rGlass breakage
CFD
Compartment fire
el d
e is
s de
ts a
men
0–2
brea
the 680 kW fire case, the model shows an earlier glass fallout time, however, the predicted glass
temperature at fallout is around 450 1C and is consistent with previous experiments. Further research
to improve the model is discussed such as on radiation modeling and the criteria of glass breakage
glass
ants’
d the p
and fa
ases ai
g such
that the glass breaking stress follows a Weibull distribution. This
effects of window assembly on glass breakage during a controlled
odel
nsfer
latest
[13].
time
discussed the use of advanced radiation modeling in the
ARTICLE IN PRESS
Contents lists availabl
.el
ty
Fire Safety Journal 44 (2009) 415–424presence of the large temperature difference between the inner
compartment fire. They tested both framed (edge protected) and
unframed (edge unprotected) glass and the results showed that
the unframed glass could sustain a higher temperature increase
prediction of glass breakage.
One of the observations by [5] and many others is that in a fire
environment, a uniform approximation to glass temperature
distribution with depth would not be valid. This is due to the
and the outer surface. Therefore, the thickness of the glass should
be taken into account. It should also be noted that the interaction
Tel.: +1212 4819460; fax: +1212 4819484.
E-mail address: kai.kang@jacobs.com0379-71
doi:10.1analytical model was later extended to double panes [7]. In the
mean time, the experiments by Skelly et al. [8] demonstrated the
of window fallout and assumed that this failure temperature
follows a Gaussian probability distribution. The other study [14]analyses by [3,4] suggested the temperature difference as the
cause of glass breakage (crack) and subsequent fallout. Joshi and
Pagni [5] derived an analytical model for glass breakage, the
BREAK1 algorithm [6]. They also quantified through experiments
verified the three-band radiation model for the zone m
BRANZFIRE. This was largely based on the radiative heat tra
model of [11] and the glass failure criterion of [5]. The
development in numerical modeling of glass breakage is by
They used the glass ‘‘failure’’ temperature to determine thedraft [1]. For a ventilation-controlled fire, the result would be a
sudden jump in heat release rate and a rapid spread of fire when
fuel vapor mixes with incoming oxygen at the right temperature.
The research work on glass breakage due to fire started with
the experiments in Harvard University [2]. The theoretical
zone models and field models. Sincaglia and Barnett [11]
presented a study on the implementation of BREAK1 glass
breakage model into a zone model. They paid special attention
to the dependence of radiative heat absorption coefficient on
wavelength, using a three-band radiation model. Parry et al. [12]1. Introduction
In a built environment, window
poses potential danger to occup
challenges fire fighting activities an
integrity. As window glass breakage
vent openings, this essentially incre
the fire inside the enclosure, causin12/$ - see front matter & 2008 Elsevier Ltd. A
016/j.firesaf.2008.09.002& 2008 Elsevier Ltd. All rights reserved.
breaking during a fire
safe evacuation, and
rotection of structural
llout create additional
r and oxygen supply to
phenomenon as back
than what the framed glass does. Another study by Strege et al. [9]
examined fire induced failure of polycarbonate windows. In a
recent experiment [10], the performance of multi-pane glazing
due to radiant heat flux has been tested at small, medium and
large-scale samples, and the radiant transmittance through the
glazing assembly was examined.
Along with experiments and theoretical analyses, numerical
modeling of glass breakage has been explored extensively for bothand fallout.Assessment of a model development fo
exposure in a field model
Kai Kang

Jacobs, 260 Madison Avenue, New York, NY 10016, USA
article info
Article history:
Received 1 August 2008
Received in revised form
27 August 2008
Accepted 5 September 2008
Available online 15 October 2008
Keywords:
abstract
This paper presents a mod
field model. Glass breakag
stress; and glass fallout i
generally good agreemen
compartment fire experi
temperature are within 1
initial occurrence of glass
journal homepage: www
Fire Safell rights reserved.window glass breakage due to fire
evelopment for the prediction of window glass breakage and fallout in a
based on the temperature difference and the allowable glass breaking
termined by a preset number of successive breakages. As a validation,
re obtained between the numerical predictions and the data from a
t. The predicted glass surface temperature and the adjacent gas
5% of the test data. For fire sizes of 170, 280 and 390 kW, the time of
kage are shown within reasonable range of the experimental results. For
e at ScienceDirect
sevier.com/locate/firesaf
Journal

compartment fire experiment [15] is discussed.
ARTICLE IN PRESS
urn2. Description of model development
2.1. Criterion of window glass breakage and fallout
The criterion of window glass breakage follows the same of [5]
and is the same as that used in BREAK1. As shown in Eq. (1), it
assumes that glass breakage occurs when the fire heat induced
thermal stress exceeds the allowable glass breaking stress, s4 s
b
.
s ¼ fbEDT (1)between fire development and enclosure confinement is impor-
tant, especially when window glass breakage could promote the
fire. Otherwise, an iterative approach would have to be taken, and
this might be impossible for a fire in an enclosed environment
that has many windows of different geometric and material
configurations. Therefore, the prediction of either the glazing
behavior or the fire development necessitates both be modeled
together. Using the fire dynamics simulator (FDS), the objective of
this study is to integrate the predictive capability of window glass
breakage with fire modeling. In this paper, the model develop-
ment is first described and a validation study with data from a
Nomenclature
f dimensionless factor
b coefficient of thermal expansion (1/1C)
E Young’s modulus (Pa)
T temperature (K)
h coefficient of convective heat transfer (w/m
2
K)
C constant
c
p
specific heat (kJ/kg K)
L local characteristic length scale (m)
l radiative decay length in glass (1/m)
I incident radiative heat flux (W/m)
Re Reynolds number
Pr Prandtl number
q total heat flux (W/m
2
)
S glass pane thickness (m)
K. Kang / Fire Safety Jo416where the factor ‘‘f’’ is to maintain over-all force balance in the
pane and takes into account glass half height and glass thickness.
If it is assumed that the shaded edge of the glass remains near the
initial temperature, the temperature change ‘‘DT’’ can be calcu-
lated as the increase in the average temperature of the pane. This
was implemented in BREAK1 [6].
As glass breakage (crack) does not necessarily mean glass
fallout, additional criterion would be needed. For window glass
fallout, this study uses the same approach as proposed by [16],
which is based on the number of successive breakages. In a
probabilistic analysis of glass behavior due to fire exposure, [16]
prescribed a fixed number of five breakages as generally indicative
of the time of glass fallout. This observation was interpreted from
the reported test data such as [15,17,18].
2.2. Implementation of window glass breakage
FDS is a special-purpose computational fluid dynamics (CFD)
program for fire-driven buoyant flows and incorporates mostly
used fire protection methods such as the modeling of heat and
smoke detectors and sprinklers. FDS is limited to structured grids
and the numerical method of finite volume technique uses secondorder spatial and temporal discretization. Turbulence flow can be
modeled by either Large Eddy Simulation (LES) or Direct
Numerical Simulation (DNS), and the fire is simulated using the
mixture fraction approach.
The wall heat transfer in FDS for thermally thick boundaries
takes into account both radiative and convective heat flux [18].
The coefficient of convective heat transfer to the wall is calculated
as the maximum of natural and forced convection,
h ¼ max C DT




1
3
;
k
L
0:037 Re
4
5
Pr
1
3

(2)
The constant C takes a value of 1.31 for vertical and 1.52 for
horizontal surfaces. DT is the temperature difference between the
wall cell and the neighboring gas cell. The Reynolds number, Re,is
based on the local characteristic length scale, L, which is 1 m by
default in FDS [18].
The convective heat flux is taken as the maximum between
convective and that based on temperature gradient using the
following:
q
c

¼ max hDT ; k
DT
DX

(3)
The boundary conditions on the fire and the non-fire side of
window panes are
t time (second)
x coordinate
D difference
r density (kg/m
3
)
e surface emissivity
s Stefan–Boltzmann constant (5.6710
8
J/m
2
/s/K
4
)
Subscript
a non-fire side
c convective
f fire side
g glass
d solid boundary
al 44 (2009) 415–424k
qT
qx




x¼0
¼ h
f
½T
f
ðtÞTð0; tÞ þ 
f
sT
4
f
ðtÞsT
4
ð0; tÞ¼q

ð0; tÞ (4)
k
qT
qx




x¼S
¼ h
a
½T
a
ðtÞTðS; tÞ þ 
a
sT
4
a
ðtÞsT
4
ðS; tÞ¼q

ðS; tÞ (5)
The one-dimensional heat conduction, including a radiative decay
term through the depth of the glass pane, is modeled as [5]
r
g
c
p
qT
qt
¼
q
qx
k
qT
qx

þ IðtÞ
e
x=l
l
(6)
where in the source term, I(t) is the incident heat flux and l is the
decay length in the glass pane. The heat conduction through other
solid interface is solved as follows:
r
d
c
p
qT
qt
¼
q
qx
k
qT
qx

(7)
Numerically, the above heat conduction equations are solved
using implicit Crank–Nicholson finite difference method over 20
grid points across the glass panes and other solid interface. This
discretization is based on the actual dimension of the specified
thickness and is calculated separately from the model grid [18].In