CALIBRATION OF THE HEAT BALANCE MODEL FOR PREDICTION
OF CAR CLIMATE
Jan POKORNÝ, Jan FIŠER and Mi osla JÍCHA•
Abs ac : In he pape , he au ho s e e o de elopmen a hea balance model o
p edic ca clima e and powe hea load. Model is de eloped in Modelica language
using Dymola as in e p e e . I is a dynamical sys em, which desc ibes a hea
exchange be ween ca cabin and ambien . Inside a ca cabin, he e is conside ed
hea exchange be ween ai zone, in e io and ai -condi ioning sys em. I is
conside ed 1D hea ans e wi h a hea accumula ion and a ela i e mo emen
Sun espec o he ca cabin, whils ca is mo ing. Measu emen s o he eal
ope a ing condi ions o ga e us da a o model calib a ion. The model was
calib a ed o Škoda Felicia pa king-summe scena ios.
1. INTRODUCTION
A ca cabin is a small enclosed space, which should p o ide com o able indoo clima e
o pe sons inside, al hough he he mal esis ance/insula ion o walls is ela i ely low
compa ed o buildings. Gene ally ca cabin clima e is mo e sensi i e o he change o
wea he condi ions. In summe he sola in ensi y subs an ially a ec s a he mal com o
and clima e in ca cabin. I is due o he high a io o anspa en su aces ansmi ing
sola adia ion ene gy inside. Clima e con ol o such compa men s equi es
conside a ion o dynamical hea ans e phenomena. Konz [3] de eloped a dynamical
model o VW Polo ca cabin o s udy a ious ai condi ioning s a egies. Wagne [5]
in oduced a me hod o p edic he empe a u e s a i ica ion inside a passenge
compa men o a ious ypes o ca s. A ici [1] de eloped a design ool o clima e
con ol sys em minimizing he ime-consuming p ocedu es o in eg a ing a p o o ype ai
condi ioning sys em. In au omo i e indus y, he e a e used comme cial so wa es as
Theseus-FE [4] o RadThe m o simula e hea ans e inside ca cabin.
The pape p esen s he ca cabin model o p edic ion o ca clima e, mainly ai zone
empe a u e o ai inside a passenge compa men . The model is designed o p edic ion
o ca clima e, when he ope a ing and wea he condi ions a e known. I is hea balance
model conside ing 1D hea exchange among ambien , passenge compa men and ai
condi ioning sys em. The model was es ed on ou es cases ep esen ing scena io o
pa king du ing summe day. The es ehicle was Škoda Felicia wi h da k blue pain ing
see Figu e 1, on he le . Mo e de ails abou measu emen s a e in he chap e 4.
2. HEAT BALANCE MODEL OF CAR CABIN
I is conside ed 1D hea ans e wi h a hea accumula ion in he nodes. The ca cabin
model consis s om ex e io (index E), in e io (index I) and ai zone (index A) nodes.
• Jan Poko ný, Jan Fiše , p o . Mi osla Jícha, CSc., Depa men o The modynamics and
En i onmen al Enginee ing, Facul y o Mechanical Enginee ing, B no Uni e si y o Technology,
Technická 2896/2, 616 69, B no, e-mail: ypoko 25@s ud. me. u b .cz
EPJ Web o Con e ences , 010 (2012)
DOI: 10.1051/epjcon /201225010
© Owned by he au ho s, published by EDP Sciences, 2012
This is an Open Access a icle dis ibu ed unde he e ms o he C ea i e Commons A ibu ion License 2.0, which
pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal wo k is p ope ly ci ed.
A icle a ailable a h p://www.epj-con e ences.o g o h p://dx.doi.o g/10.1051/epjcon /20122501077
Cabin is spli in o 10 pa s: Windshield, Rea glass, Le and Righ side glass, Bulk, T unk
doo , Le and Righ doo s (opaque su aces), Roo and Floo . Each pa has i s own
ex e io and in e io node and hea balance equa ions (1-2). I is conside ed only one
ai zone node o he whole compa men , see equa ion (3). The hea ans e model
includes an ai condi ioning sys em (index K), which egula es empe a u es and ela i e
humidi y inside a passenge compa men .
A he ou e su ace o cabin, i is conside ed hea exchange be ween ambien and
ex e io by sho wa e and longwa e adia ion and con ec ion. Hea balance (in wa s) a
ex e io su ace is de ined as
(1)
whe e c [J/kgK] is speci ic hea capaci y, m [kg] is mass, τ [s] is ime, T [°C] is mode
empe a u e and QE, ad is longwa e adia ion hea low be ween ambien and ca cabin,
QE,con is con ec i e hea low be ween ambien ai and ca cabin, bo h calcula ed by
empi ical o mulas om [3]. aQs ep esen s abso bed sola ene gy by ca
b
in su aces and
QE,cond is conduc i e hea low be ween ex e io and in e io node.
Inside a compa men i is conside ed hea exchange among in e io (con ec ion,
adia ion), ai zone, ai condi ioning (con ec ion), human ( adia ion, con ec ion
e apo a ion and espi a ion) and ambien ( ansmi ed sola adia ion). Hea balance a
in e io su ace is
(2)
whe e QI,con is con ec i e hea low be ween ai zone and in e io node. μQs ep esen s
ansmi ed sola ene gy.
Hea balance in ai zone node depends on he hea ene gy coming om ai condi ioning,
human su ace and hea ans e be ween ai and in e io su aces by con ec ion.
(3)
whe e xA is speci ic humidi y o ai zone, (iK-iA) is he change o speci ic en halpy in
ai zone, QH, ad = 70 W/m2 and QH,con = 30 W/m2. i.e each occupan p oduces 100 W/m2
(i.e. sea ing ac i i y). Bo h hea loss by espi a ion and e apo a ion a e no conside ed
in he model. A ca clima e is de ined by ai zone empe a u e and ai zone humidi y. The
speci ic humidi y o ai zone xA is calcula ed by he mois u e mass balance equa ion
(4)
3. ŠKODA FELICIA PARAMETERS
Škoda Felicia ma e ial composi ion was es ima ed om he es ehicle and he alues o
ma e ial p ope ies we e aken om Theseus-FE ma e ial p ope ies da abase. Since
mos o cabin pa s a e composed om mo e ma e ials (mul ilaye ed), The mal insula ion
,
,,, condEs con E adE
E
EE QaQQQ
τ
d
d
mc +++=
,
,,, adHcondEs con I
I
II QQQμQ
τ
d
d
mc +−+=
,)(
,, con Icon H
A
AA
A
K
AK
A
AA QQ
d dx
dx
di
m
d
dm
ii
τd
d
cm −+−−=
,
1
)1( ⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
−
+=
K
AK
AA x
xx
τd
dm
x
τd
dx
m
EPJ Web o Con e ences
01077-p.2
and speci ic hea capaci y o each pa was p e-calcula ed in Excel. Real Škoda Felicia
Combi geome y was simpli ied in o he pa ame e ized geome y, which was de ined as
ollows: α = 32°, β = 34°, γ = 66°, A = 3.3 m, B = 1.42 m, C = 0.72 m, D = 0.38 m,
see Figu e 1, on he igh .
Figu e 1: Tes ehicle Škoda Felica and i s pa ame e ized geome y
Whe e α is windshield angle, β is ea glass angle, γ is side glass angle, A is leng h, B is
wid h, C is heigh o doo panels and D is heigh o doo glasses. Black a ow deno es a
ca o ien a ion ec o . The geome y pa ame e s a e impo an o he calcula ion o
sho wa e adia ion (i depends on he mu ual posi ion o each ca body pa and Sun).
Impo an cha ac e is ics a e sho wa e adia ion abso p i i y a and ansmissi i y , and
longwa e adia ion emissi i y. The le e is equal o longwa e adia ion abso p i i y by
he Ki chho 's law o he mal adia ion. Ai zone olume o cabin is e y impo an
pa ame e o calcula ion o en ila ion. I is exp essed om he olume o pa ame e ized
geome y de ined as
(5)
whe e S [m2] a e su ace a eas. This olume includes in e io equipmen olume 0.15 m3
(sea s, dashboa d, e c), unk olume 0.45 m3 and ai zone olume, which comple es he
sum and i is equal o 3.1 m3.
4. MEASUREMENTS
Measu emen s o case Pa king-Summe was done in he backya d pa king lo o Facul y
o Mechanical Enginee ing in B no, K álo o Pole du ing 2nd and 12-15 h o Sep embe
2011. Equipmen and ha dwa e used o measu emen s:
• Da a logge s TESTO 435 and 735, ELSACO-PLC wi h PT 100 p obes, TESTO
combined p obe ( eloci y, humidi y, empe a u e) and wi eless ai empe a u e
p obes, Sola panel 12W wi h 7Ah lead-acid accumula o , ACER lap op.
Da a channels:
• Ai empe a u e: Ambien , Unde Hood, T unk, Co-d i e : Fee , Head, To so,
Passenge (behind d i e ): Fee , Head, To so
• Su ace empe a u es: Sola panel and in e io su aces as Roo , Dashboa d, Co-
d i e sea , Righ doo , Windshield, Righ glass
• Ai eloci y: a Co-d i e 's head posi ion, a ou le s o HVAC
• Rela i e humidi y: Ambien , a Co-d i e 's head posi ion
• Radian empe a u e: a Co-d i e 's head posi ion
• Global sola in ensi y on he Roo (ho izon al plane)
],[m 3.7 3
=+++⋅⋅= )(
3
loo loo oo oo cabin SSSS
D
CBAV
EFM11
01077-p.3
The sola in ensi y was de i ed om measu emen o he sola panel powe and i was
calib a ed by able o ypical sola in ensi y du ing Sep embe in B no (see Cihelka [2]).
Ai eloci y a ou le s o HVAC was measu ed o ypical en ila ion a es (II. and IV. s ep
o an con olle ) o es ima e ai mass low coming in o he cabin. Measu ed da a we e
logged in TESTOs and ELSACO da a logge s and hen we e expo ed in o he Excel and
il e ed. The il e ed measu ed da a we e used o de ine inpu s and bounda y condi ions
and also o he model calib a ion.
5. RESULTS AND DISCUSSION
A compa ison o model p edic ions and measu emen s a e p esen ed in his chap e see
Figu e 2. The compa ison is ocused on he ai zone empe a u e, because his
pa ame e is one o he mos impo an clima e pa ame e s. I was compa ed wi h he
mean ai empe a u e calcula ed as a e age o all ai empe a u es measu ed in cabin o
he es ca , namely head, o so and ee posi ion a he co-d i e and he ea le
passenge sea . Bounda y condi ions used in ca cabin model we e:
a) Cons an condi ions
• Ca posi ion: La i ude 49.2° N , Longi ude 16.6° E, Al i ude 363 m
• Ca o ien a ion: o he No h-Eas (Azimu h 67°)
• Ca speed: 0 km/h (pa king)
• Ai -condi ioning and en ila ion: swi ched o
• Occupan s: 0 pe son
b) Va iable condi ions
• Da e and Time (summe )
• Rela i e humidi y o ambien ai [%]
• Ambien adian empe a u e and ai empe a u e [°C]
• Ai empe a u e inside unk and engine space [°C]
• Sola adia ion in ensi y [W/m2]
Figu e 2: Fou summe pa king cases. Compa ison o calcula ed ai zone
empe a u e (blue line) wi h a e aged measu ed ai empe a u e ( ed line)
EPJ Web o Con e ences
01077-p.4
Measu emen s show ha he main ac o a ec ing ai zone empe a u e is he sola
adia ion and ambien ai empe a u e. The ambien adian empe a u e is also e y
impo an pa ame e , bu i is p ecise alue du ing eal ope a ing condi ions is ha d o
ob ain. I depends on many ac o s: e.g. sky condi ions (cloudiness, Linke u bidi y
ac o , e c.), empe a u es and ma e ials o su ounding coun yside, shadows e c. In he
simula ions ambien adian empe a u e was assumed o be equal ambien ai
empe a u e. The model does no ake in accoun e ec s o wind and p ecipi a ion. This
ac can be eason why in es case 14.9.-15.9. di e ences be ween simula ed and
measu ed ai empe a u e we e highe , because his day was aining om 12:05 ill
16:30 and i was ela i ely windy. The model is also limi ed by conside a ion o only one
ai zone o whole cabin, hus he ai s a i ica ion e ec (in summe pa king es case
was he empe a u e di e ence o e 20°C) canno be desc ibed. Mo eo e o simula e a
powe hea load o cabin is necessa y o calcula e empe a u es o ex e io and in e io
su aces. The ex e io su aces show a good ag eemen unlike some in e io pa s as
Dashboa d and Righ doo . I is due o he ac ha geome y o in e io is no
conside ed explici ly (no de ined geome y o sea s, dashboa d e c.). E en h ough he
e y simpli ied ca cabin geome y, he p edic ion o ai empe a u e inside ca cabin
shows a good ag eemen wi h measu ed da a.
6. CONCLUSIONS
The pa ame e ized model is able o p edic a ca clima e and a powe hea load on he
ca cabin du ing eal ope a ing condi ions. I he cha ac e is ic o HVAC sys em is known
hen i is possible o simula e hea ing/cooling powe o achie e a se poin empe a u e.
The accu acy o he model can be imp o ed by de ini ion o in e io geome y as sea s
and dashboa d. The model is alid o wea he wi hou p ecipi a ions, which s ongly
a ec he hea ans e . I was done measu emen s du ing summe (pa king case) and
measu emen s o au umn es cases (d i ing: ci y, highway) is s ill ongoing. A he
beginning o he new yea some win e es s will be ca ied ou o alida e he model o
he whole yea wea he condi ion o Cen al Eu opean clima e.
7. ACKNOWLEDGEMENT:
This wo k is ounded by Czech go e nmen p ojec GA101/09/H050 and B no Uni e si y
o Technology p ojec BD13102016/2100. Consul a ion o echnical aspec s om
Volkswagen AG Company is g ea acknowledged as well.
8. REFERENCES
[1] A ici O., Yang S., Huang D., Oke E.: Compu e Model o Au omobile Clima e
Con ol Sys em Simula ion and Applica ion. In .J. Applied The modynamics, Vol.2,
(No.2), 2010, pp. 59-68
[2] Cihelka J.: Solá ní epelná echnika, Malina – P aha 1994.
[3] Konz M.: A Gene ic Simula ion o Ene gy Consump ion o Au omobile Ai
Condi ioning Sys ems. Ph.D. hesis – Po Elizabe h Technikon, 2002
[4] Theseus-FE: Theo y Manual Ve sion 4.0, P+Z Enginee ing GmbH – Munich, 2011.
A ailable om WWW: <h p://www. heseus- e.com>
[5] Wagne S.: Idealisie e ene ge isch-analy ische Abbildungsme hode de
Tempe a u schich ung bei de passi en Au heizung in de Fah zeugkabine, PKW-
Klima isie ung VI, Haus de Technik Fachbuch 107 – Essen, 2009, pp. 94-110
EFM11
01077-p.5