Design and Fabrication of a Phase Change Material Heat Storage Device for the Thermal Control of Electronics Components of Space Applications



Ci a ion: Ga mendia, I.; Vallejo, H.;
Seco, M.; Anglada, E. Design and
Fab ica ion o a Phase Change
Ma e ial Hea S o age De ice o he
The mal Con ol o Elec onics
Componen s o Space Applica ions.
Ae ospace 2022,9, 126. h ps://
doi.o g/10.3390/ae ospace9030126
Academic Edi o : Eph aim Suhi
Recei ed: 20 Janua y 2022
Accep ed: 25 Feb ua y 2022
Published: 28 Feb ua y 2022
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ae ospace
A icle
Design and Fab ica ion o a Phase Change Ma e ial Hea
S o age De ice o he The mal Con ol o Elec onics
Componen s o Space Applica ions
Iñaki Ga mendia 1,* , Ha i z Vallejo 2, Miguel Seco 2and E a Anglada 3
1Mechanical Enginee ing Depa men , Enginee ing School o Gipuzkoa, Uni e si y o he Basque Coun y
UPV/EHU, Plaza de Eu opa, 1, E-20018 Donos ia-San Sebas ian, Spain
2TECNALIA, Basque Resea ch and Technology Alliance (BRTA), Mikele egi Pasealekua, 7,
E-20009 Donos ia-San Sebas ian, Spain; [email p o ec ed] (H.V.); [email p o ec ed] (M.S.)
3TECNALIA, Basque Resea ch and Technology Alliance (BRTA), Mikele egi Pasealekua, 2,
E-20009 Donos ia-San Sebas ian, Spain; [email p o ec ed]
*Co espondence: [email p o ec ed]; Tel.: +34-43-018630
Abs ac :
In his pape , he design and alida ion o a hea s o age de ice based on phase change
ma e ials a e p esen ed, wi h he ocus on imp o ing he he mal con ol o mic o-sa elli es. The
main objec i e o he de elopmen is o p o ide a sys em ha is able o keep elec onics wi hin
sa e empe a u e anges du ing he ope a ion o manoeu es, while educing mass and olume in
compa ison o o he he mal con ol echniques. Due o he low he mal conduc i i y o phase change
ma e ials, he conduc i i y o he de ice as a whole is one o he majo challenges o he de elopmen .
This issue has been sol ed by means o he use o a la ice o aluminium ins. The he mal beha iou
o he p oposed solu ion is assessed wi h nume ical simula ion ools, and he esul s p o e ha he
de eloped phase change ma e ial-based he mal con ol echnique is able o p o ide he sui able
in eg a ed he mal managemen o mic o-sa elli es. Fab ica ion challenges ound in he p ojec a e
also explained. Nume ical esul s a e alida ed h ough a es ing s age. The p edic ed empe a u e
p o iles a e in good ag eemen wi h expe imen al da a and inside he ange o eseen o he hea
s o age de ice.
Keywo ds: phase change ma e ials; space he mal con ol; hea s o age de ices
1. In oduc ion
Space is a e y ha sh and di icul en i onmen o spacec a and hei payloads. F om
a he mal poin o iew, spacec a and payloads mus unde go ex eme empe a u es, hea
luxes and a ia ions in hese lows depending on he o bi ype [1,2].
The mal con ol e e s o he se o echniques employed o main ain he empe a u es
o he spacec a and i s componen s inside he ange o allowed empe a u es [
3
,
4
]. This
mus be achie ed in all possible scena ios (ho cases, cold cases, s eady s a e o ansien
cases, e c.) because, o he wise, indi idual componen s can ail due o he e y high o e y
low empe a u es eached. A ailu e in one componen , e.g., he elec onics, can jeopa dize
a mission o e en make i a ailu e [5].
Phase change ma e ials (PCM) ha e been used o he mal con ol echniques since
he ea ly yea s o he 1960s. Se e al Apollo missions ca ied componen s ha used PCMs
o s abilize hei empe a u es [
6
]. O he componen s we e also used ha elied on PCM
beha io s [
7
]. The gene al app ecia ion in he space indus y o PCMs con inued also
du ing he 21s cen u y, as was shown by he call om he Eu opean Space Agency (ESA)
o he Eu opean space indus ies o design, calcula e and ab ica e a phase change ma e ial
hea s o age de ice (PCM-HSD) [8].
The physics and beha io o PCM ma e ials ha e been widely s udied in he li e a-
u e [
9
–
20
]. One in e es ing s udy showed he possibili y o using PCMs o s abilize he
Ae ospace 2022,9, 126. h ps://doi.o g/10.3390/ae ospace9030126 h ps://www.mdpi.com/jou nal/ae ospace
Ae ospace 2022,9, 126 2 o 16
empe a u e o some componen s, o ins ance, he elec onics [
1
]. When he di e en
elec onic ci cui s a e swi ched on, hea is p oduced, and empe a u es s a o ise. The
hea p oduced mus be conduc ed o he adia o and, om he e, mus be e acua ed in o
ou e space. I he powe o be disposed o is big, he su ace o he adia o mus also be
big and, consequen ly, i s weigh will be high. Howe e , i he powe p oduced by he
elec onics is somehow ‘s o ed’ in he PCM, and he empe a u e is main ained a a cons an
le el, i will be possible o dispose o he hea when he ci cui s a e swi ched o . This
means ha he a ea o he adia o will no be ha la ge, he weigh will be lowe and he
design will be be e . In ac , wha he PCM achie es is an inc ease in he he mal ine ia
o he spacec a o payload and, in his way, i will ha e a mo e s able empe a u e and
a educed weigh o he payload o spacec a .
2. Phase Change Ma e ial Hea S o age De ice (PCM-HSD)
2.1. Desc ip ion
This s udy aimed o assess he possibili y o using PCMs in space o s abilize he
empe a u es o componen s and o educe he size o he adia o in o de o educe
weigh . The sys em conside ed, shown in Figu e 1, was based on a PCM con ained in
a house, which was a ached o he elec onics whose empe a u e is o be con olled and he
adia o . E e y su ace bu he adia o was assumed o be co e ed by mul i-laye insula ion
(MLI) blanke s o a oid hea leaks. Mo eo e , he adia o was assumed o ope a e jus
when he hea needed o be eleased in o he space. The de ice was conside ed, he e o e,
o be insula ed om he en i onmen o make he s udy condi ions mo e un a o able.
Ae ospace2022,9,1262o 16


Thephysicsandbeha io o PCMma e ialsha ebeenwidelys udiedin heli e a‐
u e[9–20].Onein e es ings udyshowed hepossibili yo usingPCMs os abilize he
empe a u eo somecomponen s, o ins ance, heelec onics[1].When hedi e en elec‐
onicci cui sa eswi chedon,hea isp oduced,and empe a u ess a  o ise.Thehea 
p oducedmus beconduc ed o he adia o and, om he e,mus bee acua edin oou e 
space.I  hepowe  obedisposedo isbig, hesu aceo  he adia o mus alsobebig
and,consequen ly,i sweigh willbehigh.Howe e ,i  hepowe p oducedby heelec‐
onicsissomehow‘s o ed’in hePCM,and he empe a u eismain aineda acons an 
le el,i willbepossible odisposeo  hehea when heci cui sa eswi chedo .This
means ha  hea eao  he adia o willno be ha la ge, heweigh willbelowe and he
designwillbebe e .In ac ,wha  hePCMachie esisaninc easein he he maline ia
o  hespacec a o payloadand,in hisway,i willha eamo es able empe a u eand
a educedweigh o  hepayloado spacec a .
2.PhaseChangeMa e ialHea S o ageDe ice(PCM‐HSD)
2.1.Desc ip ion
Thiss udyaimed oassess hepossibili yo usingPCMsinspace os abilize he
empe a u eso componen sand o educe hesizeo  he adia o ino de  o educe
weigh .Thesys emconside ed,showninFigu e1,wasbasedonaPCMcon ainedina
house,whichwasa ached o heelec onicswhose empe a u eis obecon olledand
he adia o .E e ysu acebu  he adia o wasassumed obeco e edbymul i‐laye 
insula ion(MLI)blanke s oa oidhea leaks.Mo eo e , he adia o wasassumed oop‐
e a ejus when hehea needed obe eleasedin o hespace.Thede icewasconside ed,
he e o e, obeinsula ed om heen i onmen  omake hes udycondi ionsmo eun a‐
o able.

Figu e1.Phasechangema e ialhea s o agede ice(PCM‐HSD)conside ed.
Thekeyideabehind hisPCM he malcon olconcep is ocon e  he he malen‐
e gyin oaphasechange eac ion,s o inghea wheni isp oducedand eleasing his
ene gywhen heelec onicsisswi chedo .Since hephasechangep ocessoccu sa al‐
mos cons an  empe a u e,such he malcon olmeans ha  hesys em empe a u edoes
no changesigni ican lydu ing hemel ing/solidi ica ion,so ha i  hemel ingpoin is
app op ia e, heelec onicscanbee icien lyp o ec ed.
Ingene al e ms,mic o‐sa elli es(be ween10and100kginweigh )ope a eonlow
Ea hci cula o bi s(LEO,450–1200km)wi hawide angeo NASAβangles,andon
highellip icalo bi s,anda eexposed o heSun,albedoandin a edEa h adia ion.
Typicalmaximalinciden  luxes o 550kmo bi  o  la su aceswi hno mal onadi 
ajec o iesa eQ
IR
(in a ed)~200W/m
2
andQ
AL
(albedo)max~450W/m
2
(a e agedo e 
o bi <150W/m
2
).Theeclipse imecan a ybe ween0.5h(ci cula )andup ose e al
Figu e 1. Phase change ma e ial hea s o age de ice (PCM-HSD) conside ed.
The key idea behind his PCM he mal con ol concep is o con e he he mal
ene gy in o a phase change eac ion, s o ing hea when i is p oduced and eleasing his
ene gy when he elec onics is swi ched o . Since he phase change p ocess occu s a
almos cons an empe a u e, such he mal con ol means ha he sys em empe a u e does
no change signi ican ly du ing he mel ing/solidi ica ion, so ha i he mel ing poin is
app op ia e, he elec onics can be e icien ly p o ec ed.
In gene al e ms, mic o-sa elli es (be ween 10 and 100 kg in weigh ) ope a e on low
Ea h ci cula o bi s (LEO, 450–1200 km) wi h a wide ange o NASA
β
angles, and on
high ellip ical o bi s, and a e exposed o he Sun, albedo and in a ed Ea h adia ion.
Typical maximal inciden luxes o 550 km o bi o la su aces wi h no mal o nadi
ajec o ies a e Q
IR
(in a ed) ~200 W/m
2
and Q
AL
(albedo) max ~450 W/m
2
(a e aged
o e o bi <150 W/m
2
). The eclipse ime can a y be ween 0.5 h (ci cula ) and up o se e al
hou s o ellip ic o bi s. Acco ding o Ba u kin [
21
], ypical equi emen s o a e age hea
gene a ion inside he sa elli e a e in he ange o 15–40 W. This powe is p oduced mainly
by housekeeping equipmen (on boa d compu e , ansmi e , he a i ude and con ol
Ae ospace 2022,9, 126 3 o 16
sys em, ba e ies). Peak hea gene a ion coincides wi h payload ope a ion and can each
up o 200 W.
In ou case, he speci ica ions ha we e o be ollowed a e hose s a ed by he ESA [
8
].
The e we e equi emen s o unc ional and pe o mance (FPR), in e ace (IR), en i on-
men al (ER), ope a ional (OR), design (DR) and e i ica ion and es ing (VTR) ope a ions.
Howe e , he main equi emen s a e hose ela ed wi h he mal capaci y and mechanical
beha io , lis ed below:
•The de ice mus be capable o abso bing 30 W o 45 min;
•Ope a ional empe a u e ange mus be (−20/+40 ◦C);
•The de ice’s mass shall be less han 0.50 kg;
•The de ice’s i s esonance equency mus be highe han 140 Hz;
•The de ice shall sus ain a mechanical en i onmen cha ac e ized by dynamic loads.
2.2. Go e ning Equa ions and Nume ical Me hods
I is e y common o he mal con ol in spacec a o desc ibe he hea ans e
p ocess h ough he he mal lumped me hod (TLP). De ails abou he me hod can be ound
elsewhe e [22–24].
The se o nonlinea equa ions ha desc ibe he empe a u es o a ansien he mal
ma hema ical model is ( o a node i)
j=n
∑
j=1
GL(i,j)Ti−Tj+
j=n
∑
j=1
σGR(i,j)T4
i−T4
j+MiCi
dTi
d =qi(1)
whe e
n
is he numbe o nodes o he he mal ma hema ical model (TMM),
GL(i,j)
is he
conduc i e conduc ance (W/m) be ween nodes
i
and
j
,
σ
is he S e an–Bol zmann cons an
(5.67
×
10
−
8 W/(m
2·
K
4
)),
GR(i,j)
is he adia i e conduc ance (m
2
) be ween nodes
i
and
j
,
Ti
and
Tj
a e he empe a u es (K) o nodes
i
and
j
,
MiCi
is he p oduc o he
i
node mass
(kg) imes he hea capaci y (J/(kg
·
K) and
qi
is he powe (W) ha en e s in o node
i
. The
subsc ip s
i
and
j
go om 1 o
n
. I is usual o asc ibe he mal ine ia o he p oduc
MiCi
as i desc ibes he “opposi ion” o changing he empe a u e o
i
node when subjec ed o a
powe inpu .
The ime de i a i e o he empe a u e o node ican be app oxima ed by
dTi
d =Ti +∆ −Ti
∆ (2)
Fo a node iand o a gene al ime s ep +∆ , i is possible o w i e
j=n
∑
j=1
GL(i,j)Ti +∆ −Tj +∆ +
j=n
∑
j=1
σGR(i,j)Ti4 +∆ −Tj4 +∆ 
+MiCi(Ti +∆ −Ti )
∆ −qi=0
(3)
In o de o simpli y he no a ion, he ollowing will be used
Ti +∆ =Ti;Ti =Ti (4)
Addi ionally, he ollowing se o equa ions is ob ained
j=n
∑
j=1
GL(i,j)Ti−Tj+
j=n
∑
j=1
σGR(i,j)Ti4−Tj4+MiCiTi−Ti 
∆ −qi=0 (5)
Each equa ion ep esen s he he mal ins an equilib ium o a node. An in-house-
de eloped compu e p og am called TK was used o sol e he se o
n
non-linea equa ions.
These equa ions a e sol ed o each ime s ep whe e empe a u es o he di e en nodes
Ae ospace 2022,9, 126 4 o 16
a e calcula ed. The hea powe (W) ha goes om one node o ano he is also calcula ed,
as well as he hea powe (W) ha goes in o each node, which is employed in inc easing
i s empe a u e. The TK compu e p og am was modi ied o be able o deal wi h phase
change ma e ials. In he ollowing, we will assume ha he ini ial s a e o each node is solid
and ha he phase change will be mel ing.
Fo hose nodes made o PCMs, addi ional in o ma ion mus be supplied o he
compu e p og am. The PCM has a la en hea
L
, measu ed in J/kg. The mass o each node
(kg), as well as he speci ic hea (J/(kg
·
K)) o he ma e ial a e also known. By mul iplying
he mass o he node by he la en hea
L
, he p og am can ob ain he o al ene gy needed
by he node when passing om a solid o liquid phase.
The p og am uses a p edic o –co ec o me hod o ake in o accoun he la en hea o
nodes made o PCM. Fo each ime s ep, a se o empe a u es is calcula ed (p edic ed) wi h
he p e iously explained equa ions. Then, he p og am checks each node made o PCM.
I he empe a u e p edic ed o his node is highe han he s a ing empe a u e o he
change o s a e om solid o liquid, hen he ene gy used (J) is calcula ed, he empe a u e
o he node is co ec ed and he accumula ed ene gy used in ha node is calcula ed, as
is he liquid ac ion o PCM in ha node. These calcula ions a e pe o med aking in o
accoun he p oduc o he mass imes he speci ic hea o he node. I he calcula ed liquid
ac ion is lowe han 1, he p og am con inues wi h he nex node. When he o al ene gy
accumula ed in one node is highe han he o al ene gy ha he node needs o change
s a e, he s a e o he node is conside ed liquid and, in he ollowing ime s eps, i will no
ha e in luence o e he p edic ed empe a u es.
I is clea ha ime s eps sho enough mus be conside ed when phase change akes
place, o he wise signi ican e o s can appea . I is no unusual o need o make se e al
ials be o e ixing an app op ia e ime s ep leng h. Finally, he p ocedu e o conside ing
he change om liquid o solid is simila , bu wi h dec easing empe a u es.
3. Design o he Phase Change Ma e ial Hea S o age De ice (PCM-HSD)
3.1. Concep ual Design
The design e o s a e aimed a c ea ing an app op ia e hea managemen echnique
o keep he elec onics wi hin he sa e empe a u e ange and a sui able housing design
able o wi hs and he s uc u al loads speci ied. Toge he wi h he speci ica ions men ioned
in he p e ious sec ion, he main issues conside ed o he concep ual design we e he
PCM selec ion and he PCM he mal conduc i i y enhancemen . I has no been p e iously
men ioned bu , in gene al, he mal conduc i i y o PCMs is qui e low, and i is necessa y o
imp o e i o ob ain an app op ia e he mal beha io o he de ice.
3.1.1. PCM Selec ion
Rega ding he PCM selec ion, a i s calcula ion has been pe o med o ind he
minimum alue o he la en hea needed o he PCM. Following he speci ica ions,
Equa ion (6) s a es:
λmin =Emin
mmax
=30 W·45 min·60 s
1 min
0.5 kg =81000 J
0.5 kg =162 kJ
kg . (6)
In ac , he minimum alue o he la en hea o he PCM mus be bigge , because he
PCM will be posi ioned inside a con aine ha will add mass o he de ice bu almos no
la en hea (no aking in o accoun he speci ic hea ).
A box-shaped aluminum con aine wi h a,b,cdimensions and hickness has been
conside ed. Aluminum has e y good he mal conduc i i y and a ela i ely low densi y,
so as a i s app oxima ion, i has been selec ed as he con aine ma e ial. Values o
dimensions aand bha e also been selec ed as 80 mm and 20 mm, espec i ely. The eason
is ha hese dimensions a e adequa e o one o he mechanical in e aces conside ed. A
hickness o equal o 2 mm has also been selec ed because o he ab ica ion cons ain s,
so he only unknown dimension le is he heigh c. I is possible o demons a e ha he c
Ae ospace 2022,9, 126 5 o 16
maximum alue (in me e s) ha can be accep ed o he box i he maximum weigh o he
PCM-HSD has o be 0.5 kg mus be
c=0.5 −2 ·ρcon aine ab +2 (a+b)+4 2
ab·ρPCM +2 ·ρcon aine (a+b+2 ), (7)
whe e ρcon aine and ρPCM a e he densi ies o he con aine and he PCM.
Once he gene al dimensions o he PCM-HSD a e known, i is possible o calcula e
he ene gy ha he PCM-HSD can handle due o he la en hea o a pa icula PCM. I his
ene gy is highe han 81 kJ (162 kJ/kg 0.5 kg), i is possible o conclude ha he selec ed
PCM is app op ia e o he applica ion.
Se e al o ganic and ino ganic PCMs ha e been s udied, and he i s selec ion c i e ion
has been ha he ene gy calcula ed wi h Equa ion (2) is bigge han 81 kJ. In addi ion, he good
chemical compa ibili y be ween he PCM and he s uc u al ma e ial has been conside ed.
EPCM =mPCMλPCM =a·b·c·ρPCM·λPCM (8)
3.1.2. Enhancemen o he The mal Conduc i i y
As i has al eady been men ioned, he he mal conduc i i y o he PCMs is, in gene al,
low. This can pose a p oblem o he PCM-HSD because highe han desi ed empe a u es
could be eached while he phase change occu s, endange ing he unc ioning o he
elec onics. In his con ex , an in oduc o y calcula ion has been pe o med, compa ing he
beha io o he PCM alone wi h i s beha io i aluminum ins a e p esen , i aluminum
oam is used o i e en bo h o hem, ins and oam, a e used simul aneously (Figu e 2).
The calcula ion is based on he mix u e ule and ga e an ini ial idea o wha o expec om
each solu ion.
Ae ospace2022,9,1265o 16


soasa i s app oxima ion,i hasbeenselec edas hecon aine ma e ial.Values o di‐
mensionsaandbha ealsobeenselec edas80mmand20mm, espec i ely.The eason
is ha  hesedimensionsa eadequa e o oneo  hemechanicalin e acesconside ed.A
hicknesso  equal o2mmhasalsobeenselec edbecauseo  he ab ica ioncons ain s,
so heonlyunknowndimensionle is heheigh c.I ispossible odemons a e ha  hec
maximum alue(inme e s) ha canbeaccep ed o  heboxi  hemaximumweigh o 
hePCM‐HSDhas obe0.5kgmus be
𝑐.

󰇛󰇜






󰇛󰇜,(7)
whe e𝜌and𝜌a e hedensi ieso  hecon aine and hePCM.
Once hegene aldimensionso  hePCM‐HSDa eknown,i ispossible ocalcula e
heene gy ha  hePCM‐HSDcanhandledue o hela en hea  o apa icula PCM.I 
hisene gyishighe  han81kJ(162kJ/kg0.5kg),i ispossible oconclude ha  heselec ed
PCMisapp op ia e o  heapplica ion.
Se e alo ganicandino ganicPCMsha ebeens udied,and he i s selec ionc i e‐
ionhasbeen ha  heene gycalcula edwi hEqua ion(2)isbigge  han81kJ.Inaddi ion,
hegoodchemicalcompa ibili ybe ween hePCMand hes uc u alma e ialhasbeen
conside ed.
𝐸 𝑚𝜆 𝑎𝑏𝑐𝜌 𝜆(8)
3.1.2.Enhancemen o  heThe malConduc i i y
Asi hasal eadybeenmen ioned, he he malconduc i i yo  hePCMsis,ingen‐
e al,low.Thiscanposeap oblem o  hePCM‐HSDbecausehighe  handesi ed empe ‐
a u escouldbe eachedwhile hephasechangeoccu s,endange ing he unc ioningo 
heelec onics.In hiscon ex ,anin oduc o ycalcula ionhasbeenpe o med,compa ‐
ing hebeha io o  hePCMalonewi hi sbeha io i aluminum insa ep esen ,i alu‐
minum oamisusedo i e enbo ho  hem, insand oam,a eusedsimul aneously(Fig‐
u e2).Thecalcula ionisbasedon hemix u e uleandga eanini ialideao wha  o
expec  omeachsolu ion.

Figu e2.F omle  o igh ,PCM,PCMwi h ins,PCMwi h oam,PCMwi h insand oam.
Tocalcula e heequi alen  he malconduc i i y,weha e akenin oaccoun  hecon‐
duc i i yo  hePCM, heconduc i i yo  he insandalso he ans e sala eao  he ins.
In he oamcase, heappa en conduc i i yhasbeenconside ed,whichisa unc iono 
hema e ialconduc i i yand hepo edensi y:
𝑘 









_



_







_

,(9)
pe o mingsomealgeb ainEqua ion(3),i ispossible ow i e:
𝑘 𝑘
_
 𝑘 1

_



_

󰇛1𝑥󰇜𝑘 𝑥,(10)
whe e:
𝑘:PCM‐HSDequi alen  he malconduc i i y(W/(m∙K));
𝑘:Thephasechangema e ial’s he malconduc i i y(W/(m∙K));
𝑘:The ins’ he malconduc i i y(W/(m∙K));
Figu e 2. F om le o igh , PCM, PCM wi h ins, PCM wi h oam, PCM wi h ins and oam.
To calcula e he equi alen he mal conduc i i y, we ha e aken in o accoun he
conduc i i y o he PCM, he conduc i i y o he ins and also he ans e sal a ea o he
ins. In he oam case, he appa en conduc i i y has been conside ed, which is a unc ion
o he ma e ial conduc i i y and he po e densi y:
ke =kPCM·APCM +k in·A in +k eal_ oam·A eal_ oam
APCM +A in +A eal_ oam
, (9)
pe o ming some algeb a in Equa ion (3), i is possible o w i e:
ke =kappa en _ oam +kPCM·1−
ρappa en _ oam
ρ eal_ oam ·(1−x)+k in·x, (10)
whe e:
ke : PCM-HSD equi alen he mal conduc i i y (W/(m·K));
kPCM: The phase change ma e ial’s he mal conduc i i y (W/(m·K));
k in: The ins’ he mal conduc i i y (W/(m·K));
k eal_ oam: The eal oam’s he mal conduc i i y (W/(m·K));
kappa en _ oam: The appa en oam’s he mal conduc i i y (W/(m·K));
APCM: The ans e sal a ea o he PCM (m2);

Ae ospace 2022,9, 126 6 o 16
A in: The ans e sal a ea o he ins (m2);
A eal_ oam: The ans e sal a ea o he oam (m2);
ρappa en _ oam: The appa en densi y o he oam (kg/m3);
ρ eal_ oam: The eal densi y o he oam (kg/m3).
Fo his p elimina y analysis, a pa a in called RT5HC was selec ed as he PCM
(p ope ies in Table 1), wi h a me allic oam Duocel
®
(Table 2) and aluminum alloy 6101 o
he ins (Table 3).
Table 1. PCM RT5HC ma e ial p ope ies (supplie : Rubi he m).
PCM Type T usion (◦C) λ(kJ/kg) ρ(kg/m3)K (W/(m·K)) Cp (J/(kg·K)) EPCM (J)
RT5HC O ganic 6 214 880/763 0.2 1800/2400 60,553
Table 2. Duocel® oam ma e ial p ope ies.
Ma e ial ρappa en
(kg/m3)
ρ eal
(kg/m3)
Cp
(J/(kg·K))
K
(W/(m·K))
Aluminum 6101 Duocel® oam 207 2700 895 218
Table 3. Aluminum ma e ial p ope ies.
Ma e ial ρ(kg/m3)Cp (J/(kg·K)) K (W/(m·K))
Aluminum 2700 895 218
I is wo h o no ing ha he PCM (RT5HC) selec ed o his i s app oxima ion
does no ul il he condi ion imposed ega ding he minimum ene gy (i.e., be highe han
81 kJ). Howe e , he pu pose o his ini ial in es iga ion is o es ima e he a ia ion o he
equi alen conduc i i y in ela ion o he pe cen age o ille olume con en . This a ia ion,
as well as he equi alen la en hea , can be seen in Figu e 3. The do lines exp ess he
alues when oam is p esen , as well as he ins. The con inuous lines show alues wi h
only ins.
Ae ospace2022,9,1266o 16


𝑘_:The eal oam’s he malconduc i i y(W/(m∙K));
𝑘_:Theappa en  oam’s he malconduc i i y(W/(m∙K));
𝐴:The ans e sala eao  hePCM(m
2
);
𝐴:The ans e sala eao  he ins(m
2
);
𝐴_:The ans e sala eao  he oam(m
2
);
𝜌_:Theappa en densi yo  he oam(kg/m
3
);
𝜌_:The ealdensi yo  he oam(kg/m
3
).
Fo  hisp elimina yanalysis,apa a incalledRT5HCwasselec edas hePCM
(p ope iesinTable1),wi hame allic oamDuocel
®
(Table2)andaluminumalloy6101
o  he ins(Table3).
I iswo h ono ing ha  hePCM(RT5HC)selec ed o  his i s app oxima iondoes
no  ul il hecondi ionimposed ega ding heminimumene gy(i.e.,behighe  han81
kJ).Howe e , hepu poseo  hisini ialin es iga ionis oes ima e he a ia iono  he
equi alen conduc i i yin ela ion o hepe cen ageo  ille  olumecon en .This a ia‐
ion,aswellas heequi alen la en hea ,canbeseeninFigu e3.Thedo linesexp ess
he alueswhen oamisp esen ,aswellas he ins.Thecon inuouslinesshow alues
wi honly ins.
Table1.PCMRT5HCma e ialp ope ies(supplie :Rubi he m).
PCMTypeT
usion
(°C)𝝀(kJ/kg)𝝆(kg/m
3
)
𝐊
(W/(m∙K))Cp(J/(kg∙K))E
PCM
(J)
RT5HCO ganic6214880/7630.21800/240060,553
Table2.Duocel
®
 oamma e ialp ope ies.
Ma e ial𝝆𝒂𝒑𝒑𝒂𝒓𝒆𝒏𝒕
(kg/m
3
)𝝆𝒓𝒆𝒂𝒍
(kg/m
3
)
Cp
(J/(kg∙K))
K
(W/(m∙K))
Aluminum6101Duocel
®
 oam2072700895218
Table3.Aluminumma e ialp ope ies.
Ma e ial𝝆(kg/m
3
)Cp(J/(kg∙K))K(W/(m∙K))
Aluminum2700895218

Figu e3.Va ia iono equi alen conduc i i yandequi alen la en hea asa unc iono  he%o 
ille  olumecon en .
Figu e 3.
Va ia ion o equi alen conduc i i y and equi alen la en hea as a unc ion o he % o
ille olume con en .
Figu e 3shows ha he equi alen conduc i i y o he de ice imp o es a lo when
oam and ins a e p esen bu , a he same ime, he equi alen la en hea o he de ice
Ae ospace 2022,9, 126 7 o 16
dec eases signi ican ly. The inal design should be a ade-o be ween hese wo aspec s o
he hea ans e mechanism.
3.1.3. Ini ial Concep ual Design
Re e ence [
1
] p o ides a good me hod o he geome ical ini ial design o he PCM-
HSD. Assuming a geome y simila o he one shown in Figu e 4, a sp eadshee has been
p epa ed o e alua e di e en ini ial designs in a quick and e icien way.
Ae ospace2022,9,1267o 16


Figu e3shows ha  heequi alen conduc i i yo  hede iceimp o esalo when
oamand insa ep esen bu ,a  hesame ime, heequi alen la en hea o  hede ice
dec easessigni ican ly.The inaldesignshouldbea ade‐o be ween hese woaspec s
o  hehea  ans e mechanism.
3.1.3.Ini ialConcep ualDesign
Re e ence[1]p o idesagoodme hod o  hegeome icalini ialdesigno  hePCM‐
HSD.Assumingageome ysimila  o heoneshowninFigu e4,asp eadshee hasbeen
p epa ed oe alua edi e en ini ialdesignsinaquickande icien way.

Figu e4.Ini ialbasicdesigno  hePCM‐HSD.
Thebasicequa ions akenin oaccoun a e heene gyconse a ion,Fou ie ’slaw,
hemix u e uleandmassconse a ion.Theinpu s o  hesp eadshee a e hePCMp op‐
e ies,gene aldimensionso  hehousing,numbe and hicknesso  he insand hei p op‐
e iesand hep ope ieso  he oam.Theob ained esul sa e he o almasso  hede ice
(maximum0.5kg), he he malene gy ha canbedeal wi h(minimum81kJ)and he
equi alen  he malconduc i i y.
I canbeseen ha  hede ice’sweigh is0.5kgand ha  he o alene gyis87.9kJ:
bo hcons ain sa e hen ul illed.
3.2.P elimina yDesigno TwoPossiblePhaseChangeMa e ialHea S o ageDe ices
Thep ocesso elabo a inganewdesignis,wi hou adoub ,ani e a i ep ocess ha 
onlycon e geswhen he inaldesignisbuil .Inou case, wop elimina ydesigns,based
on wophasechangema e ials(RT5HCandKF.4H
2
O),ha ebeende eloped.Thegeom‐
e iesa equi edi e en ,andbo hdesignsneeded obecalcula ed he mallyandmechan‐
ically.Fo  hesakeo comple eness, hema e ialp ope ieso bo hma e ialsa ecollec ed
inTable4.
Table4.Ma e ialp ope ies o  hep eselec edphasechangema e ials.
P ope yRT5HCKF.4H
2
O
Mel ingpoin (°C)618.5
La en hea (kJ/kg)245231
Solidphasedensi y(kg/m
3
)8801455
Liquidphasedensi y(kg/m
3
)7631447
Speci ichea solidphase(J/kg/°C)18001840
Speci ichea liquidphase(J/kg/°C)24001850
The malconduc i i y(W/m/°C)0.20.2
Bo hma e ialscomplywi h heESAspeci ica ionsp e iouslymen ioned.Pe haps
hemos  ele an poin o in e es o  heKF.4H
2
Osal is ha i unde goesalmos no
changein olumewhenmel ing.
Figu e 4. Ini ial basic design o he PCM-HSD.
The basic equa ions aken in o accoun a e he ene gy conse a ion, Fou ie ’s law,
he mix u e ule and mass conse a ion. The inpu s o he sp eadshee a e he PCM
p ope ies, gene al dimensions o he housing, numbe and hickness o he ins and hei
p ope ies and he p ope ies o he oam. The ob ained esul s a e he o al mass o he
de ice (maximum 0.5 kg), he he mal ene gy ha can be deal wi h (minimum 81 kJ) and
he equi alen he mal conduc i i y.
I can be seen ha he de ice’s weigh is 0.5 kg and ha he o al ene gy is 87.9 kJ: bo h
cons ain s a e hen ul illed.
3.2. P elimina y Design o Two Possible Phase Change Ma e ial Hea S o age De ices
The p ocess o elabo a ing a new design is, wi hou a doub , an i e a i e p ocess
ha only con e ges when he inal design is buil . In ou case, wo p elimina y designs,
based on wo phase change ma e ials (RT5HC and KF
·
4H
2
O), ha e been de eloped. The
geome ies a e qui e di e en , and bo h designs needed o be calcula ed he mally and
mechanically. Fo he sake o comple eness, he ma e ial p ope ies o bo h ma e ials a e
collec ed in Table 4.
Table 4. Ma e ial p ope ies o he p eselec ed phase change ma e ials.
P ope y RT5HC KF·4H2O
Mel ing poin (◦C) 6 18.5
La en hea (kJ/kg) 245 231
Solid phase densi y (kg/m3)880 1455
Liquid phase densi y (kg/m3)763 1447
Speci ic hea solid phase (J/kg/◦C) 1800 1840
Speci ic hea liquid phase (J/kg/◦C) 2400 1850
The mal conduc i i y (W/m/◦C) 0.2 0.2
Bo h ma e ials comply wi h he ESA speci ica ions p e iously men ioned. Pe haps he
mos ele an poin o in e es o he KF
·
4H
2
O sal is ha i unde goes almos no change in
olume when mel ing.
Ae ospace 2022,9, 126 8 o 16
3.2.1. RT5HC Ma e ial
The p oposed design o his ma e ial can be seen in Figu e 5. The p e iously men-
ioned sp eadshee was used, wi h some mino adap a ions.
Ae ospace2022,9,1268o 16


3.2.1.RT5HCMa e ial
Thep oposeddesign o  hisma e ialcanbeseeninFigu e5.Thep e iouslymen‐
ionedsp eadshee wasused,wi hsomemino adap a ions.

Figu e5.P elimina ydesign o  heRT5HCma e ial.
The apezoidalgeome y ies omaximize hesu acecon ac be ween heho elec‐
onicde iceand hePCMma e ial.Thedesignhas woinne  ins oimp o e he he mal
conduc i i yo  hede ice.Thecon aine ma e ialis he6101aluminumma e ial.
3.2.2.KF.4H
2
OMa e ial
A ai lydi e en p elimina ydesignwasdepic ed o  hehyd a edsal ma e ial,see
Figu e6.Thedesignwasconcei ed o akead an ageo  healmos ‐cons an densi yo 
hePCMma e ial o solidandliquidphases.Thenumbe o inne  insisbigge in his
case,again oimp o e he he malconduc i i y.Thema e ialcon aine isagain6101alu‐
minumma e ial,and hees ima edweigh is0.5kg.

Figu e6.P elimina ydesign o  heKF.4H
2
Oma e ial.
3.3.De ailedDesign:The malandMechanicalModellingo  hePhaseChangeMa e ialHea 
S o ageDe ices
Thep elimina ydesignsp oposedin hep e ioussec iono  hepape mus unde go
ade ailed he malandmechanicalanalysisbe o ebeing ab ica ed.Thisispe o medin
o de  ocheckwhe he  hedesigns ul ill he equi emen sexp essedinSec ion2.
Figu e 5. P elimina y design o he RT5HC ma e ial.
The apezoidal geome y ies o maximize he su ace con ac be ween he ho
elec onic de ice and he PCM ma e ial. The design has wo inne ins o imp o e he
he mal conduc i i y o he de ice. The con aine ma e ial is he 6101 aluminum ma e ial.
3.2.2. KF·4H2O Ma e ial
A ai ly di e en p elimina y design was depic ed o he hyd a ed sal ma e ial, see
Figu e 6. The design was concei ed o ake ad an age o he almos -cons an densi y o he
PCM ma e ial o solid and liquid phases. The numbe o inne ins is bigge in his case,
again o imp o e he he mal conduc i i y. The ma e ial con aine is again 6101 aluminum
ma e ial, and he es ima ed weigh is 0.5 kg.
Ae ospace2022,9,1268o 16


3.2.1.RT5HCMa e ial
Thep oposeddesign o  hisma e ialcanbeseeninFigu e5.Thep e iouslymen‐
ionedsp eadshee wasused,wi hsomemino adap a ions.

Figu e5.P elimina ydesign o  heRT5HCma e ial.
The apezoidalgeome y ies omaximize hesu acecon ac be ween heho elec‐
onicde iceand hePCMma e ial.Thedesignhas woinne  ins oimp o e he he mal
conduc i i yo  hede ice.Thecon aine ma e ialis he6101aluminumma e ial.
3.2.2.KF.4H
2
OMa e ial
A ai lydi e en p elimina ydesignwasdepic ed o  hehyd a edsal ma e ial,see
Figu e6.Thedesignwasconcei ed o akead an ageo  healmos ‐cons an densi yo 
hePCMma e ial o solidandliquidphases.Thenumbe o inne  insisbigge in his
case,again oimp o e he he malconduc i i y.Thema e ialcon aine isagain6101alu‐
minumma e ial,and hees ima edweigh is0.5kg.

Figu e6.P elimina ydesign o  heKF.4H
2
Oma e ial.
3.3.De ailedDesign:The malandMechanicalModellingo  hePhaseChangeMa e ialHea 
S o ageDe ices
Thep elimina ydesignsp oposedin hep e ioussec iono  hepape mus unde go
ade ailed he malandmechanicalanalysisbe o ebeing ab ica ed.Thisispe o medin
o de  ocheckwhe he  hedesigns ul ill he equi emen sexp essedinSec ion2.
Figu e 6. P elimina y design o he KF·4H2O ma e ial.
3.3. De ailed Design: The mal and Mechanical Modelling o he Phase Change Ma e ial Hea
S o age De ices
The p elimina y designs p oposed in he p e ious sec ion o he pape mus unde go
a de ailed he mal and mechanical analysis be o e being ab ica ed. This is pe o med in
o de o check whe he he designs ul ill he equi emen s exp essed in Sec ion 2.
Ae ospace 2022,9, 126 9 o 16
3.3.1. The mal Beha io Modelling
The comme cial he mal so wa e NX-TMG om Siemens has been used o he an-
sien calcula ion o he sys em empe a u es. The employed mesh can be seen
in Figu e 7
.
Ae ospace2022,9,1269o 16


3.3.1.The malBeha io Modelling
Thecomme cial he malso wa eNX‐TMG omSiemenshasbeenused o  he an‐
sien calcula iono  hesys em empe a u es.TheemployedmeshcanbeseeninFigu e7.

Figu e7.De ailedmeshemployedin he he malcalcula ion.
TheNXTMGso wa eau oma icallycon e s he ini eelemen meshshowninFig‐
u e7in oane wo ko  he malconduc ance aluesemployedin he he mallumpedpa‐
ame e (TLP)me hod,whichis e ywellknownin hespaceindus y[24].The mal e‐
sis ancesha ebeenaddedmanually o hemodels o akein oaccoun  hecon ac be‐
ween hein e aceand hePCMcon aine .Theemployed alueis0.070∙10
−4
m
2
K/W,
aken om[25].Themesh ep esen saqua e o  he ealgeome ydue o hesymme y
p esence.Bo h he malin e aces(smallandbig)ha ebeenmodelled o comple enesso 
hecalcula ions.Theobjec i eis omain ain he empe a u ebe ween−20°Cand+40°C.
The he malloadcaseappliedineacho  he ou geome iesisahea  lowo 30W
p oducedby heelec onics,applied o 45min.Theini ial empe a u econside edis−20
°Canda imes epo 0.1swasused,whichmakesa o alo 27,000s eps.The esul s o 
hemos c i icalpoin o  hePCM‐HSD(apoin in hein e ace,nea  heelec onics)a e
showninFigu e8.

Figu e8.Highes  empe a u eo  hePCM‐HSDina ansien calcula ion.
Ascanbeseen,e en o  hemos c i icalpoin o  hedesign, hemaximumallowed
empe a u eo 40°Cisno  eached.I canbealsoconcluded omFigu e8 ha  hesmall
in e acegene a eshighe  empe a u es han hela geone,asi wouldbeexpec ed.
Figu e 7. De ailed mesh employed in he he mal calcula ion.
The NX TMG so wa e au oma ically con e s he ini e elemen mesh shown in
Figu e 7in o a ne wo k o he mal conduc ance alues employed in he he mal lumped
pa ame e (TLP) me hod, which is e y well known in he space indus y [
24
]. The mal
esis ances ha e been added manually o he models o ake in o accoun he con ac
be ween he in e ace and he PCM con aine . The employed alue is 0.070
×
10
−4
m
2
K/W,
aken om [
25
]. The mesh ep esen s a qua e o he eal geome y due o he symme y
p esence. Bo h he mal in e aces (small and big) ha e been modelled o comple eness o
he calcula ions. The objec i e is o main ain he empe a u e be ween
−
20
◦
C and +40
◦
C.
The he mal load case applied in each o he ou geome ies is a hea low o 30 W
p oduced by he elec onics, applied o 45 min. The ini ial empe a u e conside ed is
−20 ◦C
and a ime s ep o 0.1 s was used, which makes a o al o 27,000 s eps. The esul s
o he mos c i ical poin o he PCM-HSD (a poin in he in e ace, nea he elec onics)
a e shown in Figu e 8.
Ae ospace2022,9,1269o 16


3.3.1.The malBeha io Modelling
Thecomme cial he malso wa eNX‐TMG omSiemenshasbeenused o  he an‐
sien calcula iono  hesys em empe a u es.TheemployedmeshcanbeseeninFigu e7.

Figu e7.De ailedmeshemployedin he he malcalcula ion.
TheNXTMGso wa eau oma icallycon e s he ini eelemen meshshowninFig‐
u e7in oane wo ko  he malconduc ance aluesemployedin he he mallumpedpa‐
ame e (TLP)me hod,whichis e ywellknownin hespaceindus y[24].The mal e‐
sis ancesha ebeenaddedmanually o hemodels o akein oaccoun  hecon ac be‐
ween hein e aceand hePCMcon aine .Theemployed alueis0.070∙10
−4
m
2
K/W,
aken om[25].Themesh ep esen saqua e o  he ealgeome ydue o hesymme y
p esence.Bo h he malin e aces(smallandbig)ha ebeenmodelled o comple enesso 
hecalcula ions.Theobjec i eis omain ain he empe a u ebe ween−20°Cand+40°C.
The he malloadcaseappliedineacho  he ou geome iesisahea  lowo 30W
p oducedby heelec onics,applied o 45min.Theini ial empe a u econside edis−20
°Canda imes epo 0.1swasused,whichmakesa o alo 27,000s eps.The esul s o 
hemos c i icalpoin o  hePCM‐HSD(apoin in hein e ace,nea  heelec onics)a e
showninFigu e8.

Figu e8.Highes  empe a u eo  hePCM‐HSDina ansien calcula ion.
Ascanbeseen,e en o  hemos c i icalpoin o  hedesign, hemaximumallowed
empe a u eo 40°Cisno  eached.I canbealsoconcluded omFigu e8 ha  hesmall
in e acegene a eshighe  empe a u es han hela geone,asi wouldbeexpec ed.
Figu e 8. Highes empe a u e o he PCM-HSD in a ansien calcula ion.
As can be seen, e en o he mos c i ical poin o he design, he maximum allowed
empe a u e o 40
◦
C is no eached. I can be also concluded om Figu e 8 ha he small
in e ace gene a es highe empe a u es han he la ge one, as i would be expec ed.
3.3.2. Mechanical Beha io Modelling
Bo h s a ic and dynamic loads a e o eseen o he di e en mission phases whe e he
PCM-HSD can be used. As a consequence, di e en load cases a e analyzed.
Ae ospace 2022,9, 126 16 o 16
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