applied
sciences
Re iew
Insigh s in o Single D ople Impac Models upon
Liquid Films Using Al e na i e Fuels o
Ae o-Engines
Daniela F. S. Ribei o 1,*,† , And é R. R. Sil a 1,† and Miguel R. O. Panão 2,†
1AEROG, LAETA, Ae onau ics and As onau ics Resea ch Cen e , Uni e sidade da Bei a In e io ,
6201-001 Co ilhã, Po ugal; [email p o ec ed]
2
ADAI, LAETA, Associação pa a o Desen ol imen o da Ae odinâmica Indus ial, Uni e sidade de Coimb a,
3030-788 Coimb a, Po ugal; [email p o ec ed]
*Co espondence: daniela.san o. ibei [email p o ec ed]
† These au ho s con ibu ed equally o his wo k.
Recei ed: 29 Augus 2020; Accep ed: 21 Sep embe 2020; Published: 25 Sep embe 2020
Abs ac :
In ae o-engines, he in oduc ion o bio uels is among he bes al e na i es o ossil uels,
and his change is likely o a ec he impac o d ople s on in e posed su aces. Unde his amewo k,
his wo k e iews he main mo phological hyd odynamic s uc u es occu ing upon he impac
o a liquid d ople on a we ed su ace, using je uel and bio uel mix u es as al e na i e uels.
The expe imen s pe o med allow in es iga ing he e ec o he liquid ilm hickness on he dynamic
beha io o single d op impac , conside ing he ele ancy o hese phenomena o he op imiza ion o
engine ope a ing pa ame e s. Pa icula emphasis is gi en o he occu ence o c own splash, and he
mo phological di e ences in he ou comes o d op impac depending on he impac condi ions
and luid p ope ies. The ou luids es ed included pu e wa e (as e e ence), 100% Je A-1,
75%/25%, and 50%/50% mix u es o Je A-1 and NExBTL (Nes e Renewable Diesel)—wi h he
Webe impac numbe be ween 103 and 1625; Reynolds alues 1411–16,889; and dimensionless
ilm hicknesses o
δ
= 0.1, 0.5, and 1. The analysis on he seconda y a omiza ion o he di e en
luids e idences he p edominance o p omp and c own splash, and je ing o al e na i e uels.
Finally, besides a sys ema ic e iew o empi ical co ela ions o he ansi ion o splash, we in es iga e
hei uni e sali y by ex apola ing he alida ion ange o e alua e hei abili y o p edic he ou come
o impac accu a ely. One o he co ela ions s udied show he highes deg ee o uni e sali y o he
cu en expe imen al condi ions, despi e i s limi a ion o hin liquid ilms (δ=0.1).
Keywo ds:
d ople impac ; expe imen al; uel mix u es; d op impac models; liquid ilm; splashing
ansi ion
1. In oduc ion
The u u e o bio uels in he a ia ion indus y depends on how much he induced changes in
he mophysical p ope ies a ec he combus ion p ocess and all i s s ages, om sp ay o ma ion o
he p epa a ion o he uel/ai mix u e. One o he s ages which p oduces a signi ican impac on he
uel/ai mix u e p epa a ion is he impac o d ople s on in e posed su aces. Addi ionally, due o
he complexi y o he se e al phenomena in ol ed, he adequacy o nume ical models o simula e
he combus ion p ocess elies on accu a ely desc ibing he ou come o d op impac on d y o
we ed su aces. This desc ip ion includes he mo phological beha io o hyd odynamic s uc u es
leading o he deposi ion o uel o e en ual seconda y a omiza ion, e-issuing pa o he uel
o he combus ion chambe , imp o ing he uel/ai mix u e p epa a ion. Howe e , due o he
nume ous a iables ha a ec he ou come o d op impac , he bes app oach is o de elop
Appl. Sci. 2020,10, 6698; doi:10.3390/app10196698 www.mdpi.com/jou nal/applsci
Appl. Sci. 2020,10, 6698 2 o 21
empi ical co ela ions based on dimensionless numbe s exp essing he ela ion be ween he ine ial,
su ace ension, and iscous o ces in ol ed.
1.1. T ansi ion o Seconda y A omiza ion a e D op Impac on Liquid Films
The wo essen ial ou comes o d op impac on liquid ilms a e he deposi ion o a liquid d ople
in he ilm o he gene a ion o seconda y d ople s h ough hyd odynamic mechanisms, such as a
ull o pa ial ebound o he ini ial d ople , o smalle d ople s de aching om he bounding im
o an up ising c own associa ed wi h he splashing mechanism. Howe e , he classi ica ion o hese
ou comes is no always unanimous.
Rioboo e al.
[1]
de ined de ailed e minology o he se e al mo phological s uc u es eme ging
om d op impac —p omp splash, c own splash, ebound, and pa ial ebound being he mos ele an
o his s udy o d ople deposi ion. Figu e 1p esen s illus a ions o hese phenomena o ganized by
he equi ed d op impac ene gy.
Figu e 1. D op impac mechanisms.
Iden i ying he di e ences in he d ople hyd odynamic beha io depending on he liquid ilm
hickness (
h
) was a conce n. Namely, Chand a and A edisian
[2]
epo ed ha he sp eading o he
d ople changed signi ican ly due o he liquid ilm. La e , ocusing hei wo k on dis inguishing he
sp eading beha io be ween he impac on d y and we ed su aces, Rioboo e al.
[3]
showed how
main aining all he impac pa ame e s cons an , excep he su ace condi ions, esul ed in en i ely
di e en d op impac mo phological s uc u es. The e o e, i is easonable o include he e ec o he
liquid ilm cha ac e is ics in he empi ical co ela ions (in a dimensionless o m as
δ=h /D0
, whe e
D0
is he d ople diame e be o e impac ) disce ning he ansi ion be ween deposi ion and he splash
which gene a es seconda y a omiza ion.
The empi ical co ela ions ha ca ego ize he ou comes o impac s depend on dimensionless
pa ame e s, such as he Webe (
We =ρD0U2
0/σ
) and Reynolds (
Re =ρU0D0/µ
) numbe s, ollowed by
he Ohneso ge (
Oh =√We/Re
) and Laplace (
La =Oh−2
) numbe s, dependen on he o me , whe e
ρ
,
Appl. Sci. 2020,10, 6698 3 o 21
σ
, and
µ
a e he densi y, su ace ension, and dynamic iscosi y o he liquid, espec i ely, and
U0
is
he d ople impac eloci y. Mos empi ical co ela ions ollow a ela ion be ween Webe and Reynolds
numbe s exp essed as
ReαWe0.8 =Kc(1)
whe e
Kc
is he c i e ion be ween a d ople sp eading and splashing. Table 1summa izes he p oposals
o his c i e ion o we ed su aces. The e a e se e al conside a ions abou he o igin o hese c i e ia.
Table 1. T ansi ion c i e ia o Kc.
Re e ence Exponen αC i e ion, Kc
Re Valida ion δValida ion
Range Range
Bai and Gosman [4] 0.3584 1136.7 8000–33,600 †
Cossali e al. [5] 0.4 2100 +5880 ⋅δ1.44 428–1828 0.1–1
T opea and Roisman [6] 0.4 2823.6 +357.7 ln (η
1.2−η)‡150–3184 -
Vande Wal e al. [7] 0.272 756.7 988–13,900 0.1
†
Bai and Gosman
[4]
conside a we ed condi ion equi alen o he impac on a e y ough su ace;
‡
wi h
η=ms/m0
is he mass a io be ween he mass o seconda y d ople s p oduced by splash and he mass on he
ini ial impinging d ople .
The i s ela es o he c i e ion o Bai and Gosman
[4]
, which conside s he impac o a d ople on a
we ed su ace equi alen o i s impac on a e y ough su ace (
s>
12
µ
m), and he da a can be aced
back o he o iginal con ibu ion o S ow and S aine
[8]
wi h expe imen s wi hin he ange indica ed
in Table 1. The second conside a ion is he c i e ion o Cossali e al.
[5]
which conside s he in luence o
he liquid ilm hickness in he impac ou come. To enla ge hei expe imen al da a, hey used no only
pu e wa e bu also mix u es o glyce ol and wa e , he eby inc easing he ange o he mophysical
p ope ies o he luids. Addi ionally, hey pe o med expe imen s using di e en dimensionless ilm
hicknesses (
δ=h /D0
). The alida ion ange o his c i e ion can be consul ed in Table 1. The hi d
conside a ion e e s o he co ela ion o
T opea and Roisman [6]
, which includes a andom elemen
in he c i e ion
Kc
h ough he mass a io
η
. This mass a io can be abo e 1 in he sense ha pa
o he liquid ilm may con ibu e o he mass o seconda y d ople s eme ging om splash. In ac ,
Bai and Gosman [4] conside
a simila andom elemen in he nume ical model o sp ay impingemen
as
η=
0.2
+
0.9
nd(
0,1
)
. In Roisman and T opea
[9]
a alue o
Kc=
2800 is sugges ed, which would
co espond o
η≈
0.58; howe e , no explana ion o his alue is p o ided. Thus, in his e iew, we op
o he mos gene al o m o his c i e ion.
Las ly, Vande Wal e al. [7]
de e mined an empi ical
co ela ion o he sp eading/splashing ansi ion o single d ople s impinging on d y su aces and
hin liquid ilms. In he expe imen al da a ha hey used o i he co ela ion, di e en luids we e
included p o iding a wide ange o impac condi ions. Howe e , hey only es ed impac s wi h hin
liquid ilms (δ=0.1).
Figu e 2plo s he c i e ia o ganized in Table 1, showing he egion o he Cossali e al.
[5]
co ela ions depending on he dimensionless liquid ilm (
δ=h /D0
) and he egion o he T opea and
Roisman
[6]
co ela ion depending on
η
. Mos co ela ions ha e a simila loga i hmic slope, excep o
he co ela ion p oposed by Vande Wal e al.
[7]
. In scale, Vande Wall e al.’s co ela ion is close o he
dimensionless ilm hickness condi ion o
δ=
0.1. Howe e , hei expe imen s co e ed a b oade ange
o Reynolds alues, e en ually, leading o a lowe in luence o Re, as he co esponding exponen
poin s o wi h i s lowe alue.
Figu e 2also shows he measu emen egion o he d ople cha ac e is ics used in his wo k.
The egion co e s uel mix u es ha can be implemen ed in ae o-engines since he Ame ican Socie y
o Tes ing and Ma e ials (ASTM) p esen ly au ho izes je uel blends wi h 50% in olume wi h uels
de i ed om HEFA (hyd op ocessed es e s and a y acids) in a ia ion u bines [
10
,
11
]. HEFA uels
ha e p o en o be able o eplace con en ional je uels [
12
]. Gaw on and Białecki
[13]
compa ed he
pe o mance o a Je A-1/HEFA blend wi h Je A-1 on a minia u e u boje engine. The mos signi ican
Appl. Sci. 2020,10, 6698 4 o 21
di e ences in e ms o ope a ing pa ame e s conce n he uel consump ion, which is smalle o he
blend. Mo eo e , he emission indices o CO, CO2, and NOxa e smalle in compa ison o Je A-1.
Figu e 2. T ansi ion c i e ia be ween sp ead and splash a e d op impac on o a liquid ilm.
1.2. Mo phological Conside a ions on he Hyd odynamics o Splashing
The splashing mechanism is one o (i no ) he mos ele an and s udied ac o s in he li e a u e.
On a ypical e ical impac o a single d ople on a s eady liquid ilm he d ople is ini ially
sphe ical, and i does no su e any de o ma ion du ing he all. A ecen s udy [
14
], using p ecisely
he same luids, s udied he e ec o a d ople ’s ini ial de o ma ion on he splashing dynamics.
Due o he in e ac ion be ween he d ople and an ai low be o e impac , he d ople de o med and
assumed di e en shapes be o e impac . They epo ed ha sphe ical d ople s p omo e splashing,
while de o med d ople s p omo e sp eading. The physical p ocesses in ol ed in uel combus ion
include uel a omiza ion and impac , ollowed by he e apo a ion. The mix u e p epa a ion, including
he impac upon d y and we ed su aces, is ecognized as o majo impo ance. The seconda y
a omiza ion p oduced by he splashing op imizes he uel combus ion e iciency. Conside ing his,
a d ople alling e ically on a s eady liquid ilm was s udied o he luids men ioned and he
occu ence o splash was compa ed o he p edic ion o models p esen ed in he li e a u e. All models
conside ed we e designed o he impac o sphe ical d ople s upon a liquid ilm. The mo phology o
his impac mechanism includes he o ma ion o a c own wi h a im in i s uppe bound, and om
ins abili ies in his im, he cusp can eme ge, which disin eg a es in o d ople s— hus, seconda y
a omiza ion. Cossali e al.
[15]
we e among he i s o cha ac e ize he c own diame e , hickness,
and maximum heigh . The au ho s no iced ha highe alues o he Webe numbe led o smalle
seconda y d ople s. A ew yea s la e ,
Cossali e al. [16]
ocused hei wo k on he ime e olu ion
Appl. Sci. 2020,10, 6698 5 o 21
o he c own o wa e d ople s impinging upon hin liquid ilms. They eached se e al conclusions
ela ed o he c own diame e , he non-dimensional c own heigh , and he mean seconda y d ople
size. Howe e , since hey used only one luid, i is no possible o iden i y whe he hei conclusions
could be ex ended o o he luids.
Fedo chenko and Wang
[17]
s udied expe imen ally and heo e ically, he egion o he ully
de eloped splashing. They used wa e bu also a 70% glyce ol-wa e solu ion. They de eloped a
model o he cen al je o ma ion a he ca i y collapse. Some conside a ions we e made abou
he iscosi y o he luids ela ed o he ca i y, he cen al je , and he c own ejec ion. In luids wi h
low iscosi y, he in e ac ion be ween he capilla y wa e and he ca i y wall has a majo in luence
on he ca i y shape, and by consequence, on he cen al je speed. On he o he hand, o luids
wi h high iscosi y, he in luence o capilla y wa es is mino . Unde s anding he oles o he luid
physical p ope ies is essen ial o unde s anding how hey in luence he impac egimes. Fo example,
Range and Feuillebois [18] epo ed ha splashing is highly sensi i e o su ace ension alues.
A pa ame e pa icula ly ele an o he impac s o d ople s on we ed su aces is he dimensionless
hickness o he liquid ilm and i s in luence in he d ople dynamic beha io . Vande Wal e al.
[19]
s udied d ople s splashing upon liquid ilms o di e en dep hs. They epo ed ha hinne liquid ilms
dec eased he c i ical Webe numbe , se ing he ansi ion be ween deposi ion and splash. They also
ound ha he size and numbe o he splashed d ople s depend upon he p esence and hickness o
he liquid ilm, and also on he luid’s iscosi y and su ace ension. Fo
δ<
1, bo h p omp and c own
splash we e spo ed, bu o
δ>
1, p omp splash was limi ed and c own splash inhibi ed. Mo eo e ,
he numbe o ejec ed d ople s dec eased while hei mean size inc eased, an ou come a ibu ed o
he inc ease o he su ace ension and iscosi y. In addi ion, a highe iscosi y leads o an inc ease
o he damping o ces in ol ed in he mo phological de elopmen o splash, delaying bo h p omp
and c own ypes. The e o e, while iscosi y p omo es splash a e d op impac on d y su aces, in he
p esence o hin liquid ilms, i s ole e e s. Las ly, high su ace ension inhibi s splashing bo h o d y
o we ed su aces.
O e he yea s, esea che s wan ed o p oduce hinne liquid ilms and s udy hese pa icula
impac s. Fo example, Wang and Chen
[20]
did expe imen s cen e ed on he splashing o a single
d ople upon e y hin liquid ilms (
δ<
0.1). They con i med ha he c i ical Webe numbe and he
splashing dynamics emain in luenced by he hickness o he liquid ilm. Howe e , he au ho s also
no iced ha he c i ical Webe numbe con e ges o a minimum alue as
δ
dec eases, which depends
on he luid iscosi y and su ace cha ac e is ics unde nea h he liquid ilm.
In he s udy o d op impac on we ed su aces, i is impo an o unde s and whe he he
su ace unde nea h he liquid ilm in luences he ou come. Wi h ha in mind, Vande Wal e al.
[21]
combined he in luence o a ough su ace and a hin liquid ilm upon he splashing limi and dynamics.
They ecognized ha bo h cases subs an ially changed he splashing limi and dynamic. A ough
su ace dec eased he c i ical Webe numbe d as ically o he ansi ion o splash, and he su ace
opog aphy o e akes he impo ance o o he go e ning pa ame e s, especially in he splashing egime.
Fo example, conside able di e ences in he su ace ension and iscosi y became less signi ican and
made he ou come o impac e y simila . The splashing beha io o a ough su ace co e ed by a hin
liquid ilm was a combina ion o bo h cases.
Bounda ies be ween he di e en impac egimes a e common and widely epo ed.
Mo ei a e al. [22]
syn hesized se e al empi ical co ela ions in he li e a u e which es ablished
bounda ies be ween he di e en impac egimes and classi ied hem as e y dis inc . The main
di e ences we e due o he dis inc impac condi ions which o igina ed hem.
Conce ning he e ec o luid p ope ies, Zhang e al.
[23]
cen e ed hei wo k on he nume ical
simula ion o a d ople impinging upon ilms and ema ked ha while su ace ension and iscosi y
dec eases, mo e momen um is impa ed on he c own de elopmen , inc easing i s heigh and
dec easing i s hickness. In he same way, he o ma ion o p omp splashing is enhanced by he
dec ease in su ace ension and iscosi y o he luid. They ound ha Webe numbe plays a mo e

Appl. Sci. 2020,10, 6698 6 o 21
impo an ole in d ople impac beha io han he Reynolds numbe . Inc easing he Webe numbe
accele a es he impac p ocess and inc eases he numbe o splashing d ople s.
O he s udies conce n d ople impac s upon immiscible liquid ilms (e.g., wa e and oil), such as
he wo k pe o med by Che and Ma a
[24]
. Immiscibili y induces comple ely di e en hyd odynamic
beha io s. A wa e d ople impinging on an oil ilm c ea es a compound c own, ollowed by he
o ma ion o a cen al je ; con a ily, an oil d ople impinging on a wa e ilm causes quick sp eading.
They also s udied he in luences o some pa ame e s, such as he Webe and Ohneso ge numbe s,
he iscosi y a io, and he dimensionless hickness o he liquid ilm. Namely, conce ning he las
pa ame e , hicke ilms show a beha io simila o miscible liquids, wi h he imescales delayed
ela i e o hinne liquid ilms. Recen ly, Bu zynski and Bansme
[25]
s udied he d ople splashing
on a hin mo ing ilm only o high Webe numbe (
We >
2281). They epo ed ha he liquid ilm
eloci y a ec s he c own geome y conside ably. The high ine ial o ce o he d ople enla ges he
expansion o he c own, which causes a la ge diame e . Inc easing he liquid ilm eloci y leads o an
inc ease in c own hickness, and consequen ly, will dec ease he dimensionless c own diame e , due o
he highe ine ial o ces o he ilm ha al e he sp eading p ocess.
In addi ion o hose desc ibed abo e, se e al o he esea ch wo ks ha e been de eloped [
26
],
including mul iple d ople impac s, impac s upon hea ed su aces, and impac s upon inclined walls,
among many o he s. The e was some hing missing in all hose s udies. The mos common luids
used we e wa e , glyce ol, e hanol, and solu ions wi h di e en luids. Howe e , since one o he
applica ions whe e d op impac s on liquid ilms is ele an conce ns he uel injec ion in in e nal
combus ion engines, uel mix u es should be es ed. The e o e, he assessmen o empi ical models,
and he mo phological hyd odynamic s uc u es associa ed wi h d op impac on we ed su aces, a e
wo hy o u he in es iga ion.
One o he goals o his wo k is o con ibu e o he implemen a ion o bio uels in he a ia ion
sec o . Fo his eason, he wo king luids conside ed we e 100% Je A-1 and wo mix u es wi h
75%/25% and 50%/50% o Je A-1 and NExBTL (Nes e Renewable Diesel), espec i ely. Pu e wa e
was also used as e e ence luid. The designed and buil expe imen al acili y ha isualizes d op
impac ou comes, enables p ecise con ol o e he liquid ilm hickness (
h ±
0.05 mm) [
27
]. Acco ding
o i s dimensionless hickness, he liquid ilms can be classi ied as hin, in e media e, and hick,
and e en as shallow o deep pool [
28
]. In he expe imen s epo ed, h ee ela i e hicknesses we e
conside ed and iden i ied as hin (
δ=
0.1), in e media e (
δ=
0.5), and hick (
δ=
1) liquid ilms. A e his
in oduc ion, he ollowing sec ion de ails he expe imen al p ocedu e used. Sec ion 3explo es he
esul s ob ained in he expe imen s in h ee lines o esea ch: (1) he mo phology o d op impac ;
(2) i s ou come
; and (3) he applica ion o ansi ion c i e ia o e alua e hei limi a ions when uels
a e conside ed. These uel mix u es ill all he demands de ined by ci il a ia ion o be applied in
ae o-engines, and p edic ing he splashing occu ence will enhance hei e iciency in he combus ion
p ocess. Finally, he a icle ends wi h some concluding ema ks.
2. Expe imen al P ocedu e
The expe imen al acili y (Figu e 3) is composed o ou main pa s: image acquisi ion, impac
su ace, d ople dispensing sys em, and impac si e illumina ion. Fo image acquisi ion, we used a
high-speed digi al came a Pho on FASTCAM mini UX50 wi h 1.3 Megapixel esolu ion a ame a es
up o 2000 ps ( ames pe second) and a educed image esolu ion o ame a es up o 160,000 ps.
We used a Mac o Lens Tokina AT-X M100 AF PRO D wi h a minimum ocus dis ance o 0.3 m, a ocal
leng h o 100 mm, a mac o a io o 1:1, and a il e size o 55 mm. The image esolu ion a i s was
1280
×
1024, he exposu e ime was 1
/
5120 s, and he ame a e was 2000 ps. A opless igh -angled
pe spex con aine was he impac su ace and i s dimensions we e calcula ed based on he maximum
d ople diame e (edge equal o 40
D0,max
). To elease he d ople s, a sy inge pump NE-1000 was used
a a pumping a e o 0.5 mL/min. To a y he d ople diame e , i e s ainless s eel p ecision ips we e
used. They had s aigh ips and hei inne diame e s we e: 1.5 mm, 0.84 mm, 0.51 mm, 0.25 mm,
Appl. Sci. 2020,10, 6698 7 o 21
and 0.10 mm. The illumina ion o he impac si e is c ucial, and he only ligh sou ce in he oom was
a 20 W LED in on o he came a o p o ide backligh ing. A piece o di usion glass was placed
be ween he impac si e and he LED.
Figu e 3. Scheme o he expe imen al acili y.
The physical p ope ies o he h ee uels used we e measu ed o inc ease he p ecision o he
s udy (densi y, su ace ension, and dynamic iscosi y) and can be seen in Table 2. I is possible o see
ha bo h he densi ies and he su ace ensions o he h ee luids a e e y simila , he majo di e ences
being in he dynamic iscosi y alues. As men ioned, pu e wa e was also es ed as a e e ence since
i s p ope ies a e well de ined in he li e a u e.
Table 2. Physical p ope ies o he luids.
Subs ances ρ[kg/m3]σ⋅103[N/m] µ⋅103[Pa⋅s]
H2O (li e a u e) 1000 72.0 1.00
100% Je Fuel (JF) 798.3 25.4 1.12
75% JF–25% HVO 794.9 25.5 1.44
50% JF–50% HVO 792.3 24.6 1.79
The expe imen al p ocedu e has wo pa s. In he i s pa , he came a was kep pa allel o he
d ople alling plane and he d ople diame e s and impac eloci ies we e measu ed h ough he
impac upon he d y su ace o allow he de e mina ion o he liquid ilm hickness. In he second pa ,
he came a was leaned 10
○
wi h he ho izon al plane o imp o e isualiza ion. In his pa , he d ople
impinged upon a liquid ilm wi h dimensionless hicknesses (
δ
) o 0.1, 0.5, and 1. Since pe spex is a
hyd ophobic su ace, i was no possible o p oduce he hinne ilms o wa e . Wa e and pe spex a e
a non-we ing sys em. In his way, he hinne ilms p oduced o H
2
O we e de ined by he minimum
olume ha allowed he p oduc ion o a homogeneous liquid ilm and i was hen calcula ed o
e e y d ople diame e . Table A1 in he Appendix Ashows he alues o he hinne dimensionless
hicknesses o H2O.
To measu e he d ople diame e and he impac eloci y, a MATLAB algo i hm was c ea ed o
sub ac he backg ound and he bina iza ion o he image; he numbe o pixels co esponding o
he d ople diame e we e coun ed. By mul iplying ha by he pixel size, he d ople diame e was
hen de e mined. The maximum pixel size was 49.2
µ
m/pixel p o iding a maximum e o o 24.6
µ
m.
Fo he impac eloci y, he image ea men was simila , bu in his case, i was chosen he las d ople
be o e impac and he d ople 5 ms be o e and again by pixel coun ing he alues we e de e mined.
A mo e de ailed desc ip ion o he expe imen al wo k can be seen in Ribei o [27].
In e ms o he expe imen al condi ions explo ed in his wo k, he i e di e en inne diame e s
o he needle used esul ed in he d ople diame e s a ying om, app oxima ely, D0=1.7 o 4.0 mm
(see Table A2 in he Appendix A o he de ails). The di e ences be ween he h ee uels a e negligible,
and wa e egis e ed he la ges diame e s due o he highe su ace ension. Table A3 in Appendix A
Appl. Sci. 2020,10, 6698 8 o 21
con ains he in o ma ion on he impac eloci y measu ed o he h ee alling impac heigh s used
(
z1=
0.175 m,
z2=
0.500 m, and
z3=
1.000 m). Table 3shows he anges o dimensionless numbe s
calcula ed om he d ople s’ dynamic cha ac e is ics.
Table 3. Expe imen al anges o dimensionless numbe s.
Reynolds Webe Laplace Ohneso ge⋅103
1411–16,889 103–1623 27,987–28,8101 1.863–9.593
3. Resul s and Discussion
The analysis o he esul s om he high-speed isualiza ion ollows h ee esea ch ques ions.
The i s ques ion add esses he mo phological s uc u es ob ained a e d op impac . The second
ques ion di es in o he p ocesses igge ing seconda y a omiza ion. Finally, we e alua e he accu acy
o ansi ion c i e ia in p edic ing he ou come o d op’s impac on he liquid ilm using bio uels.
3.1. Mo phological S uc u es o D op Impac on Liquid Films
The impac o bio uel single d ople on o a liquid ilm esul ed in six di e en obse ed
phenomena: deposi ion, inge ing, p omp -splash, c own splash, je ing, and bubble encapsula ion.
In Figu e 4, i is possible o see wo phenomena wi hou he o ma ion o seconda y a omiza ion:
(a) sp eading o deposi ion, when he d ople me ges wi h he liquid ilm, occu ing o low
impac ene gies; (b) inge ing, i.e., ins abili ies c ea ed in he ou e im o he liquid lamella and
s uc u es inge -like in shape g ow. When he size o he inge s is la ge , hey end o b eak up
and o m d ople s by seconda y a omiza ion. The a iable
exp esses he ime be o e and a e
impac — =0 he ins an o impac .
P omp splash was also spo ed (Figu e 5) when he impac ene gy was high enough o he d ople
o disin eg a e in he i s momen s a e impac . Tiny d ople s ejec om he liquid lamella pe iphe y
while he c own s ill ises o ad ances a i s baseline. Since he sequence o images co esponds o
an impac heigh o
z3=
1 m, he impac eloci y is high
U0=
4.06 m/s). The e o e, he momen he
d ople impinges on o he liquid, a ilm appea s be ween subsequen impac ames.
Figu e 6shows wo high impac ene gy e en s: (a) he c own splash and (b) je ing o ebound.
C own splash occu s a e he s age o maximum expansion and encompasses he b eakup o he
c own shee and i is a equen e en du ing impac s o singles d ople s wi h liquid ilms. In his
phenomenon, he impac ene gy o he d ople impinging in he liquid ilm gene a es a momen um
ans e o he cylind ical liquid shee o ming an up ising c own (
=
1 ms). Conside ing he imescale
o impac measu ed om he d ople size and eloci y,
i=D0/U0=
0.78 ms, i e idences how ine ia
domina es he e olu ion o his hyd odynamic s uc u e. F om ins abili ies in he bounding im,
iny d ople s ejec om inge s o med
=
3 ms a e impac . Du ing he c own collapse (
=
14 ms),
he inge s s e ch, and e en ually b eak, gene a ing seconda y d ople s. This phenomenon p oduces
a ious sizes o seconda y d ople s, while p omp splash only p oduces iny ones. Sho ly a e he
c own collapse, a e ical ex ension o luid (je ) ises om he cen e o he impac si e—a phenomenon
iden i ied as je ing, o ebound in he cases whe e mos o he impinging mass de aches om he
su ace a e impac , which occu s mo e o en in d y su aces. The o ma ion o his cen al je was
also spo ed se e al imes in hese expe imen s, e en wi hou c own o ma ion. As isualized on he
igh sequence in Figu e 6, his je o en eaches i s maximum heigh and b eaks, ejec ing one o mo e
seconda y d ople s. The occu ence o deposi ion ollowed by je ing, as shown in he image sequence,
only happened wo imes in he expe imen s pe o med. Howe e , i was ecu en ly p eceded by
p omp and c own splash.
Appl. Sci. 2020,10, 6698 9 o 21
(a) (b)
Figu e 4.
Image sequences: (
a
) he sp eading o a single d ople in a liquid ilm o he 75% JF/25%
HVO mix u e (
D0=
2.77 mm,
z1=
0.175 m,
δ=
1); (
b
) he inge ing o a single d ople in a liquid ilm
o he 75% JF/25% HVO mix u e (D0=2.47 mm, z1=0.175 m, δ=0.1).
Appl. Sci. 2020,10, 6698 16 o 21
Figu e 12.
Compa ison o he expe imen al esul s wi h he p oposed ansi ion c i e ia es ablished
by Bai and Gosman
[4]
, Cossali e al.
[5]
, T opea and Roisman
[6]
, and Vande Wal e al.
[7]
wi hin
hei alida ion anges. Colo scheme: black— he phenomena ob ained expe imen ally ag ee wi h he
c i e ia; whi e— he phenomena ob ained expe imen ally do no ag ee wi h he p edic ed ou come;
g ay—do no belong wi hin he alida ion ange o ha c i e ion.
I we es ic he use o hese co ela ions o hei alida ion ange, he c i e ion ha be e p edic s
he ou come o d op impac on we ed su aces, wi h he uels and al e na i e uels used in he
expe imen s, is he one o mula ed by Bai and Gosman [
4
] because i i ed 100% o he expe imen al
esul s ob ained. Bo h Cossali e al.
[5]
and T opea and Roisman
[6]
ha e a simila p edic ion accu acy.
The c i e ion de ined by Cossali e al.
[5]
is he only one ha conside s he in luence o he liquid ilm
hickness, ye , i s p edic ion capabili y dec eases o highe Reynolds numbe s and high dimensionless
ilm hicknesses. Finally, Vande Wal e al.
[7]
ocus i s bounda y on hin liquid ilms. I s accu acy is
high, ailing only o he la ge d ople diame e s o bo h mix u es. As ollows, he assump ion ha
a liquid ilm beha es as a e y ough su ace is, in ac , alid and Vande Wal e al.
[7]
’s co ela ion
should include a ange o dimensionless hicknesses in o de o uni e salize he c i e ion.
Howe e , one may ques ion how a can we ex apola e hese ansi ion c i e ia o assess hei
uni e sally? The dimensionless numbe s in he c i e ia allow he use o empi ical co ela ions in

Appl. Sci. 2020,10, 6698 17 o 21
comple ely di e en impac condi ions. Conside ing his, Figu e 13 shows an in o-g aphic iden i ying
he esul s when ex apola ing he di e en ansi ion c i e ia o explo e hei ou come in egions
ou side hei alida ion domain. Simila ly o he las igu e, he impac condi ions a e iden i ied, and,
he inc ease o d ople ini ial diame e (
D0
) and d ople impac eloci y (
U0
), es ablished by he a ows.
Figu e 13.
Compa ison o he expe imen al esul s wi h he p oposed ansi ion c i e ia es ablished by
Bai and Gosman
[4]
, Cossali e al.
[5]
, T opea and Roisman
[6]
, and Vande Wal e al.
[7]
. Colo scheme:
black— he phenomena ob ained expe imen ally ag ee wi h he c i e ia wi hin he alida ion ange;
whi e— he phenomena ob ained expe imen ally do no ag ee wi h he p edic ed ou come wi hin he
alida ion ange; g ay— he phenomena ob ained expe imen ally ag ee wi h he c i e ia ou o he
alida ion ange; beige— he phenomena ob ained expe imen ally do no ag ee wi h he p edic ed
ou come ou o he alida ion ange.
The ag eemen o he expe imen al esul s and he c i e ia we e desc ibed by a new colo scheme.
Black ep esen s he cases whe e he phenomena ob ained expe imen ally ag ee wi h he c i e ia wi hin
he alida ion ange, whi e displays he cases whe e he phenomena ob ained expe imen ally do
no ag ee wi h he p edic ed ou come wi hin he alida ion ange, g ey de ines he cases whe e he
phenomena ob ained expe imen ally ag ee wi h he c i e ia ou side he alida ion ange, and beige
Appl. Sci. 2020,10, 6698 18 o 21
ep esen s he cases whe e he phenomena ob ained expe imen ally do no ag ee wi h he p edic ed
ou come ou side he alida ion ange. The e we e also wo cases iden i ied wi h an "R", which means
ebound. Since he phenomena ob ained we e di e en om he ones p edic ed by he c i e ia he
au ho s decided o iden i y i di e en ly.
Now, conside ing all he expe imen al da a, he i ing o he c i e ia changed signi ican ly.
The c i e ion p oposed by Bai and Gosman
[4]
p edic s co ec ly 83% o he da a. This shows ha he
e iciency o he co ela ion dec eases signi ican ly o da a ou o he alida ion ange.
Cossali e al. [5]
p edic accu a ely 74% o he esul s. I s p edic ion dec ease bu no subs an ially. This c i e ion i s
be e d ople impac s wi h hinne liquid ilms. Howe e , i should i equally all hicknesses since i
is he only one ha conside s he in luence o he liquid ilm hickness.
T opea and Roisman
[6]
show good ag eemen o highe Webe numbe s and i s co ec ly 89%
o he cases. In his case, he p edic ion capabili y inc eased o alues ou side he alida ion ange.
Finally, Vande Wal e al.
[7]
shows a g ea ag eemen o highe impac eloci ies. This is he c i e ion
ha be e p edic s he ou comes o ou expe imen s, i ing 93% o he cases co ec ly.
The inal assessmen om he new in o-g aphic is a o able o he Vande Wal e al.
[7]
co ela ion
as he one wi h he g ea e uni e sali y, being able o p edic co ec ly cases ou side i s alida ion
ange. Wha is so special abou Vande Wal e al.
[7]
c i e ion? I p o ed o be a uni e sal c i e ion,
bu i does no e en accoun o he in luence o he liquid ilm hickness. I we conside he insigh o
he Cossali e al.
[5]
co ela ion ega ding he in luence o he dimensionless liquid ilm, as plo ed
ea lie in Figu e 2, hicke ilms lead o a shi in he cu e o highe Webe numbe s, since he ene gy
equi ed o gene a ing splashing e en s is highe . Assuming he same p incipal in he expe imen s
pe o med by Vande Wal e al.
[7]
, one can expec ha mo e expe imen s wi h hicke ilms migh
lead o simila esul s. Figu e 14 plo s he expe imen al esul s ob ained in he p esen wo k and he
Vande Wal e al.
[7]
empi ical co ela ion. I
Kc= (δ)
, and p opo ional o i , e en i in a nonlinea
way, an inc ease o
Kc
while keeping cons an he loga i hmic slope, should imp o e he p edic ion
o he splashing ansi ion. Thus, wi h
δ=
1, a es on a 15% inc ease o
Kc
alida es his hypo hesis.
Howe e , i also poin s o he need o mo e expe imen al esea ch o e ine he c i e ion.
Figu e 14.
Expe imen al esul s in he p esen wo k and he Vande Wal e al.
[7]
empi ical co ela ion.
In he case o
δ=
1, we plo ed a quali a i e cu e ep esen ing an inc ease o 15% in he splashing
c i e ion alue Kc.
4. Conclusions
One o he ields o esea ch ha a ec he pe o mance o he combus ion p ocess in ae o-engines
is he impac o a sp ay on solid su aces. A e impac , he sp ay can o m a liquid ilm ha al e s
he ansi ion c i e ia be ween he ou comes o impac . Mo eo e , wi h he g owing in e es in using
al e na i e uels, which mix s anda d uels wi h bio uels, one may ques ion whe he he exis ing
c i e ia be ween d op impac mechanisms emain alid.
Appl. Sci. 2020,10, 6698 19 o 21
The goal o his expe imen al s udy is o e iew he empi ical models o d op impac on o
liquid ilms, iden i y he mo phological s uc u es o he d op impac on we ed su aces o a s anda d
Je Fuel (JF), and mixing i wi h NExBTL, wi h wa e expe imen s as e e ence. Pa icula ele ance
is gi en o he ansi ion o splashing wi h he p oduc ion o d ople s by seconda y a omiza ion.
The mo phological analysis ocus on he in luence o he pa ame e s in ol ed in he dynamic beha io
o he d ople , such as he luid physical p ope ies, he d ople diame e and impac eloci y, and he
ela i e hickness o he liquid ilm. Finally, he image analysis o he ou come o d op impac is
use ul o e alua e he uni e sali y o empi ical co ela ions o p edic ing he splashing ansi ion,
conside ing dimensionless ilm hicknesses o δ=0.1–1.
The expe imen al esul s e idenced he di e en ou comes, he clea in luences o he luid’s
physical p ope ies, and he e ec o he liquid ilm hickness (no malized by he diame e o he
impac ing d ople ) on he hyd odynamic mechanisms de eloping a e impac . The high-speed
images showed changes in he size and numbe o splashed p oduc s wi h he ela i e hickness
o he liquid ilm and he impac ene gy. Images also cap u ed he pa icula mo phological e en
o bubble encapsula ion o liquid ilms wi h small hicknesses. The e ec o he liquid ilm on he
c own hickness and heigh e olu ion was simila o he esul s epo ed by o he au ho s. O e all,
he beha io s induced in he hyd odynamic mechanisms a e d op impac o he 100% JF and
he 75%/25% mix u e (JF+NExBTL) we e e y simila ; he majo di e ences we e obse ed o he
50%/50% mix u e, due o i s iscosi y. Fo his luid none e en o splashing was obse ed o he
hinne liquid ilm (δ=0.1).
Finally, he phenomenon ob ained o each se o impac condi ions was compa ed wi h he
p edic ion o ou c i e ia es ablishing he sp eading/splashing ansi ion. Thei uni e sali y was
es ed and Vande Wal e al.
[7]
p o ed o p oduce he g ea es ag eemen conside ing all he
expe imen al condi ions wi hin and ou side i s alida ion domain. The eason is likely he in luence
o he dimensionless ilm hickness, simila o he co ela ion o Cossali e al.
[5]
, bu wi h a di e en
nonlinea e ec on he ansi ion c i e ia Kc.
Au ho Con ibu ions:
Concep ualiza ion, D.F.S.R., A.R.R.S., and M.R.O.P.; me hodology, D.F.S.R. and A.R.R.S.;
o mal analysis, D.F.S.R., A.R.R.S., and M.R.O.P.; da a cu a ion, D.F.S.R. and M.R.O.P.; w i ing—o iginal d a
p epa a ion, D.R. and M.R.O.P.; w i ing— e iew and edi ing, D.F.S.R., A.R.R.S., and M.R.O.P.; isualiza ion,
D.F.S.R.; supe ision, A.R.R.S.; unding acquisi ion, A.R.R.S. All au ho s ha e ead and ag eed o he published
e sion o he manusc ip .
Funding: The p esen wo k was pe o med unde he scope o Labo a ó io Associado em Ene gia T anspo es e
Ae onáu ica (LAETA)—ac i i ies, and i was suppo ed by Fundação pa a a Ciência e a Tecnologia (FCT) h ough
he p ojec s UID/EMS/50022/2019 and UIDB/50022/2020, and he g an sponso ed by Fundação pa a a Ciência
e a Tecnologia SFRH/BD/140009/2018.
Acknowledgmen s:
The au ho s would like o acknowledge Má io Cos a o all he suppo he ga e o his wo k.
His passing was unexpec ed and we would like o dedica e him his a icle as a homage o his memo y.
Con lic s o In e es : The au ho s decla e no con lic o in e es .
Abb e ia ions
The ollowing abb e ia ions a e used in his manusc ip :
ASTM Ame ican Socie y o Tes ing and Ma e ials
ps F ames pe Second
HEFA Hyd op ocessed Es e s and Fa y Acids
HVO Hyd op ocessed Vege able Oil
JF Je Fuel
NExBTL Nes e Renewable Diesel
Appl. Sci. 2020,10, 6698 20 o 21
Appendix A. Expe imen al Condi ions
Table A1. The ela i e hickness o he hinne liquid ilms o H2O.
Dn[mm] δ
1.50 0.22
0.84 0.24
0.51 0.27
0.25 0.31
0.10 0.39
Table A2. D ople diame e s.
Dn[mm] DH2O
0[mm] D100%JF
0[mm] D75%JF/25%HVO
0[mm] D50%JF/50%HVO
0[mm]
1.50 4.03 3.04 3.05 3.06
0.84 3.61 2.76 2.77 2.78
0.51 3.23 2.44 2.47 2.47
0.25 2.80 2.07 2.12 2.18
0.10 2.27 1.73 1.74 1.78
Table A3. Impac eloci ies.
z[m]Dn[mm] U0[m/s]
H2O 100% JF 75% JF / 25% HVO 50% JF / 50% HVO
z1=0.175
1.50 1.83 1.80 1.80 1.81
0.84 1.83 1.80 1.80 1.80
0.51 1.82 1.79 1.79 1.80
0.25 1.81 1.79 1.79 1.79
0.10 1.81 1.79 1.78 1.79
z2=0.5
1.50 3.07 2.97 2.99 3.00
0.84 3.05 2.96 2.97 2.97
0.51 3.04 2.93 2.94 2.95
0.25 3.02 2.90 2.93 2.93
0.10 2.96 2.88 2.90 2.91
z3= 1
1.50 4.21 4.05 4.06 4.06
0.84 4.18 4.00 4.00 4.00
0.51 4.15 3.95 3.96 3.96
0.25 4.09 3.83 3.86 3.89
0.10 3.98 3.68 3.68 3.78
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