account to make the simulation independent of the initial conditions. Figure 2 shows the time-averaged profiles of different gas species, soot concentration and temperature along the line of sight shown in Figure 1. The experimental data of spectral radiation intensity of large Kerosene pool fires reported by Erez et al. [10] has been used here to qualitatively validate the used numerical approach. They measured the spectra of Kerosene flames 23 meters away from the pools. The region
(1 k D) where D and Δh represent diameter of the pool and enthalpy of combustion. The parameter kβ and
where the local, nominal radiative loss is greater than a specified lower bound, 𝜒𝜒𝜒𝜒"𝑞𝑞𝑞𝑞$$$> 10 kW/m3 in which 𝜒𝜒𝜒𝜒" is radiative fraction defined as the fraction of the total combustion energy that is locally released in the form of thermal radiation [11]. FDS allows the user to explicitly specify the net radiative emission from the flaming region. For most of the fuels, the radiative fraction have been reported between 0.3-0.4. For n-heptane pool fire, 0.35 is used in this work.
Figure 1. An illustration of the CFD model, its computational grid with an instantaneous temperature contours and smoke at t=25 sec.
The pool is modeled as a fuel mass inflow boundary with corresponding to a heat release rate of 4316 kW/m2, calculated by an empirical correlation [15]:
(2) where 𝐷𝐷𝐷𝐷 and represent diameter of the pool and enthalpy of combustion. The parameter 𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘 and are given as 1.1 m-1, and 0.101 kg/m2s for n-heptane liquid pool fire [15]. All the domain boundaries except the pool surface and bottom boundary are considered opened.
Simulation is done for 50 seconds and time averaging of transient results for the line shown in Figure 1 has been done between 10 to 50 seconds. The first 10 seconds of the simulations is not taken into account to make the simulation independent of the initial conditions. Figure 2 shows the time-averaged profiles of different gas species, soot concentration and temperature along the line of sight shown in Figure 1. The experimental data of spectral radiation intensity of large Kerosene pool fires reported by Erez et al. [10] has been used here to qualitatively validate the used numerical approach. They measured the spectra of Kerosene flames 23 meters away from the pools. The region
(1 k D) HRRPUA m h m= D =! !¥ -e-b Dh
h D
m!¥are given as 1.1 m–1, and 0.101 kg/m2s for n-heptane liquid pool fire [15]. All the domain boundaries except the pool surface and bottom boundary are con-sidered opened.
Simulation is done for 50 seconds and time averaging of tran-sient results for the line shown in Figure 1 has been done between 10 to 50 seconds. The first 10 seconds of the simulations is not ta-ken into account to make the simulation independent of the ini-tial conditions. Figure 2 shows the time-averaged profiles of dif-ferent gas species, soot concentration and temperature along the line of sight shown in Figure 1. The experimental data of spectral radiation intensity of large Kerosene pool fires reported by Erez et al. [10] has been used here to qualitatively validate the used nu-merical approach. They measured the spectra of Kerosene flames 23 meters away from the pools. The region between the simulati-on domain boundary and the target at 23 m distance from the axis of the pool is assumed to be normal standard air, and hence it has not been included in the CFD model to reduce the computational costs. The same gas concentrations and temperature as the open boundary surfaces of CFD model have been used for the exten-ded the line up to 23 meters away from the pool. The mole fracti-on of H2O and CO2 in the extended parts of the line are assumed 0.004 and 0.0004, respectively. The time-averaged data together with this assumption for the extended part of line of sight of the sensor have been used to build up a 1D spectral radiation solver as explained in the following section.
1D spectral radiation model
To obtain the profile of spectral intensity reaching to a sensor po-sitioned 23 m away from the pool, a 1D model has been built.
Two different simplifying assumptions have been used. First, the spectral intensity directionally integrated over a hemisphere
fa-Figure 1. An illustration of the CFD model, its computational grid with an instantaneous temperature contours and smoke at t=25 sec.
where the local, nominal radiative loss is greater than a specified lower bound, 𝜒𝜒𝜒𝜒
"𝑞𝑞𝑞𝑞
$$$> 10 kW/m
3in which 𝜒𝜒𝜒𝜒
"is radiative fraction defined as the fraction of the total combustion energy that is locally released in the form of thermal radiation [11]. FDS allows the user to explicitly specify the net radiative emission from the flaming region. For most of the fuels, the radiative fraction have been reported between 0.3-0.4. For n-heptane pool fire, 0.35 is used in this work.
Figure 1. An illustration of the CFD model, its computational grid with an instantaneous temperature contours and smoke at t=25 sec.
The pool is modeled as a fuel mass inflow boundary with corresponding to a heat release rate of 4316 kW/m
2, calculated by an empirical correlation [15]:
(2) where 𝐷𝐷𝐷𝐷 and represent diameter of the pool and enthalpy of combustion. The parameter 𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘 and are given as 1.1 m
-1, and 0.101 kg/m
2s for n-heptane liquid pool fire [15]. All the domain boundaries except the pool surface and bottom boundary are considered opened.
Simulation is done for 50 seconds and time averaging of transient results for the line shown in Figure 1 has been done between 10 to 50 seconds. The first 10 seconds of the simulations is not taken into account to make the simulation independent of the initial conditions. Figure 2 shows the time-averaged profiles of different gas species, soot concentration and temperature along the line of sight shown in Figure 1. The experimental data of spectral radiation intensity of large Kerosene pool fires reported by Erez et al. [10] has been used here to qualitatively validate the used numerical approach. They measured the spectra of Kerosene flames 23 meters away from the pools. The region
(1 k D) HRRPUA m h m= D =! !¥ -e-b Dh
h D m!¥
96 Palotutkimuksen päivät 2019
cing the sensor is obtained by simplifying the three-dimensional fire to a participating media bounded between two infinite paral-lel plates, i.e. 1D slab problem. Second, it is simplified by a sing-le ray, along the sensor’s line of sight shown in Figure 1, directing from the flame to the sensor and spectral radiative transfer
equa-tion is solved along this line with the extended time averaged pro-files as described in the previous section.
To obtain the spectral intensity profile using the first assumpti-on, i.e. 1D slab problem, discrete ordinate method as described in [16,17] has been used while for the second assumption of single ray a simple finite difference approach has been used.
The spectral absorption data of the gases used in both simp-lified 1D models have been obtained by line-by-line calculation (LBL) with HITEMP 2010 [18]. The details of the LBL calcula-tions can be found in [16]. The absorption spectra have been ob-tained with resolution of 0.02 cm-1 resulting to 492500 lines bet-ween 150–10000 cm-1.
The soot spectral absorption coefficient is given as
between the simulation domain boundary and the target at 23 m distance from the axis of the pool is assumed to be normal standard air, and hence it has not been included in the CFD model to reduce the computational costs. The same gas concentrations and temperature as the open boundary surfaces of CFD model have been used for the extended the line up to 23 meters away from the pool. The mole fraction of H2O and CO2 in the extended parts of the line are assumed 0.004 and 0.0004, respectively.
The time-averaged data together with this assumption for the extended part of line of sight of the sensor have been used to build up a 1D spectral radiation solver as explained in the following section.
1D spectral radiation model
To obtain the profile of spectral intensity reaching to a sensor positioned 23 m away from the pool, a 1D model has been built. Two different simplifying assumptions have been used. First, the spectral intensity directionally integrated over a hemisphere facing the sensor is obtained by simplifying the three-dimensional fire to a participating media bounded between two infinite parallel plates, i.e. 1D slab problem. Second, it is simplified by a single ray, along the sensor’s line of sight shown in Figure 1, directing from the flame to the sensor and spectral radiative transfer equation is solved along this line with the extended time averaged profiles as described in the previous section.
To obtain the spectral intensity profile using the first assumption, i.e. 1D slab problem, discrete ordinate method as described in [16,17] has been used while for the second assumption of single ray a simple finite difference approach has been used.
The spectral absorption data of the gases used in both simplified 1D models have been obtained by line-by-line calculation (LBL) with HITEMP 2010 [18]. The details of the LBL calculations can be found in [16]. The absorption spectra have been obtained with resolution of 0.02 cm-1 resulting to 492500 lines between 150-10000 cm-1.
The soot spectral absorption coefficient is given as
(3) where and are soot volume fraction and wave number, respectively. is a fuel dependent coefficient which is set to 7.0 for n-heptane [13].
The 1D models have been built for the entire line of sight starting from a point located at 23 m away from the flame on the opposite side of the sensor to the sensor, i.e. the length of the 1D models is 46 m. The boundary condition on the opposite wall is blackbody intensity at ambient temperature (20 °C) which is assumed to have negligible effect on the intensity spectrum reaching the sensor.
RESULTS AND DISCUSSIONS
Comparison with the available experimental data
Due to lack of experimental data for the radiation spectrum out of the flame of large heptane pool fire, the results of the current modeling has been compared with the measured spectra of the large Kerosene pool fires. The comparison shows qualitatively good agreement as depicted in Figure 3.
However, quantitative comparison is not sensible here due to different fuels and sizes, used in the experiments by Erez et al. [10]. The results of the 1D model with parallel plates assumption has been used in this figure.
Figure 3 shows the strong absorption effect of atmospheric cold gases, which explains the valley like regions in both numerical and experimental spectra. However, in both spectra, an emission peak of hot
s s
k =an h
ns h a
(3) where vs and η are soot volume fraction and wave number, res-pectively. α is a fuel dependent coefficient which is set to 7.0 for n-heptane [13].
The 1D models have been built for the entire line of sight star-ting from a point located at 23 m away from the flame on the op-posite side of the sensor to the sensor, i.e. the length of the 1D models is 46 m. The boundary condition on the opposite wall is blackbody intensity at ambient temperature (20 °C) which is as-sumed to have negligible effect on the intensity spectrum reach-ing the sensor.
RESULTS AND DISCUSSIONS
Comparison with the available experimental data Due to lack of experimental data for the radiation spectrum out of the flame of large heptane pool fire, the results of the current mo-deling has been compared with the measured spectra of the lar-ge Kerosene pool fires. The comparison shows qualitatively good agreement as depicted in Figure 3. However, quantitative com-parison is not sensible here due to different fuels and sizes, used in the experiments by Erez et al. [10]. The results of the 1D mo-del with parallel plates assumption has been used in this figure.
Figure 3 shows the strong absorption effect of atmospheric cold gases, which explains the valley like regions in both numeri-cal and experimental spectra. However, in both spectra, an emis-sion peak of hot CO2 gases at ~2200 cm-1 can be seen even at 23 m away from the flame. This can, in theory, be used for detecting fires from other hot resources by optical fire detection sensors.
Blackbody profiles corresponding to three possible flame tem-peratures are also shown in Figure 3. None of them matches with all the non-absorbing regions of the spectrum. This can be exp-lained by emissions of soot at various temperatures along the li-ne of sight. In other words, soot radiation does not have a single characteristic radiation temperature.
Effect of simplification assumptions
Figure 4 shows a comparison of two different assumptions ma-de for solving spectral radiation along a line of sight in the large pool fires. The single ray assumption gives quite close results as parallel plate assumption except for the emission peak of CO2 at
~2200 cm-1 which is estimated slightly stronger by single ray as-sumption. It shows that for the large pool fires, the directional de-pendency is marginal.
Effect of pool size
By geometric scaling the time averaged data, the radiation spectra of the smaller pools are estimated. Note that this only gives an
esti-Figure 2. Time averaged profiles together with their standard deviati-on aldeviati-ong the sampling line shown in Figure 1. Top: Mole fractideviati-on of gas species. Middle: soot volume fraction. Bottom: Temperature.
Figure 2. Time averaged profiles together with their standard deviation along the sampling line shown in Figure 1. Top: Mole fraction of gas species. Middle: soot volume fraction. Bottom:
Temperature.
97 Palotutkimuksen päivät 2019
mation of the effect of size. However, a quantitative analysis needs CFD simulation of smaller pools as well which is planned for the next step of this research.
Figure 5 shows the spectra found for three different pool sizes using the single ray solution. As seen the strength of the emissi-on peak of CO2 remains quite the same for all different sizes whi-le magnitude of intensity in the other parts of the spectra is quite affected by the pool size.
Comparison with blackbody
To identify the main spectral characteristics of the fire radiation spectrum that make it distinguishable from a spectrum from a hot object, the 1D model is adopted. A blackbody with the same tem-perature as the maximum temtem-perature of fire profile, i.e. 1180 K, is assumed as the source of radiation at one end of the 1D model.
The participating media is assumed to be standard air with small fraction of H2O and CO2 at room temperature (20 °C). Mole frac-tion of H2O and CO2 are assumed to be 0.004 and 0.0004, respec-tively. Assuming parallel plate conditions, the same directional-ly integrated spectral intensity have been obtained reaching the other end of the 1D model. Figure 6 shows two different radiati-on spectra reaching to the same locatiradiati-on, radiati-one from a 2 m n-hep-tane pool fire and the other from a hot blackbody object of the same temperature as the maximum temperature of the flame. The Planck intensity profile of the same temperature is also included in the figure for comparison. It can be seen that the emission peak of CO2 is the characteristic feature of the fire spectrum compa-red to the spectrum of a hot black body. Moreover, for blackbody heat source, the Planck distribution can successfully describe the radiation profile reaching the sensors for the parts of the spect-rum outside the main absorbing bands of H2O and CO2. For fi-re spectrum, a single Planck distribution cannot be used as a sub-stitute because the profile of fire is contributed by soot emission from different temperatures.
CONCLUSIONS
The spectral radiation of a large n-heptane pool fire is numeri-cally obtained. The numerical approach is based on implemen-ting the time-averaged data of a 3D CFD model in 1D solution of
Figure 3. Spectral intensity profile obtained by the present numeri-cal approach compared with experimental data of the large Kerosene pool fire and blackbody profiles of two temperatures.
CO2 gases at ~2200 cm-1 can be seen even at 23 m away from the flame. This can, in theory, be used for detecting fires from other hot resources by optical fire detection sensors.
Figure 3. Spectral intensity profile obtained by the present numerical approach compared with experimental data of the large Kerosene pool fire and blackbody profiles of two temperatures.
Blackbody profiles corresponding to three possible flame temperatures are also shown in Figure 3.
None of them matches with all the non-absorbing regions of the spectrum. This can be explained by emissions of soot at various temperatures along the line of sight. In other words, soot radiation does not have a single characteristic radiation temperature.
Effect of simplification assumptions
Figure 4 shows a comparison of two different assumptions made for solving spectral radiation along a line of sight in the large pool fires. The single ray assumption gives quite close results as parallel plate assumption except for the emission peak of CO2 at ~2200 cm-1 which is estimated slightly stronger by single ray assumption. It shows that for the large pool fires, the directional dependency is marginal.
Effect of pool size
By geometric scaling the time averaged data, the radiation spectra of the smaller pools are estimated. Note that this only gives an estimation of the effect of size. However, a quantitative analysis needs CFD simulation of smaller pools as well which is planned for the next step of this research.
Figure 5 shows the spectra found for three different pool sizes using the single ray solution. As seen the strength of the emission peak of CO2 remains quite the same for all different sizes while magnitude of intensity in the other parts of the spectra is quite affected by the pool size.
Figure 4. The effect of two different simplification assumption in sol-ving spectral radiation in large-scale fires.
Figure 5. Effect of pool size.
Figure 4. The effect of two different simplification assumption in solving spectral radiation in large-scale fires.
Figure 5. Effect of pool size.
Comparison with blackbody
To identify the main spectral characteristics of the fire radiation spectrum that make it distinguishable from a spectrum from a hot object, the 1D model is adopted. A blackbody with the
Figure 4. The effect of two different simplification assumption in solving spectral radiation in large-scale fires.
Figure 5. Effect of pool size.
Comparison with blackbody
To identify the main spectral characteristics of the fire radiation spectrum that make it distinguishable from a spectrum from a hot object, the 1D model is adopted. A blackbody with the
Figure 6. Spectrum coming from a blackbody hot object compared with the one coming from a fire flame.
same temperature as the maximum temperature of fire profile, i.e. 1180 K, is assumed as the source of radiation at one end of the 1D model. The participating media is assumed to be standard air with small fraction of H2O and CO2 at room temperature (20 °C). Mole fraction of H2O and CO2 are assumed to be 0.004 and 0.0004, respectively. Assuming parallel plate conditions, the same directionally integrated spectral intensity have been obtained reaching the other end of the 1D model. Figure 6 shows two different radiation spectra reaching to the same location, one from a 2m n-heptane pool fire and the other from a hot blackbody object of the same temperature as the maximum temperature of the flame. The Planck intensity profile of the same temperature is also included in the figure for comparison. It can be seen that the emission peak of CO2 is the
same temperature as the maximum temperature of fire profile, i.e. 1180 K, is assumed as the source of radiation at one end of the 1D model. The participating media is assumed to be standard air with small fraction of H2O and CO2 at room temperature (20 °C). Mole fraction of H2O and CO2 are assumed to be 0.004 and 0.0004, respectively. Assuming parallel plate conditions, the same directionally integrated spectral intensity have been obtained reaching the other end of the 1D model. Figure 6 shows two different radiation spectra reaching to the same location, one from a 2m n-heptane pool fire and the other from a hot blackbody object of the same temperature as the maximum temperature of the flame. The Planck intensity profile of the same temperature is also included in the figure for comparison. It can be seen that the emission peak of CO2 is the