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Ci a ion: Tomasko a, M.; Poko ny, J.;
Kuce a, P.; Balaziko a, M.; Ma aso a,
D., J . Fi e Models as a Tool o
E alua ion o Ene gy Balance in
Bu ning Space Rela ing o Building
S uc u es. Appl. Sci. 2022,12, 2505.
h ps://doi.o g/10.3390/
app12052505
Academic Edi o s: Cesa e Bise ni and
As e ios Bakolas
Recei ed: 18 Janua y 2022
Accep ed: 25 Feb ua y 2022
Published: 28 Feb ua y 2022
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applied
sciences
A icle
Fi e Models as a Tool o E alua ion o Ene gy Balance in
Bu ning Space Rela ing o Building S uc u es
Ma ianna Tomasko a 1,*, Ji i Poko ny 2, Pe Kuce a 2, Michaela Balaziko a 1and Daniela Ma aso a, J . 3
1Depa men o Sa e y and P oduc ion Quali y, Facul y o Mechanical Enginee ing, Technical Uni e si y o
Kosice, Le na 9, 042 00 Kosice, Slo akia; [email p o ec ed]
2Facul y o Sa e y Enginee ing, VSB-Technical Uni e si y o Os a a, Lumi o a 630/13,
700 30 Os a a-Vysko ice, Czech Republic; [email p o ec ed] (J.P.); pe [email p o ec ed] (P.K.)
3Facul y o Mining, Technical Uni e si y o Kosice, Pa k Komenskeho 19, 040 01 Kosice, Slo akia;
[email p o ec ed]
*Co espondence: [email p o ec ed]
Abs ac :
Fi e is de ined as an ex emely haza dous e en , causing a h ea o li e and heal h o
pe sons, bu also damage o he economic sphe e. I has been shown many imes ha i e can occu
anywhe e and a any ime. In o de o minimize he isk o i e mani es a ions, i is necessa y o
unde s and i s cou se. In echnical p ac ice, compu a ional models a e used o de e mine he pa ial
mani es a ions o i e, such as i e sp ead a e, smoke gene a ion a e in he bu ning a ea, o ma ion
o oxic bu ning p oduc s, lame heigh , and o he s. One o he impo an cha ac e is ics is also he
ene gy balance in he bu ning a ea ela ing o he cha ac e o bu ning ma e ial, access o oxygen
necessa y o exo he mic eac ion o bu ning, and eac ion o he ins alled sa e y de ices. In his pape
we will poin ou he i e sa e y o he building. The FDS (Fi e Dynamics Simula o ) model is ecen ly
used in p ac ice, and i s ad an age is he possibili y o model i e e en in la ge and a ypical spaces.
The con ibu ion o his pape is he p ac ical applica ion o i e sa e y o cons uc ion using he FDS
Model, o educe he cos o i e sa e y o he s uc u e being cons uc ed. A en ion was paid o
e alua ing how he hea ene gy ha is eleased du ing a i e can be in luenced by he ins alled s able
i e-ex inguishing equipmen , aking in o conside a ion he i e esis ance o he building s uc u es.
Keywo ds: i e simula ion; building i e sa e y; p e en ion
1. In oduc ion
Fi es cause loss o li e, p ope y, and na u al ecosys ems e e y yea , so i is impo an
o s udy hem o p e en o limi he occu ence o po en ial i es. The basic p inciple o
i e p e en ion is o c ea e and de elop he condi ions o ensu e e ec i e p o ec ion o
li e and heal h o pe sons and p ope y om i es, as well as hei e ec i e managemen ,
including he p o ision o assis ance du ing such e en s. The a ea o i e p e en ion and
he p o ision o basic i e p e en ion measu es is cu en ly add essed in a numbe o
ways, in pa icula , he oles, esponsibili ies, and compe ences con ained in i e p o ec ion
legisla ion. Compu e simula ion o i es makes i possible o es di e en i e scena ios
and o model he cou se and consequences o a i e unde di e en condi ions, o de ec
possible isks and ci cums ances ha may lead o damage, and, whe e app op ia e, o
educe he consequences o po en ial u u e i es. I is also one o he ways o minimize he
consequences o i e and con ibu e o he i e sa e y o buildings [1].
Fi es and i e igh ing in e en ions a i es ep esen a high cos o go e nmen bud-
ge s each yea . They cause seconda y damage ha can be mo e se e e han he di ec
consequences o i e, o example, by limi ing in as uc u e by closing o a eas damaged
by i e.
Sus ainable de elopmen o he e i o y is also signi ican ly ela ed o he sa e y o
he buildings loca ed in he e i o y. The equi emen s o ensu ing he sa e y o buildings
Appl. Sci. 2022,12, 2505. h ps://doi.o g/10.3390/app12052505 h ps://www.mdpi.com/jou nal/applsci
Appl. Sci. 2022,12, 2505 2 o 15
wi hin he Eu opean Union a e based in pa icula on Regula ion (EU) No 305/2011 o
he Eu opean Pa liamen and o he Council laying down ha monized condi ions o he
ma ke ing o cons uc ion p oduc s and epealing Council Di ec i e 89/106/EEC. Among
he cha ac e is ics ha buildings mus mee a e i e sa e y equi emen s. These equi emen s
include main aining he load-bea ing capaci y o he s uc u e in he e en o i e, limi ing
he sp ead o i e inside and ou side he building, ensu ing he e acua ion and escue o
pe sons, and ensu ing he sa e y o escue uni s [2].
To assess compliance wi h he speci ied equi emen s, i is necessa y o cha ac e ize
he de elopmen o he i e. The de elopmen o a i e is usually desc ibed by ou phases,
which include he ini ial (ini ia ion) phase, he de elopmen phase, he ully de eloped
phase, and he bu n-ou phase. All phases o a i e can be desc ibed by i e pa ame e s,
he mos signi ican o which include i e a ea, i e pe ime e , linea a e o sp ead, a e o
la e-up o ma e ials, lame heigh , lame empe a u e, hea elease a e, hea lux densi y,
and o he s. Using he i e phases and hei pa ame e s, he dynamics o he de eloping i e
and i s p edic ed e ec s on he su ounding en i onmen , i.e., he building s uc u e, can
be desc ibed [3–6].
Smoke is p oduced and sp ead du ing a i e, which also has nega i e consequences.
Toxic subs ances p esen in smoke can cause poisoning o people in smoke-in es ed build-
ings in con ined spaces.
The p esence o smoke educes isibili y and, he e o e, he abili y o o ien onesel in
space, which can make i signi ican ly mo e di icul o impossible o ind escape ou es and,
as a consequence, cause panic among people escaping. Fi e is a phenomenon ha in ol es
many physical and chemical p ocesses such as he p opaga ion o adia ion, combus ion,
hea adia ion, u bulen low o gases, and o he s. Due o he in ensi ica ion o i e, i is
necessa y o s udy he cou se o i e and i s consequences, o seek means o inc easing he
sa e y o objec s h ea ened by i e.
The cou se o a i e can be de e mined by s anda dized o speci ic p ocedu es. S an-
da dized p ocedu es may include compu a ional o expe imen al app oaches p esen ed
by echnical s anda ds [
7
]. Speci ic p ocedu es can be unde s ood as he use o me hods
o he han s anda dized me hods. Fi e models ha can be used o desc ibe, in pa o
comp ehensi ely, he cou se o a i e a e used he e [8].
Compu e simula ions o i e based on empi ical and scien i ic knowledge a e com-
pa able o eal i e expe imen s. A signi ican ad an age in compa ison o i e es s is he
non-des uc i eness and lexibili y o i e simula ions. A i e can be modeled in an iden ical
space unde di e en condi ions (e.g., wi h di e en i e ini ia ion sou ces) wi hou majo
cos s. Compu e simula ion, i e p og ession, and consequence modeling a e an impo an
pa o imp o ing i e sa e y [9].
One o he c ucial p ope ies o building s uc u es is hei i e esis ance, i.e., he ime
o which he building s uc u es a e able o esis he e ec s o i e. The e a e a ious
high quali y and e ec i e p oduc s and sys ems ha ensu e he in eg i y and load-bea ing
capaci y o he a ec ed s uc u es, be o e he ac ion o i e o i s sp ead, o he pe iod o
e acua ion o he building.
In e ms o i e esis ance o building s uc u es, in he e en o a i e, he building and
i s equipmen mus p o ide:
•load-bea ing capaci y o he pe iod speci ied in he p ojec ;
• he abili y o limi he sp ead o i e and smoke in he building;
• he abili y o limi he sp ead o i e o adjacen buildings;
• he possibili y o e acua ing people om he building;
• he sa e y o he eme gency se ices.
Fi e esis ance is a a e o a building’s du abili y in he e en o a i e. The measu e o
i e esis ance is he ime (in minu es) om he i s con ac o he sys em wi h i e un il i
eaches one o he h ee limi ing c i e ia:
• i e load capaci y—R;
•in eg i y he mal insula ion capaci y—I [10].
Appl. Sci. 2022,12, 2505 3 o 15
Simula ion and aining echnologies o e new oppo uni ies o imp o e he quali y o ,
o example, eaching a uni e si ies. The in oduc ion o new p og essi e eaching is based
on simula ion and si ua ional me hods. Simula ion me hods c ea e he play ul cha ac e o
he si ua ion wi hou he con on a ional cha ac e as i is in eali y. I acili a es s uden s o
mo e o wa d and gain insigh . Si ua ional me hods a e p oblem-sol ing p ocedu es o
model si ua ions. Thei basis is based on ac ual eme gencies o c ises ha ha e happened
in he pas . A icle [
11
] emphasizes he use o simula ions in p epa ing s uden s o handle
eme gencies a he ac ical, ope a ional, and s a egic managemen le els [11].
The p esen shows ha i is also necessa y o obse e he mani es a ions and beha io
o pas i es. By s udying documen a ion o pas i es, i is possible o p edic unde wha
ci cums ances a i e will occu in a simila en i onmen and unde simila condi ions, how i
will sp ead, and how i can be loca ed and ex inguished as quickly as possible. Ne e heless,
he sp ead o a i e is in luenced by a numbe o o he ci cums ances and pa ame e s, such
as clima ic condi ions ( empe a u e, ai low, en ila ion, humidi y, p essu e), en i onmen
(in e io , ex e io , obs uc ions, openings), uel ype, and quan i y. The e o e, i should be
no ed ha in app oxima ely he same en i onmen a i e may beha e di e en ly, and, hus,
based on knowledge om pas i es, i is only possible o de e mine he occu ence and
sp ead o po en ially h ea ening i es app oxima ely, e en o buildings and condi ions o
simila ypes.
The wo king en i onmen , empe a u e changes and humidi y mus be con olled in
all p oduc ion p ocesses and places whe e employees a e p esen . Pape [
12
] objec i ely
assessed employee exposu e o mic oclima ic en i onmen al ac o s in he wo kplace.
The da a we e collec ed in eal wo king condi ions. The mal s ess due o cold and hea
exposu e a each loca ion was assessed using he we bulb globe empe a u e (WBGT)
indica o . Indoo ai quali y indica o s consis o indoo empe a u e, ai quali y, ligh ing,
dus le els, as well as chemical and biological ac o s. These da a can also be used in i e
simula ion [13].
Fi es in a con ined space a e common eme gencies in ou company. Howe e , he
di icul y o dealing wi h his complica ed eme gency si ua ion by i e and escue pe sonnel
can ha e a al consequences o hei employees. The e is, he e o e, a signi ican demand
o new me hods and echnologies o deal wi h his li e- h ea ening eme gency. Modeling
and simula ion echniques ha e been adop ed o conduc esea ch due o he complexi y o
ob aining a da abase o ac ual cases ela ed o his phenomenon. Pape [
14
] e iews he
li e a u e ela ed o modeling and simula ion o shel e i es wi h espec o he i e-jumping
phenomenon. Fu he mo e, he ela ed li e a u e o compa ing he mal came a images
wi h compu ed images is summa ized. Finally, he sui abili y o A i icial In elligence (AI)
echniques o p edic ing he i e jumping in closed p emises is in es iga ed [14].
The objec i e o he esea ch in [
15
] is o sol e he p oblem o i e e acua ion om
a s uden house using a nume ical me hod. In esea ch wi h an e acua ion unc ion
(
FDS + E ac.
), Fi e Dynamics Simula o so wa e was used. The p oblem being in es iga ed
is ela ed o a building ha has an ou doo cen e . The building ea u es include i e loo s,
wi h wo ex e io i e s ai cases loca ed on wo sides o he building. In addi ion, he e is a
single exi o he ex e io o he building, and he i e supp ession sys em is no ins alled
inside he building.
Among a ious ypes o disas e s, i e poses a signi ican h ea o li e and p ope y
in u ban and u al a eas. P o ec ion o hospi als om i e is e y impo an due o he
p esence o a ec ed pe sons, lack o awa eness, and expensi e appa a uses and de ices
in hospi als. This s udy ocused on he simula ion o i e in a hospi al [
16
]. In daily li e,
eme gency se ices such as i e igh e s, pa amedics, and police play an impo an ole.
Rescue s o en o ge abou hei own sa e y in hei wo k. O e all, his issue is neglec ed in
hese se ices, especially du ing he ac ual in e en ion. In many cases, i is he impe ec
p ocess o each escue ac i i y, o e en he ailu e o use pe sonal p o ec i e equipmen .
In [
17
], a g oup o i e and escue o ice s is speci ied, which espec s he basic ules o OHS
in hei ac i i ies such as i es, oad acciden s, na u al disas e s, and many o he s.
Appl. Sci. 2022,12, 2505 4 o 15
Acco ding o [
18
], ma hema ical models o i e ha e wo main a eas o hei use. Fi s ,
i is he design and e i ica ion o he i e sa e y o a building and nex , hey a e a ool o
simula ing he de elopmen o a i e in he ime in e al be ween he occu ence o a i e
and i s ex inc ion. One o he essen ial capabili ies o ma hema ical models is he simula ion
o smoke mo emen and he de e mina ion o i s empe a u e and concen a ion. E idence
o his capabili y is p o ided by simula ions o buildings such as he Xanadu shopping
and en e ainmen cen e in Spain, he mass ga ages in Annecy, F ance, o he Wembley
s adium. In he Czech and Slo ak epublics, ma hema ical models a e mainly used o his
pu pose in he design o ailway and oad unnels.
Inno a i eness o his a icle is based on he ollowing aspec s: on he me hodological
p ocedu e used o c ea ion o he i e scena ios and on he subsequen speci ica ion
o design i es and on hei assessmen by h ee basic a ian s, i.e., by he simpli ied
analysis, by he ma hema ical zonal model CFAST, and by he ma hema ical model o
compu a ional luid dynamics FDS. These p ocedu es we e applied o a ious ypes o
ope a ions, which a e cha ac e ized by di e en i e dynamics, assuming simul aneous
ac ing o he sp inkle i e ex inguishe . The au ho s do no dispu e ha ma hema ical
modeling o i e is, nowadays, an ac ual end in sol ing some o he p oblema ic a eas o
i e sa e y o buildings. Howe e , he au ho s emphasize in he p esen ed case s udy a
ele an ac : jus he combina ion o ma hema ical modeling o i e wi h he simul aneous
applica ion o ac i e i e-ex inguishing equipmen is a p og essi e solu ion ha can lead
o signi ican economic sa ings in sol ing o hese buildings. This solu ion is sui able,
especially in complica ed ope a ions.
The au ho s demons a e, on a p esen ed case s udy, a pe spec i e o he i e model
applica ion in he eal p ocess o building p ojec ion using ac i e elemen s o he i e
p o ec ion (in his case, i is he sp inkle p o ec ion).
1. Ma hema ical Models o Recons uc ion and In es iga ion
The aim o he pape is o p esen a case s udy ha demons a es he pe spec i e
o using i e models o i e esis ance assessmen o building s uc u es. The main idea
o his case s udy is he e alua ion o ene gy balance in he bu ning a ea and in luence
o he ins alled s able i e-ex inguishing equipmen on he ene gy balance, aking in o
conside a ion i e esis ance o he building s uc u es. The p esen ed s udy con i ms a ac
ha in addi ion o he s anda d p oposal p ocedu es i is meaning ul o use he simpli ied
calcula ions, bu abo e all also he ma hema ical models o i e. In he cases when a
s able i e-ex inguishing sys em is also ins alled, mo e de ailed e alua ion p ocedu es
(i.e., simpli ied calcula ions o i e models) can lead o a signi ican educ ion in he cos s
necessa y o ensu e he equi ed i e esis ance o he building s uc u es, while main aining
hei de ined p ope ies.
2. Ma e ials and Me hods
The i e esis ance o building s uc u es may be assessed by es , calcula ion, o a
combina ion o bo h. Wi h nominal o pa ame ic empe a u e cu es, simpli ied and
imp o ed i e models a e used o he mal analysis o s uc u es. Fo he pu pose o he
case s udy, he di e en a ian s usable o he assessmen o he i e esis ance o building
s uc u es will be desc ibed below. The desc ibed a ian s p esen s anda d p ocedu es
and speci ic p ocedu es. A he same ime, he p ocedu es ha we e used in he case s udy
a e p esen ed.
2.1. Fi e Resis ance o S uc u es De e mined by Nominal Tempe a u e Cu es
Fi e esis ance es s o building s uc u es a e ca ied ou in acc edi ed labo a o ies
whe e empe a u e cu es a e used. Nominal empe a u e cu es include he s anda d em-
pe a u e cu e, he ex e nal i e cu e, he hyd oca bon cu e, and he slow i e cu e [
19
].
The no m empe a u e cu e has he wides use.
The no m empe a u e cu e has an empi ical basis; i is also e e ed o as he “cellu-
lose cu e” and simplis ically desc ibes he si ua ion a e he o al igni ion o subs ances
Appl. Sci. 2022,12, 2505 5 o 15
in space. Speci ic empe a u e cu es a e used o speci ic buildings whe e a signi ican ly
di e en empe a u e e olu ion o he i e de elopmen can be assumed. Cha ac e is ic
cu es a e, e.g., unnel empe a u e cu es RABT o RWS.
2.2. Fi e Resis ance o S uc u es De e mined by Pa ame ic Tempe a u e Cu es
Pa ame ic empe a u e cu es a e a simple calcula ion me hod ha de e mines he
empe a u e his o y o a i e o di e en en ila ion coe icien s, i e load densi ies, and di -
e en physical p ope ies o he s uc u es bounding he i e compa men . The equa ions
o de e mining he pa ame ic empe a u e cu es we e de i ed based on he he mal
equilib ium equa ion, which desc ibes he o e all empe a u e balance in he space whe e
he i e de elops.
The use o pa ame ic empe a u e cu es is e y limi ed, and hei use is ecom-
mended only o i es wi h cellulose- ype i e loads and o ela i ely small spaces (up o
500 m
2
o loo a ea wi h a maximum clea ance o 4 m). I is also possible o apply hem o
i e compa men s wi h ho izon al openings in loo s o ceilings [19,20].
2.3. Simpli ied and Imp o ed Fi e Models
Simpli ied i e models ep esen simple compu a ional echniques o desc ibing i e,
based on he de e mina ion o a design i e load alue ha akes in o accoun he densi y o
he cha ac e is ic i e load and coe icien s e lec ing he in luence o he i e haza d and he
in luence o ac i e i e sa e y equipmen [21].
A uni o m o non-uni o m dis ibu ion o empe a u es as a unc ion o ime is as-
sumed. Unequal empe a u e dis ibu ion is cha ac e is ic o he phases o i e de elopmen .
A uni o m empe a u e dis ibu ion gene ally co esponds o a ully de eloped i e
si ua ion. The e is p esen ed, as an example o he simpli ied i e model, a calcula ion
o hea elease a e wi hou in luence o i e ex inguishing (i.e., wi hou ac i a ion o he
sp inkle p o ec ion o wi hou in e en ion o i e b igade e c.). This example is based on
a simpli ied desc ip ion o i e de elopmen , which is di ided in o h ee main phases.
The i e g ow h phase— his i s phase is usually desc ibed in a simpli ied o m by
means o -quad a ic equa ion, which is applied in he modi ied o m [7]:
Q=103
α2
, (1)
whe e Qis hea elease a e (kW),
ime (s),
α ime in e al, which is necessa y o each he hea elease a e alue 1 MW (s).
The ully de eloped i e phase— he second phase is cha ac e ized by he eached
maximum alue o he eleased hea (i.e., by i s cons an alue), whe eby he i e in his
phase is con olled ei he using en ila ion o by amoun o uel) [3,7].
An example o i e, which is con olled by he amoun o uel, is p esen ed by calcula-
ion o he hea elease a e alue Q(kW), acco ding o he ollowing ela ion:
Q=RHR ·A i, (2)
whe e A iis maximum a ea o i e (m2),
RHR
maximum hea elease a e p oduced by 1 m
2
o i e, which is con olled by he
amoun o uel (kW·m−2).
The case o i e, which is con olled using en ila ion, is illus a ed by calcula ion o
he maximum hea elease a e Qmax (MW), as ollows:
Qmax = 0.10·m·Hu·A √(heq) (3)
whe e mis coe icien o bu ning (-), usually m = 0.8,

Appl. Sci. 2022,12, 2505 6 o 15
H
u he pu e calo i ic alue o wood (MJ·kg−1), Hu= 17.5 MJ·kg−1,
A
a ea o nozzles (m2),
heq a e age heigh o nozzles (m).
The bu ning-ou phase— he las phase is ypically a linea dec ease. This phase begins
a e bu n-ou o 70% i e loading, and i is inished in he momen o comple e bu n-ou .
Ad anced i e models a e i e models based on he assessmen o changes in ene gy,
mass and momen um in he space whe e he i e de elops. These include single-zone
models, wo-zone models, and Compu a ional Fluid Dynamics (CFD)-based models [21].
2.4. Fi e Models Selec ed o he Case S udy
I is essen ial o selec he app op ia e i e model o each ask. The choice o he model
is closely ela ed o he ollowing a eas:
• he objec i es o he solu ion (e alua ion);
• he ex en and quali y o he inpu da a;
• he ex en and quali y o he equi ed ou pu da a;
• isualisa ion quali y equi emen s;
• he cha ac e is ics o he model and i s po en ial o add ess he s a ed objec i es.
The Model o Fi e and Smoke T anspo (CFAST) and he Fi e Dynamics Simula o
(FDS) we e chosen o u he e alua ion. The CFAST and FDS models enable o pe o m
simula ions when en e ing di e en sou ces o i e. In his case, he so-called -squa e
i e was used, which is cha ac e ized by di e en i e dynamics o a ious g oups o
p oduc ion and ope a ions. Howe e , his is only one op ion. As was p e iously men ioned,
he used i e models allow o pe o m simula ions o di e en i e sou ces. In gene al,
i is possible o use mo e cen e s o i es, no jus only one. I can be s a ed ha only he
i e model FDS enables o dis inguish he di e en sou ces o i e, o which i also allows
o pe o m a pa allel calcula ion, i.e., i enables o apply mo e han one p ocesso in he
calcula ion p ocess.
O cou se, each o he i e models has i s own speci ic ad an ages and disad an ages.
The ype o he sol ed ask, he scope and quali y o he inpu da a, and he equi ed scope
and quali y o he inpu da a a e he decisi e aspec s necessa y o a p ope choice o he
sui able i e model. The ac whe he he model is cu en ly being de eloped and e i ied
on a long- e m basis is absolu ely subs an ial. When e alua ing he pe o mance o he i e
models ( his a ec s he choice o he model i sel ), i is also necessa y o ake in o accoun
he basic a ibu es on which he model is based, i.e., wha kinds o he sub-models a e used
in o de o sol e he sub-p ocesses and wha a e he limi s o he model. In hei esponse,
he au ho s p esen ed only he basic aspec s ela ed o he choice o a sui able model and o
assessmen o i s pe o mance.
The u bulence was simula ed using he La ge Eddy Simula ion (LES) me hod. The
“mos used” ma hema ical CFD i e model— he FDS p og am—is based on his app oach.
CFAST is a wo-zone i e model used o calcula e he e ol ing dis ibu ion o smoke,
i e gases and empe a u e h oughou compa men s o a building du ing a i e. These
can ange om e y small con ainmen essels, on he o de o 1 m
3
o la ge spaces on he
o de o 1000 m3[22,23].
The modeling equa ions used in CFAST ake he ma hema ical o m o an ini ial
alue p oblem o a sys em o o dina y di e en ial equa ions (ODEs). These equa ions a e
de i ed using he conse a ion o mass, he conse a ion o ene gy (equi alen ly he i s
law o he modynamics), he ideal gas law and ela ions o densi y and in e nal ene gy.
These equa ions p edic as unc ions o ime quan i ies such as p essu e, laye heigh and
empe a u es gi en he accumula ion o mass and en halpy in he wo laye s. The CFAST
model hen consis s o a se o ODEs o compu e he en i onmen in each compa men
and a collec ion o algo i hms o compu e he mass and en halpy sou ce e ms equi ed by
he ODEs [22–24].
Appl. Sci. 2022,12, 2505 7 o 15
Fi e models based on Compu a ional Fluid Dynamics [
24
] a e widely used o he as-
sessmen o i e de elopmen . One o he mos p omising models based on his ounda ion
is he FDS model. The model was de eloped a he Na ional Ins i u e o S anda ds and
Technology in he USA [
25
] in collabo a ion wi h he Technical Resea ch Cen e o Finland
in Finland [
13
]. The FDS model has been alida ed du ing i s de elopmen and is also now
being u he de eloped.
To acili a e he wo k, i is possible o use he g aphical in e aces Py oSim [
14
] o
Blende FDS [15].
FDS sol es nume ically he Na ie –S okes equa ions o empe a u e-con olled low,
wi h emphasis on hea and smoke ans e om he i e.
The FDS p og am applies he so-called ne wo k me hod o a nume ical solu ion o
he pa ial di e en ial equa ions. This me hod is e y obus , bu i equi es a egula
ne wo k. C ea ing o a quali y calcula ion ne wo k is a basic p e equisi e o a quali y CFD
simula ion. Fo he sol ed ype o he ask, i is possible o conside he edge leng h o
he compu ing cell in ens o cen ime e s. Fo his s udy, he calcula ion ne wo k wi h he
dimensions 10 cm
×
10 cm
×
10 cm (cubic shape) was chosen in he FDS p og am. This
ne wo k is conside ed o be he mos sui able and op imal o he simula ion p ocess, and
a he same ime i allows nume ically app oxima e he i e well enough in e ms o spa ial
scale. The choice o ne wo k o pu poses o his s udy was, he e o e, op imal in o de o
achie e he igh esul s. In he cases whe e i is no de ined a calcula ion ne wo k sui able
wi h ega d o he simula ion, he esul s ob ained om he simula ion can be signi ican ly
“mis ep esen ed”.
I is a model ha allows o simula e many i e pa ame e s, e.g., de e mina ion o he
hea elease a e and i s sub- ac ions, he low o gases induced by he i e, de e mina ion
o he concen a ion o subs ances eleased by he i e, e c. The model can be used o
simula e i es in a ious objec s, e.g., buildings o echnical equipmen (e.g., ca s). All inpu
da a a e en e ed by means o a single ex inpu ile. The ou pu is mul iple iles whe e he
ou pu da a a e s o ed. The model can be isualized wi h Smoke iew (SMV) so wa e [
11
].
2.5. Desc ip ion o he Case S udy
2.5.1. Cha ac e is ics o Ope a ion
The con ibu ion o i e models o he assessmen o he i e esis ance o building
s uc u es is desc ibed by a case s udy o a manu ac u ing plan whe e s eel pla o ms
a e loca ed.
The p oduc ion plan is a la ge-scale au omo i e pain shop. In he p oduc ion a ea,
he e a e pain lines ha un longi udinally h ough he space unde e alua ion. The lines
a e a la ge-scale pain ing and d ying acili y.
Walking pla o ms a e loca ed in he p oduc ion a ea o allow people o a e se he
ins alled p oduc ion equipmen . Each o he pla o ms has plan dimensions o 16/16 m
and a clea heigh o 5.5 m. The suppo ing s uc u e o he pla o ms consis s o e ical
s eel columns and ho izon al s eel beams. The ceiling walkway s uc u e consis s o shee
me al. The pe ime e s uc u es o he pla o ms a e open.
The pla o ms a e designed o he mo emen o employees du ing no mal ope a ion.
In he e en o a i e, he pla o ms a e also designed o he in e ening i e igh e s.
The pla o ms ha e he cha ac e o s uc u es ha do no ensu e he s abili y o he
whole building. Due o hei use by i e igh ing uni s in he e en o a i e, i is necessa y o
ensu e he i e esis ance o he load-bea ing s uc u es o he pla o ms o he du a ion o
he ongoing in e en ion, i.e., o 30 min.
The p oduc ion plan is equipped wi h a numbe o i e sa e y de ices. Among he
mos impo an a e an elec ical i e ala m and ixed sp inkle i e-ex inguishing equipmen .
Fi e-ex inguishing equipmen is loca ed in all a eas o he p oduc ion plan and also unde
he ceiling s uc u es o he pla o ms.
Appl. Sci. 2022,12, 2505 8 o 15
2.5.2. Design Fi e Scena io and Design Fi e
The se o possible scena ios, cha ac e ized by hei p obabili y o occu ence and
expec ed consequences, is unde s ood as design i e scena ios. The p ocess o selec ing i e
scena ios is e e ed o as quali a i e analysis om a i e enginee ing pe spec i e. F om he
o e all se o scena ios, he scena ios o be u he e alua ed a e selec ed. As a ule, hese
a e he scena ios wi h he highes p obabili y o occu ence o he highes consequences.
A design i e is a quan i a i e desc ip ion o he selec ed design i e scena ios. I is
usually an exp ession o he hea elease a e and i s componen s, he densi y o he hea
elease a e, he empe a u es, he amoun o smoke gene a ed, he p essu e a ios, e c. [
3
,
4
].
The s abili y o he pla o ms was e alua ed on he basis o he expec ed i e de elop-
men in he p oduc ion plan , which can be desc ibed by he so-called cha ac e is ic i e
ypes [3,5,6].
The i e ypes we e de e mined o di e en “g oups o p oduc ion and ope a ions”,
which a e cha ac e is ic in he design o buildings o p oduc ion acili ies in he Czech
Republic. Ope a ions in p oduc ion buildings a e di ided in o se en g oups (1 o 7),
wi h he eigh h g oup consis ing o auxilia y non-p oduc ion ope a ions ha also occu in
p oduc ion buildings (e.g., d essing ooms, sani a y acili ies, o ices) [
26
,
27
]. In gene al,
as he alue o he p oduc ion ope a ion inc eases, he amoun o combus ible subs ances
inc eases and hus he dynamics o i e de elopmen also inc eases.
Fo he case s udy, he g oups 4 o 7 o p oduc ion and ope a ion acco ding o CSN 73
0804) we e chosen [
17
]. The i e ou b eak was loca ed in he middle o he pla o m a loo
le el. The hea elease a e o each p oduc ion and plan g oup we e hen de e mined in
acco dance wi h EN 1991-1-2 [7].
The sp inkle heads we e loca ed a a clea heigh o 5.4 m and hei eac ion empe a-
u e was 68 ◦C. The dis ance be ween he sp inkle heads was 3 m.
2.5.3. Me hods o Assessmen
The s abili y o he pla o ms du ing i e de elopmen was assessed by he ollow-
ing p ocedu es:
•simpli ied analysis (empi ical calcula ions);
• he CFAST i e zone model wi h he Smoke iew g aphical ex ension;
• he FDS model wi h Smoke iew g aphical ex ension and Py oSim in e ace suppo .
The CFAST zonal i e model and he FDS model ha e been desc ibed in p e ious
sec ions o his pape . The esul s o he ma hema ical i e models we e compa ed wi h he
simpli ied analysis p epa ed by empi ical calcula ions.
In he simpli ied calcula ions, he unde - loo low ela ionships de i ed by Alpe
[6,18,19]
we e used o de e mine he empe a u es unde he ho izon al pla o m s uc u e. Based
on he de e mined empe a u es, he sp inkle head esponse ime
ac
(s) was de e -
mined [20,21].
The sp inkle head esponse ime is gene ally conside ed o be he ime o eaching he
maximum-maximum alue o he hea elease a e and, he e o e, he maximum ambien
empe a u e eached. A he same ime, he hea ans e o he s eel s uc u e o he
pla o m was e alua ed.
2.5.4. De e mina ion o Limi C i e ia
In he case s udy, he ocus was on he en i onmen al and su ace empe a u es o he
s eel s uc u es. The cou se o he ambien empe a u es is signi ican ly in luenced by he
esponse o he sp inkle heads in he a ea unde e alua ion [28,29].
The i e esis ance o he ho izon al s eel pla o m s uc u e elemen s was e alua ed in
he case s udy. These a e he elemen s ha ensu e he s abili y o he pla o m and he i e
esis ance R( ) can be e alua ed on he basis o exceeding he limi ing empe a u es.
The c i ical empe a u e o he load-bea ing s eel elemen s depends on hei deg ee o
use (load on he s uc u e). In he case o hea ily loaded s uc u es, he c i ical empe a u e
is gene ally conside ed o be 463 ◦C.
Appl. Sci. 2022,12, 2505 9 o 15
The su ace empe a u e o he s uc u es e alua ed in he case s udy will be ela ed o
his limi ing empe a u e.
2.5.5. De e mined Ou pu Values
The ollowing ou pu alues we e de e mined by hese p ocedu es:
• he ac i a ion ime and empe a u e his o y o he nea es sp inkle head;
•
he maximum empe a u e and en i onmen al empe a u e p o ile a he s eel pla -
o m ceiling;
•
he maximum empe a u e and empe a u e his o y o he ho izon al s eel-bea ing s uc u e.
The ou pu alues de e mined by he abo e me hods we e hen compa ed and e alua ed.
3. Resul s
The display o he s uc u e geome y and isualiza ion a he ime o sp inkle head
ac i a ion in CFAST and FDS is shown in Figu e 1.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 9 o 15
2.5.4. De e mina ion o Limi C i e ia
In he case s udy, he ocus was on he en i onmen al and su ace empe a u es o
he s eel s uc u es. The cou se o he ambien empe a u es is signi ican ly in luenced by
he esponse o he sp inkle heads in he a ea unde e alua ion [28,29].
The i e esis ance o he ho izon al s eel pla o m s uc u e elemen s was e alua ed
in he case s udy. These a e he elemen s ha ensu e he s abili y o he pla o m and he
i e esis ance R( ) can be e alua ed on he basis o exceeding he limi ing empe a u es.
The c i ical empe a u e o he load-bea ing s eel elemen s depends on hei deg ee
o use (load on he s uc u e). In he case o hea ily loaded s uc u es, he c i ical empe -
a u e is gene ally conside ed o be 463 °C.
The su ace empe a u e o he s uc u es e alua ed in he case s udy will be ela ed
o his limi ing empe a u e.
2.5.5. De e mined Ou pu Values
The ollowing ou pu alues we e de e mined by hese p ocedu es:
 he ac i a ion ime and empe a u e his o y o he nea es sp inkle head;
 he maximum empe a u e and en i onmen al empe a u e p o ile a he s eel pla -
o m ceiling;
 he maximum empe a u e and empe a u e his o y o he ho izon al s eel-bea ing
s uc u e.
The ou pu alues de e mined by he abo e me hods we e hen compa ed and e al-
ua ed.
3. Resul s
The display o he s uc u e geome y and isualiza ion a he ime o sp inkle head
ac i a ion in CFAST and FDS is shown in Figu e 1.
(a)
(b)
(c)
(d)
Figu e 1.
Visualiza ion o he i e p og ess in he CFAST and FDS p og ams, whe e: (
a
) display o he
s uc u e geome y in he CFAST p og am; (
b
) display o he s uc u e geome y in he FDS p og am;
(
c
) isualiza ion a he ime o sp inkle head ac i a ion in he CFAST p og am; (
d
) isualiza ion a
he ime o sp inkle head ac i a ion in he FDS p og am.
The hea elease a e o each g oup o p oduc ions and ope a ions wi hou and wi h
sp inkle esponse a e shown in Figu e 2.
The esul s de e mined by he p e iously desc ibed me hods a e summa ized in
Table 1.