Ad ances in Elec ical and Elec onic Enginee ing
238
NUMERICAL SOLUTION OF THE HEAT ACCUMULATOR LAYER BY MEANS
OF FEM
P. Fiala, I. Bhunek, E. Kadleco á
Depa men o Theo e ical and Expe imen al Elec ical Enginee ing,
Uni e si y o Technology B no,Kolejní 2906/4, 612 00 B no, Czech Republic
e-mail: ialap@ eec. u b .cz
Summa y
The a icle deals wi h one laye o a hea accumula o which is sui able o sola sys ems. The e is a desc ip ion
o he ai u bulence, hea ans e , conduc ion and also phase change o CaCl2.6H2O which is used o inc ease he densi y o
s o ed ene gy. The nume ical solu ion was done wi h he help o ini e elemen me hod (FEM) in ANSYS so wa e.
1. INTRODUCTION
The model o hea accumula o is concep ually
simila o g a el accumula o . S ones o g a el we e
eplaced by plas ic enclosu es, which con ain PCM
(Phase Change Ma e ial). Accumula o has 8 laye s
equipped by he mal insula ion. In e ical duc s
he e is a sys em o swinging dis ibu ing laps. They
a e able o di ec ai low o laye s, close and isola e
laye s e c. The aim is o each empe a u e
s a i ica ion along he o e all heigh o
accumula o , s o e o pump hea o/ om any laye .
2. APPLICATION OF PCM
Phase changes o ma e ials a e a pe spec i e
way o he mal ene gy s o age. The applica ion o
PCM o e s a lo o ad an age. We can each highe
densi y o s o ed ene gy. Table 1 shows he
calcula ion o classical ma e ials and PCM. The
ini ial empe a u e 20 °C and inal empe a u e 50
°C a he end o hea ing a e supposed. Nex
ad an age is a possibili y o s o e hea a low
empe a u e. We don’ need o ha e such good
he mal insula ion and sola collec o s wo k wi h
be e e iciency so he demand o a ea o collec o s
dec eases.
Tab. 1. Compa ison o classical ma e ials and PCM
ma e iál densi y o s o age ene gy
[kWh.m
-3
]
wa e 34,5
g a el 23,0
pa a ine wax 62,4
CaCl
2
.6H
2
O 117,4
Na
2
CO
3
.10H
2
O 131,7
Na
2
HPO
4
.12H
2
O 134,7
Big la en hea , good he mal conduc i i y and
in lammabili y a e he main ad an ages o ino ganic
ma e ials. Bu hey cause co osion and su e om
loss he o wa e . Incong uen mel ing and
supe cooling a e he bigges p oblem o hei
exploi a ion. Du ing mel ing and eezing he e a e
p ecipi a ions o o he phases, which do no ake pa
in nex p ocess o cha ging and discha ging. Poo
nuclea ion, slow a e o c ys al g ow h o high a e
o hea emo al may be he eason o supe cooling.
Impu i ies ha e a s ong in luence on he cooling
cu es as well.
20
22
24
26
28
30
32
34
36
38
40
0:00 0:21 0:43 1:04 1:26 1:48 2:09
as [hodiny]
°C
5
10
15
20
25
30
35
40
0:00 0:36 1:12 1:48 2:24 3:00 3:36 4:12
as [hodiny]
°C

Fig. 1. Phase changes o CaCl2.6H2O
In he Fig. 1 he e is exhibi ed he phase change
o CaCl
2
.6H
2
O du ing hea ing and cooling. Dashed
lines would show heo e ical beha iou i mel ing
and eezing we e a cons an empe a u e T
m
– case
o pu e c ys allic subs ance. Impu i y and
me hodology o measu ing (p obe always is only in
small amoun o hexahyd a e) a e he causes o
a iances. Du ing solidi ica ion he supe cooling
occu ed because o weak nuclea ion. C ys alliza ion
was ini ia ed due o a solid pa icle o PCM which
we pu o he measu ed sample. O he wise he e
would no be any c ys alliza ion. We can use
Nume ical solu ion o he hea accumula o laye by means o FEM
239
plas ics, mild s eel o coppe o enclosu es.
Aluminium o s ainless s eel a e no sui able.
Some imes we can see empe a u e luc ua ion
abo e T
m
du ing solidi ica ion (Fig. 2). We ound an
explana ion in he bina y diag am (Fig. 3).
20
22
24
26
28
30
32
34
36
38
40
0:00 0:28 0:57 1:26 1:55 2:24 2:52
as [hodiny]
°C
Fig. 2. Phase change o CaCl2.6H2O (CaCl2.4H2O
c ys alliza ion)
Fig. 3. Bina y diag am o CaCl2.6H2O [2]
Figu e 3 shows he bina y phase diag am o calcium
chlo ide and wa e . The hexahyd a e con ains 50,66
w % CaCl
2
, and he e ahyd a e 60,63 w %. The
mel ing poin o he hexahyd a e is 29,6 °C, and o
he e ahyd a e 45,3 °C. The hexahyd a e-α
e ahyd a e pe i ec ic poin is a 49,62 w % CaCl
2
-
50,38 w % H
2
O, and 29,45 °C. In addi ion o he
s able α o m, he e a e wo mono opic polymo phs
o he e ahyd a e sal , β and γ. The la e wo a e
a ely encoun e ed when dealing wi h he
hexahyd a e composi ion; howe e , he α
e ahyd a e is s able om i s liquidus empe a u e,
32,78 °C down o he pe i ec ic poin , 29,45 °C, a
span o 3,33 °C. When liquid CaCl
6
.6H
2
O is cooled
a equilib ium, a CaCl
2
.4H
2
O can begin o c ys allize
a 32,78 °C. When he pe i ec ic is eached a 29,45
°C he e ahyd a e hyd a es u he o o m
hexahyd a e, and he ma e ial eezes. The
maximum amoun o e ahyd a e which can be
o med is 9,45 w %, calcula ed by he le e ule.
This p ocess is e e sed when solid CaCl
6
.6H
2
O is
hea ed a equilib ium. A 29,45 °C he pe i ec ic
eac ion occu s, o ming 9,45% a CaCl
2
.4H
2
O and
liquid o he pe i ec ic composi ion. As he
empe a u e inc eases u he , he e ahyd a e mel s,
disappea ing comple ely a 32,78 °C. Unde ac ual
eezing and mel ing condi ions, he equilib ium
p ocesses desc ibed abo e may occu only pa ially,
o no a all. Supe cooling o he e ahyd a e may
lead o ini ial c ys alliza ion o he hexahyd a e a
29,6 °C, o lowe i his phase also supe cools.
Modi ica ion is possible o do by addi i es.
F om numbe o po en ial candida es Ba(OH)
2
,
BaCO
3
, and S (OH)
2
we e chosen. They seemed o
be easible. When we used Ba(OH)
2
and S (OH)
2
a
1% pa by weigh he e was no supe cooling. We
could inc ease s abili y o he equilib ium condi ion
wi h addi ion o KCl (2 w %) and NaCl. NaCl is
weak soluble in CaCl
2
.6H
2
O, he e o e pa by
weigh is only abou 0,5%. Disad an age is ha
mel ing poin dec eases abou 3 °C a 26-27 °C. The
mel ing poin o pu e CaCl
2
.6H
2
O is 29,6 °C. Due o
a ailabili y on he ma ke and p ice we chose o
modi ica ion BaCO
3
. We ob ained he bes esul s
o 1,2 w %. In Fig. 1 we can see ha supe cooling
is 3-4 °C bu hen c ys alliza ion s a ed
spon aneously and empe a u e inc eased a 28-29
°C. I is ob ious ha nuclea ion is slowe in
compa ison wi h pu e c ys allic ma e .
Supe cooling is no conside ed as a disad an age. I
we use CaCl
2
.6H
2
O in he hea accumula o we will
be able o s o e ene gy a lowe empe a u e (abou
26 °C) and supp ess hea losses. Nex disad an age
o BaCO
3
is ha i ca bona es because o
a mosphe ic CO and CO
2
. This means he loss o
p ope ies. In ou case BaCO
3
will be isola ed om
su ounding en i onmen .
3. NUMERICAL MODEL OF HEAT
ACCUMULATOR LAYER
The e is geome ic model o one laye o
accumula o in he igu e 4. I consis s om 26 PVC
pipes in he squa e con igu a ion. Inside o pipes
he e a e 9,36 li e s o modi ied CaCl
2
.6H
2
O. The ai
lows h ough he laye and ans e s hea in o pipes.
P og ess o nume ical solu ion had wo pa s. Fi s
we sol ed u bulence model and go hea ans e
ilm coe icien s. These esul s we e he inpu o
solu ion o second pa when he mal model was
calcula ed. Time dependence o empe a u e
dis ibu ion in he laye is inal esul .
Ad ances in Elec ical and Elec onic Enginee ing
240
Fig. 4. Geome ic model o laye wi h mesh o elemen s
Ini ial and bounda y condi ions
• inle empe a u e o he ai is 50 °C
• inle eloci y o he ai is 0,4 m.s
-1
• ou le p essu e is 101,3 kPa + 10 Pa
• ini ial empe a u e o he ai , PVC and
CaCl
2
.6H
2
O is 20 °C
The e a e dis ibu ions o eloci y in Fig. 5 and
nex esul s o dis ibu ion o he u bulen kine ic
ene gy, dissipa ion, empe a u e, and p essu e.
Fig.5. Veloci y dis ibu ion o he ai
Fig.6. Dis ibu ion o kine ic ene gy, dissipa ion
Fig.7. Dis ibu ion o empe a u e and p essu e
Calcula ion o he mal model was done wi h he
same condi ions as p e ious u bulence model. In
Fig. 8 he e is ime dependence o CaCl
2
.6H
2
O
empe a u e in he pipe which is ma ked wi h black
c oss (see Fig. 4). We can compa e esul s ob ained
by nume ical simula ion wi h he measu ing.
Di e ences be ween simula ion and measu ing a e
caused due o inaccu acy o model wi h espec o
eali y. We used abula alues o pu e CaCl
2
.6H
2
O
bu in pipes he e is modi ied hexahyd a e wi h 1,2%
o BaCO
3
. We would need o know empe a u e
dependence o he mal conduc i i y, speci ic hea ,
and densi y du ing phase change exac ly.
20
22
24
26
28
30
32
34
36
38
40
42
44
46
0:00 0:19 0:38 0:57 1:17 1:36 1:55 2:15 2:34 2:53 3:13 3:32 3:51
ime [hou s]
empe a u e [°C]
measu ing simula ion
Fig.8. Compa ison be ween measu ing and simula ion
4. CONCLUSION
The e was p esen ed one laye o hea
accumula o in he pape which is de i ed om
g a el accumula o . We used pu e CaCl
2
.6H
2
O wi h
addi ion 1,2% o BaCO
3
o inc ease hea capaci y
and a oid a supe cooling. Nume ical model was
sol ed wi h help o FEM in ANSYS so wa e. I we
compa e esul s be ween simula ion and
expe imen al measu ing we will see qui e good
cong uence. Exac knowledge o ma e ial p ope ies
has c ucial e ec on accu acy o nume ical model.
Acknowledgemen
The pape was p epa ed wi hin amewo k o he
esea ch plan No. MSM 0021630516 o he Minis y
o Educa ion, You h and Spo s o he Czech
Republic.
REFERENCES
[1] BEHUNEK, I. P ope ies o ino ganic PCM In
Honeywell EMI con e ence and compe i ion
2005. B no: Ing. Zdenk No o ný CSc.,
Ond áko a 105, B no, 2005. ISBN 80-214-
2942-9.
[2] LANE, G.A. Sola Hea S o age: La en Hea
Ma e ials, Volume II: Technology. Boca Ra on
(Flo ida, USA): CRC P ess, Inc., 1986. ISBN 0-
8493-6586-4.
[3] WILCOX, D.C. Tu bulence modeling o CFD.
La Canada (Cali o nia, USA): DCW Indus ies,
Inc., 1994. ISBN 0-9636051-0-0.