Ene gy and exe gy analysis o an expe imen al en ila ed açade
Ana Picallo-Pe ez
⇑
, José Ma ía Sala-Liza aga
Uni e si y o he Basque Coun y, ENEDI Resea ch G oup, Ene gy Enginee ing Depa men , Pl. Ingenie o To es Que edo 1, 48013 Bilbao, Spain
a icle in o
A icle his o y:
Recei ed 19 Oc obe 2022
Re ised 8 Decembe 2022
Accep ed 19 Decembe 2022
A ailable online 21 Decembe 2022
Keywo ds:
Ven ila ed açade
Expe imen al es
Exe gy analysis
Pe o mance indexes
abs ac
This wo k, analyzes en ila ed açades h ough he i s and second law o he modynamics. In addi ion
o he ene gy-balances, i p esen s he exe gy-balances on he in e io and ex e io su ace o a açade,
aking in o accoun he di e en mechanisms o hea exchange. I p oposes wo new indexes (EQC and
ExQC) o cha ac e ize he beha io o en ila ed açades, by compa ing hei beha io wi h a e e ence
açade and conside ing he ene gy balance in one case and he exe gy balance in he o he . An expe imen-
al es o a o ced en ila ed açade se es as he case s udy, using he es -me hodology based on Paslink
cells. The es da a se e o cha ac e ize he beha io o he açade, bo h om an ene gy and exe gy poin
o iew. O e all, 53.05 kWh o hea is los o he ou side h ough he açade du ing 6 days o No embe ,
which co esponds o 0.31 kWh o exe gy-loss. The in e nal ene gy change o he açade is decomposed
acco ding o i s laye s, showing ha in e ms o ene gy he sandwich insula ion laye in luences he mos
(99.45 % o he o al change) bu in e ms o exe gy, on he con a y, he me al shee a ec s he mos
(83.66 %). The alues ob ained o he wo indexes show ha , unde he es condi ions, al hough he en-
ila ed açade and he e e ence açade p esen simila alues om he ene gy poin o iew, when he
exe gy is used, i is clea ly seen ha he beha io o he en ila ed açade is 44 % be e .
Ó2022 The Au ho s. Published by Else ie B.V. This is an open access a icle unde he CC BY license (h p://
c ea i ecommons.o g/licenses/by/4.0/).
1. In oduc ion
The popula ion does no alue com o homogeneously when
esponding abou he mal and ai quali y aspec s. The e o e, bal-
ance pa ame e s and s a egies a e es ablished o supply a com-
mon com o le el- ange wi hin a chi ec u al design. As a ule,
com o is gua an eed when he body empe a u e is wi hin a ce -
ain ange, he skin has a low humidi y and he physiological e o
o egula ion is minimum. The ac i e and passi e sys ems o build-
ings a e esponsible o main aining he mal com o by consum-
ing na u al esou ces, so hei ole is essen ial o sus aining
socie y i sel . Consuming na u al esou ces in ol es using enew-
able o ossil uels, al hough hese las emi g eenhouse gases
and con ibu e o clima e change. Cu en ly, buildings accoun
o abou 40 % o he o al ene gy consump ion and 36 % o he
CO
2
emissions in he Eu opean Union [1]. To educe hese con-
sump ions, passi e solu ions can be used by in ol ing he build-
ing’s a chi ec u e.
Ven ila ed Façades (VF) [2] a e cons uc i e solu ions, which
can be inco po a ed in e u bishmen o new buildings, and
imp o e he ene gy e iciency o he buildings o help ensu e
indoo com o . They a e based on a double skin wi h an ai cham-
be which slows down he a e o hea ans e . On he one hand,
hea is s o ed in a he mal mass-wall and is conduc ed, adia ed
and ansmi ed o he in e io space ha is being acclima ized.
On he o he hand, VF ex ac s he he mal ene gy o he hea ed
ai di ec ly o he ou side, o in oduces i in o he in e io h ough
he openings a he ends o he açade. This ai mo es be ween he
dampe s by na u al con ec ion o can be o ced and con olled by
ans. Mo e and mo e p e ab ica ed slabs and açade modules a e
becoming a ailable due o ad ances in p oduc ion, which o e
he oppo uni y o implemen VF modules mo e easily, as is he
case o Re . [3], which s udies he eno a ion o a high school build-
ing wi h p e ab ica ed VF elemen s.
The wo k in Re . [4] s udies and discusses he mos ecen and
cu ing-edge esea ch in o double-skin açades o building e o-
i . VFs p o ide a he mal bu e zone, ene gy sa ings and o he
bene i s. Re . [5] heo e ically compa es he ene gy pe o mance
o an Opaque Ven ila ed Façade agains a con en ional one h ough
a CFD analysis, conside ing wo speci ic days, di e en o ien a ions
and wo wind- eloci ies; he wo k concludes ha he VF sa es
be ween 20 and 55 % o ene gy compa ed o he con en ional
one. Re . [6] also uses CFD simula ions and op imizes a no el opa-
que dynamic açade, wi h an in eg a ed en ila ion module, phase
change ma e ials and an adjus able insula ion sys em. As an ou -
come, he ai low can inc ease o dec ease he he mal esis ance
o he açade o con ol he hea loss along he yea . Maciel and
h ps://doi.o g/10.1016/j.enbuild.2022.112737
0378-7788/Ó2022 The Au ho s. Published by Else ie B.V.
This is an open access a icle unde he CC BY license (h p://c ea i ecommons.o g/licenses/by/4.0/).
⇑
Co esponding au ho .
E-mail add ess: [email p o ec ed] (A. Picallo-Pe ez).
Ene gy & Buildings 280 (2023) 112737
Con en s lis s a ailable a ScienceDi ec
Ene gy & Buildings
jou nal homepage: www.else ie .com/loca e/enb
Ca alho [7] de elop a me hodology o compa e opaque en ila ed
açades o cladding açades based on se e al simula ions and s a-
is ical p ocessing da a. Re . [8] also s udies opaque en ila ed
açades, h ough a sensi i i y analysis, o e alua e he pe o mance
and in luence o he ou doo bounda y condi ions. The s a e-o -
he-a o e iewed in he wo k highligh s ha , a e 2011, he
expe imen al ene gy-analysis o na u ally en ila ed açades is
he mos widesp ead app oach in he li e a u e. Re . [9] s udies di -
e en wall laye p ope ies and hei e ec on he he mal pe o -
mance o en ila ed açades by measu ing hea low and
en ila ion. As a esul , he p esence o an in e nal mass inc eases
he hea ans e owa ds he indoo en i onmen . The s udy o
Re . [10] e alua es he design, cons uc ion and he mal pe o -
mance o an expe imen al VF. As i aims o keep he p inciples o
he ci cula economy, all he ma e ials a e bio-based. As a esul ,
his açade is a p omising op ion o wa m clima es. An opaque
en ila ed açade made up o ecycled ma e ials is es ed du ing
a win e pe iod in Re . [11]. This wo k does a hyg o- he mal anal-
ysis o accoun o hea losses as well as o con ol he mois u e.
As men ioned abo e, h oughou he published li e a u e
e iew, a la ge numbe o wo ks analyze expe imen ally he
beha io o VFs; he mos ecen wo ks design VFs wi h inno a i e
ma e ials and special cha ac e is ics, and many o he wo ks pe -
o m he analysis dynamically. Howe e , all he li e a u e ocuses
on ene gy s udies, based on he i s law o he modynamics, bu
no wo k has been ound ha applies he second law in oducing
he exe gy p ope y in en ila ed açades solu ions.
Indeed, he exe gy me hod is a well-es ablished he modynamic
me hod ha helps o imp o e he e iciency o p ocesses. Howe e ,
i s applica ion in buildings is no as popula as ene gy analyses. This
exe gy analysis can be applied ei he a acili y le el, building le el
o e en o u ban planning. One o he mos de ailed publica ions
applying exe gy in buildings appea s in Re . [12], which de ails he
applica ion o exe gy, bo h in he building en elope and in i s acil-
i ies. As wi h ene gy analysis, exe gy analysis aims o sea ch o
echniques ha educe ossil uel consump ion, inc ease he use o
enewable ene gy and use ene gy mo e e icien ly. In addi ion, i
p o ides addi ional in o ma ion o con en ional ene gy analysis,
hus unco e ing ene gy and en i onmen al p oblems and he e o e
b inging abou be e design solu ions.
Al hough VF exe gy analyses a ely appea in he li e a u e,
he e a e a ew pape s ha e e o he second law o he mody-
namics applied o buildings en elope. Re . [13] simula es a
iangula - oo enclosu e o ob ain he nume ical solu ion o he
en opy p oduc ion due o na u al con ec ion. Re . [14] also deals
wi h ma hema ical app oaches and ema ks he impo ance o sec-
ond law analyses o e alua e he quali y o ene gy sou ces in o de
o ge be e s a egies o building designs. The e o e, he wo k
analyzes he mal exe gy lows h ough he building and de ines
he human body exe gy balance. Human body exe gy balances
a e also deeply de eloped in Re . [15]. Low-exe gy buildings a e
de ined and simula ed in Re . [16] and he de ailed analysis o a
building en elope appea s in Re . [17]; his wo k simula es ou
di e en building en elops and compa es he exe gy analysis
esul s. Re . [18] analyzes he en elope and he hea ing sys em o
a nZEB in Spain unde he exe gy poin o iew; he esul s show
he possibili ies o ene gy e iciency imp o emen ha canno
be app ecia ed wi h pu e ene gy analysis. The en i e hea ing p o-
cess in buildings is in es iga ed in Re . [19], om he exe gy o
he building en elope, oom ai , hea ene gy emission sys em, dis-
ibu ion, s o age, gene a ion sys em, un il he p ima y ene gy
ans o ma ion, dealing wi h he simula ion esul s. Some hing
simila is done in Re . [20], which compa es he ene gy and exe gy
pe o mances o an old and a e o i ed building in Spain, om he
en elope un il he p ima y ene gy, o in Re . [21] which s udies a
low exe gy hea ing sys em om he g ound-sou ce hea pump o
he building en elope. Re . [22] de ines he ma hema ical model
o applying dynamic exe gy and exe goeconomic analyses o he
building en elope, o calcula e he hea ing and cooling demands.
Uns eady-s a e exe gy analysis, based on a ini e di e ence so -
wa e, a e also applied in Re . [23] on ex e nally and in e nally insu-
la ed en elopes o ha e new insigh s o he buildings design.
The e iew o hea ans e and ene gy low cha ac e is ics o
he building en elopes in Re . [24] concludes ha exe gy analysis
becomes mo e signi ican and help ul wi h ac i e en elops, i.e.,
in buildings wi h in eg a ed PV (BIPV) o he mal (BIPV-T) solu-
ions. In a simila way, Re . [25] e iews he p esen day applica-
ion o BIPV and BIPV-T echnologies unde he ene gy and
exe gy pe spec i es. The pe o mance o semi- anspa en hyb id
pho o ol aic he mal double pass açades (HPVT-DPF) a e ene ge -
ically and exe ge ically analyzed in Re . [26] by esul s ob ained
om simula ions. In addi ion, Re . [27] e alua es he building in e-
g a ed semi anspa en pho o ol aic (BISPV) modules o oo and
açade, o de e mine he ene gy and exe gy pe o mance o he
building. A building wi h BIPV-T is also simula ed in Re . [28]
whe e he dynamic exe gy analyses o all he sys em componen s
is done and is compa ed o a e e ence building model, i.e., a build-
ing wi hou BIPV-T. The wo k poin s ou ha usually exe gy s ud-
ies a e ocused only on he BIPV-T collec o i sel , dis ega ding he
whole building-plan .
2. Objec i e and me hodology
As jus i ied in he p e ious in oduc ion sec ion, some wo ks (1)
analyze he VFs om an ene gy poin o iew and (2) se e al s ud-
ies ela e he en elope he mal losses o he exe gy analysis; how-
e e , we ha e no ound wo ks linking hese wo ields oge he .
The ollowing poin s summa ize he e iewed li e a u e in o de
o ge a gene ic pic u e o he s a e o he a :
Re e ing o (1) VFs analysis:
o As desc ibed in Re s.[4–11], he ecen wo ks expe imen-
ally cha ac e ize en ila ed açades only om he ene gy
poin o iew; all hese pape s a e published du ing he las
wo yea s, 2020–2022.
Re e ing o (2) exe gy analyses in buildings en elope:
o These wo ks a e sca ce so he li e a u e e iew has been
ex ended om 2009 o 2020, and no wo k has been ound
a e ha 2020 yea .
o As ma ked in Re s.[22,23], he majo i y o s udies in he li -
e a u e ollow a s eady-s a e app oach when conduc ing an
exe gy analysis by ixing a cons an e e ence empe a u e.
Ne e heless, he e is a necessi y o making a dynamic anal-
ysis because o he en i onmen al condi ions change.
o Mos o he wo ks [13,17,19,21–23,26,28] a e associa ed
wi h simula ion esul s, since i is o en no possible o al-
ida e he ene gy and exe gy pe o mance wi h expe imen al
da a.
o The wo ks o Re s.[13–16,18–21,24–28] de elop he ma he-
ma ical o mulae o de ine he exe gy losses h ough
açades, ocusing exclusi ely on he losses om he in e io
o he ex e io , wi hou conside ing he ype o açade unde
analysis no he composi ion o i s speci ic laye s.
The e o e, his wo k aims o ill he esea ch gap o VFs analysis
wi h he ollowing objec i es and no el ies:
To de ine he ma hema ical o mulae o applying dynamic
ene gy and exe gy analyses in VFs.
To p opose new indexes, EQC and ExQC, o cha ac e ize he
ene gy and exe gy beha iou o a VF e sus a con en ional one.
A. Picallo-Pe ez and José Ma ía Sala-Liza aga Ene gy & Buildings 280 (2023) 112737
2
To ca y ou an expe imen al dynamic essay o a o ced VF in a
Paslink es -cell, o ob ain he co esponding dynamic da a a
each laye o he açade.
To apply he p oposed balances and indexes o he o ced VF
es ed.
The e o e, his wo k explains how o apply he exe gy me hod-
ology o cha ac e ize he he mal beha io o a VF, a e doing he
co esponding ene gy analysis.
The s uc u e o he wo k appea s in Fig. 1. A e he in o-
duc ion o Sec ion 1 and he wo k jus i ica ion in Sec ion 2,
Sec ion 3 de elops he ene gy and exe gy balances in he in e -
nal and ex e nal su aces o a con en ional açade, aking in o
accoun all he di e en hea ans e mechanisms. Based on
hese exp essions, he wo k o mula es he ene gy and exe gy
balances o a VF in Sec ion 4 and de ines some indexes ha
cha ac e ize i s beha io e sus a con en ional açade. Sec ion 5
desc ibes he cha ac e is ics o he es pe o med on a VF in a
PASLINK es -cell, oge he wi h hei co esponding da a
ob ained. Sec ion 6 p esen s he nume ical esul s o he ene gy
and exe gy beha io and shows he alues o he pe o mance
coe icien s and inally, Sec ion 7 highligh s he conclusions o
he wo k and Sec ion 8 con ains he discussion.
3. Ene gy and exe gy balances in he su aces o a con en ional
açade
The ollowing sec ion con ains he ma hema ical app oach o
cha ac e ize a açade h ough i s ene gy and exe gy balances.
Acco ding o he adop ed sign con en ion, he hea lux ha
eaches he su ace is conside ed posi i e and he lux ha comes
ou is nega i e.
3.1. Ene gy balance in he in e nal su ace
I an ene gy balance is applied o he in e nal su ace o he
açade in win e condi ions, when he ou doo empe a u e T
0
is
lowe han he indoo empe a u e T
i
(T
0
<T
i
), hea goes om
he inside h ough he açade, see Fig. 2 (a):
_
Q
;lw;is
þ
_
Q
;sw;is
þ
_
Q
c ;is
¼
_
Q
cd;is
ð1Þ
whe e:
_
Q
;lw;is
: co esponds o he exchanged longwa e adia ion (by
abso p ion - emission). This e m includes he exchanges wi h
he o he in e io su aces a di e en empe a u es, as well
as he adian exchange wi h he in e nal hea sou ces, wi hou
conside ing ligh ing.
_
Q
;sw;is
: ep esen s he edis ibu ed and abso bed sho wa e
adia ion; i conside s con ibu ions om he sun ( h ough
he openings) and om in e nal sou ces, such as ligh ing.
_
Q
c
;is
: ep esen s he hea exchanged by con ec ion wi h he
indoo ai .
_
Q
cd;is
: e e s o he hea ans e by conduc ion h ough he
açade.
The analysis o he adian exchange o in e io su aces is com-
plex due o he di e en su aces and na u es o his adia ion.
The e o e, he
_
Q
c
;is
con ec ion and (
_
Q
;lw;is
þ
_
Q
;sw;is
) adia ion
luxes a e conside ed o be pa allel, so a combined con ec ion-
adia ion coe icien h
c
;is
is used o simpli y he calcula ion and
o conside he hea lux di ec ly h ough New on’s cooling
equa ion.
h
c ;is
¼h
c
þh
ð2Þ
_
Q
is
¼Ah
c ;is
ðT
i
T
si
Þð3Þ
whe e A is he hea ans e a ea and h
is an equi alen adia-
ion coe icien , being h
¼4
e
is
T
3
m
;T
m
¼ðT
si
þT
sj
Þ=2 and T
sj
is
he a e age o he o he in e nal su ace empe a u es ha
exchange adia ion wi h he su ace conside ed,
is he Bol z-
mann cons an , and e
is
is he emissi i y o he in e nal su ace
conside ed.
In Spain, he Technical Building Code (CTE) [29] limi s he max-
imum he mal ansmi ance alues K
lim
W=m
2
K
ha buildings
can ha e h ough s anda dized con ec ion- adia ion coe icien s
h
c
;is
, whose alues ake in o accoun whe he he low is ho izon-
al o e ical (ascending o descending), see Table 1.
In o de o calcula e K
lim
, he cha ac e is ics o each elemen
ha make up he he mal en elope need o be included, aking in o
accoun he compac ness and i s hea exchange su ace wi h he
ex e io . The e o e, he calcula ion is on he basis o each elemen ,
which in u n mus comply wi h a limi ing he mal ansmi ance
(U
lim
W=m
2
K
)[30].
Knowing he h
c
;is
coe icien and he in e nal su ace empe -
a u e T
is
, he ene gy balance esul s as:
Ah
c ;is
ðT
i
T
is
Þ¼
_
Q
cd;is
ð4Þ
3.2. Exe gy balance in he in e nal su ace
Re e ing now o he exe gy balance in he in e io su ace:
_
B
;lw;is
þ
_
B
;sw;is
þ
_
Q
c ;is
1T
0
T
i
¼
_
Q
cd;is
1T
0
T
is
þ
_
D
is
ð5Þ
Fig. 1. Summa y o he wo k s uc u e.
A. Picallo-Pe ez and José Ma ía Sala-Liza aga Ene gy & Buildings 280 (2023) 112737
3
whe e
_
B
;lw;is
and
_
B
;sw;is
designa e he exe gy o longwa e and sho -
wa e adia ion exchanged by he in e nal su ace espec i ely, T
0
is
he dead s a e empe a u e, and
_
D
is
is he a e o exe gy des uc ion
a he in e nal su ace. This des uc ion is due o (1) abso p ion o
longwa e adia ion om he es o he in e io su aces, (2) emis-
sion om he su ace i sel , (3) edis ibu ed sho wa e abso p ion
om he sun, (4) om ligh s and (5) exe gy des uc ion associa ed
wi h con ec ion in he bounda y laye be ween he ai and he
su ace.
Annex 49 [31] ecommends using he p ope ies o he ‘‘ai
a ound he building” o de ine he dead s a e empe a u e, because
when he indoo ai (in imbalance wi h he ou doo ai ) passes
h ough he açade, i des oys all i s exe gy un il i eaches equi-
lib ium wi h he ou doo en i onmen . The e o e, as said, he su -
ounding ambien -ai can be conside ed as he sou ce o sink o
he ene gy p ocesses o buildings and hei acili ies, always keep-
ing in mind he dynamic beha io o he building and o he ou -
doo empe a u e.
Al hough he adia ion and con ec ion exchanged ha e di e -
en he modynamic quali ies, in a i s app oxima ion, he
con ec ion- adia ion coe icien h
c
;is
is conside ed o a com-
bined
_
Q
is
e m. Then, as he exe gy lux ha a i es on one side
o he su ace is g ea e han he exe gy lux ha lea es on he
o he side, he di e ence is he a e o exe gy des uc ion ha
akes place on he su ace:
Ah
c ;is
T
i
T
is
ðÞ1T
0
T
is
¼
_
Q
is
1T
0
T
is
¼
_
Q
cd;is
1T
0
T
is
þ
_
D
is
ð6Þ
In summe , when T
0
>T
i
, he same exe gy balance equa ion
applies, bu now he exe gy associa ed wi h he ene gy exchanged
has he opposi e sense and his can be seen algeb aically in eq. (6),
as he coe icien 1
T
0
T
is
has a nega i e sign.
3.3. Ene gy balance in he ex e nal su ace
I he o mulae ocus on he ex e nal su ace o he açade,
unde win e condi ions, he e will be a ne hea low by conduc-
ion om inside he açade o he ex e nal su ace, see Fig. 2 (b),
and as he hea lux is he same on one side o he su ace as on
he o he :
_
Q
cd;es
¼
_
Q
;lw;sky
þ
_
Q
;lw;su
þ
_
Q
c ;es
_
Q
;sun;ab
ð7Þ
whe e:
_
Q
cd;es
co esponds o he a e o hea by conduc ion om he
in e io o he wall o he ex e nal su ace.
_
Q
c
;es
is he a e o hea exchanged by con ec ion wi h he ou -
side ai .
_
Q
;sun;ab
is he a e o sho wa e adia ion abso bed om he sun
(inwa d (-)).
_
Q
;lw;sky
is he a e o longwa e adia ion exchanged wi h he
sky.
_
Q
;lw;su
is he a e o longwa e adia ion exchanged wi h he
su oundings, such as he g ound, o he buildings, e c.
In he same way as in he in e io su ace, a h
c
;es
coe icien
can be de ined o combine
_
Q
c
;es
con ec ion and (
_
Q
;lw;sky
þ
_
Q
;su
)
longwa e adia ion, and in oducing he equi alen empe a u e
T
eq
[12]:
h
c ;es
¼h
c
þ4
e
es
T
3
m
ð8Þ
T
eq
¼T
0
þ
e
es
T
4
0
F
es;sky
e
sky
þF
es;su
1
h
c ;es
ð9Þ
_
Q
;lw;sky
þ
_
Q
;lw;su
þ
_
Q
c ;es
¼h
c ;es
T
eq
T
es
ð10Þ
Fig. 2. (a) Ene gy balance in he in e nal su ace and (b) in he ex e nal su ace o he açade.
Table 1
Maximum he mal ansmi ance alues acco ding o CTE.
K
lim
W=m
2
K
Compac ness Win e clima e zone
V/A [m
3
/m
2
]
a
ABCDE
New buildings and expansions V/A 1 0.67 0.6 0.58 0.53 0.48 0.43
V/A 4 0.86 0.8 0.77 0.72 0.67 0.62
Changes in use V/A 1 1 0.87 0.83 0.73 0.63 0.54
Reno a ions o mo e han 25 % o he o al en elope a ea. V/A 4 1.07 0.94 0.9 0.81 0.7 0.62
A. Picallo-Pe ez and José Ma ía Sala-Liza aga Ene gy & Buildings 280 (2023) 112737
4
whe e:
e
es
is he emissi i y o he ex e nal su ace,
is he S e an-Bol zmann coe icien ,
T
m
is he a i hme ic mean o T
es
and T
0
o linea ize he T
4
es
T
4
0
exp ession,
e
sky
is he emissi i y o he celes ial aul calcula ed as
e
sky
¼
e
0
þ0:81
e
0
ðÞC
cloud
,C
cloud
being he cloudiness ac o and
e
0
he equi alen emissi i y co esponding o a clea sky [32].
F
es;sky
and F
es;su
a e he ision ac o s su ace/sky and su ace/
su oundings espec i ely.
Then eq. (7) becomes:
_
Q
cd;es
¼h
c ;es
T
eq
T
es
_
Q
;sun;ab
ð11Þ
The sho wa e adia ion om he sun abso bed by he ex e io
su ace
_
Q
;sun;ab
is:
_
Q
;sun;ab
¼
a
es
G
T
Að12Þ
whe e a
es
is he abso p i i y o sho wa e adia ion o he ex e io
su ace, G
T
is he sola i adia ion
W
m
2
;and A is he su ace. I is
composed o di ec and di use adia ion (wi h di e en associa ed
exe gies) and i s alue depends on loca ion, o ien a ion, day and
ime.
3.4. Exe gy balance in he ex e nal su ace
In he same way as eq.(7), an exe gy balance on he ex e nal
su ace gi es:
_
Q
cd;es
1T
0
T
es
¼
_
B
;lw;sky
þ
_
B
;lw;su
þ
_
Q
c ;es
1T
0
T
es
_
B
;sun;ab
þ
_
D
es
ð13Þ
The exe gy luxes e e ing o he exchange o longwa e adia-
ion be ween he sky
_
B
;lw;sky
and he ex e io su ace-su oundings
_
B
;lw;su
can be combined h ough he ic i ious empe a u e T
;sky
as
ollows:
T
;sky
¼1F
es;sky
T
su
þF
es;sky
T
sky
ð14Þ
and, using he Pe ela exp ession o calcula e he exe gy o
adia ion:
_
B
;lw;sky
þ
_
B
;lw;su
¼A
e
es
T
4
es
T
4
;sky
14
3T
0
T
3
es
T
3
;sky
T
4
es
T
4
;sky
2
43
5ð15Þ
Many ene gy analyses also combine he sho and longwa e
adia ion mechanisms wi h con ec ion in o a single e m, o apply
New on’s cooling law by he con ec ion- adia ion coe icien , and
he sun-ai empe a u e [12]. Howe e , al hough using he h
c
;is
coe icien in he exe gy balance o he in e nal su ace (eq. (6)),
encompassing sho - and longwa e mechanisms in he ex e nal
su ace is no adequa e o he exe gy calcula ion, due o he a i-
ous he modynamic quali ies o hese ene gy ans e s. Ne e he-
less, longwa e adia ion exe gy lows can be joined wi h he
ex e nal con ec ion mechanism h ough he h
c
;es
con ec ion-
adia ion coe icien in he
_
B
es
e m,
_
B
es
¼
_
B
;lw;sky
þ
_
B
;lw;su
þ
_
Q
c ;es
1T
0
T
es
¼Ah
c ;es
T
eq
T
es
1T
0
T
es
ð16Þ
Thus, summa izing he exe gy balance s ays as ollows:
_
Q
cd;es
1T
0
T
es
¼
_
B
es
_
B
;sun;ab
þ
_
D
es
ð17Þ
whe e, ollowing Pe ela
_
B
;sun;ab
¼
a
es
AG
T
1þ1
3
T
0
T
sun
4
4
3
T
0
T
sun
()
ð18Þ
andT
sun
= 5.700 K is he sola adia ion empe a u e app oxi-
ma ed o a black body. As men ioned abo e, o a mo e accu a e
analysis, G
T
should be decomposed in o di ec and di use i adi-
ance [12].
The ne hea -loss h ough he ex e io su ace is inally
exchanged wi h he en i onmen by con ec ion and longwa e
adia ion un il i eaches he ambien empe a u e T
0
( he dead
s a e). Thus, he exe gy o his hea -loss is comple ely des oyed
in he en i onmen , esul ing in an exe gy loss:
_
Q
cd;es
1T
0
T
es
þ
_
B
;sun;ab
¼
_
L
es
ð19Þ
In win e , he conduc ion hea lux in he ex e nal su ace and
i s exe gy ha e he same sense, bo h a e om he in e io o he
ex e io , while in summe he conduc ion hea lux in he ex e nal
su ace is inwa d, whe eas i s associa ed exe gy low, on he con-
a y, is ou wa d.
4. The modynamic analysis o a en ila ed açade
Ven ila ed açades inco po a e insula ion oge he wi h a en i-
la ed ai chambe , wi h an ou e shee joined o he in e io by
means o a subs uc u e, see he scheme o Fig. 3.
The ai chambe is he p ima y componen o he sys em, pe -
o ming a ious unc ions: i p e en s he dynamic o ces o he
wind om eaching he in e io componen s, i ac s as a d ainage
sys em agains e en ual in il a ions, i allows he e acua ion o
wa e apo coming om he pe spi a ion o he enclosu e o he
building and, likewise, he ci cula ion o ai cools he excess o
sola adia ion inciden on he skin o he cladding.
4.1. Ene gy and exe gy balances in a en ila ed açade
Acco ding o he abo e nomencla u e, om an ene gy balance
in a non-s a iona y s a e, conside ing he whole açade as a con ol
olume and ha hea goes om he ex e io o he in e io , he ol-
lowing equa ion is w i en:
dU
VF
d ¼
_
Q
;sun;ab
þ
_
Q
c ;es
_
Q
c ;is
þ
_
H
in
_
H
ou
ð20Þ
dU
VF
d ¼A
a
es
G
T
þAh
c ;es
T
eq
T
es
Ah
c ;is
T
is
T
i
ðÞ
þ
_
H
in
_
H
ou
ð21Þ
whe e U
VF
is he in e nal ene gy accumula ed in he ma e ials ha
make up he açade, which can be calcula ed knowing he empe -
a u e T
j
, he he mal capaci y c
P
j
and he mass m
j
o each j- laye ;
and
_
H
in
and
_
H
ou
a e he a e o ai en halpy a he en ance and exi
o he en ila ed açade.
U
VF
¼Xðm
j
c
P
j
ðT
j
T
0
ÞÞ ð22Þ
dU
VF
d
D
U
VF
D
¼Xm
j
c
P
j
T
j
T
j
D
D
T
0
T
0
D
D
ð23Þ
_
H
in
_
H
ou
¼_
m
ai
c
P
T
in
T
ou
ðÞ ð24Þ
A. Picallo-Pe ez and José Ma ía Sala-Liza aga Ene gy & Buildings 280 (2023) 112737
5
I an exe gy balance is pe o med hen:
dB
VF
d ¼
_
B
;sun;ab
þ
_
Q
c ;es
1T
0
T
es
_
Q
c ;is
1T
0
T
is
þ
_
B
in
_
B
ou
_
D
T
ð25Þ
whe e
_
B
in
_
B
ou
is he exe gy change o he ai en e ing in he cham-
be (
_
B
in
_
B
ou
¼_
m
ai
c
P
ai
T
in
T
ou
ðÞ
T
0
ln
T
in
T
ou
);
_
D
T
is he a e
o o al exe gy des uc ion in he açade, including all he hea
exchange mechanisms and he i e e sibili ies associa ed wi h he
ai low in he chambe , and B
VF
is he exe gy accumula ed in he
ma e ials:
B
VF
¼Xm
j
uu
0
ðÞjT
0
ðss
0
ÞðÞj
¼Xm
j
c
P
j
T
j
T
0
T
0
ln T
j
T
0
ð26Þ
dB
VF
d
D
B
VF
D
¼
Xm
j
c
P
j
D
T
j
D
D
T
0
D
D
T
0
D
ln T
j
T
0
T
0
D
T
j
D
T
0
T
j
D
T
0
D
T
j
T
0
! !"#
ð27Þ
4.2. Pe o mance coe icien s o a en ila ed açade
As said in he li e a u e e iew, no exe gy index is ound o
cha ac e ize he he mal beha io o en ila ed açades o oo s.
The mos common exe gy indica o s ocus on indus ial p ocesses
o ene gy gene a ion sys ems. Among hem, he ollowing a e
ound: he exe gy e iciency used by Boelman & Sakupipa sin
[33], and Co nelissen & Hi s [34], o he unc ional e iciency o
Ko as [35] and Tsa sa onis [36].
The e o e, a coe icien o cha ac e ize he beha io o build-
ing en elopes needs o be de ined in e ms o exe gy, pa icu-
la ly o VFs. Fu he mo e, his coe icien has o conside he
en elope as a dynamic sys em and mus be easy o in e p e
and no dis an om he ene gy coe icien s. Conside ing he
equi emen s, he Doc o al Thesis o I. Flo es [37] de ines i e
possible pa ame e s. A e analyzing he esul s o di e en
walls, clima es, e c., he mos in e es ing is he one based on
he ISO 9869-1 s anda d exp ession [38], o he ‘‘in si u” de e -
mina ion o he he mal esis ance o a wall, and is called ‘‘dy-
namic exe gy ansmi ance”.
In his wo k, a di e en poin o iew is adop ed. In o de o
assess he in e es o inco po a ing o no a VF, i s he mal beha -
io is compa ed wi h ha o a con en ional açade ha mee s he
minimum equi emen s equi ed by he egula ions, and he e o e
depending on he geog aphical a ea and clima ic condi ions.
Unde he poin o iew o he i s law, his wo k de ines a coe -
icien ha ela es he ene gy los h ough he con en ional ( e e -
ence) açade e sus ha los in he VF. Fo win e condi ions,
which a e he mos ele an in ou zone, he hea low
_
Q
is
¼Ah
c
;is
T
i
T
is
ðÞgoes om he indoo ai a T
i
o he in e nal
su ace a T
is
, being T
e
is
he in e nal su ace empe a u e in he e -
e ence açade. The hea exchanged by he e e ence açade in e nal
su ace h ough con ec ion and longwa e adia ion is
_
Q
e
is
¼Ah
c
;is
T
i
T
e
is
,Fig. 4 (b).
This wo k p oposes naming his a io he Ene gy Quali y Coe i-
cien (EQC) so,
Fig. 3. Scheme o a simple en ila ed açade (summe ).
A. Picallo-Pe ez and José Ma ía Sala-Liza aga Ene gy & Buildings 280 (2023) 112737
6
EQC ¼P
n
j¼1
Q
e
is
j
P
n
j¼1
Q
is
j
ð28Þ
whe e n¼1jco esponds o he hea ans e ed du ing he n
pe iods o ime conside ed. Applying he ene gy balance, he abo e
de ini ion can be exp essed wi h e e ence o he ex e nal su ace
‘‘es”, by conside ing in he e m Q
es
j
he sola abso p ion (Q
;sun;ab
j
)
and he con ec ion- adia ion (Q
c
;es
j
), hen,
EQC ¼P
n
j¼1
Q
e
es
j
þ
D
U
e
j
hi
P
n
j¼1
Q
es
j
þH
ou
H
in
ðÞ
j
þ
D
U
j
hi ð29Þ
I EQC is g ea e han one, he VF is he mally p e e able o he
e e ence- açade de ined by he applica ion o he Spanish Techni-
cal Code (CTE) limi ing alues. In win e condi ions, i he p e-
hea ed ai o he chambe is used in he building,
H
ou
H
in
should appea in he denomina o o eq. (28), so ha
P
n
j¼1
Q
is
ðH
ou
H
in
Þis now he hea -loss.
Compa ing he exe gy los by such a e e ence- açade wi h he
exe gy los by he VF, we can simila ly de ine an exe gy quali y coe -
icien ExQC, as ollows
ExQC ¼P
n
j¼1
Q
e
is
j
1
T
0j
T
e
isj
!
P
n
j¼1
Q
is
j
1
T
0j
T
isj
ð30Þ
Re e ing his coe icien o he ex e nal su ace ‘‘es” o he FV,
h ough he exe gy balance equa ion:
ExQC ¼P
n
j¼1
B
e
es
j
þ
D
B
e
j
þD
e
j
hi
P
n
j¼1
B
es
j
þB
ou
B
in
ðÞ
j
þ
D
B
VF
j
þD
j
hi
ð31Þ
In summe , when T
0
>T
is
, he hea lux-gain
_
Q
is
supposes an
exe gy ou pu om indoo equal o
_
Q
is
1
T
0
T
is
, so he hea lux
and i s co esponding exe gy ha e opposi e senses. The objec i e
now is o educe he hea low
_
Q
is
so ha he exe gy associa ed
wi h i and ha goes ou om he indoo ai is as low as possible.
In hese condi ions, he ho ai in he chambe is sen ou doo s.
5. Case s udy
5.1. Cha ac e is ics o he paslink cell- es s
PASLINK dynamic cell- es s a e highly s anda dized es s ha
allow cons uc ion solu ions o be he mally cha ac e ized unde
eal dynamic condi ions hanks o hei nume ous and s a egic
senso s. The de elopmen o PASLINK es s s a ed mo e han
20 yea s ago, h ough in e na ional wo k coo dina ed and unded
by EU esea ch p ojec s [39]. PASLINK cells consis o a es oom
whe e he sample o be es ed is placed, and an adjacen se ice
oom whe e he hea exchange h ough he sample is measu ed
wi h high p ecision, see Fig. 5.
5.2. Desc ip ion o he o ced en ila ed açade es ed
The cons uc ion-solu ion es ed as he case s udy in he
PASLINK cell is a ligh and indus ialized en ila ed açade wi h
d y assembly and p e ab ica ed ma e ials, see Fig. 6. I is a simple
açade consis ing o a 2 mm gal anized s eel shee , a 3 cm ai
chambe and a sandwich panel wi h a 6 cm polyu e hane co e.
The ai inside he en ila ed chambe mo es in a o ced way by
means o h ee ex ac ion hoppe s loca ed in he uppe pa o
he sample.
Fig. 7 shows he loca ion o he empe a u e senso s (P 100) in
he a ious laye s o he en ila ed açade; as i can be seen, he ai
chambe has a calib a ed he mopile wi h nume ous senso s o
measu e he inc ease in he ai empe a u e ac oss i . In addi ion
o he senso s in he sample he e a e: 12 P 100 senso s o ambi-
en empe a u e, 3 Kypp and Zonnen CMP11 Sola ime e s o mea-
su e he o al e ical and ho izon al sola adia ion and 1 shadow
ing o measu e di use adia ion, 1 senso o he ou side wind
di ec ion and ano he one o i s speed, 1 di e en ial p essu e
me e , 1 ai low me e , and 1 powe ansduce .
Fig. 4. (a) Ene gy loss in en ila ed açade s (b) e e ence açade.
A. Picallo-Pe ez and José Ma ía Sala-Liza aga Ene gy & Buildings 280 (2023) 112737
7
5.3. Da a ob ained om he es
The es was ca ied ou a he Building Quali y Con ol Labo a-
o y o he Basque Go e nmen (LCCE) in Vi o ia/Gas eiz, no he n
Spain, o e 6 days ( om No embe 8 h o 13 h) and da a we e col-
lec ed e e y 10 min.
Fig. 8 shows he da a collec ed di ec ly om he senso s in
each laye . All empe a u es show a simila end, which allows
he alues o be a e aged o a single su ace- empe a u e alue
(excep o he ai empe a u e inside he chambe , which
inc eases i s alue e ically om T
in
a he en ance o T
ou
a he exi ).
The a e age s anda d de ia ions
a
g
;when a e aging he em-
pe a u es o each su ace a a single su ace empe a u e T
s;j
;a e
ga he ed in Table 2.
Fig. 9 shows he ou doo and indoo empe a u es, and he
a e age in e nal and ex e nal su ace empe a u es o he VF, as
well as he sola i adia ion ( e ical global, ho izon al global,
and ho izon al di use) and he ai low a e h ough he ai
chambe .
6. Resul s
This sec ion shows he esul s o he analysis pe o med wi h
he da a ob ained in he es . The esul s a e p esen ed in h ee sec-
ions: 6.1 Ene gy Analysis, 6.2 Exe gy Analysis and 6.3 Pe o mance
Coe icien s.
6.1. Ene gy analysis
This sec ion con ains he dynamic and global esul s o ene gy
analysis.
6.1.1. Dynamic ene gy analysis o he VF
Calcula ing he componen s o he ene gy balance equa ion in
he açade, eq. (20), he alues ob ained a e shown in Fig. 10. The
ollowing ends a e obse ed:
When he e is sola i adia ion G
T
, he ex e nal su ace empe -
a u e T
es
ises ma kedly, making
_
Q
c
;es
nega i e (i.e., loss) as
T
eq
<T
es
;
On he o he hand, he ai - low empe a u e in he chambe
ises om inle T
in
o ou le T
ou
, pa icipa ing in he hea ans-
e , which makes
_
H
in
<
_
H
ou
and he e o e p ehea ing he ai o
be a e inse ed inside he house.
Fu he mo e, as he coe icien h
c
;is
is low, he e is ha dly any
empe a u e di e ence be ween he indoo empe a u e T
i
and
he in e nal su ace empe a u e T
is
. In addi ion, as T
i
>T
is
,
_
Q
c
;is
lows ou wa ds (i has a nega i e sign).
When he sola adia ion abso bed
_
Q
;sun;ab
ises and he ex e nal
su ace empe a u e T
es
inc eases, he VF loses hea o he ou -
side, so i s in e nal ene gy dec eases
dU
VF
d
<0:Fig. 11 jus i ies
his ac by depic ing he sola i adia ion s he change in in e -
Fig. 5. S uc u e o a Paslink cell.
Fig. 6. (a) Laye s o he en ila ed açade, (b) PASLINK cell, (c) ma e ials.
A. Picallo-Pe ez and José Ma ía Sala-Liza aga Ene gy & Buildings 280 (2023) 112737
8
nal ene gy. I can be seen ha he sola i adia ion abso bed
no iceably s imula es he in e nal ene gy inc ease and dec ease
o he VF.
6.1.2. Ene gy analysis o he VF o e he es pe iod
As a summa y, Table 3 shows he accumula ed ene gy du ing
he 6-day es pe iod o each o he ene gy balance e ms.
Fig. 7. a) Loca ion o senso s in he di e en laye s o he en ila ed açade. b) Zoom in he inside o he ai chambe .
Fig. 8. Tempe a u es o each laye acco ding o senso loca ion.
A. Picallo-Pe ez and José Ma ía Sala-Liza aga Ene gy & Buildings 280 (2023) 112737
9
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