Expe imen al de e mina ion o he hea ans e coe icien o he op imal design
o he cooling sys em o a PEM uel cell placed inside he uselage o an UAV
Jo ge Ba oso 1, Jo di Renau 2, An onio Lozano 1, José Mi alles 2, Jesús Ma ín 1,
Fe nando Sánchez 2, Félix Ba e as 1,*
1 LIFTEC, CSIC – Uni e sidad de Za agoza. Ma ia de Luna 10, 50018 – Za agoza. SPAIN
2 UCH CEU. Uni e sidad CEU Ca denal He e a. C/ San Ba olomé, 55, 461150 – Al a a
del Pa ia ca, Valencia. SPAIN
Abs ac
The objec i e o his esea ch is o calcula e he hea ans e coe icien s needed o
he u he design o he op imal cooling sys em o a high- empe a u e polyme
elec oly e memb ane uel cell (HT-PEMFC) s ack ha will be inco po a ed o he
powe plan o a ligh unmanned ae ial ehicle (UAV) capable o eaching an al i ude
o 10,000 m. Expe imen s a e pe o med in wo ec angula unnels, o h ee
di e en o m ac o s, in expe imen al condi ions as close as possible o he ac ual
ones in he HT-PEMFC s ack. Fo he calcula ions, all he ele an he mal p ocesses
a e conside ed. Di e en pa ame e s a e measu ed, such as ai mass low a e, inle
and ou le ai empe a u es, and wall empe a u es o bipola pla es and endpla es.
Di e en nume ical models a e i ed e ealing he in luence o he di e se ele an
non-dimensional g oups on he Nussel numbe . Hea ans e coe icien s
calcula ed o he ai cooling low a y om 8 o 44 W m-2 K-1. Resul s ob ained a
sea le el a e ex apola ed o a ligh ceiling o 10 km. The low sec ion is op imized
as a unc ion o he powe equi ed o cool he s ack down o he empe a u e
ecommended by he memb ane-elec ode assembly (MEA) manu ac u e using a
nume ical code speci ically de eloped o his pu pose.
Keywo ds: Hea ans e coe icien , PEM uel cell, Hyd ogen, Hea ans e
managemen , UAV
* Co esponding au ho . E-Mail: elix@li ec.csic.es
Nomencla u e
La in alphabe
A a ea (m2)
a nume ical coe icien
Bi Bio numbe
b exponen o Reynolds numbe
C cons an
c exponen o P and l numbe
Cp speci ic hea (J kg-1 K-1)
Deq equi alen diame e (m)
F hea ans e a ea (m2)
g g a i y accele a ion a sea le el
(9.80665 m s-2)
H ai en halpy (J kg-1)
h hea ans e coe icien
(W m-2K-1)
K mino losses coe icien
k he mal conduc i i y
(W m-3K-1)
L leng h o he s ack (m)
LC cha ac e is ic leng h (m)
m
mass low a e (g s-1)
Nu Nussel numbe
∆
p p essu e d op (Pa)
P pe ime e (m)
P P and l numbe
Q hea lux (W)
R ai gas cons an (287 m2 s-2 K-1)
Re Reynolds numbe
T empe a u e (K)
V eloci y (m s-1)
W
powe consump ion (W)
Z al i ude (m)
G eek le e s
α
empe a u e g adien in he
oposphe e (−0.0065 K m-1)
𝜖𝜖 emissi i y
δ plas ic hickness (m)
ρ
densi y (kg m-3)
σ
S e an-Bol zmann cons an
(5.67x10-8W m-2 K-4)
λ
he mal conduc i i y
(W m-1K-1)
Subsc ip s
a,i ai inle
a,o ai ou le
ai ai
con con ec ion
dis dissipa ed hea
duc wind unnel
low
FC uel cell
me me al
log loga i mic
plas plas ic
ad adia ion
SL sea le el
w wall
we we
1
1. In oduc ion
An impo an pe cen age o he ala ming amoun o CO2 cu en ly emi ed o he
a mosphe e co esponds o he anspo sec o . In pa icula , a ia ion-gene a ed
CO2 is p ojec ed o g ow in app oxima ely 6% by 2050, due o he inc ease in global
a el demand [1]. Fuel cells can be a clean al e na i e o hei use in he ae onau ic
sec o [2]. Fo unmanned ae ial ehicles (UAVs), powe plan s based on p o on
exchange memb ane uel cells (PEMFCs) ha e been ecen ly es ed in ligh s o e y
sho du a ion a low ceiling [3-5]. Howe e , ligh s o small UAVs a a c uising
al i ude o 10 km pose some challenges ela ed o he a ia ion in a mosphe ic
condi ions, namely: e y low a mosphe ic and pa ial oxygen p essu es,
empe a u e below −50°C, and e y d y ai humidi y [6]. E iciency and du abili y o
a PEMFC is mainly a ec ed by he accu a e managemen o he mass and hea
ans e p ocesses ha ake place inside he de ice. Focusing on hea ans e , he
wo king empe a u e o a PEMFC is no mally adjus ed o he one ecommended by
he memb ane-elec ode assembly (MEA) manu ac u e . In he p esen esea ch, a
high empe a u e (HT) PEMFC s ack is conside ed, which allows aising he
ope a ing empe a u e abo e 140°C. This acili a es hea ejec ion due o he la ge
empe a u e di e ence be ween uel cell and ambien en i onmen [7]. As a esul ,
he cooling sys em can be simple , inc easing he powe plan mass-speci ic and
olume-speci ic powe densi ies. This is a e y impo an poin o ligh UAVs whe e
weigh is an essen ial issue.
The hea ans e p oblem analyzed in he p esen esea ch is o con ol he
wo king empe a u e o a HT-PEMFC s ack in he ange om 140°C o 180°C when
a cons an elec ic powe is demanded. The s ack will be loca ed inside he uselage
o he UAV, in o de o p o ec he di e en elemen s o he powe plan om he
e y low ambien empe a u e du ing ligh s a an al i ude o 10 km. The UAV
conside ed has a o al ai ame mass o 3 kg, a wingspan o 4 m, and he uselage has
a diame e o 200 mm and a leng h o 1.6 m [8]. A pho o o his UAV is depic ed in
Fig. 1 in a low al i ude ligh wi h an in e nal combus ion engine.
2
Figu e 1. Pho o o he UAV conside ed in he p esen esea ch.
In a b oade sense, he p oblem unde s udy consis s in he de e mina ion o
he hea ans e coe icien o a p isma ic h ee-dimensional objec inside an
enclosu e. The expe imen al es ima ion o he hea ans e coe icien implies he
measu emen o he hea ans e ed by ei he di ec (s eady s a e) o indi ec
( ansien ) echniques [9]. T ansien echniques in ol e he measu emen o he
empe a u e change wi h ime a a loca ion nea o o a he body. An example o
his me hod is he de e mina ion o he su ace empe a u e analyzing he emi ed
adia ion in ensi y and wa eleng h using in a ed came as [10,11]. A di ec hea
ans e measu emen me hod is he ene gy supply echnique, in which he
empe a u e o a solid su ace is measu ed while ac i ely p o iding hea [12,13].
O he me hods o he di ec measu emen o he hea ans e coe icien a e he
use o hin ilm hea lux senso s [14-16] o he one based on naph halene
sublima ion ha has been used o measu e he con ec i e hea ans e coe icien
on he ho izon al oo o a eal building [17].
Fi s s udies on he de e mina ion o he hea ans e coe icien da e back o
he i s hal o he XX Cen u y [18-20]. Since hen, a la ge numbe o pape s ha e
been published desc ibing co ela ions o he hea ans e coe icien as a unc ion
o he objec geome y and he low cha ac e is ics, as summa ized in many
ex books [21,22]. Calcula ion o he hea ans e coe icien is widely epo ed in
he li e a u e o uncon ined lows in an ample a ie y o applica ion p oblems such
as in machine ools and manu ac u ing p ocesses [23-27], cooling o he human
body [28-29], o e ige a e buildings [30-32] and elec onic de ices [33-35], o
o e cylinde s o sphe es [36-38]. In all hese s udies, ei he Nussel numbe (Nu)
is exp essed as a unc ion o non-dimensional g oups, ypically Reynolds (Re) and
P and l (P ) numbe s, o he hea ans e coe icien is gi en as a unc ion o
dimensional a iables including empe a u e di e ence o coolan eloci y.
3
Howe e , hey a e likely o be inaccu a e in his case, because hey do no conside
o m ac o s o unnel blockage e ec s. In ac , many o hem ha e been es ed in
his wo k wi h poo esul s. Ano he la ge g oup o s udies e e o con ined lows
in channels o duc s [39-41], and o annula geome ies as desc ibed in a ecen
e iew in [42], bu hey no mally conside ully de eloped low. In his s udy, he
hea ans e om he HT-PEMFC s ack occu s in a non-de eloped low inside a
ese oi wi h he walls qui e close o he objec . Besides, he objec leng h in he
low di ec ion is compa able o he dimensions in he di ec ion no mal o he low,
and Re numbe s a e in he ange co esponding o lamina and ansi ional-
u bulen egimes, cons i u ing a a he pa icula case. All he es ed co ela ions
a ailable in he li e a u e ha e p o en o be unsui able.
The objec i e o his esea ch is o ob ain eliable and accu a e models o
calcula e he hea ans e coe icien needed o he u he design o he op imal
cooling sys em o a high- empe a u e PEMFC s ack ha will be inco po a ed o he
powe plan o a ligh UAV capable o eaching an al i ude o 10,000 m using he
ene gy supply echnique. To his end, expe imen s a e pe o med in wo ec angula
unnels, o h ee di e en o m ac o s, in condi ions simila o hose expec ed o
he HT-PEMFC s ack. Fo calcula ions, con ec i e and adia i e p ocesses a e
conside ed. Di e en pa ame e s a e measu ed, such as ai mass low a e, inle and
ou le ai empe a u es, and wall empe a u es o bipola and endpla es, among
o he s.
2. Hea ans e analysis. Non-dimensional conside a ions
Once he HT-PEMFC s ack is wo king unde a s a iona y egime, he cooling sys em
has o be capable o g an ing a s able empe a u e in he ange be ween 140°C and
180°C. In mos cases, he coolan used is a mosphe ic ai , and hea ans e
mechanisms a e con ec ion and adia ion. Ini ially i will be assumed ha
conduc ion be ween he di e en elemen s o he s ack is su icien ly as o
cha ac e ize i by a single ep esen a i e empe a u e. The accu acy o his
assump ion will be checked a e ob aining he expe imen al esul s.
Excess hea gene a ed o any speci ic s ack powe has o be ex ac ed h ough
he ou e walls o keep a cons an empe a u e. F om an ene gy balance, once he
4
sys em is in equilib ium, all he hea dissipa ed om he s ack (𝑄𝑄𝑑𝑑𝑑𝑑𝑑𝑑) has o be equal
o ha abso bed by he ai (𝑄𝑄𝑎𝑎𝑑𝑑𝑎𝑎). I can be exp essed as
𝑄𝑄𝑑𝑑𝑑𝑑𝑑𝑑 =𝑄𝑄𝑎𝑎𝑑𝑑𝑎𝑎 =𝑚𝑚𝑎𝑎𝑑𝑑𝑎𝑎�𝐻𝐻𝑎𝑎,𝑜𝑜−𝐻𝐻𝑎𝑎,𝑑𝑑� (1)
whe e (𝑚𝑚𝑎𝑎𝑑𝑑𝑎𝑎) is he cooling ai mass low a e, while 𝐻𝐻𝑎𝑎,𝑑𝑑 and 𝐻𝐻𝑎𝑎,𝑜𝑜a e ai inle and
ou le en halpy espec i ely. Hea abso bed by he ai is he sum o he con ec i e
and he adia i e componen s
𝑄𝑄𝑎𝑎𝑑𝑑𝑎𝑎 =𝑄𝑄𝑐𝑐𝑜𝑜𝑐𝑐𝑐𝑐 +𝑄𝑄𝑎𝑎𝑎𝑎𝑑𝑑 (2)
The hea ha he s ack exchanges by adia ion can be exp essed as
𝑄𝑄𝑎𝑎𝑎𝑎𝑑𝑑 =𝜎𝜎 𝜖𝜖𝐹𝐹𝐹𝐹 𝐹𝐹𝐹𝐹𝐹𝐹(𝑇𝑇𝐹𝐹𝐹𝐹
4−𝑇𝑇
�𝑎𝑎𝑑𝑑𝑎𝑎
4) (3)
whe e
σ
is he S e an-Bol zmann cons an , 𝜖𝜖𝐹𝐹𝐹𝐹 he s ack emissi i y, 𝐹𝐹𝐹𝐹𝐹𝐹 he hea
ans e a ea, TFC i s absolu e empe a u e, and 𝑇𝑇
�𝑎𝑎𝑑𝑑𝑎𝑎 he ai empe a u e a e aged
be ween inle and ou le o he cooling sys em. Equa ion (3) includes he ene gy
adia ed by he s ack and he adia i e ene gy ha i abso bs. I assumes ha he
s ack abso p ion coe icien is equal o i s emissi i y, acco ding o Ki cho ´s law o
a g ey body. In his s ep, he HT-PEMFC s ack is conside ed as a unique body, bu as
i is o med by di e en ma e ials, Eq. (3) will la e be modi ied.
Hea ans e ed by con ec ion is de ined by
𝑄𝑄𝑐𝑐𝑜𝑜𝑐𝑐𝑐𝑐 =ℎ 𝐹𝐹𝐹𝐹𝐹𝐹 ∆𝑇𝑇
�
�
�
�
𝑙𝑙𝑜𝑜𝑙𝑙 (4)
whe e ℎ is he con ec i e hea ans e coe icien , and ∆𝑇𝑇
�
�
�
�
𝑙𝑙𝑜𝑜𝑙𝑙 he mean loga i hmic
empe a u e di e ence ha is calcula ed by
∆𝑇𝑇
�
�
�
�
𝑙𝑙𝑜𝑜𝑙𝑙 =�𝑇𝑇𝑤𝑤−𝑇𝑇𝑎𝑎,𝑖𝑖�−�𝑇𝑇𝑤𝑤−𝑇𝑇𝑎𝑎,𝑜𝑜�
ln�𝑇𝑇𝑤𝑤−𝑇𝑇𝑎𝑎,𝑖𝑖
𝑇𝑇𝑤𝑤−𝑇𝑇𝑎𝑎,𝑜𝑜� (5)
𝑇𝑇𝑎𝑎,𝑑𝑑 and 𝑇𝑇𝑎𝑎,𝑜𝑜 a e he ai inle and ou le empe a u e, and 𝑇𝑇𝑤𝑤 he s ack su ace
empe a u e,
The con ec i e hea ans e coe icien ℎ o o ced ai lowing along an
annula space su ounding a PEM uel cell s ack will depend on
ℎ=𝑓𝑓�𝐿𝐿,𝜆𝜆,𝜌𝜌,𝑉𝑉,𝐷𝐷𝑒𝑒𝑒𝑒,𝜇𝜇,𝐶𝐶𝑝𝑝� (6)
whe e 𝜆𝜆, 𝜌𝜌, 𝜇𝜇, 𝐶𝐶𝑝𝑝 and 𝑉𝑉 a e he mal conduc i i y, densi y, iscosi y, speci ic hea and
eloci y o he cooling low, espec i ely; 𝐿𝐿 is he s ack leng h in he low di ec ion
and 𝐷𝐷𝑒𝑒𝑒𝑒 is he equi alen diame e o he c oss-sec ional a ea o he cooling luid
low
𝐷𝐷𝑒𝑒𝑒𝑒 =4𝐴𝐴𝑓𝑓
𝑃𝑃𝑤𝑤𝑤𝑤𝑤𝑤 =4 (𝐴𝐴𝑑𝑑𝑑𝑑𝑑𝑑𝑤𝑤−𝐴𝐴𝐹𝐹𝐹𝐹)
𝑃𝑃𝑑𝑑𝑑𝑑𝑑𝑑𝑤𝑤+𝑃𝑃𝐹𝐹𝐹𝐹 (7)
5
in which 𝐴𝐴 and 𝑃𝑃 e e o a ea and pe ime e , espec i ely. Subsc ip s “𝑓𝑓”, “𝑤𝑤𝑤𝑤𝑤𝑤”, and
“𝑑𝑑𝑑𝑑𝑑𝑑𝑤𝑤” indica e low, we ed (whe he in con ac o no wi h he hea ans e
su ace), and he wind unnel ha encloses he s ack ac ing as he cooling duc ,
espec i ely.
Applying he Buckingham pi heo em, ou dimensionless g oups a e ob ained:
Nussel , Reynolds and P and l numbe s, and a o m ac o
Nu =ℎ 𝐷𝐷𝑤𝑤𝑒𝑒
𝜆𝜆 (8)
Re =𝜌𝜌 𝑉𝑉 𝐷𝐷𝑤𝑤𝑒𝑒
𝜇𝜇 (9)
P =𝜇𝜇 𝐹𝐹𝑝𝑝
𝜆𝜆 (10)
𝐷𝐷𝑤𝑤𝑒𝑒
𝐿𝐿 (11)
Consequen ly,
Nu =𝑓𝑓�Re,P ,𝐷𝐷𝑤𝑤𝑒𝑒
𝐿𝐿� (12)
The con ec i e hea ans e coe icien is no mally de e mined om
empi ical exp essions, ob ained expe imen ally o di e en hea ans e su aces
and low con igu a ions. Howe e , he al eady discussed lack o models o
accu a ely desc ibe he hea ans e coe icien o he p ac ical case s udied in he
p esen esea ch, has o ced o ob ain he ela ion in Eq. (12), om a se o
expe imen s speci ically designed.
3. Expe imen al se up
The expe imen al se up in his p oblem includes a 3-D p isma ic hea sou ce ha
will simula e he HT-PEMFC s ack, he wind unnels ha will ac as he uselage o
he UAV, and he di e en elemen s used o measu e he physical pa ame e s
ele an o he p oblem. A desc ip ion o all o hem will be gi en below.
3.1. Fuel cell s ack
Al hough he uel cell s ack is s ill in he design s age, a b ie summa y o i s
main cha ac e is ics will be included. F om ae odynamic calcula ions [8], i is
conside ed ha he powe ha has o be supplied by he elec ochemical de ice is
a ound 650 W. The de ice will include comme cial 5-laye high empe a u e
Cel ec®-P 1100 memb ane elec ode assemblies (MEAs) manu ac u ed by BASF Fuel
6
Cells wi h an ac i e a ea o 81.28 cm2 and a wo king empe a u e o 160°C. A
pola iza ion cu e expe imen ally ob ained in ou esea ch acili ies o a single cell
is p esen ed in Fig. 2.
Figu e 2. Pola iza ion cu e o a single cell.
Following he ecommenda ions o he MEA’s manu ac u e , he ope a ing
poin is ixed a a cu en densi y o 0.45 A cm-2 ha yields a o al cu en o 36.58
A. Acco ding o he pola iza ion cu e, a ol age o 0.45 V pe cell is ob ained o his
cu en . Then, s acking 40 cells, he esul ing uel cell powe is 658 W. A ske ch o
he 40-cells s ack is shown in Fig. 3, indica ing he dis ibu ion o gases, he
mo emen o he di e en species and elec ons, and he hea ans e . As depic ed
in he zoomed-in sec ion, each s ack cell is o med by wo pla es ha sepa a e he
indi idual cells, and a 5-laye MEA. This elemen is o med, om he ou side, by wo
gas di usion laye s ollowed by he ca hodic and anodic ca alys laye s ha a e in
close con ac wi h he p o on conduc i e polyme ic memb ane. The hea is
gene a ed a he ca alys laye s o each cell.
To educe he weigh o he s ack i will be cons uc ed wi h monopola
aluminum pla es, coa ed wi h ch omium ni ide by physical apo deposi ion o
p o ec hem om co osion [43,44]. Compa ed o g aphi e elemen s, he use o
me allic pla es imp o es he hea ans e p ocess and simpli ies he cooling sys em.
The sealing and eac an gas supply sys ems will be simila o hose in a 2.5 kW HT-
7
PEMFC s ack designed as a CHP-uni [45]. Finally e y ligh endpla es will be used
o close he s ack, manu ac u ed in a high- empe a u e esis an plas ic. Wi h hese
elemen s, he o al s ack mass is 3.86 kg, which could be u he educed using
ligh e ma e ials e.g. a magnesium alloy o he monopola pla es.
Figu e 3. Ske ch o he 40-cells s ack wi h a zoomed-in sec ion o one o he cells
indica ing he exchange o gases and hea ans e .
When s udying he hea ans e p ocess om he s ack su ace o he ai , he
way in which he elec ochemical de ice is hea ed up is no ele an . To a oid wo k
complexi y, he s ack is eplaced by a solid aluminum block wi h a o al leng h o
140 mm, a heigh o 168 mm, and a wid h o 81 mm exac ly ma ching he dimensions
14
As can be obse ed, he dependence o he non-dimensional g oups is
collapsed in wo s aigh lines. I is o be no ed ha bo h slope and in e sec poin o
he wo s aigh lines a e no ably di e en . Conside ing ha he a iable
ep esen ed in he ho izon al axis is he p oduc o he Reynolds numbe by he o m
ac o (Deq/L), he exis ence o he wo zones is associa ed o a ansi ion be ween
lamina and ansi ion- u bulen egime acco ding o he ange o Re numbe s,
coupled wi h he de elopmen o he bounda y laye dependen on he o m ac o
g oup.
App oxima ing he exponen s o simple ac ions, Eqs. (16) and (17) can be
ew i en as
Nu = 0.6155 Re(2/3)�𝐷𝐷𝑤𝑤𝑒𝑒
𝐿𝐿�(3/4)
P (1 3
⁄) (19)
o Re �𝐷𝐷𝑤𝑤𝑒𝑒
𝐿𝐿�≥640 and
Nu = 0.002149 Re(3/2)�𝐷𝐷𝑤𝑤𝑒𝑒
𝐿𝐿�(4/3)
P (1 3
⁄) (20)
o Re �𝐷𝐷𝑤𝑤𝑒𝑒
𝐿𝐿�≤560.
The i o he expe imen al measu emen s using Eqs. (16) and (17) has an
a e age e o o 3.34%. Using he simpli ied Eqs. (19) and (20), he e o sligh ly
inc eases o 4.33%.
Fo he Re �𝐷𝐷𝑤𝑤𝑒𝑒
𝐿𝐿�≥640 egion, he ob ained dependence o he Nussel numbe
on he o m ac o is simila o ha desc ibed in o he p e ious s udies epo ed in
he li e a u e o con ined low con igu a ions [53,54]. Howe e , o Re �𝐷𝐷𝑤𝑤𝑒𝑒
𝐿𝐿�≤560,
ou esul s indica e a s onge in luence o he o m ac o han he one no mally
epo ed in o he pape s [19,55]. I should be no ed ha i he models in he
li e a u e a e used, e o s a ound 50% a e ob ained when es ima ing he hea
ans e coe icien e en when hey ha e been ob ained o low con igu a ions
simila (al hough no iden ical) o he es ed one, bu di e en low condi ions.
4.2. Model alida ion
Wi h all he equa ions desc ibed up o his poin , s a ing om a educed se o inpu
alues (hea gene a ed by he s ack, ai low a e and ai inle empe a u e), an
a e age s ack su ace empe a u e and ai ou le empe a u e can be calcula ed
using he EES nume ical code. Howe e , i he empe a u e o he plas ic endpla es
15
and ha o he me al s ack su ace ha e o be de e mined sepa a ely, a hea balance
has o be sequen ially applied o each one o hese elemen s. In his way,
in e media e empe a u es and hea ans e coe icien s can be ob ained o he
on plas ic endpla e, he me al su ace in he middle, and he ea endpla e.
Figu e 9. P edic ed (lines) and expe imen al (symbols) me al empe a u es a sea
le el.
Figu e 9 shows bo h expe imen al and p edic ed me al empe a u e as a
unc ion o he cooling ai low a e a sea le el condi ions. All expe imen al poin s
ha e been eplica ed a leas i e imes. E o be ween p edic ed and measu ed
alues is below 10% in all cases. As expec ed, s ack cooling becomes mo e di icul
as Deq/L inc eases, due o he dec ease in ai eloci y and, hence, in he con ec i e
hea ans e coe icien .
I he uel cell s ack is going o be ins alled in a UAV, i is in e es ing o
de e mine he dependence o he equi ed cooling ai mass low a e on al i ude (Z).
Ai densi y and empe a u e a ia ion will be desc ibed by he o mulas o a
s anda d ISO a mosphe e [56],
𝑇𝑇=𝑇𝑇𝑆𝑆𝐿𝐿 +𝛼𝛼 𝑍𝑍 (21)
𝜌𝜌=𝜌𝜌𝑆𝑆𝐿𝐿 �1 + 𝛼𝛼 𝑍𝑍
𝑇𝑇𝑆𝑆𝑆𝑆�−𝑔𝑔
𝛼𝛼𝛼𝛼−1 (22)
16
These exp essions a e applicable up o 10,000 m. In hem,
ρ
SL and TSL a e he
densi y and empe a u e alues a sea le el (1.225 kg m-3 and 288.15 K
espec i ely), g is he g a i y accele a ion a sea le el assumed o be cons an and
equal o 9.80665 m s-2, R is he ai gas cons an (287 m2 s-2 K-1), and
α
is he
empe a u e g adien in he oposphe e aken o be −0.0065 K m-1.
Figu e 10. Cooling ai low a e (do ed lines) and Reynolds numbe (solid lines) o
wo di e en hea eleased powe s. G ey colo co esponds o 500 W, and black o
600 W.
Resul s depic ed in Fig. 10 a e inally ob ained o wo hea eleased powe
alues, 500 W and 600 W. The change in ai p ope ies wi h al i ude leads o an
inc ease in bo h ai eloci y and olume ic low a e equi ed o a sui able cooling.
Howe e , as he ai densi y dec eases, he cooling ai low a e also dec eases wi h
heigh . In he same way, as he ai eloci y inc ease is smalle han he densi y
a ia ion, Re also dec eases.
4.3. Op imiza ion o he cooling low sec ion
Va ia ions in he cooling low sec ion a e in luen ial on he hea ans e , because
he o m ac o , Deq/L, and he con ec i e hea ans e coe icien can be modi ied.
On he o he hand, p essu e losses in he cooling low also depend on he low c oss-
17
sec ional a ea. The equi ed cooling low a e, aking in o accoun p essu e losses,
de e mines he powe equi ed o ci cula e he low along he cooling ci cui :
𝑊𝑊=∆𝑝𝑝𝑓𝑓 𝑉𝑉 𝐴𝐴𝑎𝑎𝑑𝑑𝑎𝑎 (23)
P essu e losses ∆𝑝𝑝𝑓𝑓 can be e alua ed acco ding o
∆𝑝𝑝𝑓𝑓=𝜌𝜌 𝐾𝐾𝑉𝑉2
2 (24)
whe e ic ion losses ha e been neglec ed compa ed o hose due o sudden changes
in low sec ion and di ec ion. The coe icien o mino losses, K, can be conside ed o
be a unc ion o he a io be ween he wind unnel sec ion and he low sec ion
a ound he s ack
𝐾𝐾=𝐶𝐶�1−𝐴𝐴𝑎𝑎𝑖𝑖𝑎𝑎
𝐴𝐴𝑑𝑑𝑑𝑑𝑑𝑑𝑤𝑤� (25)
Figu e 11. Beha io o he powe consump ion o he ai cooling sys em.
F om he expe imen al measu emen s, an a e age C alue o 10.73±0.4 is
ob ained. I should be no ed ha his esul does no ag ee wi h hose epo ed in
he li e a u e o ei he an expansion o a con ac ion, because he es ed
con igu a ion includes a combina ion o con ac ions, expansions and changes in
low di ec ion. Adding hese equa ions o he EES nume ical code, he o m ac o
ha minimizes he cooling sys em powe consump ion can be ob ained. As can be
obse ed in Fig. 11, he cu es ha e a ela i ely la egion nea he minimum, so o
18
o m ac o s anging be ween 0.35 and 0.55 low powe will be equi ed o cool he
s ack down. Ob iously, he selec ed o m ac o (Deq/L) has o be compa ible wi h
he space a ailable in he ai c a ame, usually qui e limi ed. Fo his eason, i will
be unp ac ical o u he inc ease he low c oss sec ion. The e ical line ma ks he
maximum o m ac o used in he expe imen al measu emen s.
Figu e 12. Beha io o ai olume ic low a e.
The equi ed ai low a e as a unc ion o he o m ac o in shown in Fig. 12.
I is o be no ed ha o he o m ac o ange conside ed, he co esponding ai
eloci y a an al i ude o 10 km is always below 7 m/s. This means ha cooling he
s ack down o he ope a ing empe a u e (160°C), can be achie ed ei he by ac i e
o passi e sys ems. Fo he passi e s a egy, he eloci y o he ai low induced by
he mo emen o he UAV du ing ligh can be used o cooling pu poses. Axial
compac ans wi h e y low powe consump ion can be conside ed o he ac i e
me hod [57-59]. I should be no ed ha he calcula ed ai c a s all eloci y when
lying a 10 km is abo e 25 m s-1. In any case, he way o pass he ai low h ough
he uselage o he UAV has o be ca e ully designed accoun ing o speci ic
ae odynamic conside a ions.
19
5. Conclusions
A se o expe imen s has been comple ed o de e mine he con ec i e hea ans e
coe icien o cool a HT-PEMFC s ack down ins alled in he uselage o an UAV. The
calcula ed hea ans e coe icien a ies om 8 o 44 W m-2 K-1. Two new models
ha e been ob ained ha allow he accu a e calcula ion o he Nussel numbe as a
unc ion o he h ee ele an non-dimensional g oups, Re, P , and o m ac o
(Deq/L). I o he models a ailable in he li e a u e a e used, e o s a ound 50% a e
ob ained when es ima ing he hea ans e coe icien . Wi h a non-dimensional
app oach, esul s ob ained a sea le el a e sui ably ex apola ed o a a ge al i ude
o 10 km. Using a nume ical code speci ically de eloped, he cooling low sec ion is
op imized, esul ing in o m ac o s om 0.35 o 0.55. This ange will ensu e a
cooling sys em wi h low powe consump ion, and is compa ible wi h he space
a ailabili y in he ac ual ai c a uselage. Resul s indica e ha bo h passi e and
ac i e cooling s a egies could be p ac ically conside ed.
The de eloped p ocedu e and he models ob ained (conside ing he alidi y ange)
will be applicable o any si ua ion in which a uel cell s ack loca ed in an enclosu e
is cooled down by an ai low su ounding i . This is a ypical si ua ion o ei he
high- empe a u e o low- empe a u e PEMFC s acks used in anspo a ion o in
combined hea and powe uni s.
6. Acknowledgmen s
This wo k has been unded by he Sec e a ia o S a e o Resea ch o he Spanish
Minis y o Economy and Compe i i eness unde p ojec ENE2012-38642-C02-
01/CON.
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