Nume ical In es iga ion on An i-Icing Pe o mance o Hea ing Su ace o NACA0012 Ai oilK Fukudome, S U anai, H Mamo i and M Yamamo o
VIII In e na ional Con e ence on Compu a ional Me hods o Coupled P oblems in Science and Enginee ing
COUPLED PROBLEMS 2019
E. Oña e, M. Papad akakis and B. Sch e le (Eds)
NUMERICAL INVESTIGATION ON ANTI-ICING PERFORMANCE OF
HEATING SURFACE FOR NACA0012 AIRFOIL
K. FUKUDOME*, S. URANAI*, H. MAMORI† AND M. YAMAMOTO*
* Depa men o Mechanical Enginee ing, Facul y o Enginee ing
Tokyo Uni e si y o Science
6-3-1 Niijuku, Ka sushika-ku, Tokyo 125-8585, Japan
e-mail: k ukudom[email p o ec ed], www. s.kagu. us.ac.jp/yamamo o/
† G adua e School o In o ma ics and Enginee ing, School o In o ma ics and Enginee ing
The Uni e si y o Elec o-Communica ions
1-5-1, Cho ugaoka, Cho u, Tokyo 182-8585, Japan
email: mamo [email protected], h p://www.mamo ilab.mi.uec.ac.jp/
Key wo ds: Ice Acc e ion, An i-Icing Me hod, Ai oil, Hea ing Su ace, Supe -Cooled Wa e
D ople .
Abs ac . Ice acc e ion is a phenomenon ha supe -cooled wa e d ople s impinge and acc e e
on wall su aces. I is known ha icing can cause se e e acciden s. To p e en he icing, an
elec o- he mal hea e is ecen ly adop ed as he de- and an i-icing de ice o wings. In he
p esen s udy, we conduc ed icing simula ions o a wo-dimensional NACA0012 ai oil wi h an
elec o- he mal hea e on he leading-edge su ace o op imize he hea ing a ea. The a ack angle
and he hea ing a ea we e changed om 0 o 4 deg ees and om 0 o 2.0% cho d leng h,
espec i ely. Th ough he simula ions, we ound ha he li coe icien was signi ican ly
imp o ed by he hea ing, he d ag coe icien gene ally dec eased wi h inc easing he hea ing
a ea, and a he a ack angle o 0 deg ee and he hea ing a ea o 1.0% cho d leng h, he d ag
coe icien excep ionally became wo se because o he esidual ice shape wi h ho ns.
1 INTRODUCTION
Icing is a phenomenon ha supe -cooled wa e d ople s collide on a solid su ace and i
o ms an ice laye on he su ace. The icing p oblem occu s o many indus ial appa a uses
such as powe lines, buildings, ca s, ships, ai c a wings, je engines and so on. Fo ai c a
wings, he icing makes ice laye and oughness on he su ace and hey lead a d as ic dec ease
o ae odynamic pe o mance. The e o e, he icing is one o he easons o cause a a al acciden
o ai c a . To p e en he acciden , he p edic ion o icing and he de elopmen o de- and an i-
icing echniques a e e y impo an om he iewpoin s o ai c a sa e y. As he de- and an i-
icing echniques, bleed ai , an i- eezing liquid and an elec ic hea e ha e been p oposed and
implemen ed o ai c a . Because o he easy se ing and he low en i onmen al bu den, he
elec ic hea e has ecen ly been adop ed in cu en ai c a . We can ind a numbe o echnical
pape s on icing in he li e a u e. Fo example, Al-Khalil e al. [1] pe o med expe imen al and
nume ical s udies o icing on he wing wi h he elec ic hea e . They epo ed he e ec o he
di e en hea ing empe a u es o he elec ic hea e . Bu e al. [2] conduc ed he icing simula ion
673
K. Fukudome, S. U anai, H. Mamo i AND M. Yamamo o.
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o a wing wi h conside ing hea lux om he wing su ace. Reid e al. [3] pe o med he
nume ical simula ion o an elec ic- he mal de-icing sys em, and hey epo ed he empo al
a ia ion o su ace empe a u e o he de-icing p ocess. Howe e , he esea ch ocusing on
he hea ing a ea o he elec ic hea e has no been conduc ed ye .
Taking in o accoun hese backg ounds, in he p esen s udy, we pe o m wo-dimensional
icing simula ions o NACA0012 ai oil o in es iga e he e ec o he hea ing a ea on he
ae odynamic pe o mance. Th ough his s udy, he in luences o hea ing a ea on he esidual
ice o ma ion, he d ag and he li o he ai oil and ene gy consump ion a e cla i ied.
2 NUMERICAL PROCEDURE
The nume ical simula ion consis s o ou s eps: (1) gene a ion o compu a ional g ids; (2)
compu a ion o low ield; (3) compu a ion o d ople ajec o ies and collec ion e iciency; (4)
he modynamics compu a ion. Acco ding o hem, we can ob ain ice shape on he ai oil. In he
ollowing, he de ails o each nume ical p ocedu e a e b ie ly explained.
The compu a ional a ge is a NACA0012 ai oil. The compu a ional g id is shown in Fig. 1.
The o e lap g id is employed. The main is used o simula e he whole low ield a ound he
ai oil, and as shown in Fig. 1, he sub g id has high esolu ion o co ec ly ob ain he ice shape
a ound he leading edge and he bounda y laye on he ai oil. The o al numbe o g id poin s
is abou 26,000. The con e gence o he ice shape by he g id poin s has p elimina ily been
con i med h ough he g id independen s udy.
The low a ound he ai oil is assumed o be wo-dimensional, comp essible, and ully
u bulen . The go e ning equa ions a e he con inui y, Na ie -S okes, ene gy equa ions and
anspo equa ions o he u bulen kine ic ene gy k and i s dissipa ion a e ε. The Ka o-Launde
k-ε u bulen model [4] is employed o supp ess he o e -p oduc ion o u bulence a ound he
leading edge egion.
The d ople ajec o y is compu ed based on he Lag angian app oach. Since he size o
d ople and he concen a ion a e small enough, a one-way coupling me hod is employed. Tha
is, he d ople mo ion is a ec ed om he low ield, whe eas he d ople does no a ec he
low ield. The mo ion equa ion o a d ople is a simpli ied BBO equa ion as
dd
g
D
dUU
d
C
d
Ud 1
4
3
=
.
(1)
He e,
d
U
is he eloci y o a d ople and
U
is he ela i e eloci y be ween he low and he
d ople .
g and
d a e he densi y o he gas (i.e. ai ) and he d ople espec i ely, dd is he
diame e o he d ople , and CD is he d ag coe icien . Since we suppose ha he d ople does
no de o m and o a e, as he d ag coe icien o a sphe e, Schile model [5] is used, which is
de ined as
( )
687.0
Re15.01
Re
24 +=
D
C
,
(2)
whe e Re is he d ople Reynolds numbe based on he d ople diame e , he ela i e eloci y,
densi y o he luid
, and iscosi y o he luid
.
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K. Fukudome, S. U anai, H. Mamo i AND M. Yamamo o.
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In he he modynamics compu a ion, since he ime scales o he low ield and he icing a e
signi ican ly di e en , we use he weak coupling me hod. The Ex ended Messinge Model [6]
( e e ed as EMM, he ea e ) is adop ed as he icing model. The EMM is based on he mass and
ene gy conse a ion law o he ice and wa e and he equa ion o phase change a he in e ace
be ween he ice and he wa e . Al hough he EMM is widely used in icing simula ions, he
su ace hea ing and he empe a u e o un-back wa e a e no conside ed. Thus, in he p esen
s udy, we imp o e he EMM o ep oduce hem as ollows. Fi s , he hea lux is compu ed by
he empe a u e o he colliding d ople . Second, he empe a u e and hickness o he ice o
wa e ilm a e compu ed. I he empe a u e is o e 0 deg ee Celsius, he adhe ed d ople is
ea ed as a wa e ilm.
Figu e 1 Compu a ional domain and g id. Le and igh igu es ep esen he en i e compu a ional domain and
he enla ged iew o sub-g id a ound ai oil, espec i ely. Main and sub g ids a e colo ed in ed and blue,
espec i ely.
The compu a ional condi ions a e abula ed in Table 1, which a e se in acco dance wi h he
expe imen al s udy pe o med by Olsen e al. [6]. In he p esen s udy, he an i-icing simula ion
o he NACA ai oil is ca ied ou and he e o e he su ace o he ai oil is pa ially hea ed. A
he hea ed egion, he cons an empe a u e is ixed, and a he o he egion, he adiaba ic
condi ion is imposed. The h ee di e en angle o a ack and hea ing- egion cases a e examined
as abula ed in Table 2. The hea e empe a u e is se o be 5.0 oC o all cases wi h hea ing.
Table 1: Compu a ional condi ions
S a ic Tempe a u e
[oC]
-27.8
Acc e ion Time
[sec.]
480
In low Veloci y
[m/s]
58.1
MVD (Median Volume Diame e )
[
m]
20.0
LWC (Liquid Wa e Con en )
[g/m3]
1.3
Cho d Leng h
[m]
0.53
A ack Angle
[deg.]
0.0
Ambien P essu e
[kPa]
95.6
Exposu e Time
[s]
480
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K. Fukudome, S. U anai, H. Mamo i AND M. Yamamo o.
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Table 2: Pa ame e s o es cases
Case
A00
A01
A02
A20
A21
A22
A40
A41
A42
A ack Angle [deg]
0.0
2.0
4.0
Hea ing A ea x/c [%]
0.0
1.0
2.0
0.0
1.0
2.0
0.0
1.0
2.0
Figu e 2 S eamline and ice shape o he ai oil. Whi e egions ep esen adhe ed ice shape, and he colo o he
s eamlines deno es he low speed.
3 RESULT AND DISCUSSION
Figu e 2 shows he acc e ed ice shapes and s eamlines o cases consis ing o clean, A20,
A21, and A22. The colo o he s eamlines deno es he low speed. In Fig. 2 (b), he la ge ice
is o med a ound he leading edge, and eci cula ion egions appea behind he ice. Owing o
add he hea e , as shown in Fig. 2 (c) and (d), he ice a he leading edge o he wing anished,
hough he small ice emains a he downs eam o hea e . Howe e , he eci cula ion egions
disappea in applying he hea e . Ob iously, ice o ma ion s ongly depends on he hea ing a ea
and he a ack angle.
Figu e 3 indica es li coe icien Cl and no malized d ag o ep esen he ae odynamic
pe o mance. Wi hou hea ing, Cl inc ease non-linea ly wi h he inc ease o he a ack angle.
By applying he hea e , Cl d as ically eco e s and inc eases almos linea ly wi h he inc ease
o he a ack angle. The e o e, he hea e wo ks well o p e en a li loss e en in applying 2.0%
cho d leng h. On he o he hand, he d ag dis ibu es mo e complexly. In e es ingly, in case ha
he a ack angle is 0.0 deg ee, he d ag inc eases by se ing he 1.0% hea e in compa ison o
he wi hou hea ing case. Then, he d ag dec eases by applying he 2.0% hea e . In he cases
76.4 [m/s]
0.0
(b) CaseA20 (w/o hea ing)
(a) Clean Ai oil
(c) CaseA21
(Hea ing A ea 1.0[%])
(d) CaseA22
(Hea ing A ea 2.0[%])
Hea ing A ea Hea ing A ea
Ice
Ai oil
Ai oil
Ai oil
Ai oil
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K. Fukudome, S. U anai, H. Mamo i AND M. Yamamo o.
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ha he a ack angle is 2.0 deg ees, he d ag dec eases wi h expanding hea ing a ea. Howe e ,
in case ha he a ack angle is 4.0 deg ees, he d ag inc eases wi h expanding hea ing a ea.
Clea ly, he d ag dis ibu ion changes i egula ly by he hea ing a ea.
Figu e 4 shows he hea ing powe a io no malized by he h us powe . The hea ing powe
a io dec eases by inc easing he a ack angle and hea ing a ea. I is con i med ha he hea ing
a io is less han 0.4%, he e o e, he hea ing powe is ex emely lowe han he us powe .
Figu e 3: Li coe icien (le ) and d ag change om he clean ai oil ( igh ). The d ag is no malized by he d ag
o clean ai oil a he same a ack angle.
Figu e 4: Hea ing powe a io agains h us powe .
Angle o A ack [deg.]
(D - D
clean
) / D
clean
×100 [%]
0 2 4
0
10
20
un egis e ed
○：w/o Hea ing
□：Hea ing A ea=1.0%
◇：Hea ing A ea=2.0%
Angle o A ack [deg.]
Li Coe icien C
l
0.0 2.0 4.0
0.0
0.2
0.4
○：w/o Hea ing
□：Hea ing A ea=1.0%
◇：Hea ing A ea=2.0%
0 2 4
0.1
0.2
0.3
●：Hea ing A ea=1.0%
●：Hea ing A ea=2.0%
Angle o A ack [deg.]
R
hea ing
[%]
677
K. Fukudome, S. U anai, H. Mamo i AND M. Yamamo o.
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4 CONCLUDING REMARKS
The icing simula ion o a NACA0012 ai oil is pe o med o in es iga e he e ec o he
su ace hea ing a ea on he icing and he ae odynamic pe o mance. The Ex ended Messinge
model o he he modynamics calcula ion is modi ied o simula e he hea ed su ace. As a esul ,
he indings ob ained in his s udy a e as ollows.
➢ Ice o ma ion s ongly depends on he hea ing a ea and he a ack angle o he ai oil.
➢ In he unhea ed case, he la ge ice o ms a ound he leading edge and induces he low
sepa a ion behind he ice. I esul s in he inc ease o he luid d ag.
➢ The hea e applied a he leading edge p e en s he ice o ma ion, and i signi ican ly
imp o es he ae odynamics pe o mance, i.e., inc ease o li coe icien .
➢ Fo he case ha a ack angle is 0.0 deg ee, he d ag coe icien inc eases a he case o
1.0% hea ing a ea, while i dec eases a he case o 2.0% hea ing a ea.
➢ The hea ing powe is e y small compa ing he h us powe .
REFERENCES
[1] Al-Khalil K. M. e al., “Valida ion o NASA he mal ice p o ec ion compu e codes pa 3:
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de-icing”. J. Ai c a , 49(4), (2012), pp. 1101-1109.
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4-6.
[5] Schille L. and Naumann A., “A d ag coe icien co ela ion”, Z. Ve . Deu sch, Vol. 77,
(1935), pp. 318-320.
[6] Özgen S. and Canibek M., “Ice acc e ion simula ion on mul i-elemen ai oils using
ex ended Messinge model”, J. Hea Mass T ans e , Vol. 45, No. 3 (2009), pp. 305-322.
[7] Olsen W. e al., “Ice shapes and he esul ing d ag inc ease o a NACA 0012 ai oil”,
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