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An experimental study and numerical simulation of horizontal flame spread over polyoxymethylene in still air
Fire Safety Journal 111 (2020) 102924
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An experimental study and numerical simulation of horizontal flame spread over polyoxymethylene in still air O. Korobeinichev a, *, R. Glaznev a, b, A. Karpov c, A. Shaklein c, A. Shmakov a, b, A. Paletsky a, S. Trubachev a, b, Y. Hu d, X. Wang d, W. Hu d a
Voevodsky Institute of Chemical Kinetics and Combustion, Novosibirsk, 630090, Russia Novosibirsk State University, Novosibirsk, 630090, Russia Udmurt Federal Research Center, Izhevsk, 426067, Russia d University of Science and Technology of China, State Key Laboratory of Fire Science, Hefei, 230026, PR China b c
A R T I C L E I N F O
A B S T R A C T
Keywords: Flame spread Heat fluxes Polymer Polyoxymethylene Numerical simulation Probing mass spectrometry Micro thermocouple Flame structure Flammability Polymer pyrolysis kinetics
A comprehensive study of thermal decomposition and combustion of a horizontally placed polyoxymethylene (POM) slab was performed. The kinetic parameters of thermal degradation of POM in supposition of two parallel reactions were determined and were used for simulation of the flame spread over the POM. The following main characteristics of the POM slab’s combustion were measured: the flame spread rate, the slab’s mass loss rate, the width of the pyrolysis zone, the flame height, the temperature profile of the upper and lower surfaces of the slab, the temperature field and the fields of the main flame species concentrations over the burning slab, and the conductive heat flux from the flame onto the fuel surface. It was concluded from analysis of experimental data that two global gas phase reactions may be identified: the reaction of formaldehyde pyrolysis with light combustible gas formed (with the properties close to those of СО) and the subsequent reaction of its oxidation in the flame to the end combustion products (СО2þH2O). This approach was implemented as the coupled com bustion model was modified, taking into account a two-step reaction in the gas phase. The results of the cal culations made showed good agreement with the experimental data.
1. Introduction Polymers find extensive applications in the day-to-day life owing to their low production costs and unique properties, such as corrosion resistance, a low friction coefficient, low density, very low electrical and thermal conductivity, and high modulus-to-weight ratios, to name just a few [1,2]. Important characteristics of polymers determining their application in various areas are their flammability and thermal stability. Therefore, the study of the kinetics and of the mechanism of thermal decomposition and combustion of polymers is essential. Many studies are devoted to this issue. Combustion of polymers is a diffusion process, which includes their pyrolysis, with volatile and non-volatile (char) products formed, followed by diffusion combustion of the volatile combustion products and by oxidation of char. To study the kinetics of polymer pyrolysis, thermal analysis methods are used. The method of linear pyrolysis of polymers in air counterflow [3–5] was applied to obtain data on the kinetics of polymer degradation under combustion conditions and to compare these data with bulk-pyrolysis data for the
same polymers. McAlevy et al. [6], and Blazowski et al. [4] reported the burning characteristics of polymethyl methacrylate (PMMA) impinged by an O2–N2 mixture gas jet; the burning surface temperature was measured with a thermocouple and an optical detector. Ishihara et al. [7, 8] applied the same method to measure the polymer regression rate. The activation energies of PMMA degradation measured in these works vary within 90–1000 kJ/mol. Korobeinichev et al. [9], Seshadri and Williams [10] used this method to study the structure of the polyethylene and PMMA flame. Holve and Sawyerе [3] used this approach to measure the Spalding mass transfer number B, which characterizes intensity of the heat and mass exchange at diffusion combustion of polymers and which is an important characteristic for evaluating the degree of polymer flamma bility. Beckel and Matthews [11] applied this method to investigate the main parameters of ignition of polyoxymethylene (POM), depending on the intensity of the heater radiation and the composition and the oxidant flux rate. The flame structure of trioxane in air counterflow was studied by numeric simulation using a detailed kinetic mechanism [12]. The
* Corresponding author. E-mail address: [email protected] (O. Korobeinichev). https://doi.org/10.1016/j.firesaf.2019.102924 Received 12 July 2019; Received in revised form 13 November 2019; Accepted 22 November 2019 Available online 6 December 2019 0379-7112/© 2019 Elsevier Ltd. All rights reserved.
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Fig. 1. Configuration of the experimental setup.
flame structure of POM Aldrich in air counterflow was studied in Ref. [13] experimentally and by numerical modeling also using a detailed kinetic mechanism. The ignition time and the flame spread rate are important characteristics determining the polymer flammability. The study of the mechanism of flame spread over polymers, the flame spread rate, and the ignition time have been the subject of numerous experimental and theoretical studies [14–18]. Polyoxymethylene OH[–CH2O–]nH is one of the most commonly used polymers. Such properties of this polymer as elasticity, rigidity, cracking strength, chemical resistance to organic solvents and many others ensure its application in machine-building and electrical engi neering. Flammability of POM, as well as of a number of other polymers, is an essential disadvantage. Formation of a formaldehyde monomer during degradation and combustion of POM makes its a convenient model object for studying the mechanism of polymer combustion. Formaldehyde is a poisonous gas with a low molecular weight. There fore, special attention should be paid to reduction of flammability of POM. Formaldehyde is one of the intermediate species formed in the process of combustion of many organic substances [19–22], and the mechanism of its combustion is well studied. POM is one of the most difficult polymers in terms of reducing its flammability [23], as it is characterized by the relatively low ignition temperature (~400� С) and by a low oxygen index, 15%, compared to most polymers (~18%) [23]. A detailed study of thermal decomposition and combustion of POM is of great interest from the practical and fundamental viewpoints. There are many papers in literature devoted to its thermal decomposition [23–31]. The maximum rate of thermal decomposition of different modifications of POM in a flow of nitrogen at the heating rate of ~1 K/min is observed at temperatures from 200 to 320� С [27], at 20 K/min – from 330 to 380� С [23,29,31]. Decomposition of three different modifications of POM in Ref. [27] occurred in two phases, whereas in Refs. [23,30,31] only one evident phase was observed at decomposition of POM. According to Refs. [29–31], the activation energy of the thermal decomposition reaction in inert media of different modifications of POM differs significantly: 121, 159, and 381 kJ/mol. This is related to the fact that, depending on the method of POM production, POM has essentially different physical and chemical properties, which affects the kinetics of the thermal decomposition reaction and the burning rate. These differ ences suggest the challenges connected with comparison of the results of thermal degradation and combustion of POM samples obtained by different researchers. Therefore, the study of thermal decomposition and combustion of the same POM samples is of special interest. Despite the large number of studies of flame propagation over
polymers [14–18], there is only one experimental study of flame spread over POM Delrin [16]. In it, data were first obtained on the flame spread rate, temperature and species concentration fields. This study is devoted to investigation of the kinetics of thermal decomposition of POM Delrin and horizontal flame spread over it, as well numerical simulation of these processes. 2. Experimental 2.1. Materials Polyoxymethylene (POM) slabs (100 � 200 � 5 mm in size, with the density of 1380 kg/m3) were manufactured out of POM homopolymer granules DuPont Delrin 100T (USA) by the hot pressing method at the pressure of 100 atm and at the temperature of 170� С. The melting point of Delrin 100T is 178� С at the heating rate of 10 K/min [32]. The DSC (differential scanning calorimetry) results showed the melting point of the POM slab to be 166� С at the heating rate of 10 K/min in the flow of helium. The number average molecular weight and the weight-average molecular weight for Delrin 100T were approximately 70000 and 140000 g/mol, respectively [33]. 2.2. Experimental methods 2.2.1. Thermogravimetric analysis Thermal degradation of POM was investigated by the method of thermogravimetric analysis (TGA) using a synchronous TG/DSC analyzer Netzsch STA 409 PC. Fragments taken from different parts of the POM slab were crushed to the condition of powder, placed into an aluminum cap and heated in a flow of helium (27 cm3/min under normal conditions) from 30 to 550� С at the heating rates of 30 and 50 K/ min. The sample mass was 2–3 mg. 2.2.2. The mass spectrometric and thermocouple methods The study of the flame spreading over the surface of a horizontally placed POM slab was conducted by the mass spectrometric and micro thermocouple methods. Shown in Fig. 1 is configuration of the experi mental setup. POM slabs 200х100х5 mm in size were placed into a thin steel frame serving to prevent flame spread over the side surfaces, fixated to an insulation board 10 mm thick, which was positioned on an electronic balance placed on a movable platform. The specific heat and thermal conductivity of the insulation board were, respectively, 950 J/ (kg⋅m⋅K) and 0.15W/(m⋅K). Horizontal marks were made on the 2
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specimen’s surface with a 5 mm step to determine the spread rate of the flame over the slab. A video camera was used to monitor the specimen’s burning. A signal from the balance was transferred to the analogue-todigital converter ADC E 14-140-M. The first-centimeter of POM surface was ignited with a gas burner. To prevent flame spread across the entire slab, a fire-proof plate was placed onto the specimen, which was instrumental in forming a homogeneous flame front across the entire width of the slab. After visual control of the homogeneity of the flame front, the plate was removed, and the flame spread over the POM surface began. Scanning of the flame started after the combustion regime for the slab was stabilized, this moment was determined in the previous experiments. In the stationary regime of combustion, the slab’s mass loss rate did not change with the time, and the flame propagation rates of the flame front and flame rear were equal. The ignition of the POM slab and the scanning of the POM slab’s flame is shown in Video 1 (online version only). Supplementary video related to this article can be found at https:// doi.org/10.1016/j.firesaf.2019.102924. The chemical structure of the flame was investigated using micro probe mass spectrometry on the basis of a quadrupole mass spectrometer Hiden HPR 60 with a three-step pumping system. Probe sampling was carried out with a quartz microprobe with the aperture diameter of 55 � 7 μm, the internal angle of 20� and wall thickness near the aperture equal to 0.14 mm. The sample from the microprobe entered the inlet system of the mass spectrometer as a molecular flow through a poly ethylene tube 1.5 m long with the internal diameter of 4 mm. The measured ions intensities were recalculated to the species mole fractions using calibration tests. The mole fraction accuracy for all the flame compounds was ~15%, but for water it was ~20%. The thermal flame structure was studied with a Pt–Ptþ10%Rh thermocouple, made of wire 50 μm thick (Appendix A). The junction diameter was 70 � 10 μm. The temperature measurement accuracy was �50� С. The signal from the thermocouple was recorded by the ADC E 14-140-M. The probe or the thermocouple were moved by the computer oper ated 3D positioning device. Fig. 1 demonstrates the movement trajectory of the probe/thermocouple. Before the start of scanning, the probe and the thermocouple were at the distance of 10 mm from the flame front and at the distance of 25 mm (the thermocouple) and 35 mm (the probe) from the specimen’s surface. The characteristic dimensions of the flame were determined from the previous experiments: along the horizontal axis (~65 mm) and along the vertical axis (~35 mm). The probe/ther mocouple was descended to the level of the polymer surface at the rate of 0.5/2 mm/s. In the experiments on the study of the thermal structure of the flame, the movable platform stood still, and the thermocouple moved up and down at a fixed distance from the slab’s edge. Thus, the thermocouple scanned the flame which was spreading over the slab’s surface. As the polymer burnt, the thermocouple went further down to the distance required for the contact with the slab’s surface in accor dance with the movement code prescribed. The surface shape required for that was achieved after extinguishing the burning polymer during the preliminary experiments. To raise the resolution capacity in the experiments on the study of the chemical structure of flame, the movable platform with the specimen was moved at the velocity of (~0.08 mm/s), close to the flame spread rate, but in the opposite direction. Thus, flame stabilization was achieved in space, which allowed us to scan the chemical flame structure. To measure the temperature near the surfaces of the burning slab in the condensed phase (~0.2 mm) on the upper and lower surfaces of the POM slab at the distance of 50 mm from the ignition place, grooves were made 0.2–0.3 mm deep, 0.3–0.4 mm wide and 10 mm long. In them, Pt–Ptþ10%Rh thermocouples were placed, made of wire 50 μm in diameter, with the junction 80 μm in diameter. The thermocouples were welded on the specimen’s surface by heating. The signal from all the thermocouples was recorded by the ADC E 14-140-M.
3. Numerical The mathematical formulation is primarily based on the model [18] developed for the flame spread over horizontal surface of polymeric fuel, which is generally employed for such process (e.g. Refs. [34,35]). Regarding the chemical aspect of this model, one-step reactions are considered both for the solid fuel pyrolysis and gas-phase combustion. As shown below, kinetic parameters of two-step reaction for POM py rolysis has been established experimentally with better understanding of physics of process. Also, the comparison of experimental and numerical results of downward flame spread over PMMA surface [17] has shown the disagreement for the profiles of flame temperature: it has been found that predicted position of the maximal flame temperature stands noticeably closer to the solid fuel’s burning surface than the measured one. Experiments show that gaseous pyrolysis products of various polymers (such as polymethylmethacrylate [17], polystyrene [36], polyoxymethylene [13]) decompose into low-weight combustible gases. Thus, at least two-step reaction is expected to occur in the gas-phase. Such a model employing two-step reaction for the gas-phase combus tion has been developed [37] and tested on the downward flame spread over PMMA surface showing better agreement between predicted and measured temperature profiles. Following these premises the governing equations are as follows. For the gas phase [18,37]:
∂ρ ∂ρuj ¼ 0; þ ∂t ∂xj ρ
∂ui ∂ui þ ρuj ¼ ∂t ∂xj
ρC
(1)
∂p ∂ ∂ui þ μ þ ðρa ∂xi ∂xj ∂xj
∂T ∂T ∂ ∂T ¼ λ þ ρW1 Q1 þ ρW2 Q2 þ ρuj C ∂t ∂xj ∂xj ∂xj
ρ
∂YF1 ∂YF1 ∂ ∂Y ¼ ρD F1 þ ρuj ∂xj ∂t ∂xj ∂xj
ρ
∂YF2 ∂YF2 ∂ ∂Y ¼ ρD F2 þ ρW1 þ ρuj ∂xj ∂t ∂xj ∂xj
ρ
∂YO ∂YO ∂ ∂Y ¼ ρD O þ ρu j ∂t ∂xj ∂xj ∂xj
ρ
∂YP ∂YP ∂ ∂YP ¼ ρD þ ðνF þ νO ÞρW2 þ ρu j ∂t ∂xj ∂xj ∂xj
ρi ¼
(2)
ρÞgi ; ∂qrj ; ∂xj
(3) (4)
ρW1
νF ρW2
νO ρW2
pMi R0 T
(5) (6) (7) (8)
Here xi ¼ fx; yg, ui ¼ fu; vg, gi ¼ fg; 0g, Yi ¼ fYF1 ; YF2 ; YO ; YP g, Mi ¼ fMF1 ; MF2 ; MO ; MP g, ρi ¼ fρF1 ; ρF2 ; ρO ; ρP g, Two-step gas-phase reactions scheme is considered as follows [37]: (9)
F1→F2
νF F2 þ νO O þ I→νP P þ I
(10)
where F1 ¼ CH2O, F2 ¼ gaseous fuel, oxidizer O ¼ O2, product P ¼ CO2þH2O, inert component I ¼ N2, YI ¼ 1 YF1 YF2 YO YP . Gasphase reactions rates are expressed as W1 ¼ k1 YF1 expð W2 ¼ k2 YF2 YO expð
E1 = R0 TÞ E2 = R0 TÞ
(11) (12)
Heat transfer in solid fuel is described by two-dimensional elliptic equation:
ρs C s 3
∂Ts ∂ ∂Ts þ ρs Qs ðη1 Ws1 þ η2 Ws2 Þ ¼ λ ∂t ∂xj s ∂xj
(13)
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Table 1 Kinetic parameters of thermal degradation of POM. Es1 , kJ/ mol
Es2 , kJ/ mol
lg(ks1 ), [ks1 ] ¼ 1/s
lg(ks2 ), [ks2 ] ¼ 1/s
n1
n2
с1 a
Φa
251,3
208,0
17,6
15,7
0,54
2,09
0,25
0,02
a
с1 is the fraction of the first pseudo component, Φis the deviation parameter (Appendix B).
Fig. 3. Solid fuel temperature distribution along the burning surface; solid curves – experimental temperature, dashed curves – calculated temperature.
4. Results and discussion 4.1. Thermal degradation Dots in Fig. 2 represent the dependences obtained from the TGA experiments between the conversion degree αðTÞ ¼ ðm0 mðTÞÞ=ðm0 mfin Þ and the rate of the thermal degradation reaction dαðTÞ=dt on temperature Т, where m0 is the initial mass, mðTÞ is the mass at temperature Т, mfin is the final mass. Reproducibility of the reaction rate was �5%, and the temperature of the maximum reaction rate was reproduced with the accuracy �3 K. It can be seen from Fig. 2 that thermal degradation of POM occurs in two stages: the first peak of the thermal degradation rate is observed in the temperature range from 270 to 390� С, and the second one takes place from 390 to 460� С. The kinetic parameters of the thermal degradation reaction were obtained by optimizing the experimental reaction rates using the MATLAB genetic algorithm optimization tool [13,40,41] in supposition of two parallel degradation reactions of two pseudocomponents of the polymer. The optimization details are described in Appendix B. The kinetic parameters obtained as a result of optimization with minimum deviation from the experiment are shown in Table 1 and the reaction rates corresponding to them are shown in Fig. 2. It can be seen from Fig. 2 that the calculated reaction rates are in satisfactory agreement with the experiment. The kinetic parameters obtained were used in developing a coupled model of flame propagation over a POM slab.
Fig. 2. The conversion degree and reaction rate of POM degradation versus temperature (helium, 30 and 50 K/min).
Two-step pyrolysis reaction is considered as � Wsk ¼ ð1 αk Þnk ksk expð Esk R0 Ts Þ as:
(14)
For non-zero pyrolysis reaction order conversion degree is expressed
∂αk ¼ Wsk ∂t
(15)
Here k ¼ f1; 2g. The surface regression rate for each cross-section normal to the burning surface is expressed as Z Ls ðxÞ vs ðxÞ ¼ ðη1 Ws1 þ η2 Ws2 Þdy (16) 0
where Ls ðx; tÞ ¼ Ls;0
Z 0
t
vs ðxÞ dt is the variable thickness decreasing in
time due to burnout. Notations of symbols used above are generally accepted [18]. Boundary conditions for Eqs. (1)–(7), (13) have conventional form (e.g. Ref. [18]). The physical properties of solid fuel (POM) are: specific heat Cs ¼ 1:11 þ 0:00811T J/(g∙� C) for T < Tm and Cs ¼ 1:34 þ 0:00275T J/(g∙� C) for T > Tm [38], thermal conductivity λs ¼ 0:292 W/(m∙K) for T < Tm and λs ¼ 0:07 W/(m∙K) for T > Tm [11], where Tm ¼ 165 � C is the melting temperature [38], density ρs ¼ 1380 kg/m3, heat of gasifi cation Qs ¼ 2:68 MJ/kg [38]. Pyrolysis kinetic parameters are deter mined below (Table 1). The monomer CH2O is assigned as the pyrolysis product of POM. The second step of gas-phase reaction (combustion of low-weight gas) have the following kinetic parameters: E2 ¼ 90 kJ/mol (e.g. Refs. [17,18,34]), preexponential factor has been determined to match experimental flame spread rate, which resulted in k2 ¼ 1.0∙1010 1/s. Heat of combustion Q2 ¼ 16 MJ/kg. Kinetic parameters of formal dehyde decomposition are obtained through the comparison of detailed and two step mechanisms of POM combustion in counterflow calculated using the Cantera code [39], which resulted in following values: E1 ¼ 190 kJ/mol, k1 ¼ 5.88∙1011 1/s. Heat of CH2O decomposition Q1 ¼ 0:16 MJ/kg.
4.2. The flame spread rate and the temperature of the surface of a horizontally placed POM slab For combustion of polymer slabs, two types of the burning rates are normally identified: the moving rate of the flame front (the linear ve locity) and the mass loss rate (the mass velocity for slabs of the given width and thickness). In the course of the experiment, the linear velocity of the flame reached the constant value equal to 0.077 � 0.002 mm/s at the 6th minute of the experiment, when the flame front was at the dis tance of ~30 mm from the edge of the specimen. The mass velocity of burning reached the stationary value equal to 0.053 � 0.003 g/s 13 min after the start of the experiment, when the flame front was at the dis tance of ~60 mm from the edge of the specimen. The width of the py rolysis zone was 65 mm. In the experiment, dependence of temperature near the slab surfaces on time was measured with a thermocouple, when was then converted into dependence of temperature on the distance from the flame front considering the velocity of the flame front propagation. The measured temperature profiles in the condensed phase are shown in Fig. 3. The temperature under the flame front near the upper surface of the spec imen was 450� С, and the temperature near the lower surface of the slab was found to be 80� С. At the distance from 4 to 3.5 mm before the flame 4
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chemical flame structure, signal intensities were measured, corre sponding to the following ratios of the ion masses to their charge number (m/z): 2(H2), 14(N – fragment of N2), 18(H2O), 28(N2 and CO), 29 (CH2O), 32(O2), 44(CO2). Based on the intensities measured, the mole fractions and the species concentration fields (of mole fractions) of H2, H2O, N2, CO, CO2, O2 and CH2O, presented in Fig. 6, were calculated. No oxygen was found at the distance from 0 to 50 mm from the flame front near the POM surface, indicating that in this region thermal decomposition of POM proceeds in inert medium. For this reason, the kinetic parameters of thermal degradation of POM in inert medium were used for the coupled model in this study. The maximum mole fraction of formaldehyde was observed at the height up to 3 mm over the POM surface at the distance from 10 to 40 mm from the flame front. In this region, the mole fraction of СО reached the values of 0.15–0.2 at the distance of 5–8 mm from the slab’s surface. The maximum concentration of CO2 was observed at the height from 0 to 15 mm above the surface at the distance from 0 to 30 mm from the flame front. The mole fractions of CO2 and H2O decreased to 0 together with the increase of the mole fraction of oxygen near the flame boundary. Thus, analysis of the spatial distribution of the main species of the flame showed that in combustion of POM near the polymer surface, consumption of formaldehyde takes place, with СО and H2 formed, which are later oxidized to become CO2 and H2O. Analysis of the reaction pathways of the diffusion flame of formaldehyde indicates the same [13]. For this reason, a two-stage global reaction in the gas phase was used in this work, as contrasted to the one-stage global gas phase reaction, common for the flame spread on polymers.
Table 2 Macroscopic parameters of flame spread.
Experiment Prediction
Flame spread rate uf , mm/s
_ Mass burning rate m, g/s
Pyrolysis zone length Lp , mm
0.077 0.065
0.053 0.059
65 58
front, the temperature of the flame front near the upper surface varied from 55 to 70� С, with the heating rate varying within 0.5–5 K/s. The maximum heating rate of the upper surface near the flame front proved to be ~20 K/s. Table 2 presents the macroscopic characteristics of flame spread process showing a reasonable agreement between calculations and measurements. 4.3. The thermal flame structure of a horizontally placed POM slab Shown in Fig. 4 is a two-dimensional field of flame temperatures of a horizontally placed POM slab’s flame in still air. In the process of combustion of this slab, we observed melting of the polymer, with boiling melt formed in the pyrolysis zone. The maximum flame tem perature was 1650� С considering the radiation correction: it was observed near the rear flame front. The width of the pyrolysis zone was ~65 mm, and the flame height was ~35 mm. Fig. 5 presents the temperature profiles in the flame. It can be noted that one-step reaction in the gas phase showed poor agreement with the measurements (left plot), while proposed two-step mechanism provides noticeably better distribution of calculated temperature (right plot), especially concerning the position of maximal temperature in flame.
4.5. Heat flux onto the burning surface The conductive heat flux from the flame onto the surface of the POM slab was calculated from the temperature gradient in the gas phase near the polymer surface according to the formula:
4.4. The chemical flame structure of a horizontally placed POM slab During the mass-spectrometric experiments on the study of the
Fig. 4. Two-dimensional temperature field of the POM slab’s flame.
Fig. 5. Temperature profiles in the flame. Number of curve corresponds to distance from the flame front (in mm). Solid lines – calculation, dashed lines – experiment. Left: one-step gas phase reaction; right: two-step gas phase reaction. 5
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Fig. 6. Two-dimensional main species concentration fields of the POM slab’s flame.
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Fig. 7. Conductive heat flux (left) and estimation of radiative heat flux (right) from the flame onto the surface of the POM slab; Exp. – experiment, Calc. – calculations.
q¼λ
∂T ∂y
width of the pyrolysis zone, the flame height, the temperature profile of the upper and lower surfaces of the slab, the temperature field and the fields of the main flame species concentrations over the burning slab, the conductive heat flux from the flame onto the fuel surface. The following species were detected in the POM flame: H2, H2O, N2, CO, CO2, O2 and CH2O. It was concluded from analysis of the spatial distribution of the main flame species that in combustion of POM at least two global re actions in the gas phase may be identified: the reaction of formaldehyde pyrolysis in the absence of oxygen with light combustible gas formed (with the properties close to those of СО) and the subsequent reaction of its oxidation in the flame to the end combustion products (СО2þH2O). This approach was implemented as the couple combustion model was modified, taking into account a two-step reaction in the gas phase. The results of the calculations made showed good agreement with the experimental data for macroscopic parameters, as well as much better agreement for the temperature profiles in flame compared to the onestep gas-phase reaction.
(17)
where ∂T=∂y– is the maximum temperature gradient in the gas phase near the slab surface, calculated by the experimentally measured tem P P perature profiles, λ ¼ 0:5ð λi Xi þ ð Xi =λi Þ 1 Þ– is the thermal con ductivity of the gas mixture [42], λi ¼ λi ðTÞ is the thermal conductivity of the i-th gas mixture component [43], Xi is the mass fraction of the i-th gas mixture component near the slab surface, recalculated from the experimental mole fraction. The heat flux distribution along the burning surface presented in Fig. 7 (left) showed the reasonable agreement between predictions and measurements. The maximum heat flux was observed near the flame front, where flame is most close to the surface, resulting in the highest temperature growth at the shortest distance from the polymer specimen. The estimation of radiative heat flux showed its maximal value of order 3 kW/m2 (Fig. 7), occurring at the distance of around 40 mm from the flame front, where the flame has a large size as shown in Fig. 4.
Declarations of interest
5. Conclusion
None.
A comprehensive study of thermal decomposition and combustion of a horizontally placed polyoxymethylene (POM) slab was performed. The kinetic parameters of thermal degradation of POM in inert medium in supposition of two parallel reactions were determined. The kinetic pa rameters obtained were used to develop a coupled model and to make calculations for the flame spread over the POM. The following main characteristics of the POM slab’s combustion in the stationary mode were measured: the flame spread rate, the slab’s mass loss rate, the
Acknowledgments This work was supported by the RFBR under Grants #19-58-53016 and by the NNSF of China under Grant 51120165001. The authors acknowledge the utility of the Multi-Access Chemical Service Center SB RAS in the spectral and analytical measurements made. The authors are thankful to Dr. I. Shundrina for TGA and DSC measurements.
Appendix A. Configuration of the gas-phase thermocouple The thermal flame structure was studied using a Pt–Ptþ10%Rh thermocouple, made of wire 50 μm thick, shown in Fig. A1. The junction diameter was 70 � 10 μm, the thermocouple’s arm was 5.5 mm. The thermocouple’s arms were welded to the Pt and Ptþ10%Rh wires 0.2 mm in diameter. The wires were placed into quartz capillaries 0.7 mm in diameter, inserted into a ceramic tube 3 mm in diameter and 70 mm long. The length of the external parts of the capillaries was 40 mm. The thermocouple was coated with a SiO2 layer to prevent catalytic reactions on the thermocouple’s surface. Correction for the heat loss by the thermocouple due to radiation was calculated by Kaskan’s formula [44].
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Fig. A.1. Configuration of the gas-phase thermocouple.
Appendix B The kinetic parameters of the thermal decomposition reaction were obtained by optimizing the experimental reaction rates using the MATLAB genetic algorithm optimization tool [13,40,41] in supposition of two parallel decomposition reactions of two pseudo components of the polymer. The rate of each reaction with the known activation energy Es , preexponential factor ks and reaction order n in supposition of the power conversion function fðαÞ may be presented as [13,45]. 2 31 n n � � Es dα 1 dα ks REsT ks REsT ks REsT 6 ks R0 T 2 2R0 T 7 n (B.1) 1 e R0 T 5 ¼ ¼ e 0 f ðαÞ ¼ e 0 ð1 αÞ ¼ e 0 41 ð1 nÞ Es dT β dt β β β βEs
where α ¼ mm∞0
m m0
is the conversion degree, T is the temperature, β is the heating rate, t is time, R0 is the universal gas constant, n 6¼ 1.
Then the kinetic parameters of thermal decomposition may be determined by the highest degree of matching between the experimental reaction rate and the modeled general reaction rate: d αΣ dα1 d α2 ¼ с1 þ с2 dT dT dT
(B.2)
where с1 is the fraction of the first pseudo component, с2 ¼ 1 с1 is the fraction of the second pseudo component. To raise the accuracy, the calculated reaction rate was compared to the experimental reaction rate for two heating rates. As the value charac terizing the degree of matching of the experimental and modeled reaction rates for the heating rate β, a dimensionless parameter based on the squared differences was used [41]. � �β;calc �2 �� � P dα β;exp dαΣ Φβ ¼
i
P
dT
dα dT
i
where
dT
i
�� �β;exp
dα dT
i
dα dT
i
� �β;exp
(B.3)
i
� �β;average �2
� is the experimental reaction rate at the i-th temperature for the heating rate β,
temperature for the heating rate β,
� �β;average dα dT
dαΣ dT
�β;calc i
is the calculated reaction rate at the i-th
is the average experimental reaction rate for the heating rate β.
In the process of optimization, the calculated and experimental reaction rates were simultaneously compared for two heating rates using one parameter Φ¼
� 1 30 Φ þ Φ50 2
(B.4)
where Φ30 is the deviation at the heating rate of 30 K/min, Φ50 is the deviation at the heating rate of 50 K/min. To raise the degree of accuracy, 10 independent genetic algorithm optimization calculations were carried out followed by the selection of the result with the smallest deviation.
8
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References
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9
Contents lists available at ScienceDirect
Fire Safety Journal journal homepage: http://www.elsevier.com/locate/firesaf
An experimental study and numerical simulation of horizontal flame spread over polyoxymethylene in still air O. Korobeinichev a, *, R. Glaznev a, b, A. Karpov c, A. Shaklein c, A. Shmakov a, b, A. Paletsky a, S. Trubachev a, b, Y. Hu d, X. Wang d, W. Hu d a
Voevodsky Institute of Chemical Kinetics and Combustion, Novosibirsk, 630090, Russia Novosibirsk State University, Novosibirsk, 630090, Russia Udmurt Federal Research Center, Izhevsk, 426067, Russia d University of Science and Technology of China, State Key Laboratory of Fire Science, Hefei, 230026, PR China b c
A R T I C L E I N F O
A B S T R A C T
Keywords: Flame spread Heat fluxes Polymer Polyoxymethylene Numerical simulation Probing mass spectrometry Micro thermocouple Flame structure Flammability Polymer pyrolysis kinetics
A comprehensive study of thermal decomposition and combustion of a horizontally placed polyoxymethylene (POM) slab was performed. The kinetic parameters of thermal degradation of POM in supposition of two parallel reactions were determined and were used for simulation of the flame spread over the POM. The following main characteristics of the POM slab’s combustion were measured: the flame spread rate, the slab’s mass loss rate, the width of the pyrolysis zone, the flame height, the temperature profile of the upper and lower surfaces of the slab, the temperature field and the fields of the main flame species concentrations over the burning slab, and the conductive heat flux from the flame onto the fuel surface. It was concluded from analysis of experimental data that two global gas phase reactions may be identified: the reaction of formaldehyde pyrolysis with light combustible gas formed (with the properties close to those of СО) and the subsequent reaction of its oxidation in the flame to the end combustion products (СО2þH2O). This approach was implemented as the coupled com bustion model was modified, taking into account a two-step reaction in the gas phase. The results of the cal culations made showed good agreement with the experimental data.
1. Introduction Polymers find extensive applications in the day-to-day life owing to their low production costs and unique properties, such as corrosion resistance, a low friction coefficient, low density, very low electrical and thermal conductivity, and high modulus-to-weight ratios, to name just a few [1,2]. Important characteristics of polymers determining their application in various areas are their flammability and thermal stability. Therefore, the study of the kinetics and of the mechanism of thermal decomposition and combustion of polymers is essential. Many studies are devoted to this issue. Combustion of polymers is a diffusion process, which includes their pyrolysis, with volatile and non-volatile (char) products formed, followed by diffusion combustion of the volatile combustion products and by oxidation of char. To study the kinetics of polymer pyrolysis, thermal analysis methods are used. The method of linear pyrolysis of polymers in air counterflow [3–5] was applied to obtain data on the kinetics of polymer degradation under combustion conditions and to compare these data with bulk-pyrolysis data for the
same polymers. McAlevy et al. [6], and Blazowski et al. [4] reported the burning characteristics of polymethyl methacrylate (PMMA) impinged by an O2–N2 mixture gas jet; the burning surface temperature was measured with a thermocouple and an optical detector. Ishihara et al. [7, 8] applied the same method to measure the polymer regression rate. The activation energies of PMMA degradation measured in these works vary within 90–1000 kJ/mol. Korobeinichev et al. [9], Seshadri and Williams [10] used this method to study the structure of the polyethylene and PMMA flame. Holve and Sawyerе [3] used this approach to measure the Spalding mass transfer number B, which characterizes intensity of the heat and mass exchange at diffusion combustion of polymers and which is an important characteristic for evaluating the degree of polymer flamma bility. Beckel and Matthews [11] applied this method to investigate the main parameters of ignition of polyoxymethylene (POM), depending on the intensity of the heater radiation and the composition and the oxidant flux rate. The flame structure of trioxane in air counterflow was studied by numeric simulation using a detailed kinetic mechanism [12]. The
* Corresponding author. E-mail address: [email protected] (O. Korobeinichev). https://doi.org/10.1016/j.firesaf.2019.102924 Received 12 July 2019; Received in revised form 13 November 2019; Accepted 22 November 2019 Available online 6 December 2019 0379-7112/© 2019 Elsevier Ltd. All rights reserved.
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Fig. 1. Configuration of the experimental setup.
flame structure of POM Aldrich in air counterflow was studied in Ref. [13] experimentally and by numerical modeling also using a detailed kinetic mechanism. The ignition time and the flame spread rate are important characteristics determining the polymer flammability. The study of the mechanism of flame spread over polymers, the flame spread rate, and the ignition time have been the subject of numerous experimental and theoretical studies [14–18]. Polyoxymethylene OH[–CH2O–]nH is one of the most commonly used polymers. Such properties of this polymer as elasticity, rigidity, cracking strength, chemical resistance to organic solvents and many others ensure its application in machine-building and electrical engi neering. Flammability of POM, as well as of a number of other polymers, is an essential disadvantage. Formation of a formaldehyde monomer during degradation and combustion of POM makes its a convenient model object for studying the mechanism of polymer combustion. Formaldehyde is a poisonous gas with a low molecular weight. There fore, special attention should be paid to reduction of flammability of POM. Formaldehyde is one of the intermediate species formed in the process of combustion of many organic substances [19–22], and the mechanism of its combustion is well studied. POM is one of the most difficult polymers in terms of reducing its flammability [23], as it is characterized by the relatively low ignition temperature (~400� С) and by a low oxygen index, 15%, compared to most polymers (~18%) [23]. A detailed study of thermal decomposition and combustion of POM is of great interest from the practical and fundamental viewpoints. There are many papers in literature devoted to its thermal decomposition [23–31]. The maximum rate of thermal decomposition of different modifications of POM in a flow of nitrogen at the heating rate of ~1 K/min is observed at temperatures from 200 to 320� С [27], at 20 K/min – from 330 to 380� С [23,29,31]. Decomposition of three different modifications of POM in Ref. [27] occurred in two phases, whereas in Refs. [23,30,31] only one evident phase was observed at decomposition of POM. According to Refs. [29–31], the activation energy of the thermal decomposition reaction in inert media of different modifications of POM differs significantly: 121, 159, and 381 kJ/mol. This is related to the fact that, depending on the method of POM production, POM has essentially different physical and chemical properties, which affects the kinetics of the thermal decomposition reaction and the burning rate. These differ ences suggest the challenges connected with comparison of the results of thermal degradation and combustion of POM samples obtained by different researchers. Therefore, the study of thermal decomposition and combustion of the same POM samples is of special interest. Despite the large number of studies of flame propagation over
polymers [14–18], there is only one experimental study of flame spread over POM Delrin [16]. In it, data were first obtained on the flame spread rate, temperature and species concentration fields. This study is devoted to investigation of the kinetics of thermal decomposition of POM Delrin and horizontal flame spread over it, as well numerical simulation of these processes. 2. Experimental 2.1. Materials Polyoxymethylene (POM) slabs (100 � 200 � 5 mm in size, with the density of 1380 kg/m3) were manufactured out of POM homopolymer granules DuPont Delrin 100T (USA) by the hot pressing method at the pressure of 100 atm and at the temperature of 170� С. The melting point of Delrin 100T is 178� С at the heating rate of 10 K/min [32]. The DSC (differential scanning calorimetry) results showed the melting point of the POM slab to be 166� С at the heating rate of 10 K/min in the flow of helium. The number average molecular weight and the weight-average molecular weight for Delrin 100T were approximately 70000 and 140000 g/mol, respectively [33]. 2.2. Experimental methods 2.2.1. Thermogravimetric analysis Thermal degradation of POM was investigated by the method of thermogravimetric analysis (TGA) using a synchronous TG/DSC analyzer Netzsch STA 409 PC. Fragments taken from different parts of the POM slab were crushed to the condition of powder, placed into an aluminum cap and heated in a flow of helium (27 cm3/min under normal conditions) from 30 to 550� С at the heating rates of 30 and 50 K/ min. The sample mass was 2–3 mg. 2.2.2. The mass spectrometric and thermocouple methods The study of the flame spreading over the surface of a horizontally placed POM slab was conducted by the mass spectrometric and micro thermocouple methods. Shown in Fig. 1 is configuration of the experi mental setup. POM slabs 200х100х5 mm in size were placed into a thin steel frame serving to prevent flame spread over the side surfaces, fixated to an insulation board 10 mm thick, which was positioned on an electronic balance placed on a movable platform. The specific heat and thermal conductivity of the insulation board were, respectively, 950 J/ (kg⋅m⋅K) and 0.15W/(m⋅K). Horizontal marks were made on the 2
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specimen’s surface with a 5 mm step to determine the spread rate of the flame over the slab. A video camera was used to monitor the specimen’s burning. A signal from the balance was transferred to the analogue-todigital converter ADC E 14-140-M. The first-centimeter of POM surface was ignited with a gas burner. To prevent flame spread across the entire slab, a fire-proof plate was placed onto the specimen, which was instrumental in forming a homogeneous flame front across the entire width of the slab. After visual control of the homogeneity of the flame front, the plate was removed, and the flame spread over the POM surface began. Scanning of the flame started after the combustion regime for the slab was stabilized, this moment was determined in the previous experiments. In the stationary regime of combustion, the slab’s mass loss rate did not change with the time, and the flame propagation rates of the flame front and flame rear were equal. The ignition of the POM slab and the scanning of the POM slab’s flame is shown in Video 1 (online version only). Supplementary video related to this article can be found at https:// doi.org/10.1016/j.firesaf.2019.102924. The chemical structure of the flame was investigated using micro probe mass spectrometry on the basis of a quadrupole mass spectrometer Hiden HPR 60 with a three-step pumping system. Probe sampling was carried out with a quartz microprobe with the aperture diameter of 55 � 7 μm, the internal angle of 20� and wall thickness near the aperture equal to 0.14 mm. The sample from the microprobe entered the inlet system of the mass spectrometer as a molecular flow through a poly ethylene tube 1.5 m long with the internal diameter of 4 mm. The measured ions intensities were recalculated to the species mole fractions using calibration tests. The mole fraction accuracy for all the flame compounds was ~15%, but for water it was ~20%. The thermal flame structure was studied with a Pt–Ptþ10%Rh thermocouple, made of wire 50 μm thick (Appendix A). The junction diameter was 70 � 10 μm. The temperature measurement accuracy was �50� С. The signal from the thermocouple was recorded by the ADC E 14-140-M. The probe or the thermocouple were moved by the computer oper ated 3D positioning device. Fig. 1 demonstrates the movement trajectory of the probe/thermocouple. Before the start of scanning, the probe and the thermocouple were at the distance of 10 mm from the flame front and at the distance of 25 mm (the thermocouple) and 35 mm (the probe) from the specimen’s surface. The characteristic dimensions of the flame were determined from the previous experiments: along the horizontal axis (~65 mm) and along the vertical axis (~35 mm). The probe/ther mocouple was descended to the level of the polymer surface at the rate of 0.5/2 mm/s. In the experiments on the study of the thermal structure of the flame, the movable platform stood still, and the thermocouple moved up and down at a fixed distance from the slab’s edge. Thus, the thermocouple scanned the flame which was spreading over the slab’s surface. As the polymer burnt, the thermocouple went further down to the distance required for the contact with the slab’s surface in accor dance with the movement code prescribed. The surface shape required for that was achieved after extinguishing the burning polymer during the preliminary experiments. To raise the resolution capacity in the experiments on the study of the chemical structure of flame, the movable platform with the specimen was moved at the velocity of (~0.08 mm/s), close to the flame spread rate, but in the opposite direction. Thus, flame stabilization was achieved in space, which allowed us to scan the chemical flame structure. To measure the temperature near the surfaces of the burning slab in the condensed phase (~0.2 mm) on the upper and lower surfaces of the POM slab at the distance of 50 mm from the ignition place, grooves were made 0.2–0.3 mm deep, 0.3–0.4 mm wide and 10 mm long. In them, Pt–Ptþ10%Rh thermocouples were placed, made of wire 50 μm in diameter, with the junction 80 μm in diameter. The thermocouples were welded on the specimen’s surface by heating. The signal from all the thermocouples was recorded by the ADC E 14-140-M.
3. Numerical The mathematical formulation is primarily based on the model [18] developed for the flame spread over horizontal surface of polymeric fuel, which is generally employed for such process (e.g. Refs. [34,35]). Regarding the chemical aspect of this model, one-step reactions are considered both for the solid fuel pyrolysis and gas-phase combustion. As shown below, kinetic parameters of two-step reaction for POM py rolysis has been established experimentally with better understanding of physics of process. Also, the comparison of experimental and numerical results of downward flame spread over PMMA surface [17] has shown the disagreement for the profiles of flame temperature: it has been found that predicted position of the maximal flame temperature stands noticeably closer to the solid fuel’s burning surface than the measured one. Experiments show that gaseous pyrolysis products of various polymers (such as polymethylmethacrylate [17], polystyrene [36], polyoxymethylene [13]) decompose into low-weight combustible gases. Thus, at least two-step reaction is expected to occur in the gas-phase. Such a model employing two-step reaction for the gas-phase combus tion has been developed [37] and tested on the downward flame spread over PMMA surface showing better agreement between predicted and measured temperature profiles. Following these premises the governing equations are as follows. For the gas phase [18,37]:
∂ρ ∂ρuj ¼ 0; þ ∂t ∂xj ρ
∂ui ∂ui þ ρuj ¼ ∂t ∂xj
ρC
(1)
∂p ∂ ∂ui þ μ þ ðρa ∂xi ∂xj ∂xj
∂T ∂T ∂ ∂T ¼ λ þ ρW1 Q1 þ ρW2 Q2 þ ρuj C ∂t ∂xj ∂xj ∂xj
ρ
∂YF1 ∂YF1 ∂ ∂Y ¼ ρD F1 þ ρuj ∂xj ∂t ∂xj ∂xj
ρ
∂YF2 ∂YF2 ∂ ∂Y ¼ ρD F2 þ ρW1 þ ρuj ∂xj ∂t ∂xj ∂xj
ρ
∂YO ∂YO ∂ ∂Y ¼ ρD O þ ρu j ∂t ∂xj ∂xj ∂xj
ρ
∂YP ∂YP ∂ ∂YP ¼ ρD þ ðνF þ νO ÞρW2 þ ρu j ∂t ∂xj ∂xj ∂xj
ρi ¼
(2)
ρÞgi ; ∂qrj ; ∂xj
(3) (4)
ρW1
νF ρW2
νO ρW2
pMi R0 T
(5) (6) (7) (8)
Here xi ¼ fx; yg, ui ¼ fu; vg, gi ¼ fg; 0g, Yi ¼ fYF1 ; YF2 ; YO ; YP g, Mi ¼ fMF1 ; MF2 ; MO ; MP g, ρi ¼ fρF1 ; ρF2 ; ρO ; ρP g, Two-step gas-phase reactions scheme is considered as follows [37]: (9)
F1→F2
νF F2 þ νO O þ I→νP P þ I
(10)
where F1 ¼ CH2O, F2 ¼ gaseous fuel, oxidizer O ¼ O2, product P ¼ CO2þH2O, inert component I ¼ N2, YI ¼ 1 YF1 YF2 YO YP . Gasphase reactions rates are expressed as W1 ¼ k1 YF1 expð W2 ¼ k2 YF2 YO expð
E1 = R0 TÞ E2 = R0 TÞ
(11) (12)
Heat transfer in solid fuel is described by two-dimensional elliptic equation:
ρs C s 3
∂Ts ∂ ∂Ts þ ρs Qs ðη1 Ws1 þ η2 Ws2 Þ ¼ λ ∂t ∂xj s ∂xj
(13)
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Table 1 Kinetic parameters of thermal degradation of POM. Es1 , kJ/ mol
Es2 , kJ/ mol
lg(ks1 ), [ks1 ] ¼ 1/s
lg(ks2 ), [ks2 ] ¼ 1/s
n1
n2
с1 a
Φa
251,3
208,0
17,6
15,7
0,54
2,09
0,25
0,02
a
с1 is the fraction of the first pseudo component, Φis the deviation parameter (Appendix B).
Fig. 3. Solid fuel temperature distribution along the burning surface; solid curves – experimental temperature, dashed curves – calculated temperature.
4. Results and discussion 4.1. Thermal degradation Dots in Fig. 2 represent the dependences obtained from the TGA experiments between the conversion degree αðTÞ ¼ ðm0 mðTÞÞ=ðm0 mfin Þ and the rate of the thermal degradation reaction dαðTÞ=dt on temperature Т, where m0 is the initial mass, mðTÞ is the mass at temperature Т, mfin is the final mass. Reproducibility of the reaction rate was �5%, and the temperature of the maximum reaction rate was reproduced with the accuracy �3 K. It can be seen from Fig. 2 that thermal degradation of POM occurs in two stages: the first peak of the thermal degradation rate is observed in the temperature range from 270 to 390� С, and the second one takes place from 390 to 460� С. The kinetic parameters of the thermal degradation reaction were obtained by optimizing the experimental reaction rates using the MATLAB genetic algorithm optimization tool [13,40,41] in supposition of two parallel degradation reactions of two pseudocomponents of the polymer. The optimization details are described in Appendix B. The kinetic parameters obtained as a result of optimization with minimum deviation from the experiment are shown in Table 1 and the reaction rates corresponding to them are shown in Fig. 2. It can be seen from Fig. 2 that the calculated reaction rates are in satisfactory agreement with the experiment. The kinetic parameters obtained were used in developing a coupled model of flame propagation over a POM slab.
Fig. 2. The conversion degree and reaction rate of POM degradation versus temperature (helium, 30 and 50 K/min).
Two-step pyrolysis reaction is considered as � Wsk ¼ ð1 αk Þnk ksk expð Esk R0 Ts Þ as:
(14)
For non-zero pyrolysis reaction order conversion degree is expressed
∂αk ¼ Wsk ∂t
(15)
Here k ¼ f1; 2g. The surface regression rate for each cross-section normal to the burning surface is expressed as Z Ls ðxÞ vs ðxÞ ¼ ðη1 Ws1 þ η2 Ws2 Þdy (16) 0
where Ls ðx; tÞ ¼ Ls;0
Z 0
t
vs ðxÞ dt is the variable thickness decreasing in
time due to burnout. Notations of symbols used above are generally accepted [18]. Boundary conditions for Eqs. (1)–(7), (13) have conventional form (e.g. Ref. [18]). The physical properties of solid fuel (POM) are: specific heat Cs ¼ 1:11 þ 0:00811T J/(g∙� C) for T < Tm and Cs ¼ 1:34 þ 0:00275T J/(g∙� C) for T > Tm [38], thermal conductivity λs ¼ 0:292 W/(m∙K) for T < Tm and λs ¼ 0:07 W/(m∙K) for T > Tm [11], where Tm ¼ 165 � C is the melting temperature [38], density ρs ¼ 1380 kg/m3, heat of gasifi cation Qs ¼ 2:68 MJ/kg [38]. Pyrolysis kinetic parameters are deter mined below (Table 1). The monomer CH2O is assigned as the pyrolysis product of POM. The second step of gas-phase reaction (combustion of low-weight gas) have the following kinetic parameters: E2 ¼ 90 kJ/mol (e.g. Refs. [17,18,34]), preexponential factor has been determined to match experimental flame spread rate, which resulted in k2 ¼ 1.0∙1010 1/s. Heat of combustion Q2 ¼ 16 MJ/kg. Kinetic parameters of formal dehyde decomposition are obtained through the comparison of detailed and two step mechanisms of POM combustion in counterflow calculated using the Cantera code [39], which resulted in following values: E1 ¼ 190 kJ/mol, k1 ¼ 5.88∙1011 1/s. Heat of CH2O decomposition Q1 ¼ 0:16 MJ/kg.
4.2. The flame spread rate and the temperature of the surface of a horizontally placed POM slab For combustion of polymer slabs, two types of the burning rates are normally identified: the moving rate of the flame front (the linear ve locity) and the mass loss rate (the mass velocity for slabs of the given width and thickness). In the course of the experiment, the linear velocity of the flame reached the constant value equal to 0.077 � 0.002 mm/s at the 6th minute of the experiment, when the flame front was at the dis tance of ~30 mm from the edge of the specimen. The mass velocity of burning reached the stationary value equal to 0.053 � 0.003 g/s 13 min after the start of the experiment, when the flame front was at the dis tance of ~60 mm from the edge of the specimen. The width of the py rolysis zone was 65 mm. In the experiment, dependence of temperature near the slab surfaces on time was measured with a thermocouple, when was then converted into dependence of temperature on the distance from the flame front considering the velocity of the flame front propagation. The measured temperature profiles in the condensed phase are shown in Fig. 3. The temperature under the flame front near the upper surface of the spec imen was 450� С, and the temperature near the lower surface of the slab was found to be 80� С. At the distance from 4 to 3.5 mm before the flame 4
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chemical flame structure, signal intensities were measured, corre sponding to the following ratios of the ion masses to their charge number (m/z): 2(H2), 14(N – fragment of N2), 18(H2O), 28(N2 and CO), 29 (CH2O), 32(O2), 44(CO2). Based on the intensities measured, the mole fractions and the species concentration fields (of mole fractions) of H2, H2O, N2, CO, CO2, O2 and CH2O, presented in Fig. 6, were calculated. No oxygen was found at the distance from 0 to 50 mm from the flame front near the POM surface, indicating that in this region thermal decomposition of POM proceeds in inert medium. For this reason, the kinetic parameters of thermal degradation of POM in inert medium were used for the coupled model in this study. The maximum mole fraction of formaldehyde was observed at the height up to 3 mm over the POM surface at the distance from 10 to 40 mm from the flame front. In this region, the mole fraction of СО reached the values of 0.15–0.2 at the distance of 5–8 mm from the slab’s surface. The maximum concentration of CO2 was observed at the height from 0 to 15 mm above the surface at the distance from 0 to 30 mm from the flame front. The mole fractions of CO2 and H2O decreased to 0 together with the increase of the mole fraction of oxygen near the flame boundary. Thus, analysis of the spatial distribution of the main species of the flame showed that in combustion of POM near the polymer surface, consumption of formaldehyde takes place, with СО and H2 formed, which are later oxidized to become CO2 and H2O. Analysis of the reaction pathways of the diffusion flame of formaldehyde indicates the same [13]. For this reason, a two-stage global reaction in the gas phase was used in this work, as contrasted to the one-stage global gas phase reaction, common for the flame spread on polymers.
Table 2 Macroscopic parameters of flame spread.
Experiment Prediction
Flame spread rate uf , mm/s
_ Mass burning rate m, g/s
Pyrolysis zone length Lp , mm
0.077 0.065
0.053 0.059
65 58
front, the temperature of the flame front near the upper surface varied from 55 to 70� С, with the heating rate varying within 0.5–5 K/s. The maximum heating rate of the upper surface near the flame front proved to be ~20 K/s. Table 2 presents the macroscopic characteristics of flame spread process showing a reasonable agreement between calculations and measurements. 4.3. The thermal flame structure of a horizontally placed POM slab Shown in Fig. 4 is a two-dimensional field of flame temperatures of a horizontally placed POM slab’s flame in still air. In the process of combustion of this slab, we observed melting of the polymer, with boiling melt formed in the pyrolysis zone. The maximum flame tem perature was 1650� С considering the radiation correction: it was observed near the rear flame front. The width of the pyrolysis zone was ~65 mm, and the flame height was ~35 mm. Fig. 5 presents the temperature profiles in the flame. It can be noted that one-step reaction in the gas phase showed poor agreement with the measurements (left plot), while proposed two-step mechanism provides noticeably better distribution of calculated temperature (right plot), especially concerning the position of maximal temperature in flame.
4.5. Heat flux onto the burning surface The conductive heat flux from the flame onto the surface of the POM slab was calculated from the temperature gradient in the gas phase near the polymer surface according to the formula:
4.4. The chemical flame structure of a horizontally placed POM slab During the mass-spectrometric experiments on the study of the
Fig. 4. Two-dimensional temperature field of the POM slab’s flame.
Fig. 5. Temperature profiles in the flame. Number of curve corresponds to distance from the flame front (in mm). Solid lines – calculation, dashed lines – experiment. Left: one-step gas phase reaction; right: two-step gas phase reaction. 5
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Fig. 6. Two-dimensional main species concentration fields of the POM slab’s flame.
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Fig. 7. Conductive heat flux (left) and estimation of radiative heat flux (right) from the flame onto the surface of the POM slab; Exp. – experiment, Calc. – calculations.
q¼λ
∂T ∂y
width of the pyrolysis zone, the flame height, the temperature profile of the upper and lower surfaces of the slab, the temperature field and the fields of the main flame species concentrations over the burning slab, the conductive heat flux from the flame onto the fuel surface. The following species were detected in the POM flame: H2, H2O, N2, CO, CO2, O2 and CH2O. It was concluded from analysis of the spatial distribution of the main flame species that in combustion of POM at least two global re actions in the gas phase may be identified: the reaction of formaldehyde pyrolysis in the absence of oxygen with light combustible gas formed (with the properties close to those of СО) and the subsequent reaction of its oxidation in the flame to the end combustion products (СО2þH2O). This approach was implemented as the couple combustion model was modified, taking into account a two-step reaction in the gas phase. The results of the calculations made showed good agreement with the experimental data for macroscopic parameters, as well as much better agreement for the temperature profiles in flame compared to the onestep gas-phase reaction.
(17)
where ∂T=∂y– is the maximum temperature gradient in the gas phase near the slab surface, calculated by the experimentally measured tem P P perature profiles, λ ¼ 0:5ð λi Xi þ ð Xi =λi Þ 1 Þ– is the thermal con ductivity of the gas mixture [42], λi ¼ λi ðTÞ is the thermal conductivity of the i-th gas mixture component [43], Xi is the mass fraction of the i-th gas mixture component near the slab surface, recalculated from the experimental mole fraction. The heat flux distribution along the burning surface presented in Fig. 7 (left) showed the reasonable agreement between predictions and measurements. The maximum heat flux was observed near the flame front, where flame is most close to the surface, resulting in the highest temperature growth at the shortest distance from the polymer specimen. The estimation of radiative heat flux showed its maximal value of order 3 kW/m2 (Fig. 7), occurring at the distance of around 40 mm from the flame front, where the flame has a large size as shown in Fig. 4.
Declarations of interest
5. Conclusion
None.
A comprehensive study of thermal decomposition and combustion of a horizontally placed polyoxymethylene (POM) slab was performed. The kinetic parameters of thermal degradation of POM in inert medium in supposition of two parallel reactions were determined. The kinetic pa rameters obtained were used to develop a coupled model and to make calculations for the flame spread over the POM. The following main characteristics of the POM slab’s combustion in the stationary mode were measured: the flame spread rate, the slab’s mass loss rate, the
Acknowledgments This work was supported by the RFBR under Grants #19-58-53016 and by the NNSF of China under Grant 51120165001. The authors acknowledge the utility of the Multi-Access Chemical Service Center SB RAS in the spectral and analytical measurements made. The authors are thankful to Dr. I. Shundrina for TGA and DSC measurements.
Appendix A. Configuration of the gas-phase thermocouple The thermal flame structure was studied using a Pt–Ptþ10%Rh thermocouple, made of wire 50 μm thick, shown in Fig. A1. The junction diameter was 70 � 10 μm, the thermocouple’s arm was 5.5 mm. The thermocouple’s arms were welded to the Pt and Ptþ10%Rh wires 0.2 mm in diameter. The wires were placed into quartz capillaries 0.7 mm in diameter, inserted into a ceramic tube 3 mm in diameter and 70 mm long. The length of the external parts of the capillaries was 40 mm. The thermocouple was coated with a SiO2 layer to prevent catalytic reactions on the thermocouple’s surface. Correction for the heat loss by the thermocouple due to radiation was calculated by Kaskan’s formula [44].
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Fig. A.1. Configuration of the gas-phase thermocouple.
Appendix B The kinetic parameters of the thermal decomposition reaction were obtained by optimizing the experimental reaction rates using the MATLAB genetic algorithm optimization tool [13,40,41] in supposition of two parallel decomposition reactions of two pseudo components of the polymer. The rate of each reaction with the known activation energy Es , preexponential factor ks and reaction order n in supposition of the power conversion function fðαÞ may be presented as [13,45]. 2 31 n n � � Es dα 1 dα ks REsT ks REsT ks REsT 6 ks R0 T 2 2R0 T 7 n (B.1) 1 e R0 T 5 ¼ ¼ e 0 f ðαÞ ¼ e 0 ð1 αÞ ¼ e 0 41 ð1 nÞ Es dT β dt β β β βEs
where α ¼ mm∞0
m m0
is the conversion degree, T is the temperature, β is the heating rate, t is time, R0 is the universal gas constant, n 6¼ 1.
Then the kinetic parameters of thermal decomposition may be determined by the highest degree of matching between the experimental reaction rate and the modeled general reaction rate: d αΣ dα1 d α2 ¼ с1 þ с2 dT dT dT
(B.2)
where с1 is the fraction of the first pseudo component, с2 ¼ 1 с1 is the fraction of the second pseudo component. To raise the accuracy, the calculated reaction rate was compared to the experimental reaction rate for two heating rates. As the value charac terizing the degree of matching of the experimental and modeled reaction rates for the heating rate β, a dimensionless parameter based on the squared differences was used [41]. � �β;calc �2 �� � P dα β;exp dαΣ Φβ ¼
i
P
dT
dα dT
i
where
dT
i
�� �β;exp
dα dT
i
dα dT
i
� �β;exp
(B.3)
i
� �β;average �2
� is the experimental reaction rate at the i-th temperature for the heating rate β,
temperature for the heating rate β,
� �β;average dα dT
dαΣ dT
�β;calc i
is the calculated reaction rate at the i-th
is the average experimental reaction rate for the heating rate β.
In the process of optimization, the calculated and experimental reaction rates were simultaneously compared for two heating rates using one parameter Φ¼
� 1 30 Φ þ Φ50 2
(B.4)
where Φ30 is the deviation at the heating rate of 30 K/min, Φ50 is the deviation at the heating rate of 50 K/min. To raise the degree of accuracy, 10 independent genetic algorithm optimization calculations were carried out followed by the selection of the result with the smallest deviation.
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