# Numerical Simulation of Coupled Pyrolysis and Combustion Reactions with Directly Measured Fire Properties

^{*}

## Abstract

**:**

^{2}irradiance. The inputs of chemical kinetics and the heat of reaction were obtained from sample mass change and enthalpy data in TGA and differential scanning calorimetry (DSC) tests and the flammability parameters were obtained from cone calorimeter experiments. An iso-conversional analytical model was used to obtain the kinetic triplet of the above materials. The thermal properties related to heat transfer were also mostly obtained in house. All these directly measured fire properties were inputted to FDS in order to model the coupled pyrolysis–combustion reactions to obtain the heat release rate (HRR) or mass loss. The comparison of the results from the simulations of non-prescribed fires show that experimental HRR or mass loss curve can be reasonably predicted if input parameters are directly measured and appropriately used. Some guidance to the optimization and inverse analysis technique to generate fire properties is provided.

## 1. Introduction

## 2. Fire Properties

_{2}yield [24]. The thermo-physical properties required to model coupled pyrolysis and combustion reaction are density, thermal conductivity, specific heat capacity, absorption coefficient and emissivity. The pyrolysis, combustion and thermo-physical parameters are together often called fire properties. Kinetic triplets or parameters are obtained by postprocessing raw data from the TGA data and the process is described below.

## 3. Kinetic Parameters of PMMA, Pine, Cotton and Wool

^{−3}kJ/mol.K). Equation (3) is used in FDS by default. By applying appropriate data reduction methodology on the TGA data A, E and n can be obtained.

_{10}heating rate (β) against 1/${T}_{\alpha}$ for each heating rate at a fixed degree of conversion, $\alpha $, which should give a straight line [28]. The gradient of this is equal to $\u20130.4567\left(\frac{{E}_{a}}{R}\right)$ which is re-arranged to find the activation energy [28]. This is based on the equation below as given by the OFW method [29]:

_{a}/R) to solve for E.

## 4. Flammability and Thermo-Physical Parameters

^{2}are listed in Table 3. The effective heat of combustion (EHoC) for non-charring material (PMMA) was also taken from [23]. For charring materials (pine, cotton and wool), a different approach was undertaken for EHoC. The cone calorimeter experiments also give the total mass loss and total heat release data. The EHoC for charring materials, listed in Table 3, were obtained by dividing the total heat release (kJ) with total mass loss (kg). However, given the small mass sample of cotton and wool, the HRR and total heat release measured may not be accurate and there may be up to 40% uncertainty. Additionally, the presence of moisture can affect the effective heat of combustion which in turn affects the simulation outcome. Therefore, during the numerical modelling (with FDS), the measured EHoC was increased gradually until ignition occurred. Moisture fractions were taken from the TGA data of [23,24].

## 5. Numerical Analysis of Pyrolysis

#### 5.1. Classical Theory (Arrhenius Equation)

#### 5.2. TGA Modelling Using FDS

## 6. Numerical Simulation of Cone Calorimeter

#### 6.1. Model Set-Up

#### 6.2. Results

^{2}irradiation are compared with the experimental results in Figure 6. It can be seen that at 50 kW/m

^{2}irradiation, with A and HoR values corresponding to the heating rates of 10 and 20 K/min, the simulated results match the experimental outcome quite well. Better results are obtained with values corresponding to 20 K/min. At 30 kW/m

^{2}irradiation, with 10 and 20 K/min values, initially the HRR was under predicted up to ~500 s, then well predicted up to ~1250 s and then over predicted. Overall, a good prediction was obtained with 20 K/min values at this irradiation. At both irradiations, times of ignition match well with the experiments of three sets of values presented here. Figure 6 also shows that for the PMMA simulations, the results with A and HoR values obtained at lower heating rates yield higher HRR values. Higher HoR values at a higher heating rate (explained in detail in Abu Bakar et al. [23]) is likely to be the primary reason. It can be seen from the cotton simulations (Figure 9), where HoR and E values are fixed, with the variation of A, no significant difference was observed.

^{2}irradiation, the HRR results from the FDS simulations for pine are compared with experimental results. Generally, we see the same sort of trend of decreased HRR with the increased HoR associated with higher heating rates. This implies that the kinetics parameters obtained at high heating rates provide less conservative estimations of HRRPUA. The ignition occurs 10 s earlier in the simulation compared to the experiment at 50 kW/m

^{2}irradiation. The first peak is also significantly higher in the simulation. The first peak appears to correspond with the initial pyrolysis from the top layer. However, after ~60 s the simulated HRR values are closer to experimental values and the second peak value is also close. The second peak is associated with the thermal wave in the fuel hitting the insulation bottom [38,39]. Overall, A and HoR values associated with 30 K/min give the closest result. At 30 kW/m

^{2}irradiation, ignition occurs ~60 s earlier in the simulation, which is quite significant. A comparison with HRR time series is made by shifting the experimental HRR time series by 60 s. Simulations, at this irradiation, yield overall higher HRR which may be considered conservative in relation to fire severity [40]. However, the simulation with A and HoR values associated with 100 K/min provide a lower HRR and a longer burning duration.

^{2}irradiation, the simulation results are quite close to the experimental results. On the other hand, when the sample is exposed to a lower heat flux of 30 kW/m

^{2}, the simulation results are underpredicted during most part of the burning. The sensitivity of charring properties in wool can have a significant effect on the numerical model as wool char properties could not be measured. We used the properties of pine char. As shown in Table 3, the moisture content of 6% and char of 3.8%were modelled for Wool in line with the experimental results.

^{2}irradiation, ignition and thereby, a simulated curve occurred ~14 s later than the experimental curve. For the lower irradiation, closer simulation results were obtained. Besides charring properties, physical properties like porosity could play a role in the simulation. This property is not used in FDS [22]. Furthermore, for the pyrolysis of cotton, we considered a single “effective” reaction as opposed to two reactions.

## 7. Conclusions

^{2}. The results of the experimental HRR compared to the FDS modelled HRR show that the PMMA experiments can mostly be accurately represented by directly measured fire properties. The simulations of pine, wool and cotton also show close comparisons between the experimental and simulation results, however, not to the same degree as PMMA as in each case the result varied with the incident heat flux. For pine, at 30 kW/m

^{2}irradiance, the ignition occurred ~60 s earlier and a higher HRR was yielded. From a fire safety modelling perspective, it may not be problematic due to the conservative fire severity predictions. For cotton, at 50 kW/m

^{2}irradiance, ignition occurs later than in the experiment. The use of a thin sample, uncertainty with char properties, “effective” single pyrolysis reaction assumption, etc., can be the reasons for the difference. Furthermore, porosity is not modelled in FDS. However, the shapes of the profiles are similar between the experiment and simulation. Overall, HoR measured at 20 K/min for non-charring and at 30 K/min for charring materials provide the closest result with the experimental findings. For further improvement, it was recommended that for uncertain fire properties, the optimization method be used, keeping directly measured fire properties unchanged and the porosity model be implemented in FDS. Optimization and inverse analysis can also play a role in making calibrations of data from mg scale thermal analysis (TGA/DSC) for large-scale fire simulations, keeping the directly measured values as the base values. A further study with the cone calorimeter testing of thicker fabric samples can be carried out. Char properties of specific fabrics can be determined as well.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The Ozawa–Flynn–Wall (OFW) method plots for the TGA tests with PMMA, pine, wool and cotton.

**Figure 5.**Modelled flaming combustion of four materials within domains. Visualization is done by using FDS’s companion software Smokeview based on volumetric heat release rate (HRR) in the gas phase.

Sl. No. | Kinetic Model | Equation (1/df(α)/dα) |
---|---|---|

1 | P1 Power Law | α^{1/n} |

2 | E1 Exponential law | ln(α) |

3 | A2 Avrami–Erofeev Model | [−ln(1 − α)]^{1/2} |

4 | A3 Avrami–Erofeev Model | [−ln(1 − α)]^{1/3} |

5 | A4 Avrami–Erofeev Model | [–ln(1 − α)]^{1/4} |

6 | B1 Prout–Tompkins | [−ln(α/(1 − α))] + C |

7 | R1 Contracting area | 1 − (1 − α)^{1/2} |

8 | R3 Contracting volume | 1 − (1 − α)^{1/3} |

9 | D1 One dimensional | α^{2} |

10 | D2 Two dimensional | (1 − α)ln(1 − α) + α |

11 | D3 Three dimensional | [1 − (1 − α)^{1/3}]^{2} |

12 | D4 Ginstling–Brounshtein | (1 − 2α/3) − (1 − α)^{2/3} |

13 | F1 First order | −ln(1 − α) |

14 | F2 Second order | 1/(1 − α) |

15 | F3 Third order | 1/(1 − α)^{2} |

**Table 2.**Activation Energy (E) and Pre-exponential Factor (A) at Each Heating Rate and Heat of Reaction (HoR).

Material | Heating Rate | E (kJ/mol) | A (1/s) | HoR (kJ/kg) | Material | Heating Rate | E (kJ/mol) | A (1/s) | HoR (kJ/kg) |
---|---|---|---|---|---|---|---|---|---|

Pine | 10 K/min | 185.67 | 2.05 × 10^{13} | 97.4 | Cotton | 5 K/min | 221.54 | 2.06 × 10^{16} | 385 |

20 K/min | 2.09 × 10^{13} | 137.2 | 10 K/min | 1.84 × 10^{16} | |||||

30 K/min | 2.04 × 10^{13} | 172.5 | 50 K/min | 1.76 × 10^{16} | |||||

50 K/min | 2.13 × 10^{13} | 254.3 | 100 K/min | 2.05 × 10^{16} | |||||

100 K/min | 2.13 × 10^{13} | 357.8 | 200 K/min | 2.16 × 10^{16} | |||||

200 K/min | 2.55 × 10^{13} | 461.4 | Wool | 10 K/min | 114.72 | 1.45 × 10^{8} | 314.8 | ||

PMMA | 10 K/min | 183.44 | 7.25 × 10^{12} | 1747.2 | 20 K/min | 1.53 × 10^{8} | 346.3 | ||

20 K/min | 7.79 × 10^{12} | 2019.9 | 30 K/min | 1.57 × 10^{8} | 377.7 | ||||

30 K/min | 7.94 × 10^{12} | 2335.1 | 40 K/min | 1.45 × 10^{8} | 409.2 | ||||

50 K /min | 7.6 × 10^{12} | 3120.6 | 50 K/min | 1.45 × 10^{8} | 440.7 | ||||

100 K/min | 6.9 × 10^{12} | 6443.3 | 100 K min | 1.36 × 10^{8} | 598.2 | ||||

200 K/min | 6.26 × 10^{12} | 27468.4 | 200 K/min | 1.84 × 10^{8} | 913.2 |

Material | Irradiation | EHoC (kJ/kg) | CO Yield (kg/kg) | Soot Yield (kg/kg) | Moisture (Fraction) | Char Residue (Fraction) |
---|---|---|---|---|---|---|

Pine | 30 kW/m^{2} | 11,210 | 0.007 | 0.006 | 0.035 | 0.105 |

50 kW/m^{2} | 11,210 | 0.007 | 0.006 | 0.035 | 0.126 | |

PMMA | 30 kW/m^{2} | 21,295 | 0.007 | 0.14 | - | - |

50 kW/m^{2} | 21,295 | 0.007 | 0.14 | - | - | |

Cotton | 30 kW/m^{2} | 8927 | 0.013 | 0.022 | 0.012 | 0.025 |

50 kW/m^{2} | 5363 + 40% ^{1} | 0.013 | 0.022 | 0.012 | 0.025 | |

Wool | 30 kW/m^{2} | 6300 + 28% ^{1} | 0.01 | 0.039 | 0.06 | 0.038 |

50 kW/m^{2} | 7687 + 5% ^{1} | 0.01 | 0.039 | 0.06 | 0.038 |

^{1}% increase for Fire Dynamic Simulator (FDS) modelling.

Material | Properties | Value | Unit | Value | Material |
---|---|---|---|---|---|

Pine | Thermal Conductivity | 0.168; 20 > T 0.0002T + 0.1649; 20 ≤ T ≤ 225 0.2; T > 225 | W/m/K | 0.1945 | PMMA |

Specific heat | 0.756; 25 > T 0.004T + 0.6544; 25 ≤ T≤240 1.614; T > 240 | kJ/kg/K | 1.47 | ||

Emissivity | 1 | 0.85 [34] | |||

Absorption Coefficient | Default | m^{−1} | 2700 [35] | ||

Density | 403 | kg/m^{3} | 1210 | ||

Char ^{1} | Thermal Conductivity | 0.069; 20 > T 0.0001T + 0.0661; 20 ≤ T ≤ 225 0.102; T > 225 | W/m/K | 48; 20 > T −23.107T + 1139; 20 ≤ T ≤ 677 30; T > 677 | Steel [36] |

Specific Heat | 0.927; 25 > T 0.0028T + 0.8587; 25 ≤ T ≤300 1.697; T > 300 | kJ/kg/K | 0.45; 20 > T 6 × 10 ^{−07} T^{2} + 0.0002T + 4463; 20 ≤ T ≤ 2000.85; T > 677 | ||

Emissivity | 1 | 0.9 | |||

Density | 110 | kg/m^{3} | 7850 | ||

Wool | Thermal Conductivity | 0.0846; 20 > T 1× 10 ^{−06} T^{2} − 0.0002T + 0.0882; 20 ≤ T ≤ 2000.0882; T > 200 | W/m/K | 0.142; 20 > T 0.0002T + 0.1378; 20 ≤ T ≤ 200 0.178; T > 200 | Cotton |

Specific Heat | 1.773; 20 > T 9 × 10 ^{−06} T^{3} − 0.000355T^{2} + 0.04237T − 0.06137; 20 ≤ T ≤ 2753.583; T > 275 | kJ/kg/K | 1.672; 20 > T 0.0024T + 1.6238; 20 ≤ T ≤ 300 2.344; T > 300 | ||

Emissivity | 1 | 1 | |||

Absorption Coefficient | 50000 | m^{−1} | 50000 | ||

Density | 220 | kg/m^{3} | 254 |

^{1}These are properties of pine char. As thin cotton and wool samples were burned, char could not be collected for hot disk analyser (HDA) measurements. Therefore, for the cotton and wool simulations, the properties of pine char were used.

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**MDPI and ACS Style**

Moinuddin, K.; Razzaque, Q.S.; Thomas, A. Numerical Simulation of Coupled Pyrolysis and Combustion Reactions with Directly Measured Fire Properties. *Polymers* **2020**, *12*, 2075.
https://doi.org/10.3390/polym12092075

**AMA Style**

Moinuddin K, Razzaque QS, Thomas A. Numerical Simulation of Coupled Pyrolysis and Combustion Reactions with Directly Measured Fire Properties. *Polymers*. 2020; 12(9):2075.
https://doi.org/10.3390/polym12092075

**Chicago/Turabian Style**

Moinuddin, Khalid, Qazi Samia Razzaque, and Ananya Thomas. 2020. "Numerical Simulation of Coupled Pyrolysis and Combustion Reactions with Directly Measured Fire Properties" *Polymers* 12, no. 9: 2075.
https://doi.org/10.3390/polym12092075