Assessment study of different radiation models in the simulation of 1 m methanol pool fire

Qianjun Zhou; Yong Hu; Yong Jiang

doi:10.52396/JUSTC-2023-0021

JUSTC > 2023 > 53(10): 1005. > DOI: 10.52396/JUSTC-2023-0021 CSTR: 32290.14.JUSTC-2023-0021

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Open Access JUSTC Engineering & Materials Article 25 June 2023

Assessment study of different radiation models in the simulation of 1 m methanol pool fire

State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei 230027, China

Cite this: JUSTC, 2023, 53(10): 1005

https://doi.org/10.52396/JUSTC-2023-0021

CSTR: 32290.14.JUSTC-2023-0021

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Author Bio:
Qianjun Zhou is a master of science at the University of Science and Technology of China. His research interest includes CFD, radiation modeling in fire simulation, and spectral modeling

Yong Hu is currently a Researcher at the University of Science and Technology of China. He received his Ph.D. degree in Physical Chemistry from the University of Heidelberg, Germany. His research interests include large-scale computation, high-precision model construction, simulation of fire combustion dynamics evolution, intelligent prediction, and machine learning

Yong Jiang is a Professor at the University of Science and Technology of China (USTC). He received his Ph.D. degree in Engineering in 1998. Afterwards, he worked as a postdoctoral fellow at USTC. His research interests include computer simulation, modeling, and precision measurement techniques of fire and combustion
Corresponding author:
Yong Hu, E-mail: yhu18@ustc.edu.cn

Yong Jiang, E-mail: yjjiang@ustc.edu.cn
Received Date: February 12, 2023
Accepted Date: April 29, 2023
Available Online: June 25, 2023

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Abstract

Abstract

Pool fires are one of the most commonly encountered flame types in fire disasters, and the accurate and detailed modeling of pool fires is beneficial for the hazard analysis and assessment of liquid-related fire accidents. The radiation model is known to be the critical component in the accurate simulation of various fire scenarios. Therefore, to develop a proper radiation model, an LES study of a large-scale methanol pool fire was performed in this work by coupling four different radiation models into the open-source fire simulation code FDS and solving the radiation intensity transport equation using the discrete ordinates method. The impact characteristics of different radiation models are evaluated in detail with the NIST experiments, where the comparative analysis was carried out. Regarding the temperature calculations, the WSGG (weighted-sum-of-gray-gases)-based radiation model and Cassol’s model performed better. In addition, all models predict pulsation frequencies well. However, regarding the prediction of the radiative heat fluxes, Cassol’s two models and the FDS default model outperformed the other models, which indicates that the database for obtaining the spectral information of each species and the method to determine the WSGG coefficient of mixed gases are significant factors for the successful prediction of flame radiation.

Graphical Abstract

By comparing the improved models, the WCassol model and Cassol model have the best performance.

Abstract

Pool fires are one of the most commonly encountered flame types in fire disasters, and the accurate and detailed modeling of pool fires is beneficial for the hazard analysis and assessment of liquid-related fire accidents. The radiation model is known to be the critical component in the accurate simulation of various fire scenarios. Therefore, to develop a proper radiation model, an LES study of a large-scale methanol pool fire was performed in this work by coupling four different radiation models into the open-source fire simulation code FDS and solving the radiation intensity transport equation using the discrete ordinates method. The impact characteristics of different radiation models are evaluated in detail with the NIST experiments, where the comparative analysis was carried out. Regarding the temperature calculations, the WSGG (weighted-sum-of-gray-gases)-based radiation model and Cassol’s model performed better. In addition, all models predict pulsation frequencies well. However, regarding the prediction of the radiative heat fluxes, Cassol’s two models and the FDS default model outperformed the other models, which indicates that the database for obtaining the spectral information of each species and the method to determine the WSGG coefficient of mixed gases are significant factors for the successful prediction of flame radiation.
Public Summary
- Based on the source code of FDS, different radiation model calculation modules have been developed for detailed large eddy simulations of pool fires. This provides a reference for the secondary development of the professional fire simulation program FDS.
- The performance and accuracy of different radiation models are evaluated, guiding for further improving the reliability of large-scale pool fire simulations.

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1. Introduction

Since the early 1930s, the first polyethylene product (low-density polyethylene) was generated by free radical polymerization^[1]. More importantly, in the 1950s, Nata et al.^[2] and Ziegler et al.^[3] used coordination polymerization catalysts to achieve olefin polymerization under mild conditions, thereby promoting the vigorous development of the polyolefin industry. Over seventy years later, polyolefins were widely used in food packaging, healthcare, machinery, automotive manufacturing, and other applications due to their excellent chemical corrosion resistance and mechanical properties^[4].

The transition metal catalysts required for coordinating polymerization to prepare polyolefins have attracted widespread attention from both industry and academia with the continuous development of the polyolefin industry^[5]. Among them, late transition metal catalysts such as nickel and palladium have been widely studied in the copolymerization of olefins and polar monomers due to their high tolerance to polar groups and low hydrophilicity^[6]. For example, these nickel/palladium catalysts include [N,N] catalysts^[7], [N,O] catalysts^[8,9], [P,O] catalysts^[10–12], etc. Among them, α-diimine nickel/palladium catalysts (Fig. 1a) was first reported by Johnson et al.^[13] in 1995 and is known for its unique chain walking mechanism; these catalysts can be utilized to synthesize polyolefins with branched chain structures and diverse polymer topologies.

Figure 1. Representative diimide catalysts (a–e) and novel structures used in this work (f).

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Since then, domestic and foreign scholars have extensively designed and researched this type of highly distinctive [N,N]-type catalyst by designing and synthesizing a series of novel α-diimine nickel/palladium catalysts with varying degrees of electronic effects and steric hindrance^[14–17]. For example, one important progress was the introduction of a diisopropylphenyl substituent, which significantly increased the axial steric hindrance of the metal center of the catalysts, thereby suppressing β-H elimination and improving the stability of the catalyst, allowing it to maintain high activity at 100 °C (Fig. 1b)^[18]. Dai et al.^[19] also studied the electronic effect of metal center coordination based on this large steric hindrance α-diimine palladium catalyst, further regulating the polymerization performance of the catalyst. In addition, Brookhart, Daugulis, and Coates et al.^[20] synthesized a “sandwich” type with increased axial steric hindrance using an 8-(p-tolyl) naphthalene-1-amine α-diimine nickel catalyst (Fig. 1c), which can prepare polyethylene with a high branching density (up to 150 branches per 1000 carbons) in ethylene polymerization.

By further adjusting the electronic effects and steric hindrance of the complex center, Wang et al.^[21] synthesized a chiral α-diimine nickel catalyst with paraphenylethyl compounds that exhibited high ethylene polymerization activity (up to 2.85 × 10⁶ g·mol⁻¹·h⁻¹·bar⁻¹) and produced polyethylene with a branching density of up to 117 branches per 1000 carbons at high temperatures. In addition, Coates et al.^[22–24] introduced similar chiral structures into α-diimine nickel catalysts and used them for the polymerization of propylene and 1-butene to improve the regularity of the polymer. The steric hindrance of these nickel catalysts was significantly different from that of classical 2,6-diisopropyl nickel catalysts and 2,6-diisopropylphenyl nickel catalysts, with only half of the steric hindrance present. On the basis of these works, we designed new nickel catalysts with asymmetric steric hindrance and studied the polymerization performance and physical properties of the generated polyethylene in detail.

2. Results and discussion

2.1 Synthesis and characterization

According to Scheme 1, aniline derivatives were prepared from precursors and p-anisidine by Friedel-Crafts alkylation. Subsequently, acetic acid was used as a catalyst, and ligand L1−L3 in high yield was easily prepared by the condensation of two equivalent aniline derivatives and one equivalent of 1,2-acenaphthenedione (Scheme 1). The ligands were reacted with equimolar amounts of (DME)NiBr₂ to prepare the corresponding α-diimine nickel complex Ni1–Ni3, which was a reddish-brown solid in almost quantitative yield. These complexes were characterized by elemental analysis, ¹H NMR and ¹³C NMR. The purity and identity of the two ortho-phenyl-substituted nickel complexes were determined by elemental analysis and XRD.

1. Synthetic route to nickel complexes Ni1−Ni3.

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Single crystals of complexes Ni1 and Ni2 were prepared by treating toluene solution with n-pentane at 0 °C on the top layer (Figs. 1 and 2, Tables S1 and S2). X-ray crystallographic analysis showed that the nickel dibromide complexes Ni1 and Ni2 (Figs. 2 and 3) crystallized symmetrically at two nickel centers with a twisted tetrahedral geometry at the center of the bromine-bridged dimer, where each nickel atom is connected to two bridged bromine atoms and an α-diimine ligand. The two nickel atoms in complexes Ni1 and Ni2 are connected by a quaternary ring.

Figure 2. Crystal structure of Ni1. The selected bond lengths (Å) and angles (°) were as follows: Br2–Ni1 = 2.3442(13), Br1–Ni1 = 2.3577(13), Ni1–N1 = 2.043(5), Ni1–N2 = 0.055(6), Br2–Ni1–Br1 = 110.57(5), N1–Ni1–N2 = 83.0(2), N1–Ni1–Br2 = 97.94(17), N1–Ni1–Br1 = 134.85(18), and N2–Ni1–Br1 = 99.18(16).

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Figure 3. Crystal structure of Ni2. The selected bond lengths (Å) and angles (°) are as follows: Br1–Ni1 = 2.3451(9), Ni1–Br2 = 2.3256(9), Ni1–N2 = 2.020(4), Ni1–N1 = 2.020(4), Br2–Ni1–Br1 = 122.07(4), N2–Ni1–Br1 = 115.23(10), N2–Ni1–Br2 = 107.94(10), N1–Ni1–Br1 = 101.99(10), N1–Ni1–Br2 = 120.38(10), and N1–Ni1–N2 = 82.98(15).

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2.2 Ethylene polymerization

Under fixed aggregation conditions and with the assistance of the AlEt₂Cl catalyst, the effect of the Ni1‒Ni3 catalysts on ethylene polymerization was investigated by altering the temperature (0–90 °C) while maintaining a [Al]/[Ni] ratio of 500 (Table 1). As shown in Table 1, Ni1 exhibited a high activity of up to 6.51 × 10⁶ g·mol⁻¹·h⁻¹ and produced polyethylene with a high molecular weight of up to 38.2 × 10⁴ g·mol⁻¹ (Table 1, Entries 1–4). For Ni1, as the polymerization temperature increased, the polymerization activity, molecular weight and melting point changed. The polymerization activity reached its maximum value at 30 °C, while the molecular weight of the polymer decreased with increasing temperature (from 38.2 × 10⁴ g·mol⁻¹ to 16.6 × 10⁴ g·mol⁻¹), the melting point of the polyethylene decreased with increasing polymerization temperature (from 128.2 to 114.0 °C), and the branching density increased to 41 branches per 1000 carbons. Compared with Ni1, Ni2 was obtained by replacing 2-phenylpropan-2-yl with 1-phenylethyl, and the steric hindrance of the nickel metal center decreased due to the reduction in the number of methyl groups. Compared with those of Ni1, the polymerization activity of Ni2 and the molecular weight of the prepared polyethylene slightly decreased, while the branching density increased to 61 branches per 1000 carbons (Table 1, Entries 5–8). Compared to Ni1 and Ni2, Ni3 obtained by completely removing the substituent at this position significantly reduced the ethylene polymerization activity, especially at high temperatures (90 °C), where it almost became inactive. The molecular weight of the polymer was reduced by more than half compared to that of Ni1 and Ni2 (with a maximum value of only 16.2 × 10⁴ g·mol⁻¹). However, due to the sharp decrease in the steric hindrance of Ni3, chain transfer and chain walking accelerated, and the branching density of polyethylene increased to 94 branches per 1000 carbons (Table 1, Entries 9–12). Furthermore, we investigated the temperature-dependent polymerization activity of the Ni1 and Ni2 catalysts at 90 °C (Fig. 4), and the results showed that the Ni1 and Ni2 catalysts could maintain their polymerization activity for up to 40 min at 90 °C, with Ni1 exhibiting the best performance.

Table 1. Ethylene homopolymerization catalyzed by nickel catalyst Ni1−Ni3^a.

Entry	Catalyst	T(°C)	Yield^b (g)	Activity^b (10⁶)	M_n^c(10⁴)	PDI^c	Branch^d	T_m^e(°C)
1	Ni1	0	2.65	3.18	38.2	1.8	7	128.2
2	Ni1	30	5.43	6.51	33.6	2.1	21	118.0
3	Ni1	60	2.52	3.02	21.9	2.0	40	114.4
4	Ni1	90	2.01	2.41	16.6	2.1	41	114.0
5	Ni2	0	2.35	2.82	37.6	1.8	15	120.2
6	Ni2	30	4.11	4.93	29.7	1.9	26	117.0
7	Ni2	60	2.76	3.31	17.3	2.1	46	113.6
8	Ni2	90	0.90	1.08	14.8	2.1	61	80.9
9	Ni3	0	1.10	1.32	16.2	2.3	36	115.1
10	Ni3	30	1.94	2.33	12.8	2.6	51	106.1
11	Ni3	60	0.80	0.96	11.9	3.1	72	69.1
12	Ni3	90	0.02	0.02	11.5	3.2	94	–
^a 1 μmol of catalyst in CH₂Cl₂ (2 mL), [Al]/[Ni] = 500. V_n_-heptane = 20 mL, t_{polymerization} = 10 min, P_ethylene = 8 atm. ^b Activity is in units of 10⁶ g·mol⁻¹·h⁻¹. ^c Determined by Gel Permeation Chromatography (GPC) in 1,2,4-trichlorobenzene at 150 °C. ^d Branches per 1000 carbons, determined by ¹H NMR. ^e Determined by differential scanning calorimetry.

| Show Table

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Figure 4. The polymerization performance of catalysts. (a) Polymer weight comparisons of generated polyethylene at 0 °C, 30 °C, 60 °C and 90 °C. (b) Molecular weight comparisons of generated polyethylene at 0 °C, 30 °C, 60 °C and 90 °C. (c) Branching density comparisons of generated polyethylene at 0 °C, 30 °C, 60 °C and 90 °C. (d) Time-dependent studies (polymer yields vs polymerization time) at 90 °C.

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2.3 Mechanical properties of synthesized polyethylene

Subsequently, as shown in Fig. 5, we investigated the tensile properties of polyethylene prepared with these nickel catalysts and found that the stress distribution of these polyethylene materials was between 15 and 30 MPa and that the strain distribution was between 400% and 800%. These polyethylene materials exhibit excellent tensile properties, which may be attributed to their high molecular weight (M_n greater than 17.3 × 10⁴ g·mol⁻¹). For the polyethylene samples prepared from Ni1 and Ni2, the sample with the highest stress was obtained at 30 °C, while the polyethylene sample obtained at 0 °C had the lowest stress, which may be related to its branching density.

Figure 5. Tensile curve of polyethylene prepared with nickel catalysts.

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3. Conclusions

We synthesized a series of novel α-diimine nickel complexes with asymmetric steric hindrance and studied their catalytic performance for ethylene polymerization. The polymerization activity of these catalysts can reach up to 6.51 × 10⁶ g·mol⁻¹·h⁻¹ and can be used to prepare high-molecular-weight polyethylene with adjustable branching density distributions between 7 and 94 branches per 1000 carbons. More importantly, the polyethylene prepared from these α-diimine nickel catalysts exhibited excellent tensile properties.

Supporting information

The supporting information for this article can be found online at https://doi.org/10.52396/JUSTC-2024-0001. The supporting information includes 34 figures. Experimental details, figures, and characterization data for the nickel catalysts and polymers are provided in the supporting information.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (52006151), the National Key R&D Program of China (2022YFC3003100), and the Civil Aircraft Scientific Research Project of the Industry and Information Technology (BB2320000045, DD2320009001).

Conflict of interest

The authors declare that they have no conflict of interest.

Based on the source code of FDS, different radiation model calculation modules have been developed for detailed large eddy simulations of pool fires. This provides a reference for the secondary development of the professional fire simulation program FDS. The performance and accuracy of different radiation models are evaluated, guiding for further improving the reliability of large-scale pool fire simulations.

References (30)

References

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[2]	Fang J, Wang J, Tu R, et al. Optical thickness of emissivity for pool fire radiation. International Journal of Thermal Sciences, 2018, 124: 338–343. DOI: 10.1016/j.ijthermalsci.2017.10.023
[3]	Sacadura J F. Radiative heat transfer in fire safety science. Journal of Quantitative Spectroscopy and Radiative Transfer, 2005, 93: 5–24. DOI: 10.1016/j.jqsrt.2004.08.011
[4]	Yao Y, Li Y Z, Ingason H, et al. Scale effect of mass loss rates for pool fires in an open environment and in tunnels with wind. Fire Safety Journal, 2019, 105: 41–50. DOI: 10.1016/j.firesaf.2019.02.004
[5]	Fernandes C S, Fraga G C, França F H R, et al. Radiative transfer calculations in fire simulations: An assessment of different gray gas models using the software FDS. Fire Safety Journal, 2021, 120: 103103. DOI: 10.1016/j.firesaf.2020.103103
[6]	Barlow R S, Karpetis A N, Frank J H, et al. Scalar profiles and NO formation in laminar opposed-flow partially premixed methane/air flames. Combustion and Flame, 2001, 127: 2102–2118. DOI: 10.1016/S0010-2180(01)00313-3
[7]	Cassol F, Brittes R, Centeno F R, et al. Evaluation of the gray gas model to compute radiative transfer in non-isothermal, non-homogeneous participating medium containing CO₂, H₂O, and soot. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2015, 37: 163–172. DOI: 10.1007/s40430-014-0168-5
[8]	Hostikka S, Mcgrattan K, Hamins A. Numerical modeling of pool fires using les and finite volume method for radiation. Fire Safety Science, 2003, 7: 383–394. DOI: 10.3801/IAFSS.FSS.7-383
[9]	Krishnamoorthy G, Borodai S, Rawat R, et al. Numerical modeling of radiative heat transfer in pool fire simulations. In: Proceedings of ASME 2005 International Mechanical Engineering Congress and Exposition. Orlando, Florida, USA: ASME, 2008: 327–337.
[10]	McGrattan K, McDermott R, Weinschenk C, et al. Fire Dynamics Simulator Users Guide, Sixth Edition, Special Publication (NIST SP). Gaithersburg, MD, USA: National Institute of Standards and Technology, 2013.
[11]	Sung K, Chen J, Bundy M, et al. The characteristics of a 1 m methanol pool fire. Fire Safety Journal, 2021, 120: 103121. DOI: 10.1016/j.firesaf.2020.103121
[12]	Grosshandler W L. Radcal: A Narrow-Band Model for Radiation Calculations in a Combustion Environment. Washington, DC: NIST, 2018.
[13]	Rothman L S, Gordon I E, Barber R J, et al. HITEMP, the high-temperature molecular spectroscopic database. Journal of Quantitative Spectroscopy and Radiative Transfer, 2010, 111: 2139–2150. DOI: 10.1016/j.jqsrt.2010.05.001
[14]	Smith T F, Shen Z F, Friedman J N. Evaluation of coefficients for the weighted sum of gray gases model. Journal of Heat Transfer, 1982, 104: 602–608. DOI: 10.1115/1.3245174
[15]	Cassol F, Brittes R, França F H R, et al. Application of the weighted-sum-of-gray-gases model for media composed of arbitrary concentrations of H₂O, CO₂ and soot. International Journal of Heat and Mass Transfer, 2014, 79: 796–806. DOI: 10.1016/j.ijheatmasstransfer.2014.08.032
[16]	Denison M K, Webb B W. The spectral-line weighted-sum-of-gray-gases model for H₂O/CO₂ mixtures. Journal of Heat Transfer, 1995, 117: 788–792. DOI: 10.1115/1.2822652
[17]	Johansson N, Ekholm M. Variation in results due to user effects in a simulation with FDS. Fire Technology, 2018, 54: 97–116. DOI: 10.1007/s10694-017-0674-y
[18]	McGrattan K, Hostikka S, McDermott R, et al. Fire Dynamics Simulator Technical Reference Guide Volume 1: Mathematical Model. Washington, DC: NIST, 2013.
[19]	Rehm R G, Baum H R. The equations of motion for thermally driven, buoyant flows. Journal of Research of the National Bureau of Standards, 1978, 83: 297. DOI: 10.6028/jres.083.019
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Figure 1. Schematic diagram of the computational domain.

Figure 2. Validation of the results of 1D RTE calculations for the newly coupled radiation models.

Figure 3. Temperature distribution along the central axis of the pool fire.

Figure 4. Frequency amplitude plots of velocities under different radiation models: (a) Barlow model, (b) Cassol model, (c) WSmith model, (d) WCassol model, and (e) FDS model, respectively.

Figure 5. Transient velocity vector, temperature, radiation heat flux (Q_r), absorption coefficient (κ_p), and concentrations of H₂O and CO₂ predicted by different radiation models.

Figure 6. Vertical distribution of radiation flux at 2.8 m from the center of the pool.

References

[1]	Abdolhamidzadeh B, Abbasi T, Rashtchian D, et al. Domino effect in process-industry accidents —An inventory of past events and identification of some patterns. Journal of Loss Prevention in the Process Industries, 2011, 24: 575–593. DOI: 10.1016/j.jlp.2010.06.013
[2]	Fang J, Wang J, Tu R, et al. Optical thickness of emissivity for pool fire radiation. International Journal of Thermal Sciences, 2018, 124: 338–343. DOI: 10.1016/j.ijthermalsci.2017.10.023
[3]	Sacadura J F. Radiative heat transfer in fire safety science. Journal of Quantitative Spectroscopy and Radiative Transfer, 2005, 93: 5–24. DOI: 10.1016/j.jqsrt.2004.08.011
[4]	Yao Y, Li Y Z, Ingason H, et al. Scale effect of mass loss rates for pool fires in an open environment and in tunnels with wind. Fire Safety Journal, 2019, 105: 41–50. DOI: 10.1016/j.firesaf.2019.02.004
[5]	Fernandes C S, Fraga G C, França F H R, et al. Radiative transfer calculations in fire simulations: An assessment of different gray gas models using the software FDS. Fire Safety Journal, 2021, 120: 103103. DOI: 10.1016/j.firesaf.2020.103103
[6]	Barlow R S, Karpetis A N, Frank J H, et al. Scalar profiles and NO formation in laminar opposed-flow partially premixed methane/air flames. Combustion and Flame, 2001, 127: 2102–2118. DOI: 10.1016/S0010-2180(01)00313-3
[7]	Cassol F, Brittes R, Centeno F R, et al. Evaluation of the gray gas model to compute radiative transfer in non-isothermal, non-homogeneous participating medium containing CO₂, H₂O, and soot. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2015, 37: 163–172. DOI: 10.1007/s40430-014-0168-5
[8]	Hostikka S, Mcgrattan K, Hamins A. Numerical modeling of pool fires using les and finite volume method for radiation. Fire Safety Science, 2003, 7: 383–394. DOI: 10.3801/IAFSS.FSS.7-383
[9]	Krishnamoorthy G, Borodai S, Rawat R, et al. Numerical modeling of radiative heat transfer in pool fire simulations. In: Proceedings of ASME 2005 International Mechanical Engineering Congress and Exposition. Orlando, Florida, USA: ASME, 2008: 327–337.
[10]	McGrattan K, McDermott R, Weinschenk C, et al. Fire Dynamics Simulator Users Guide, Sixth Edition, Special Publication (NIST SP). Gaithersburg, MD, USA: National Institute of Standards and Technology, 2013.
[11]	Sung K, Chen J, Bundy M, et al. The characteristics of a 1 m methanol pool fire. Fire Safety Journal, 2021, 120: 103121. DOI: 10.1016/j.firesaf.2020.103121
[12]	Grosshandler W L. Radcal: A Narrow-Band Model for Radiation Calculations in a Combustion Environment. Washington, DC: NIST, 2018.
[13]	Rothman L S, Gordon I E, Barber R J, et al. HITEMP, the high-temperature molecular spectroscopic database. Journal of Quantitative Spectroscopy and Radiative Transfer, 2010, 111: 2139–2150. DOI: 10.1016/j.jqsrt.2010.05.001
[14]	Smith T F, Shen Z F, Friedman J N. Evaluation of coefficients for the weighted sum of gray gases model. Journal of Heat Transfer, 1982, 104: 602–608. DOI: 10.1115/1.3245174
[15]	Cassol F, Brittes R, França F H R, et al. Application of the weighted-sum-of-gray-gases model for media composed of arbitrary concentrations of H₂O, CO₂ and soot. International Journal of Heat and Mass Transfer, 2014, 79: 796–806. DOI: 10.1016/j.ijheatmasstransfer.2014.08.032
[16]	Denison M K, Webb B W. The spectral-line weighted-sum-of-gray-gases model for H₂O/CO₂ mixtures. Journal of Heat Transfer, 1995, 117: 788–792. DOI: 10.1115/1.2822652
[17]	Johansson N, Ekholm M. Variation in results due to user effects in a simulation with FDS. Fire Technology, 2018, 54: 97–116. DOI: 10.1007/s10694-017-0674-y
[18]	McGrattan K, Hostikka S, McDermott R, et al. Fire Dynamics Simulator Technical Reference Guide Volume 1: Mathematical Model. Washington, DC: NIST, 2013.
[19]	Rehm R G, Baum H R. The equations of motion for thermally driven, buoyant flows. Journal of Research of the National Bureau of Standards, 1978, 83: 297. DOI: 10.6028/jres.083.019
[20]	Gottuk D T, White D A. Liquid fuel fires. In: Hurley M J, editor. SFPE Handbook of Fire Protection Engineering. New York: Springer, 2016: 2552−2590.
[21]	Fraga G C, Zannoni L, Centeno F R, et al. Evaluation of different gray gas formulations against line-by-line calculations in two- and three-dimensional configurations for participating media composed by CO₂, H₂O and soot. Fire Safety Journal, 2019, 108: 102843. DOI: 10.1016/j.firesaf.2019.102843
[22]	Dorigon L J, Duciak G, Brittes R, et al. WSGG correlations based on HITEMP2010 for computation of thermal radiation in non-isothermal, non-homogeneous H₂O/CO₂ mixtures. International Journal of Heat and Mass Transfer, 2013, 64: 863–873. DOI: 10.1016/j.ijheatmasstransfer.2013.05.010
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Assessment study of different radiation models in the simulation of 1 m methanol pool fire

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