha D can
be excellen ly a omized wi hou p ehea ing while RO has o be in oduced well abo e
100 °C in o he combus ion chambe o ha e a su icien ly ine sp ay o liquid uel
combus ion. Among he in es iga ed liquids, he limi ing iscosi y was ound only in
he case o LHO since only his liquid passes υl,lim om he in es iga ed ones. Such a
ansi ional cha ac e is ic was expec ed based on he esul s o D and W compa ed o
RO.
2. The o e shoo ing phenomenon was shown a he cen e o he sp ay and z = 60 mm;
namely, when he la ge d ople s possess a highe eloci y han he smalle ones and
hence hey accele a e he su ounding medium, he y eloci y componen , uy o he
la ge d ople s was negligible while uz was high. As he d ople size dec eases, uz is
educed and uy inc eases. Since uy o igina es om he p esence o u bulence, i s mean
alue is ze o.
3. SMD-es ima ing Eqs. (6d), (7), (9), and (10) showed he bes i by adjus ing hei
expe imen al pa ame e s ia he Sca e Sea ch MATLAB algo i hm. Howe e , he
coe icien o he dynamic e m o Eq. (9) s a ed om a nega i e alue, which is
physically in alid. Since Eqs. (7) and (10) con ain adjus ed exponen s, Eq. (6d) is he
mos widely applicable SMD-es ima ing equa ion o da e o ai blas a omiza ion.
4. To es ima e SMD a ele a ed liquid empe a u es, he pa ame e s measu ed a ambien
empe a u e ha e o be adjus ed as ollows. The coe icien o he Webe numbe
should be mul iplied by he desi ed empe a u e and di ided by he e e ence
empe a u e i he limi ing iscosi y is no eached. I eached, hen he coe icien
does no change any u he and emains cons an as a unc ion o liquid p ehea ing
empe a u e. Howe e , he Ohneso ge numbe should be mul iplied by he squa e oo
o he a io o he liquid iscosi y a he e e ence empe a u e di ided by he ac ual
iscosi y a he desi ed liquid p ehea ing empe a u e.
The iabili y o he abo e indings is suppo ed by he ac ha he in es iga ed o mulae
we e de eloped o a ious a omize designs and liquids; mo eo e , he p esen condi ions
ega ding he a omizing ai discha ge eloci y a exceeded he alidi y o he ci ed li e a u e
da a. Liquid p ehea ing was no examined by he esea che s who expe imen ally de i ed he
espec i e equa ions. Howe e , he p esen esea ch highligh ed which SMD-es ima ing o mulae
a e alid unde he p esen ly applied ex eme condi ions. In numbe s, hey a e summa ized in
Table 3. The p esen esea che s sugges modele s using Eq. (16) o es ima ing SMD o an
ai blas a omize while suppo ing o deba ing he expe imen al esul s a e highly welcome o
u he de elop he models.
Acknowledgmen s
This wo k has been suppo ed by he p ojec №. GA18-15839S unded by he Czech
Science Founda ion and he p ojec LO1202 NETME CENTRE PLUS wi h he inancial suppo
om he Minis y o Educa ion, You h and Spo s o he Czech Republic unde he "Na ional
Sus ainabili y P og am I" ( unding o he Czech esea che s), Na ional Resea ch, De elopmen
and Inno a ion Fund o Hunga y, p ojec №. FIEK 16-1-2016-0007 and OTKA-FK 124704, New
Na ional Excellence P og am o he Minis y o Human Capaci ies p ojec № ÚNKP-18-4-BME-
195, and he János Bolyai Resea ch Schola ship o he Hunga ian Academy o Sciences ( unding
o he Hunga ian esea che s).
Con lic o in e es
The au ho s decla e ha he e is no con lic o in e es .
Appendix A. Measu emen o empe a u e-dependen physical p ope ies o liquids
The ollowing empe a u e-dependen physical p ope ies we e equi ed o de e mine he
a omiza ion cha ac e is ics o he liquids: ρ, σ, and υ. As o W and D, hey a e well known in he
li e a u e. Besides he densi y, he o he wo pa ame e s a e a ely discussed o LHO and RO. I
is known ha he a y acid composi ion o RO a ies by he clima e and he wea he , besides
cul i a ion me hods [57–59]. Consequen ly, i was manda o y o measu e he men ioned
p ope ies o he cu en ly used samples. The in es iga ion empe a u es ollowed he p: 25, 40,
55, 70, and 100 °C while he highes empe a u e o W was 90 °C o a oid boiling. Only σ was
measu ed a 75 °C ins ead o 70 °C. I is well-known ha W and D a e New onian liquids. Fasina
and Colley [60] concluded ha c ude ege able oils also exhibi New onian beha io , including
RO. As o a ligh c ude oil – which is mo e complex han LHO – i was p o en by A i in e al.
[61] ha abo e 200 1/s shea a e i beha es as a New onian liquid in he empe a u e ange o
20-90 °C. The shea a e in he p esen case is es ima ed as O (100.000) 1/s.
Tempe a u e-dependen densi ies we e de e mined using a 10-ml 3.3 bo osilica e glass
pycnome e , which was pu on a Sa o ius L610 D ype scale. The de ice was calib a ed wi h
known weigh s. The measu emen esul s o all liquids we e shown in Fig A.1. The combined
expanded unce ain y a 95% le el o signi icance was uni o mly 4.8 kg/m3. The esul s o W
di e by 0.7% om he li e a u e da a a 90 °C while he measu emen e o was unde ec able a
25 °C. This indi ec way o measu emen e o es ima ion p o ides an independen basis o he
accu acy o densi y measu emen s. All he measu emen s we e epea ed i e imes, and he
densi y calcula ion was pe o med by hei a i hme ic a e age.
Fig. A.1. The measu ed densi y o he in es iga ed liquids.
An Os wald- ype iscome e was used o de e mining he kinema ic iscosi ies o he
liquids. A la ge empe ed ank illed wi h silicone oil hos ed he iscome e s. To ha e a
homogeneous empe a u e dis ibu ion, a small pump con inuously ci cula ed he liquid. Since
he ins umen has a calib a ion cons an which is alid a 25 °C, he measu emen da a o W was
used o adjus he calib a ion cons an o he o he empe a u es. The e o e, W has no e o ba s
in Fig A.2, and i s alues ollow he li e a u e da a. The e o ba s show he combined expanded
unce ain ies a a 95% le el o signi icance o he h ee o he liquids. These measu emen s we e
epea ed h ee imes, and he iscosi y calcula ion was pe o med by hei a i hme ic a e age.
800
850
900
950
1000
20 40 60 80 100
ρl[kg/m3]
p
[°C]
DLHO RO W

Fig A.2. The measu ed kinema ic iscosi y o he in es iga ed liquids. No e he loga i hmic scale on he
o dina e.
As o su ace ension measu emen , he Wilhelmy pla e me hod was used in he open
a mosphe e a a ious p by using a double walled empe ed po . The hea ing medium was silicone
oil o enable measu emen s a 100 °C o D, LHO, and RO. Calib a ion o he load cell was
pe o med wi h known weigh s p io o ins alling he pla e on he hook. The measu emen s we e
pe o med i e imes a each poin , and hei a i hme ic a e age was p esen ed in Fig. A.3. A e
hea ing he po up om 25 °C o 100 °C, a check was pe o med a 75 °C wi h h ee indi idual
measu emen s o all liquids. The es ima ed unce ain y o he su ace ension measu emen a
95% le el o signi icance was uni o mly 0.2 mN/m.
Fig. A.3. The measu ed su ace ension o he in es iga ed liquids.
0,25
0,5
1
2
4
8
16
32
64
20 40 60 80 100
υl[mm2/s]
p
[°C]
DLHO RO W
0
20
40
60
80
20 40 60 80 100
σ[mN/m]
p
[°C]
DLHO RO W
Tempe a u e measu emen s had < 1 °C unce ain y. All he measu emen da a was in
good ag eemen wi h he li e a u e da a whe e a compa ison was possible [15,62–64]. In he case
o W, IAPWS-IF97 was used as an in e na ionally accep ed e e ence o he p ope ies o H2O.
Ne e heless, none o he equi ed empe a u e-dependen da a o LHO was ound in he public
li e a u e.
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