Chapter 6
Glazing Response in Fires
Table of Contents
1. Introduction.............................................................................. 125 2. State of the Art ........................................................................ 125 2.1 Existing Computing Models ................................................. 126 2.2 Physical Characteristics of Glass.......................................... 127 2.3 Behaviour of Glazing in Enclosure Fire................................ 128 3. Theoretical Analysis of Glazing Response in Fire ..................... 128 3.1 Mechanical Stress Model: Pagni and Joshi’s Criterion ......... 129 3.2 Heat Transfer Model ............................................................ 130 3.2.1 Conductive Heat Transfer .............................................. 131 3.2.2 Convective Heat Transfer............................................... 131 3.2.3 Radiation Heat Transfer: Sincaglia and Barnett............. 133 3.2.4 Flame Emissivity............................................................ 134 3.2.5 View Factor from the Flame to the Opening.................. 134 3.2.5. Thermal Distribution in the Glass Body ....................... 135
3.3.6 Stability of the Thermal Model ...................................... 140 4. Parametric Study: Glazing Response in Fires ........................... 140 4.1 Definition of the Reference Case .......................................... 140 4.2 Summary of the Results ....................................................... 140 4.1.1 Shade Edge .................................................................... 141 4.1.2 Thickness ....................................................................... 142 4.1.3 Tensile Strength ............................................................. 142 4.1.4 Conductivity .................................................................. 142 4.1.5 Young’s Modulus............................................................ 142 4.1.6 Half-Width ..................................................................... 142 5. Influence of Glass Breakage in a Fire Compartment ................. 143 5.1 Definition of the Reference Case .......................................... 144 5.2 Results of the Simulations.................................................... 144 6. Validation of the Model ............................................................ 146 7. Graphical Method for Glazing Response Submitted to ISO Curve ..................................................................................................... 146 7.1 Methodology ........................................................................ 146 7.2 Identification of the Main Parameters.................................. 147 7.3 Graphical Method ................................................................ 147 8. Application of Graphical Model for a Single-Paned Window .... 149 9. Limitation of the Model and the Graphical Method.................. 150 10. Conclusion .............................................................................. 151
6. Glazing Response in Fires
1. Introduction Window glass plays an important role in compartment fire dynamics as it acts as a wall before breaking and as a vent after breaking. Typical breakage events occur at critical stages of fire growth. The resulting wall openings provide an inlet for fresh air and an exit for the hot gases. The increased ventilation changes the burning rate and consequently alters the course of a fire, possibly resulting in backdraft or flashover. In several of the fire safety engineering calculations concerned with the growth and development of room fires, it is assumed that the glazing system will completely and instantaneously fail when the upper glass layer temperature exceeds 500ºC (Decicco, R., 2001). However, this assumption is not accurate enough for predicting the fire evolution that could lead to backdraft. Other hypotheses are needed. Research on the behaviour of glazing response during enclosure fires has shown that the temperature differential and the resulting thermal expansion that exist between the shaded and unshaded part of the glass are responsible for the glass’s breaking. Several models have been developed based on this fundamental concept (see Section 2.1: “Existing Computing Models”). In this section, a single-pane window fracture model, BRANZfire, based on Joshi and Pagni’s criterion, is extended to multipane windows and then implemented in OZone. The simplest and most common geometry is considered in this project: rectangular glass windows fixed in a window frame and completely subjected to a thermal field.
2. State of the Art Emmons, 1985 was the first to identify the need for research into the problem of glass breaking when submitted to external flux. Pagni, 1988 followed up on Emmon’s suggestion and he quantified the mechanism of the glass fracture problem, suggesting a failure criterion in terms of the glass temperature increase in the centre of a windowpane. Cuzillo and Pagni, 1994 summarised three possible models of the heat transfer model. The simplest one treats the glass as a lumped mass and uses constant heat transfer coefficients. However, it is not suitable for application to rapid heating from fire. A more sophisticated approach is to treat the glass as a distributed mass that absorbs radiation throughout its thickness. The temperature profile can be calculated in two dimensions, but a singledimensional model that calculates the temperature profile through the thickness of the glass is sufficient if a uniform heat flux is assumed. Later, they extended this analysis to accommodate double-paned windows and exterior heating (Cuzillo and Pagni, 1998). 125
6. Glazing Response in Fires Keski-Rahkonem, 1988 analysed the case of rectangular glass heated by radiation, i.e. in the case of a fire burning in close proximity to a window. Later they extended this study to rectangular panes in 1991. Sincaglia and Barnett, 1997 developed a model for calculating glass window fracture for implementation in a zone-type computer fire model. Sincaglia and Barnett pay great attention to radiant energy absorption, transmission and emission within the glass and its functional dependence on wavelength. Ulster University during the duration of the FIRENET project performed an experimental investigation of glazing system response exposed to underventilated enclosure conditions. This research was focused mainly on the measurement of the heat flux from flames and hot gases to the pane.
2.1 Existing Computing Models The most widely known glass-fracture model is BREAK1 (Joshi and Pagni, 1992). This program is based on the heat transfer solution from Joshi and Pagni ,1991a and it models the glass as a distributed mass with through-thickness radiation absorption and a non-linear radiative boundary condition. The user is required to enter the flame radiation flux history for windows close to the fire source, the hot layer temperature development, the heat transfer coefficient for the unexposed side (constant), the time-varying heat transfer coefficient for the fire-exposed side, the emissivity of the gas layer, the dimensions and thermo-physical properties of the glass, these latter two being considered as constants. The program then reports the temperature of both sides of the glass, the average non-dimensionalised temperature and the non-dimensionalised time for each time step as well as the time when the window fractures. BREAK1 is not capable of running interactively with any zone modelling software. Cuzillo and Pagni, 1998 extended BREAK1 in order to model double-paned windows. The new program was called McBreak. Interpane radiant and convective heat transfers are taken into account and the windowpanes can break sequentially. Sincaglia and Barnett, 1997 developed a single windowpane glass fracture model based on the explicit finite difference method. This model provides a better evaluation of the radiant heat transfer by separately considering the incident radiation in the three wavelength bands (see Section 3.3.3: “Radiation Heat Transfer: Sincaglia and Barnett�). This last model is called BRANZfire and is suitable for being implemented into any zone-based computer fire model. For this reason and in order to provide a
126
6. Glazing Response in Fires better evaluation of the radiant heat transfer, this model has been chosen for extending to multipane windows and has been implemented in OZone.
2.2 Physical Characteristics of Glass Glass is a brittle, non-isotropic and non-homogeneous material. It is a mixture of materials, predominantly silica (72%) with various additives: soda (15%), lime (9%), magnesia (3%), and various oxides (1%). Although the variety of composition results in some variation in material properties, the most significant factor in material property variation is the manufacturing and installation process. The material property that varies the most widely is the maximum allowable tensile stress (maximum tensile stress prior to fracture). The reason for this is that glass strength depends strongly upon the treatment and handling of its surface. The manufacture of plate glass leaves surface imperfections of varying size and geometry. These defects such as notches, chipping, etc., along the edge of the glass that are caused by cutting and handling, may result in high stress concentrations (see Figure 6-1). This then aids the initiation of cracking along the edge of the glass at levels of breaking stress lower than the glass tensile strength.
Notches and chipping
Figure 6-1: Schematic representation of notches and chipping formed during the manufacture of plate glass. There is also a “size effect� on the strength of the glass: the smaller the specimen size is, the more the average stress on a fracture tends to increase. However, since larger specimens can contain more defects than smaller ones, the probability of a more severe defect existing in the glass is higher for a larger specimen. Michael J. Skelly et al., 1991 gives some common values of properties for typical glass windows in Table 6.1. These values can change according to different authors.
127
6. Glazing Response in Fires
2.3 Behaviour of Glazing in Enclosure Fire All window glass has its surrounding edge covered by an opaque frame or gasket; therefore, when speaking about window glass submitted to fire, two regions must be defined: the shaded and unshaded regions.
Property Value Fracture strength, σf 47 Young’s modulus, E 70 Expansion coefficient,β 9.5·10-6 Thermal diffusivity, α 3.6·10-7 Thermal conductivity, λ 0.76 * Thickness , L 6 * For typical construction as could be houses, schools…
Units [MPa] [GPa], [K-1], [m2/s], [W/mK] [mm] seen in offices,
Table 6.1: Common properties for typical window glass. Only the unshaded region is heated by the heat mechanism developed in a fire. The reasons for this are indicated below: • • •
The covered edge of the glass is shielded by the window frame from incident radiant and convective heating. Also, the window frame may act as a heat sink and contribute to keep the shaded area of the glass at a lower temperature. Glass is a poor conductor and hence heat from the area exposed to the thermal environment is not readily conducted to the edge region. (Conductivity of common glass, 0.76 W/mK; conductivity of carbon steel 420, 26.6 W/mK )
The temperature differentials between these regions (shaded and unshaded) will induce differential thermal expansion. The thermal expansion of the heated region (unshaded) is constrained by the cooler edge region (shaded) resulting in stresses within the body of the glass. When the tensile stresses at the edges reach a value higher than the glass strength, cracking occurs.
3. Theoretical Analysis of Glazing Response in Fire The glass fracture problem can be solved by separately considering two physical processes. The first one is the heat transfer process from the flames and the hot gas to the window glass and the second one is the mechanical stress distribution and the consequent fracturing of the glass created by the difference in temperature between the shaded and unshaded regions. •
Mechanical stress and fracturing model explained in Section 3.1: “Mechanical Stress Model: Pagni and Joshi’s Criterion”.
128
6. Glazing Response in Fires •
Heat transfer model explained in Section 3.2: “Heat Transfer Model”.
Figure 6.2 shows the sequential process for calculating the breaking time as well as the input data needed to obtain it.
Input
Properties of the window glass
Thermal mechanism heating the
data
window glass
Thermal analysis
Mechanical analysis
(finite difference)
Pagni & Joshi’s criterion Internal data
Average temperature of
Maximum Tfrac
the pane
Output BREAK?
data
Figure 6.2: Sequential process for calculating the time until breakage.
3.1 Mechanical Stress Model: Pagni and Joshi’s Criterion Fracture occurs when thermally induced tensile stresses along the shaded edge reach the tensile defect strength. Pagni and Joshi, 1991 obtained a simple relationship describing the temperature distribution within the glass pane at which a window will fracture, Eq. (6-1). The relationship is expressed as follows: ∆T =
1 s σ Ti − T0 ≥ 1 + f ∑ N i H Eβ
(6-1)
Note that this expression comes from Hooke’s law, Eq. (6-2).
∆T =
σf Eβ
(6-2)
Ti is the temperature at the ith node, N is the number of nodes, T0 is the initial temperature, s is the shaded length, H is the half-width of the window, E is Young's modulus of the glass, β is the coefficient of thermal expansion and σf is the fracture strength. The term (1+s/H) is a factor close to unity that accounts for the small amount of compression found in the central heated panes.
129
6. Glazing Response in Fires
This relationship may be altered slightly if the frame is so tight as to restrict expansion or to impose edge stresses prior to heating.
Half-width, H
Shaded edge, s
Window glass
Window frame Shaded part
Exposed area Unshaded part
Figure 7.3: Window dimensions. Eq. (6.1) is used to assess the maximum temperature that a window submitted to a fire can stand as well as the critical time at which the window cracks. Two conditions must be met for using Eq. (6.1) correctly:
•
The dimension of the shaded edge of the pane must be greater than or equal to twice the thickness of the pane, Eq. (6.3). This ensures that the edge of the glass is significantly covered by the frame and thereby insulated. s ≤ 2·t
•
(6-3)
The time of glass fracture, tfrac, must be less than the product of the square of the dimension of the shaded edge and the inverse of the thermal diffusivity, Eq. (6.4). This ensures that the heating of the glass is not so gradual that the edges of the pane are heated along with the majority of the pane, thereby eliminating the thermal stresses.
tfrac <
s2 α
(6-4)
3.2 Heat Transfer Model The heat transfer mechanisms affecting the glass are convection on the interior surface and radiation absorption throughout the thickness of the glass. Heat is also transferred through the glass by conduction. Finally, heat is transferred from the heated glass to the external environment by means of convection on the exterior surface.
130
6. Glazing Response in Fires
In the next section, the heat transfer mechanisms are explained as well as the finite difference method used to obtain the temperature distribution in the body of the pane(s).
3.2.1 Conductive Heat Transfer Eq. (6-5) represents the conduction heat flux per unit of area, W/m2: qɺ cond =
k' ∆T L
(6-5)
where k’ is the Endry and Turzik’s apparent conductivity correlation expressed in W/mK (Eq. (6-6)), L is the thickness of the glass in m, and ∆T is the temperature difference between consecutive nodes of the glass in K. k' (TU ) = 0.7222 + 0.001583TU
(6-6)
Above TU is the temperature of the hot gases in K. Turzik’s apparent conductivity correlation takes into account the fact that the heated glass will also emit radiation, some of which will be reabsorbed by the pane resulting in some redistribution of energy within the glass.
3.2.2 Convective Heat Transfer Eq. (6-7) represents the convective heat flux per unit of area, W/m2: qɺ = h·∆T
(6-7)
Three different convective heat transfer coefficients can be defined in W/m2·K: • • •
hI, between the hot smoke and the fire-side of the glass. hj, in the interpane gap. hE, between the cool side of the glass and the exterior ambient.
The convective heat transfer coefficients are dependent on the temperature and on the velocity of the hot gases. The most likely to benefit from the enhanced dependence is the fire-side transfer coefficient, hI, as the condition here may vary significantly during the course of exposure. Eq. (6-8) is used to estimate this coefficient as follows (Sincaglia and Barnett, 1997):
h I = h min + (h max − h min )
(TU − 300) 100
(6-8)
131
6. Glazing Response in Fires where, the temperature of the upper layer, TU is measured in Kelvin and the values of hmin and hmax are 5 and 50 W/m2·K, respectively. This correlation describes a linear increase in the coefficient between hmin at 300K and hmax at 400K. hI is capped at hmax and cannot drop below hmin (see Figure 6.4). The convective heat transfer coefficient at the cool-side is not exposed to a large variation in temperature and is simply taken as a constant value of hE = 10 W/m2·K. The inter-pane air gap will be minimally affected by fire and, therefore, during the pre-breakage phase, the flow here will be nearly laminar because of the small temperature differences and the value of the inter-pane air gap convective heat transfer will be considered as hj= 4W/m2k. 60 50
hi hext
[W/m2K]
40 30 20 10 0 290
310
330
350
370
390
410
Temperature [K] Figure 6.4: Variation of the fire-side and cool side convective heat transfer coefficient. The model only considers the case of having a window submitted to a uniform heat flux (coming from the flames and the hot gas, in our case TU). During a fire, the glass may be submitted to different temperatures i.e., when the hot layer is found in between the sill and soffit of the window. The author makes the following hypothesis: • •
If the upper layer (smoke) is above the soffit of the window, TU is considered the average value of the lower layer temperature and the upper layer temperature. If the upper layer is below the soffit, TU is considered the value of the upper layer temperature.
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6. Glazing Response in Fires
3.2.3 Radiation Heat Transfer: Sincaglia and Barnett A glass window acts as a semitransparent medium, reflecting, transmitting and absorbing radiant energy. Only the energy that is absorbed contributes to the heating of the window glass. The rate of radiant energy transfer is a strong function of the temperature of the upper gas layer and is also proportional to the emissivity of the layer. Radiation may also be contributed from the flames and the bed of the fire, with the significance of this source depending on the distance between the flames and the window. Michael J. Skelly, 1991 developed a model for radiant heat transfer from a radiating source by isolating the directional and then monochromatic radiant energy behaviour. This model is based on the fact that the total irradiation from the environment to the window glass pane can be divided into three parts: the reflectivity (ρ), the transmissivity (τ) and absorptivity (α). Eq. (6-9) represents the radiant heat transfer from a radiating source. qɺ = qɺ 1 + qɺ 2 + qɺ 3 qɺ i = (1 − ρ)(1 − e −γ i l )fλi −1 →λi ε U σTU4
(6-9)
fλi−1→λi = f0→λi − f0→λi−1 Above qɺ 1 , qɺ 2 , qɺ 3 represent the energy transfer evaluated over three wavelength bands, λ . εu is the emissivity of the upper layer. σ is the Stefan-Boltzmann constant, f is the fractional energy function in the wavelength region limited by λ i−1 → λ i . ρ is the average reflectivity considered to be 5.7% for glass. l is the average path length, ( l =1.077·L). The energy transfer is evaluated over three wavelength bands, given that the fraction of the radiant energy of each band is known. The fractional energy function, f0 λ, can be used to calculate the fraction of energy contained in the band from λ=0 to λ=λ1 as follows: ξ
f0→λT = 1 − ξ λT =
15 ξ 3 dξ dξ π4 ∫0 eξ − 1
C2 λT
(6-10) (6-11)
T is the temperature of the radiation source (e.i. the upper layer) and C2 is a constant equal to 14387.69 µmK. A solution to this equation can be obtained using the following converging series (Siegel and Howell, 1992)
f0→λT
15 ∞ e− nξ = 1− 4 ∑ π n =1 n
3 3ξ2 6ξ 6 ξ + n2 + n2 + n 3
(6-12)
Sincaglia and Barnett use the following stepped function for typical window glass: 133
6. Glazing Response in Fires
γ1 = 35.0 m −1 → 0 ≤ λ ≤ 2.75 µm γ 2 = 475.0 m −1 → 2.75 ≤ λ ≤ 4.5 µm
(6-13)
γ 3 = ∞ m −1 → λ > 4.5 µm
Air
ρG αG
θ2 τG
θ1
G
Glass
G = ρG + αG+ τG
Figure 6-5: (a) Components of irradiation interacting with a semitransparent medium (b) Refraction of radiation at an interface between transparent media.
3.2.4 Flame Emissivity If flames are considered in the calculation, it is possible to obtain its emissivity by Eq. (6-14): εfl = (1 − e −κD )
(6-14)
Where D is the flame diameter and is a property of the fuel in [m]. A default value of 0.8 is used for k, but the formula easily accepts alternative values. To calculate the heat flux coming from the flames Eq. (6-9) is used assuming a flame temperature of 1073 K (Ross P., 2002).
3.2.5 View Factor from the Flame to the Opening Heskestad’s flame height correlation is used to estimate the diameter and height of an imaginary cylinder of the flame. The view factor from the cylinder to the window is then calculated using the following formula (SFPE Handbook, Appendix D):
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6. Glazing Response in Fires
F12 =
L A − 2D 1 L A(D − 1) 1 D −1 tan −1 tan −1 − tan −1 + 2 πD B(D + 1) D D + 1 D − 1 π D AB (6.15)
D=
d R
(6-16)
A = (D + 1)2 + L2
(6-17)
B = (D − 1)2 + L2
(6-18)
H = −1.02·D + 0.235·Q0.4
(6-19)
If the distance between the flame and the window is less than the diameter of the fuel the view factor is 1.0. All units are expressed in [m]. Figure 6-6 indicates the parameters used in the previous equations.
Figure 6-6: Cylindrical radiator to parallel receiver. [Source: Heat Transfer in Fires, P. Blackshear, ed., Scripta Book Company, Washington, DC (1974)].
3.2.5. Thermal Distribution in the Glass Body A one-dimensional finite difference method is used to obtain the temperature distribution through the thickness of the glass and the gap of air between the panes. Nodes are selected on the interior and exterior surfaces of the glass spaced evenly through the thickness of the glass (Figure 6-7). The temperature at each node is calculated at each time step using transient explicit finite difference formulae that can be written by considering the energy balance for each node, Eq. (6-20):
135
6. Glazing Response in Fires
Eɺ in + Eɺ generated = Eɺ stored
(6-20)
In this section the following nomenclature is used: • • • • •
P indicates the current time step. P+1 indicates the next time step. The internal node is defined as the node in contact with the hot smoke. The interior node is defined as the node inside the body of the glass. The external node is defined as the node in contact with the air gap or atmospheric air. I is the number of panes in the window.
•
The explicit finite difference formula for the temperature of the internal node is obtained by solving Eq. (6.21): P +1 0,I
T
2∆t k ' P P =T + − (T1,IP − T0,I ) + h I ( TU − T0,I + qɺ rad ) cpρ∆x ∆x P 0,I
(6-21)
The explicit finite difference formula for the temperature of the interior nodes of glass i is obtained by solving Eq. (6.22): Ti,IP+1 = Ti,IP +
2∆t k' (TiP−1,I + TiP+1,I − 2Ti,IP ) + qɺ rad cpρ∆x ∆x
(6-22)
The explicit finite difference formula for the temperature of the external nodes is obtained by solving Eq. (6.23): P +1 P Tm,I = Tm,I +
2∆t k' P (TmP−1,I − Tm,I ) + qɺ co nv + qɺ rad cpρ∆x ∆x
(6-23)
The temperature of the air in the gap is shown in Eq. (6-24). No conduction and no storage of energy are taken into consideration.
P +1 Air gap
T
=
P P Tm,I − T0,II
2
(6-24)
Additional comments: The formulas are valid for single-pane windows and for multi-pane windows, by only changing “I” to “II”. Attention must be paid in the convective, qɺ co nv , and radiative, qɺ rad , heat transfer of Eq. (6-21)-(6-23). Radiation from walls is not evaluated because the difference of temperature between glass and wall is small.
136
6. Glazing Response in Fires
Radiative Heat Transfer •
For the internal node: qɺ rad = qɺ 1 + qɺ 2 + qɺ 3 All evaluated with l = 1.077·(∆x / 2) .
(6-25) (6-26)
•
For the interior node: qɺ rad = qɺ 1 + qɺ 2 All evaluated with l = 1.077·∆x .
(6-27) (6-28)
The quantity qɺ 3 is not included because it represents radiant energy in the spectral band for which glass is opaque. •
For the external node: qɺ rad = qɺ 1 + qɺ 2 + qɺ ∞ All evaluated with l = 1.077·(∆x / 2) .
(6-29) (6-30)
The quantity qɺ ∞ is surface absorbed radiant energy from the external environment (or the gap). This radiant energy is treated as surface absorbed because the ambient temperature is considered low enough that most of the energy is within the spectral range for which glass is opaque.
Radiative Heat Transfer •
For the exterior node of the last pane: qɺ conv = h E ( Tm − T∞ )
•
For the gap: qɺ conv = h j ( Tm,I − TAirgap )
(6-32)
qɺ conv = h j ( TAirgap − Tm,II )
Glass
(6-33) Glass
I
II
Air
Eɺ generated
I-II
h T0,I
Ti,I ∆xI
T0,I
Tm,I
∆xI
Ti,II
Tm,II Node
∆xII ∆xII Eɺ in
∆y
ThicknessI
(6-31)
Eɺ stored
ThicknessII
Figure 6-7: Finite difference model diagram.
137
6. Glazing Response in Fires Note that ∆y of Figure 6-7 does not appear in the formulations. Calculations are independent of the depth of the gap. Figure 6-8 represents the glazing response of a single-paned window of 10 mm when heated by hot gases. In the same figure the temperature of the hot gases is shown. The properties of the glass are listed in Table 6-2. Figure 6-9 shows the variation in temperature of each node as a function of time. Time frames of 0 s, 120 s, 180 s, 240 s and 300 s are represented. A difference of approximately 46ºC can be found between the internal and external node of the glass for time 300 s. The glass breaks at 320 s.
Property Value Fracture strength, 47 σf Young’s modulus, 70 E Expansion 9.5·10-6 coefficient, β Thermal 3.6·10-7 diffusivity, α Thermal 0.76 conductivity, λ
Units [MPa] [GPa]
Geometry Shade edge, s Width
Value Units 20 [mm]
[K-1]
Height
2 [m]
[m2/s]
Half-width
1 [m]
[W/mK]
Thickness*
10 [mm]
2 [m]
Table 6-2: Properties and dimensions of the glass simulated. 700 600
TU [ｰC]
[C]
500
Taver [C]
400 300 200 100 0 0
75
150
225
300
375
450
Time [s]
Figure 6-8: Gas temperature evolution and average temperature of the glass.
138
6. Glazing Response in Fires 120 100
[C]
80 300 sec
60 240 sec
40 180 sec 120 sec
20
0 sec
0 1
2
3
4
5
6
7
8
9
10
11
Node number
Figure 6-9: Temperature of the node at different times [0 s, 120 s, 180 s, 240 s, 300 s]. 14000 12000
Total Total Reflected Reflec
2 [W/m ] []
10000
Refracted Incide Inside Inside
8000
Opaque Opaque
Absorbe Absorbed
6000
Transmit Transmitt
4000 2000 0 0
75
150
225
300
375
Time [s]
Figure 6-10: Total radiative energy coming from the temperature of the hot gases and the different forms it can take (reflected, absorbed, transmitted, refracted, opaque and inside).
Figure 6-10 represents the total radiative energy coming from the temperature of the hot gases and the different forms it can take (reflected, absorbed, transmited, refracted, opaque and inside). See Annex III. A value of 1.0 and of 10 W/m2K is given for the smoke emissivity and the convective heat transfer coefficient for the external air, respectively.
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6. Glazing Response in Fires
3.3.6 Stability of the Thermal Model With the set of formulas given above, mathematical problems occur when a certain relation of ∆t/∆x is superseded. The calculation then gives an error as a result. The relation between ∆t and ∆x is expressed in Eq. (6-34): ∆t ≤
(∆x)2
(6-34)
∆x 2α ' (h + ε U σT03 ) + 1 k
4. Parametric Study: Glazing Response in Fires 4.1 Definition of the Reference Case Here, the influence of the properties of the windowpane on the time of breakage when it is submitted to a hot gas temperature is analysed and commented on (see Figure 6-10). This is carried out by changing a single parameter (property) at once from a reference case when all other parameters remain constant. The properties and the range are: • • • • • •
The shading width, s, from 20.0 mm to 40.0 mm. The thickness, L, from 3.0 mm to 15.0 mm. The tensile strength, σ, from 10 MPa to 100 MPa The conductivity, λ, from 0.1 W/mK to 2 W/mK. Young’s modulus, E, from 50 GPa to 100 GPa. The half-width, H, from 0.1 m to 3.0 m.
The following table shows the properties of the reference glass pane.
Property Value Fracture strength, 47 σf Young’s modulus, 70 E Expansion 9.5·10-6 coefficient, β Thermal 3.6·10-7 diffusivity, α Thermal 0.76 conductivity, λ
Units [MPa]
Geometry Value Units Shade edge 20 [mm]
[GPa]
Width
2 [m]
[K-1]
Height
2 [m]
[m2/s]
Half-width
1 [m]
[W/mK]
Thickness*
6 [mm]
Table 6-3: Properties and dimensions of the reference glass.
4.2 Summary of the Results Table 6-4 represents a summary of the results obtained in the following sections.
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6. Glazing Response in Fires
Parameter Tendency of parameter Time to breakage Shading width ↑ ≈ Thickness ↑ ↑ Half-width ↑ ↓ Tensile strength ↑ ↑ Conductivity ↑ ↑ Young’s modulus ↑ ↓ Legend: ↑ increase; ↓ decrease; ≈ not significant. Table 6-4: Influence of several parameters on the time of breakage. 700 Gas temperature (a) [ｰC]
600 Gas temperature (b) [ｰC]
500
[C]
400 300 200 100 0
0
100
200
300
400
500
Time [s]
Figure 6-11: Different gas temperature curves affecting the glass.
4.1.1 Shade Edge For higher areas of shaded edge, the time of breakage is increased. However, this rise in the breaking time of the glass is not significantly. It can be seen in Figure 6-12 that varying this value from 20 mm to 40 mm, the major difference in time of breakage is 3.0 and 5.0 seconds for curves (a) and (b), respectively. The shaded edge value must fulfil the following conditions in order to ensure: • •
that the frame significantly covers the edge of the glass, thereby insulating it. that the heating of the glass is not so gradual that the edges of the pane are heated along with the majority of the pane, thereby eliminating the thermal stress.
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6. Glazing Response in Fires
4.1.2 Thickness If the thickness is increased, the time of glass fracture also increases (Figure 612). The greater the thickness, the more time is needed to raise the average temperature of the glass and consequently to reach the temperature that leads to fracture.
4.1.3 Tensile Strength If the tensile strength is increased, the time of glass fracture also increased as is shown in Figure 6-12. At a higher tensile strength, the windowpane can withstand higher temperatures (Hooke’s law).
4.1.4 Conductivity As in the previous parameters, if the value of conductivity is increased, the time of glass fracture also increases (see Figure 6-12). For smaller values, a larger quantity of the heat coming from the hot gases accumulates in the glass. However for large values, this heat is transmitted through the glass to the outside air.
4.1.5 Young’s Modulus If Young’s modulus is increased, the time of glass fracture decreases (see Figure 6-12). For a higher Young’s modulus, the maximum temperature that the glass can withstand is lower.
4.1.6 Half-Width If the half-width, defined as the minimum value between Height/2 and Width/2, is increased, the time of glass fracture decreases. However, it is observed in Figure 6-12 that from a certain value (1.0 m) its influence is negligible. 500
500 Gas temperature (a)
Gas temperature (a) Gas temperature (b)
400 300
Gas temperature (b)
400 300
[s]
[s]
Reference case
200
200
100
100
0
0
0.0
0.2
0.4
0.6
0.8
1.0 1.2 [W/mK]
1.4
1.6
1.8
2.0
Influence of the conductivity of the glass on the time of fracture
Reference case
10
20
30
40
50
60
70
80
90
[MPa]
Influence of the value of the strength on the time of glass fracture
142
100
6. Glazing Response in Fires 400
450
350
400
Gas temperature (b)
350
300
300
250
Reference case
[s]
[s]
Gas temperature (a)
200 150
250
Reference case
200 150
Gas temperature (a)
100
100
Gas temperature (b)
50
50
0
0
0.0
0.5
1.0
1.5
2.0
2.5
3
3.0
4
5
6
7
8
9
10
11
12
13
14
15
[mm]
[m]
Influence of the half-width of the glass on the time of fracture
Influence of the dimension of the thickness on the time of glass fracture
350
400 350 300
300
250
Gas temperature (b)
[s]
[s]
Gas temperature (a) Reference case
250
Reference case
200 150 Gas temperature (a)
100
200
Gas temperature (b)
50 0
150 20
22
24
26
28
30
32
34
36
38
40
50
55
60
65
70
Influence of the dimension of the shaded edge on the time of glass fracture
75
80
85
90
95
[GPa]
[mm]
Influence of Youngâ&#x20AC;&#x2122;s modulus of the glass on the time of fracture
Figure 6-12: Results of the parametric study for glazing response in fire.
5. Influence of Glass Breakage in a Fire Compartment This section shows the influence of glass breakage in a fire scenario. Three scenarios are simulated. The only difference among them is the opening conditions. In the first case, the window is open from the beginning of the fire. In the second case, a single-pane window is analysed. In the last case, a doublepane window is considered. In the latter cases the window will be opened at the moment the crack is created. The results are obtained by OZone. It is observed how this phenomenon can lead to situations such as flashover or backdraft.
143
100
6. Glazing Response in Fires
5.1 Definition of the Reference Case The input data used in the simulation are the following: • • •
The compartment is used as an office (height 3 m, depth 3 m and length 3 m.) All the partitions are made of heavy wood (unit mass: 720 kg/m3; conductivity: 0.2 W/mK; specific heat: 900 J/kgK) and are 12 cm thick. Three openings are considered. Opening I is considered to be open all the time; Opening II is a single pane; Opening III is a double-paned window. Both panes have the same properties and dimensions (sill at 0.2 m, soffit at 0.8 m; width at 1 m).
The suggested values of the NFSC method (Scheilch and Cajot, 2001, Eurocode 1, 2002) for a library are: • • •
Fire load uniformly distributed with a characteristic value qf,k = 511 MJ/m2 The fire growth rate is 300 s. The maximum rate of heat release density is 250.0 kW/m2.
Shaded edge, s
20 mm
Glass thickness, L
10.0 mm
Half-width, H Fracture strength, σf Young’s Modulus, E Exterior conv. Coeff, Hext
1m 47 MPa 70 GPa 10 W/m2K
Thermal expansion coeff, 9.5·10-6 K-1 β Thermal diffusivity, α 3.60·10-7 m2/s Thermal conductivity, λ 0.76 W/mK Enclosure temperature, T 20 ºC Exterior temperature, Text 15 ºC Exterior emissivity, ε 1
Table 6-5: Properties of both glass panes.
5.2 Results of the Simulations Figure 6-13 represents the temperature histories of the three cases. The blue line represents both the single-pane case and the double-pane case. The blue represents the single-pane case or the first pane of the double-pane case and red is used the second pane.
144
6. Glazing Response in Fires 380 370 360
Pane II 350 340
[K]
Pane I 330 320 310 300 290 0
50
100
150
200
250
300
350
400
450
500
Time [s]
Figure 6-13: Average temperature evolution for both panes. The first pane breaks at 320 s from the beginning of the fire and then the direct heating of the second pane begins. The average temperature of pane II has increased approximately by 4K at 320 s. It may be observed in Figure 6-13 that from time 320 s the average temperature of pane II starts to rise rapidly. That depends on the considered convective heat coefficient, in our case, 4 W/m2K. Pane II breaks at 430 s. Figure 6-14 shows the temperature evolution in the compartment in all three cases. 800 700 Single pane window
600
[ยบC]
500 400
Double pane window
300 200
No breakage
100 Rapid spread flame process 0 0
250
500
750
1000
1250
1500
1750
2000
2250
2500
Time [s]
Figure 6-14: Temperature evolution according to the breakage time. It is clearly observed how a rapid flame spread process may occur when creating an opening (see Figure 6-14). 145
6. Glazing Response in Fires
6. Validation of the Model Before implementing the model in OZone, a validation for glass panes with the results provided by other models such as BREAK1 and BRANZFIRE was carried out. For this purpose, three different type of glass (properties and size) submitted to the same gas temperature were simulated with each model and the results were checked. A maximum relative error of 4% was found.
7. Graphical Method for Glazing Response Submitted to ISO Curve The main reasons for using this graphical method are the following: • •
•
There is not currently any graphical method to calculate the breaking time of glass when it is submitted to a fire. A graphical method gives us a rapid way of obtaining a value of time at which the glass window will crack. There is neither a method nor a recommendation in the Eurocode or in the NFSC that allows us to obtain or suppose a fracture time of a glass window submitted to a fire. Thus, a graphical method could be very easily used for engineers to obtain results. Most computational programs (one- or two-zone models) used for predicting the fire development in a fire scenario have the option of creating an opening at a time defined by the user. This graphical method could be used as input data in these programs in order to obtain accurate results in predicting the evolution of fire.
7.1 Methodology The aim of the present method is, first, to solve the heat transfer process in order to obtain the evolution of the average temperature of the glass. Then, the time at which the glass window breaks can be calculated by comparing the average glass temperature obtained in the first process with the maximum temperature the glass can withstand, obtained by solving the second process. For developing this method: • • • •
Both process are dealt with separately. The most influential parameters must be identified: the average temperature of the glass submitted to fire and the maximum temperature the window glass can withstand. All the parameters dependent on one will be grouped. The parameters with little influence on the results are replaced by constant values.
146
6. Glazing Response in Fires
7.2 Identification of the Main Parameters The left term of Eq. (6-35) represents the heat transfer process and the right term represents the mechanical process. ∆T =
1 s σ Ti − T0 ≥ 1 + f ∑ N i H Eβ
(6-35)
Ti can be written as: properties gas temperature Cons tan t values glass Ti = Function cp ·ρ, L , h i , k' , ε U , h E , h j, T∞ , qɺ rad
cons tan ts glass properties gas temperature = function ε UL , σ, γ, ρ , l,
(6-36)
Thickness(L)
qɺ rad
(6-37)
It is clearly seen that there are two groups to consider, namely “Glass properties” and “Gas temperature”. Density and specific heat are always multiplied (cp·ρ) in Eqs. (6-21) to (6-23). That is why they are considered as a single parameter. One should note that the value of cp·ρ is the same as λ/α. εu is considered constant even if it depends on the temperature (εu = 1.0). Other parameters are: the ultimate strength (σf), Young’s modulus (E), the thermal expansion (β) and a correction parameter represented by (1+s/H). These are included in the group “Glass properties”. According to this, the graphical method can be expressed as a function of cp·ρ and the thickness of the glass, since the rest depends on the temperature of the gas (ISO curve).
7.3 Graphical Method The following method has been developed for a glass window submitted to the ISO Curve, whose analytical formula is: 8·t Tgas = 20 + 345·log + 1 60
(6-38)
Only one graph is shown here. More results for different thicknesses are found in Annex III.
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6. Glazing Response in Fires
ISO CURVE
MAXIMUM TEMPERATURE: THICKNESS Tg
2 mm
s σf 1+ H Eβ
Time
Average glass temperature 600
cp·den 0.06 cp·den 0.11
500
cp·den 0.17 cp·den 0.22 cp·den 0.28
400
cp·den 0.33
[C]
cp·den 0.44
300
cp·den 0.50 cp·den 0.56 cp·den 0.61
200
cp·den 0.72 cp·den 0.83 cp·den 0.97
100
cp·den 1.11 cp·den 1.39
0 0
100
200
300
400
500
600
Time [s]
Average glass temperature 150
cp·den 0.06 cp·den 0.11
125
cp·den 0.17 cp·den 0.22 cp·den 0.28
100
cp·den 0.33
[C]
cp·den 0.44
75
cp·den 0.50 cp·den 0.56 cp·den 0.61
50
cp·den 0.72 cp·den 0.83 cp·den 0.97
25
cp·den 1.11 cp·den 1.39
0 0
25
50
75
100
125
150
Time [s]
148
6. Glazing Response in Fires
8. Application of Graphical Model for a Single-Paned Window Definition of the single-paned window, Table 6-6:
Shaded edge, s Glass thickness, L Half-width, H Fracture strength, σf Young’s Modulus, E Exterior conv. Coeff.
20 mm 10.0 mm 1m 47 MPa 70 GPa 10 W/m2K
Thermal expansion coeff Thermal diffusivity, α Thermal conductivity, λ Enclosure temperature, T Exterior temperature, Text Exterior emissivity, ε
9.5·10-6 K-1 3.60·10-7 m2/s 0.8 W/mK 20 ºC 15 ºC 1
Table 6-6: Properties of the single-pane window Pagni and Joshi’s criterion: ∆T =
1 s σ Ti − T0 ≥ 1 + f ∑ N i H Eβ
∆T =
1 0.02m 47Mpa Ti ≥ 1 + = ∑ N i 1m 70000MPa·9.5·10−6 K−1
(6-39)
72.09K + T0 = 345.09K → 92.09º C
(6-40)
Applying Graphic c p ·ρ·10 7
250
Curve standard Thickness 10 mm
200
0.72 1.44 2.16 2.88
Temperature [C]
3.6 4.32 150
5.04 5.76 6.48 7.2
100
7.92 9
92.09ºC
10.8
50
12.6 14.4 18
127 s
0 0
75
150
225
Time [s]
Figure 6-15: Curve Standard, thickness 10 mm. The pane breaks at 127 s when it is submitted to the ISO curve.
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6. Glazing Response in Fires
9. Limitation of the Model and the Graphical Method The developed physical model introduced in OZone has the following limitations: 1. Non-uniform heating. The fracture criterion assumes full immersion of the glass in the hot layer and thus uniform heating of the exposed surface. 2. Non-uniform shape. The fracture criterion application is limited to the case of a rectangular window. Circular or oval windows cannot be modelled. 3. Non-planar windows. Only planar windows can be assessed. 4. Thermal shock. The model is not applicable to thermal shock modelling such as might be encountered in explosions or during sprinkler activation. 5. External fire exposure. The model is suited to heating from internal compartment fires only and can not be used to assess fracture caused by external fires such as wildfires or flames from lower floors. 6. Double glazing. Double glazed windows are capable of maintaining their integrity for much longer than single panes. In BRANZFire, significant heating of the second pane does not occur until the first pane has begun to fall out, unlike in Ozone. 7. Multi-paned glazing. Significant heating of the second pane does not occur until the first pane has begun to fall out, unlike in Ozone. 8. Fall−out prediction. There is no model available for predicting glass fall−out time. The model predicts time to first fracture only. Some experiments have shown that windows may take a very long time to fall out following first fracture. 9. Out−of−plane loading. The joint action of thermal stresses and out−of− plane loading is not considered. Out−of−plane loading may occur due to pressure on the pane from sources such as wind or explosions. Thermal and pressure fractures are unlikely to affect each other, but pressure loading may affect fall−out times following first fracture. 10. The same limitations are applicable for the graphical method. Furthermore, it is only applicable for ISO curve fire. Its only purpose is to provide in a rapid way an approximate value of the fracture time.
150
6. Glazing Response in Fires
10. Conclusion A model for single and multi-paned window response in fires based on the theory of Pagni and Joshi and a thermal model by finite difference has been developed and implemented in OZone. The model provides the time at which the pane cracks. However, that does not means that the pane falls. There is no model in literature that allows us to predict the time at which a glass pane falls out. Further research is needed in this field. The influence of parameters such as the shaded edge, the thickness, the halfwidth, the tensile strength, the conductivity and Youngâ&#x20AC;&#x2122;s modulus on the time to fracture has been obtained. This knowlegde may be used for safety recommendations when facing a fire, i.e. as a reference to evaluate the time at which a glass could fall out creating an influx of air that may cause backdraft. A graphical method for glazing submitted to ISO-curve has been developed with the goal of having a quick idea of the time to fracture and its possible consequences. This time can be use as input data to those fire programs that are able to create an opening during fire development but they cannot calculate the time to fracture. Future research is needed for glass windows with shapes other than rectangular and for glass submitted to heat flux not uniformly distributed over the exposed area, i.e. glass submitted to the upper and lower layer.
151
6. Glazing Response in Fires
152