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Numerical modelling of ignition in TNT deflagration

Lecturer Dr. Eng. Ioan Sorin Leoveanu1

Assistant Prof. Dr. Eng. Kamila Kotrasova2

1University “Transilvania” from Braşov2Tecnical University of !osice

REZUMAT: Asigurarea unei cit mai bune comortari in e!loatare a cladirilor imune mai ales entru constructii cudestinatie seciala un roces de cercetare in continua de"voltare# Astfel metodele numerice de anali"a s$au de"voltat intr$unritm alert atit in domeniul modelarii neliniare a comortarii structurilor de re"istenta cit si in evaluarea incarcarilore!cetionale e care anumite structuri va trebuii sa le reia# In acest sens% lucrarea de fata isi roune determinareaconditiilor initiale legate de amorsarea unei incarcaturi e!lo"ive in incinta unei cladiri% cu scoul de a determinacaracteristicile initiale ale undelor de soc roduse de o incarcatura e!lo"iva# Astfel de incarcari intra in categoriaincarcarilor e!cetionale iar resiunile% vita"ele si temeraturile cu care acestea se manifesta asure eretilor cladirii suntinfluentate de o multitudine de factori# Asigurarea unui model matematic si a uneii modelari numerice cit mai e!acte fiind

scoul acestei lucrari#

&uvinte c'eie: Ecuatii "e stare #$L% fenomene "e trans&ort% mo"elarea e'&lo(iilor% meto"a volumelor finite

ABSTRACT: Te researc &rocess in civil engineering are )ecame more an" more most com&le'es an" te numerical

meto"s &lay an im&ortant role in te "evelo&ment of te "esign an" catastro&e estimations effects *n te &resent stage of

"esign an" verifications of civil engineering &rocesses te numerical meto"s are currently use" an" almost all te art+or,ing &ro-ects are "esigne" an" verifie" using "e"icate" soft+are &rograms. Te &resent &a&er an" soft+are a&&lication is

"e"icate to )last +aves effect on a room +all mo"elling an" is )ut consist in te estimation of te e'ce&tional loa"s tat are

not inclu"e" in any ,no+n "e"icate" soft+are.

Ke( )ords: #$L state euations% trans&ort &enomenon% e'&losion mo"elling% volume finite meto"s.

*# Introduction

Te insi"e )uil"ings room e'&losion are e'tremely "angerous an" "ifficult to )e estimate an" mo"elling. Te )last

+aves generate )y te e'&losion an" te insi"e room &ressure ave a uic, mo"ification an" intensity variation.

Usually% some e'&erimental +ave/s &ressure time re&artition is use" for simulation te im&act of an e'&losion on an

environmental structure. 01.0.03. As all te e'&erimental +or,s te stu"y are ma"e in &articularly con"itions an" all

te measure" +aves )last front s&ee" an" &ressure are ma"e from te first front of +aves% for e'terior "eflagration an"

freuently in 1D. Base" on te e'&erimental +or,s% some )uil"ings )eaviour are verifie" using general finite elementssoft+are )ut tat ty&e of analyse is limite" )y te cemical com&osition of su)stance use" for )lasting% te "istance

)et+een source of "eflagration an" te )uil"ing% te )uil"ing neig)ours an" te vertical &osition of "eflagration

source. As te autors ,no+% te insi"e room "eflagration cases are not yet covere" )y e'&erimental stu"y &u)lise"until no+. 4or esta)lis te &articularity of te insi"e room +aves )lasts in te &resent &a&ers is consi"erate% te

cemical com&osition of "eflagrate source% te room "imensions an" source &osition insi"e a &articularly room. Tese

as&ects generate a &ro)lem tat )ecome more com&le'es an" nee" a "evelo&ment of s&ecifically area. Te "evelo&ment

+as "one using numerical meto"s )ase" on 5olume 4inite 6eto" 75468 for eat an" flo+ estimation of soli"

"eflagrate cemical com&osition an" Total 5anise" Diminise" 6eto" 7T5D8 for manage te +aves )last

&ro&agation an" +aves reflections "ynamics. 4or esta)lis te insi"e room )last +aves flo+s +e consi"er tat te +alls

a" rigi" an" te "eflection of +alls is neglecte". Te effects of te )last +aves on te structure are not consi"erate in

tis &a&er.

+# ,overning E-uations of )aves blast



Te )last +ave/s &rocess is generate )y te energy eats a)sor)e" on te s&ecimen surface a)ove its melting &oint to

te va&ori(ation tem&erature an" ten gaseous "iffuse" generate a surroun"ing cemical va&ours unsta)le atmos&ere.

Te euili)rium of tat &rocess is atten"e" )y gases sta)le at current &ressure an" tem&erature values% figure 1.

.ig#*. The ignition and burning consideration process. a) Schematic ignition process. b) Gas movement in the ignition

process.

Te initial eating an" &ressure )uil"9u& stage can )e "escri)e" )y a com)ination of follo+ing governing euations:

conservation of mass euation 718% ;avier 9 <to,es euations for momentum euation in te liui" (ones 728% eat flo+

in flui" euation 78% an" s&ecies transfer euations 7=89738:

( ) >=⋅∇+∂∂

V t

ρ

ρ 718

( ) ( ) g pV V V t

⋅+−∇=×⋅∇+⋅

∂∂

ρ ρ ρ 728

( ) ( )T V p E E t

∇⋅∇=⋅+⋅∇+⋅∂∂

λ ρ ρ

87 78

( ) ( ) >=⋅⋅∇+⋅∂∂

iiii C V C t

ρ ρ 7=8

( )∑+

=⋅1

1

n

ii C ρ ρ 738

+ere ρ is te "ensity of gas &ase% C i te concentrations of te cemical elements% ρ i te "ensity of va&ors an"

siel"e" gas in te area of alloye" element e'&ulse"% V te velocity of te com&onents% p te &ressure% E te ental&y of

te gases &ase% λ te eat con"uctivity of te gases &ase% T te tem&erature. Te euations 718978 are use" for

mo"elling te siel"e" gas movement an" teir results are serve" as a first a&&ro'imation of te initial con"itions on te

surface of soli" &art 7te melte" film creation8. Te s,etc of tis first ste& of numerical simulation &rocess can )e seen

in figure 2.

Fig. 2. The chemical reactions ones



+#* T'e ignition rocess modelling

Te ignition &rocess is consi"erate as a s&ot intensity &o+er source an" +ill )e e'&resse" as follo+s:

2

22

>8%7r ! "

! " e# #

+−⋅= 7?8

$ere # re&resent te &lane re&artition of eat flu'es accor"ingly +it te ignition &astille si(e% # $ re&resent te

ignition &astille eat flu' in is central area. Te initial tem&erature of te &rocess can )e estimate for te area of te

&astille using te relation:

⋅⋅⋅=−

≤

at

ier%cat

# T T

t t %or

t

p

22 >

>8%7λ

7@8

$ere λ is te eat con"uctivity% # > is te a)sor)e" ignition eat flu'es% t is current time% tp is te ignition "uration%

is "istance from te to& surface. T $ is te initial tem&erature% ier%c&u) "efine te com&lementary error function.

( )( )uer% uu

uier%c −−−

= 18e'&7

872

π 78

Using te a)ove euation can )e calculate" te 1D eat con"uction into a semi9infinite )o"y +it a single ignition

&astille +it fi'e" location an" constant am&litu"e eat source. *n tis tem&erature "istri)ution calculation% te

va&ori(ation an" melting &enomena on te soli" )last material +as not consi"ere". *n or"er to account for tese

&enomena% te latent eats of melting an" va&ori(ation +ill )e inclu"e" insi"e te control volume in te &rogram of

mo"eling &enomenon.

Using energy )alance relationsi&% i.e.% increase of store" energy in a volume of material = energy in&ut energy

generation in tis volume 9 energy out&ut% +e can "erive a general "ifferential form of tree "imensional eatcon"uction euation.

st out g in E E E E ∆=−+ 7C8

$e consi"er tat te material is omogenous an" ave uniform &ro&erty

t

T

adt

d'

T

!

T

"

T (

∂∂

=+∂∂

+∂∂

+∂∂ 11

2

2

2

2

2

2

λ 71>8

+ere a is te termal "iffusivity an" te term d' ( dt corres&on"s to te eat generation insi"e te control volume%accounting +it te melting or va&ori(ation &rocesses. Te tem&erature a&&ro'imations in te melting &rocess

consi"erations for te surface of soli" state )lasting material area. a8 ase +en )ot tem&eratures are +itin soli"us

an" liui"us tem&eratures at moment ∆t F t29t1 % )8 an" c8 +en only one tem&erature is outsi"e te melting range. Te

latent eat of melting generate" insi"e te control volume% ∆' ( is e'&resse" as follo+ +it a variation of liui" fraction

% ( "uring a time ste& ∆t % te latent eat of melting of te control volume material * ( % control volume V i an" "ensity G.

Te liui" fraction can )e e'&resse" as a function of tem&erature T +it &ases cange soli"us an" liui"us

tem&eratures T S an" T (% res&ectively 03

(i (iV ( % V *T V c' ∆⋅⋅⋅=∆⋅⋅⋅=∆ ρ ρ

( ) ( ) S S (S ( % T T T T % −=−−= 1 711%128



*n or"er to account for te melting )eavior% tem&eratureH

2T calculate" from te euations 7@8 in te eate" (one )y

laser s&ot at time t + soul" )e correcte" to a ne+ tem&erature 2T at time t +. *n tis analysis% only te cases &resente" in

figure +ere consi"ere"% +ic results in te follo+ing e'&ressions:

4or case a8:

∫ ∆−⋅∂∂

⋅=2

1

t

t

(V

,,

i 'dt t

T c E ρ 718

$e can +rite te energy e'&ression in tem&erature integration:

∫ ∫ ⋅∂∂

⋅+⋅=2

1

2

1

T

T

( (

T

T

V

,,

i dT T

% *dT c E ρ ρ 71=8

∫ ∫ ⋅⋅=∂∂

⋅=

H2

1

2

1

T

T

V

t

t

V

,

i dT cdt t

T c E ρ ρ 7138

An" e'&ression of energy )alance )ecomes

∫ ∫ ∫ ⋅⋅=∂∂⋅+⋅⋅

H2

1

2

1

2

1

T

T

V

T

T

( (

T

T

V dT cdT T

% *dT c ρ ρ ρ 71?8

Te )8 case )ecomes:

∫ ∫ ∫ ⋅⋅=∂∂⋅+⋅⋅

H2

1

2 2 T

T

V

T

T

T

T

( (V dT cdT

T % *dT c

S S

ρ ρ ρ 71@8

Te c8 case )ecomes:

∫ ∫ ∫ ⋅⋅=∂∂

⋅+⋅⋅H

2

1

2 2 T

T

V

T

T

T

T

( (V dT cdT

T

% *dT c

( (

ρ ρ ρ 718

.ig# /# The temperature appro"imations in the melting processes considerations %or the ignition heated area



2.2 Governing equations in the fuid fow area.

Te momentum an" mass conservation euations in flui" flo+ area for te melte" material can )e e'&resse" as

follo+s:

( ) ( ) v pvvt v

∆+∇−=⋅∇⋅+

∂∂ Ie 718

>=∇v71C8

Te system of euations +as solve" use" 6A meto" an" te results are "one for an e'am&le. An e'am&le of gas

&ase mo"el solutions for an ignition &o+er of - F = ,$ an" >.>3 µs are so+n in figure =.

Tis information is use" for te )oun"ary con"itions on te free surface of te melte" area an" te surface of te &art

esta)lises &rocess. Te D free surfaces mo"el euations use" in tis &rogram "o not consi"er transversal stresses.Te &ressure an" s&ee" on te surface +as consi"ere" to )e eual to tose of te gases on te interfaces )et+een liui" an"

gases. *n 2D s,etc &lanes% for ignition )last &rocess% te free )oun"aries )ecome:

ga ! ! " "li' pn !

vnn "

v

!

un "

u p −=∂∂+

∂∂+

∂∂+

∂∂+− 22 222 µ µ µ 72>8

( ) >2 22 =−⋅

∂∂

+∂∂

+

∂∂

−∂∂

" ! ! " nn "

v

!

u

"

v

!

unn µ µ 7218

$ere% n "% n ! re&resent te outsi"e normal vectors "irections% pli' an" p gas te &ressure in melte" su)stance an" te

va&ors on te surfaces &ases% µ te viscosity of melt an" u v te s&ee"s in te surface cell. After te melting front

&ro&agation te liui" "omain +as a&&ro'imate as D "omain an" te &ressure an" te tem&erature on te liui" &ase

surfaces in"uce" 6aragoni con"itions an" te recoil gases &ro"uce" )y e'&losion mo"ify te uic, )urn &rocess. To

avoi" tat &enomenon +ill )e use" te va&ors &ressure recoil estimate" )y te relation:

⋅⋅

⋅−⋅

⋅= S B A

V a

S

VapT / 0

( 1

T

B A

p e'&>

7228

+ere A is Anisimov material coefficient 0% B$ te va&ori(ation constant% 1 a te molecular mass% (V te latent eat of

va&ori(ation% 0 A te Avoga"ro num)er% 2 Bte Bolt(mann constant% T S te tem&erature of te liui" surface% p5a& te recoil &ressure of va&ors% V 0 s&ee" of va&ors%

3 V va&or/s e'&ulse" flu'es. Te tem&erature T S use" for pVap estimation +as esta)lise" +it te tin &late solution. Te

va&ors s&ee" normal on liui" surface is com&ute using te relation:

ρ

Vap

0

pV = 728

Te va&ors flu'es +ere esta)lise" using te relation:

0

Vap

V V

p 3 = 72=8

Tese "ates estimate te tem&erature an" &ressure in te (one of cemical reactions an" )last +ave formation. Te

cemical &rocesses +ill )e analy(e" using te classical mo"el )ase" on euili)rium of cemical &ossi)le reactions.

2.2 Governing equations in the waves blast ormation.

Te conce&tual mo"el consists of a liui" lengt tat as )een intro"uce" )ase" on te va&ors flu'es 3 V .



+#+#*# 0roosed mode.

Te liui" lengt can )e correlate" +it tem&erature an" &ressure an" e'&losive &ro&erties. *t is no+ ,no+n tat

"ro&lets "o not &enetrate )eyon" te liui" lengt. Tis is "ifferent from te &revious vie+ of a liui" core &enetrating

"ee& into te s&ray. Te conce&tual mo"el involves a t+o 9ste& com)ustion &rocess tat is s&atially se&arate" an" not asingle "iffusion flame )urne" &rocess. Te ne+ conce&tual mo"el as so+n tat soot forms +itin te ric &remi'e" &ro"uct (one an" )urns out as it &asses troug te flame seat% ;J is not forme" insi"e of te flame )ut only on te

lean si"e of te flame seat. A su)9mo"el tat "escri)es te tem&erature an" stoiciometry of tese t+o (ones +ere

soot an" ;J forme" e'ist in current mo"els. Descri)ing te tem&erature of tese (ones +it a (ero "imensional mo"el

+ill allo+ te com&utational &o+er to )e use" on com&reensive ,inetic mecanisms "escri)ing ;J an" soot

formation. Te ne+ (ones conce&tual mo"el &ro&ose" as )een use" to create a ne+ multi9(one% (ero9"imensional%

com&uter mo"el +ritten in language. Te uasi9stea"y mo"el is se&arate" into five (ones 74ig. =8.

4ig. =. Aspect o% the 4aves blast model ones

Te cemical com&osition of te "eflagrate an" te &ossi)le euili)rium &rocess are

C C55 6 0 5 0 6 C @@32 22?3@ +++→ 723a8

C C5 6 0 5 0 6 C 21232 22?3@ +++→ 723)8

Te reaction as ig activation energy an" is e'otermic. Because of te &ro"uction of car)on% T;T e'&losions ave a

sooty a&&earance.

+#+#+# T'e secies anal("e#

Te ;A<A9Le+is euili)rium co"e is use" to "etermine te most im&ortant s&ecies to consi"er. *t +as e'ecute" at

various ig euivalence ratio con"itions. Te s&ecies +it significant mole fractions +ere a""e" to te euili)rium

mo"el. Te ;A<A9Le+is co"e &re"icte" a significant amount of soli" car)on a)ove an euivalence ratio of .3. Due to

increase" com&le'ity of calculation soli" car)on +as neglecte". Te s&ecies inclu"e" are so+n in Ta)le 1.

Ta)le 1.K JK K2J K ;K2

J J J2 K= ;K

; ;J ;2 2K2 K;

K2 J2 Ar 2K= KJ

$it te s&ecies "etermine" te glo)al reaction euation is so+n in euation



6 C 0 6C5 0 6C0 0 06 0 06 0

6 C 0 6 C 0 C6 0 C6 0 Ar 0 0 0 C5 0 5 6 0 5 0 05 0 C5 0

56 0 6 0 0 0 5 0 6 0 Ar 0 5l mn

0 5 6 C / l mn

2212>1C1A21@

=21?2213=1=11221121>2C2A@?

32=2122 8>===.>@2@=.73.>23.>

+++++

++++++++++

+++++→++−+

+φ

72?8

*n tis euation i 0 are te num)ers of moles of eac s&ecies. Te fuel com&osition 7n% m% l an" / 8 an" euivalence

ratio 7φ8 are ,no+n an" te euation is +ritten assuming 1 mole to )urn. Tis leaves te moles of eac of te 21 s&ecies

as un,no+ns. *n or"er to solve tis &ro)lem tere must )e 21 euations. Te first 3 euations are te car)on% y"rogen%

o'ygen% nitrogen% an" argon )alances. Te rest of te euations come from te 1? euili)rium reactions so+n in Ta)le

2. Tese reactions can )e use" to +rite te remaining euations to solve te system.

Ta)le 2.

K2⇔2K J2⇔2J

;2⇔2; K2J2⇔2JK

J2;2⇔2;J 2K2J2⇔2K2J

2JJ2⇔2J2 J2K2⇔KJK

KK⇔K= 2JK2⇔2K2J2

2K2K2⇔2K= ;K2⇔ ;K2

;K2K⇔ ;K K;⇔K;K2

JK⇔KJ 2JK⇔2KJ2

+#+#/# Establis'ing e-uilibrium constants

4or an ar)itrary euili)rium reaction

d7cC bBaA +⇔+ 72@8

te reaction constant% 2 p% for initial &ressure - $ F 1 atm can )e +ritten as

( ) ( )

( ) ( )

87

1

bad c

i

i

b

B

a

A

d

7

c

C

p

0

-

0 0

0 0 2

−−+

=

∑728

Te value of 2 p is a function of tem&erature. Tis form +as use" for te 1? euili)rium reactions &rovi"ing 2>

euations for te 2> un,no+ns in te glo)al reaction. Te set of 2> euations &ro"uce" are non9linear an" can )e uite

"ifficult to solve. urve fits for 2 p are inclu"e" in 01 for te @ reactions consi"ere" in tat +or,. Te fits for te

remaining reactions +ere calculate" using "ata from te #A;A4 termocemical ta)les 01 an" are inclu"e" in te

co"e. Te same form of euation +as use" for all of te fits. Te ;e+ton9Ia&son meto" +as use" to fin" te solution

to te euation set. <olving te system of nonlinear euations nee" to rearrange te ec. 728 in ec 72C8.An isentro&ic &rocess calculates te )urning (one con"itions trougout te com&ression an" e'&ansion &rocesses. 4or te com&ression front te com&osition in te "omain is air.

( ) ( ) ( ) ( ) >

87

1 =

⋅−

−−+

∑d cba

i

ib

B

a

A p

d

7

c

C -

0

0 0 2 0 0 72C8

During te e'&ansion )last +aves te com&osition is air an" i"eal &ro"ucts of com)ustion. Te mole fractions of

&ro"uct gasses are calculate" )ase" on te overall euivalence ratio. Te "ifference in com&osition% +ic is use" to

o)tain te termo"ynamic &ro&erty / F CpCv% is te only "istinction )et+een te com&ression an" e'&ansion &rocess.



Miven e'&losion velocity 3 7 % &ressure e'&losion 3 - cemical energy > E of te given e'&losive% te &arameters of

#$L EJ< euations +ill )e o)taine" accor"ing to te # con"ition an" te conservation relation of mass% momentum%

an" energy. Accor"ing to # con"ition

2

> 7V

-

3 V

S

ρ =

∂∂

−7>8

it can )e o)taine" tat:

( ) ( ) 2

>

1

21 121 7V C e BRe AR 3

V RV R 3 3 ρ ω ω =+++ +−−−

718

$ere te volume ave te e'&ression:

( )1L += γ γ 3 V

1L2

> −= 3 3 - 7 ρ γ

Te Kugoniot relation )ecomes:

( ) 3 3 3

V RV R V - E V C

e R

Be

R

A 3 3 −+=++ −−−

12

1>

21

21 ω

ω 728

Jr in con"ense" format:( )

3 3

V RV R pCV Be Ae 3 3 =++ +−−− ω 1

21

78

Te o)taine" values of &arameters A% B% % I1% I2% ω are given in te ta)le .

Ta)le .

offs Iesults )ase"

on te 3 (ones )urning

Iesults

"ocuments

A .@2 .@12

B >.> >.>2

>.>1>=?>C >.>1>=32@

I1 =.1=C@ =.13

I2 >.C==? >.C3

ω >.>>1 >.

Te euations 71..38 +ill )e use" for simulation te front +aves )last &ro&agation an" te ga(es com&osition. Base" on

initial con"itions% E $ F =.=? 1>? #,g% ρ $ F 13?> ,gm% 7 3 F ?C> ms% pa F 1 atm% T $ F 2C >!.

/# Results and &onclusions

Te governing euations an" &resent mo"el +as use" to +rite a &rogram "esignate" to analyse insi"e )uil"ing

e'&losions. Te "iverse "etonator +it ,no+n cemical com&osition can )e mo"elle" )ase" on &resent mo"el an" te

&ressure% "eflagration energy% "etonation s&ee" an" soli" state "ensity may )e esta)lis. Te soft+are &rogram +as

ma"e in 6icrosoft visual an" te results +as &re&are" for A6TE Tec&lot 2> &ost&rocessor.

Te "iverse environmental situations can )e analy(e"% un"er+ater e'&losions for e'am&le or "iverse &ressure

an" tem&eratures am)ient.

Te &rogram is usefully in te case of structures "esigne" es&ecially for ig ris, to "iverse scenario of e'&losiveloa"s.

4igure 3 so+ te va&ours &ressure T;T "istri)ution in te ignition area of e'&losion.



4ig. 3. Vapors pressure in the e"plosion

initialiation

4ig. ?. 7ensit! variation in the ignition

stage o% e"plosion

4ig. @. 1elting speed on 58

direction

None of mi'ing an" )urning &rocesses 9;9+ ave te values of &ressure an" tem&erature as in 4ig. until in te

)urning (one of te 9< area te tem&erature an" te &ressure increase uic,ly as in 4ig. C.

.ig# 1. The pressure =1-a> and temperature = oC> in the

9;9+ blast 4ave?s %ormation.ig# 2. The pressure =1-a> and temperature = $C>

repartition in the 4ave %ormation in ones 9@ and 9<



.ig# *3. Enthalp! %ormation E =/3/g> and E + =/32g> and mi"ed vapors and li'uid e"plosive burning length ('

=mm> in 9@ and 9< o% e"plosion ignition

References

1. Tomsen% #.L. Iul% <.4.%: 1itigation o% e"plosion bubble pulsation caused b! the deep under4ater detonation o% a

tapered charge. *n: 7e%ense 0uclear Agenc! inal Report % $asington. D.% 1C>% &g. 191>=.

2. Baytos% #.4.%: Speci%ic 6eat and Thermal Conductivit! o% E"plosives 1i"tures and -lastic;Bonded E"plosives 7etermined E"perimentall!. *n: niversit! o% Cali%ornia (os Alamos (aborator! re&ort% Pag 191>

. Iaften)erg% 6. ;% 6oc, #r% 6% !ri)y M. %: 1odeling the impact de%ormation o% rods o% a pressed Al -T E

composite mi"ture =3> . *n: 3ournal o% ,mpact Eng 2>>%;r. 3:&ag. 1@3 91@==

=. Denisaev% A.A% <tein)erg% A.<% Berlin% A.A%: ,nitiation o% a reaction in aluminum te%lon multila!er thin %ilm samples

b! drop hammer impact loading=3>. *n: Russian 3ournal o% -h!sical Chemistr!% 2>>% 278: =C19=C@.

3. Kong %. P% Ume"a% T% !imura% O: 1etall Trans.% vol 13B

Lecturer dr# eng# Ioan Sorin LE45EANUUniversit( 6Transilvania7 from 8ra9ovemail: leoveanuunit)v.ro

6ecanical Engineer of te University Transilvania from Brasov% te 6anagerial *n"ustrial Program +it $el"ing Es&eciality an" PD in

resi"ual stresses an" strains mo"elling an" tecnology o&timisation. Ke +or,e" at te *n"ustrial Tractors Design an" Iesearc *nstitute at*PATT Brasov to avy an" me"iun Bull"o(ers &rototi&s "esign an" oter Eart 6oving 6acineries &rototi&es an" series &ro"ucts.

4rom 1C e +or, at Transilvania University at 6aterials <cience an" Engineering 4aculty an" from 2>1> e +or, in te area of ivile

Engineering at Transilvania University. Ke &u)lis monogra&is in te area of J&timi(ation Tecnology an" Trans&ort Penomenon

involve" in te $el"ing an" Engineering area an" articles in "iverses -ournals an" national an" international conferences.

Kere researc to&ics. 6o"elling te &ysical &rocesses involve" in +el"ing &enomenons using 4inite 5olume an" 4inite Elements

6eto" for 6o"elling te E'ce&tional Loa"s in"uce" in Builings )y Eart Qua,es% $in" an" E'&losions.

Assis# Eng# Kamila K4TRAS45% 0';# %Tec'nical Universit( of Ko<ice% &ivil Engineering .acult(% Institute of Structural Engineering% ;eartment of Structural Mec'anics% 5(so=o<=ols=> ?% 3?3 3* Ko<ice% Slova=ia#email: ,amila.,otrasovatu,e.s,

mailto:[email protected]

mailto:[email protected]



Mra"uate" at te Tecnical University of !oRice% ivil Engineering 4aculty% stu"y &rogram 9 Buil"ing onstruction. After finisingof te university se starte" to +or, at IB in <&iRs,S ;ovS 5es as "esigner an" ten at te Tecnical Tecnical University of

!oRice% 4aculty of 6ecanical Engineering% stu"y &rogram A&&lie" 6ecanics. Te researc to&ics: seismic "esign of liui"

storage groun"9su&&orte" tan,s% interaction &ro)lems of flui" an" soli".

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