1. Introduction
Polymer materials are widely used in various applications, including building interiors, electronic device casings, and industrial components. However, they act as a major fuel source in the event of a fire; specifically, polymer fuels release large amounts of soot, flammable volatile substances, and toxic gases during pyrolysis, significantly impacting the speed of fire spread and human safety[1]. The combustion reactivity of these polymeric materials varies considerably depending on their chemical compositions and physical properties, and research results that quantify this are used as essential data for indoor fire prediction, risk analysis, and fire protection design.
The thermal reaction of polymer fuels is largely dependent on the material's chemical decomposition characteristics, the composition of the product gases, whether char is produced, and heat transfer conditions. In particular, the thermal thickness of a specimen significantly affects the pyrolysis mechanism and the shape of the heat release rate (HRR) curve. Thermal thickness is a concept used to determine whether a specimen is relatively thin or thick in terms of the characteristic of heat reaching the interior via radiation or conduction. Specimens are generally categorized into thermally thin and thermally thick based on the Biot and Fourier numbers[2]. Under thermally thin conditions, radiant heat is rapidly transferred throughout the specimen, causing the surface and interior to heat and decompose almost simultaneously, and the HRR curve exhibits a single peak. Under thermally thick conditions, heat absorbed at the surface is slowly conducted inward, causing decomposition to progress in layers and inducing complex HRR patterns such as double peaks depending on whether char is formed[2-5].
Along with thermal thickness, the charring of a material is a key factor determining the combustion characteristics of polymer fuels. Polymethyl methacrylate (PMMA), a non-charring material, transforms mostly into volatile products upon combustion, exhibiting simple HRR behavior and lacking a complex char formation process; thus, it is relatively easy to model numerically. Hong et al. conducted cone calorimeter experiments based on ISO 5660-1 and pyrolysis characteristic analysis on PMMA and quantitatively predicted single-peak HRR behavior using an experiment-based pyrolysis model within the fire dynamics simulator (FDS)[6]. Acrylonitrile butadiene styrene (ABS) forms solid residues (char) upon decomposition; these residues inhibit heat transfer and lower the burning rate, inducing a typical double-peak structure in the HRR curve. The pyrolysis characteristics of these charring polymers involve complex reaction mechanisms and thermal-material interactions, and various studies have proposed pyrolysis models to simulate them numerically[3].
The pyrolysis mechanism of polyvinyl chloride (PVC) is different from those of PMMA and ABS because PVC releases a large amount of hydrogen chloride (HCl) during decomposition, which induces a combustion-inhibiting effect. At this stage, a distinct char layer does not form on the surface; instead, black, discolored, and swollen residues or carbonaceous residues remain, inhibiting heat transfer and oxygen diffusion on the surface[7]. Huggett et al. reported that during the pyrolysis of PVC, over 30% of the total mass is released in the form of HCl, which significantly reduces combustion reactivity[1]. Wang et al. implemented a numerical model for HCl release during PVC decomposition and analyzed the temporal changes in the HCl concentration and the diffusion characteristics of toxic gases in a fire[8]. However, they primarily focused on the HCl concentration distribution and toxicity prediction, with few examples of quantitatively analyzing actual HRR changes and flame-weakening effects or implementing them in numerical models.
The development of pyrolysis models for polymer fuels typically involves obtaining experimental thermophysical data, constructing a rate model, and quantifying evaporation and carbonization characteristics. In particular, researchers widely use methods for estimating pyrolysis parameters based on data such as the HRR, residual mass, and soot production rate obtained from ISO 5660-1 cone calorimeter experiments. Experimental thermal properties obtained through differential scanning calorimetry, thermogravimetric analysis, and other techniques serve as the foundation for numerical modeling that can be directly applied to fire simulators such as the FDS[3,6].
Utilizing this procedure for developing pyrolysis models, we experimentally analyzed heat-release characteristics under thermally thick conditions, where the thermal thickness is sufficiently large, for ABS and PVC, which are representative polymer fuels with different pyrolysis characteristics. Specifically for PVC, we assessed the impact of HCl generated during decomposition on the flame temperature and HRR and to numerically implement the combustion suppression behavior observed during actual combustion. We conducted FDS simulations reflecting experimentally based parameters and compared the results with the results of the ISO 5660-1 cone calorimeter experiments.
2. Experimental and Numerical Setup
2.1. Cone Calorimeter Experimental Setup
We conducted combustion experiments using a cone calorimeter based on ISO 5660-1 to compare and analyze the pyrolysis and combustion characteristics of polymer fuels ABS and PVC. The cone calorimeter is an instrument that can quantitatively measure key thermal reaction characteristics, such as the HRR and mass loss rate (MLR), based on oxygen consumption calorimetry. It is widely used to obtain experimental data for modeling the pyrolysis of solid fuels[7,9].
For the experiment, 10-mm-thick ABS and PVC specimens were used to ensure thermally thick conditions. The specimens were fabricated as 100 mm × 100 mm squares having a heating area of 100 mm × 100 mm, and the edges were wrapped in aluminum foil to prevent deformation and damage. A metal mesh was attached to the top of the specimens to suppress shape changes and surface spalling caused by swelling during combustion.
Similar experimental conditions were set when comparing the pyrolysis characteristics of the two fuels. The heat flux was set to 50 kW/m², and radiant heat was applied vertically from the top of the specimens. The heat-flux value is appropriate for simulating the harsh conditions acting on walls or ceilings during the mid-to-late stages of an indoor fire, and it is commonly adopted in relevant standards and numerous studies[10-12]. The specimens were ignited by removing the standard pilot pin from ISO 5660-1 to induce self-ignition, with the aim of analyzing the spontaneous pyrolysis and combustion behavior under conditions without an external ignition source.
The combustion products generated during the experiment were removed through the exhaust system at the top of the hood, with the duct flow rate set at 24 L/s. These flow conditions provided a stable exhaust environment for measuring the oxygen concentration and combustion products and were applied identically in the numerical analysis (FDS).
The experiments for each condition were performed three times, and the effective heat of combustion (∆He), soot yield (Ysoot), CO yield (YCO), and residue fraction (νs) were calculated as the average values of the experimental results and used as FDS input values. The residue fraction was calculated by comparing the remaining mass after combustion with the initial mass and was incorporated into the FDS's solid pyrolysis model.
Figure 1(a) shows the appearance of the PVC specimen before combustion; a uniform gray surface indicates PVC’s pre-combustion state. Figure 1(b) displays the pre-combustion state of the ABS specimens, which have the same shape and size but exhibit slight differences in terms of color and density of the surface. Figure 1(c) depicts the experimental setup where the specimen is exposed to radiant heat within the cone calorimeter. The specimen is installed below the radiant panel, and the exhaust system is located above. Figure 1(d) presents the surface condition of the PVC specimen after combustion. Extensive discoloration and non-uniform residues are observed, and some parts of the surface are rough and swollen, appearing puffed up. Figure 1(e) shows the surface of the ABS specimen after combustion, with a thin residue remaining on some parts of the surface and exhibiting a relatively uniform shrinkage pattern. This indicates that ABS is a non-charring fuel; it does not form a thick carbonized layer after combustion and leaves only a small amount of carbonaceous residues. Meanwhile, the HRR and MLR measured in the experiment were used as criteria to validate the pyrolysis and combustion models by comparing them with the numerical analysis results.
Specifically, this experiment was a small-scale study conducted under fixed-oxygen-concentration (atmospheric conditions) and radiative-heat-transfer conditions in a cone calorimeter. Therefore, it did not reflect the effects of the convective heat transfer, oxygen concentration reduction, and complex thermal environments that occur in real large-space fires. Thus, the experimental results are intended for comparing fuel characteristics under these limited conditions, and the scope of interpretation must be considered.
2.2. Pyrolysis-Combustion Modeling and FDS Input Parameters
The FDS supports two methods for inputting combustion characteristics to numerically simulate the pyrolysis and combustion processes of solid fuels. The first method is to directly input the experimental heat release rate per unit area (HRRPUA); this involves a simple model that assumes a fixed pyrolysis reaction. The second is to use a pyrolysis model that is employed to dynamically calculate the heat and mass transfer phenomena occurring during combustion based on the material's physical properties and reaction parameters. We adopted the latter approach and precisely reproduced the pyrolysis and combustion processes based on the experimental characteristics of ABS and PVC fuels.
Energy conservation analysis was performed using the FDS's pyrolysis model, considering heat transfer at the solid fuel surface, mass release into the gas phase, external radiative and convective heat fluxes, and latent heat loss. As shown in Figure 2, before ignition, external radiative heat (q ˙ e x t ′ ′ q ˙ c o n v ′ ′ q ˙ r a d ′ ′ q ˙ ≠ t ′ ′ q ˙ f l a m e ′ ′
The temperature distribution within a solid fuel is expressed using the following one-dimensional heat conduction Eq. [13]:
where ρs,cp,s and ks denote the density, specific heat, and thermal conductivity of the solid fuel, respectively, and q ˙ s ′ ′ ' ρ s c s ∂ T s ∂ t
where q ˙ e x t ′ ′ q ˙ f l a m e ′ ′ q ˙ r a d ′ ′ q ˙ c o n v ′ ′
where q ˙ r a d ′ ′ q ˙ c o n v ′ ′
The MLR per unit area, m ˙ ″
where As is the pre-exponential factor, Es is the activation energy, R is the gas constant, Ts is the fuel surface temperature, and ρ0 is the initial density. This equation is used to estimate the amount of volatile gases produced via pyrolysis. These parameters are adjusted based on experimentally obtained thermogravimetric (derivative thermogravimetric) curves and HRR results, and they are defined in the REAC and MATL blocks within the FDS input file.
The calculated MLR per unit area is multiplied with ∆He which is the effective heat released during combustion, to calculate the HRRPUA (Heat release rate per area), q ˙ ″
The FDS treats combustion reactions using the mixing-controlled method, based on the assumption that chemical reaction rates are infinitely high. Accordingly, combustion reaction equations are constructed based on the mixing ratio of fuel and air and the product yield. In this study, the combustion reaction equations for ABS and PVC are defined as follows[14]:
(6)
(7)
Here, soot is modeled as a carbon-hydrogen composite particle, with a hydrogen mole fraction of XH = 0.1, and it is calculated as a molar mass as follows:
The formation coefficients of soot and CO are calculated from the following experiment-based equation:
where mF is the mass of 1 mole of fuel, mCO and mSoot are the molar masses of each product, and yCO and ySoot are the product yields obtained from cone calorimeter experiments, which were used to set up the combustion reaction equation.
To numerically simulate the pyrolysis and combustion characteristics of solid fuels, the FDS was utilized based on the energy-conservation equation described earlier. Figure 3 depicts the analysis domain and grid configuration for simulating the cone calorimeter experimental conditions, with the same heat-flux conditions (50 kW/m²), fuel type (ABS and PVC), and ventilation flow rate (24 L/s) as those used in the experiment. The grid size was set to capture the fire characteristics adequately within the analysis domain, and the entire analysis domain was configured as 0.26 m × 0.26 m × 0.61 m. The grid size was set to 5.78 mm to adequately capture heat and soot behavior within the combustion zone. The appropriate grid resolution was evaluated based on the characteristic fire diameter (D*), which represents the characteristic scale of a fire. D* is defined as follows:
where ρ∞, cp, and T∞ represent the density, specific heat, and temperature of the atmospheric state, respectively, and g is acceleration due to gravity. D* calculated based on Q̇ =7 kW (the HRR) is approximately 0.132 m. Applying a grid size (() of 5.78 mm results in a grid number ratio () of approximately 22.76. This is a high-resolution condition exceeding FDS's recommended resolution range (4-16), which is sufficient to ensure the accuracy of thermal and soot behavior analyses[15,16].
The thermophysical and pyrolysis properties of ABS and PVC under these conditions were compiled based on experimental results and previous studies and standardized to the FDS input format. Specifically, the residue fraction (νs), effective heat of combustion (∆Hv), soot yield (ySoot), and CO yield (yCO) were directly estimated from the ISO 5660-1 cone calorimeter experiments conducted in this study, whereas thermal properties such as the density (ρs), specific heat (cp,s), thermal conductivity (ks), and Arrhenius coefficients (As and Es) were obtained from data reported in previous experimental studies[14,17]. The relevant key material properties are summarized in Table 1.
3. Results and Discussion
3.1. Comparison and Interpretation of FDS Predictions Versus Experimental Results
The predictive accuracy of the numerical model was examined by comparing the key combustion characteristics obtained from cone calorimeter experiments, including the HRR, THR, and MLR, with the results of FDS simulations. Figures 4 and 5 show the HRR curves obtained from the experiments and simulations for ABS and PVC specimens, respectively, enabling a time-series comparison of the heat release patterns and quantitative levels. In the case of ABS, both the experiment and FDS showed similar characteristics, with the peak HRR reaching approximately 7 kW around 60 s after ignition before a gently decreasing decay phase, which is also predicted well, is observed. This is because ABS exhibits simple pyrolysis characteristics, with a single pyrolysis reaction pathway, low residue formation rate, and slight inhibitory effect from combustion products. Therefore, the FDS reaction model can effectively reproduce the actual combustion behavior of ABS.
By contrast, for PVC, the HRR curves shown in Figure 5 exhibit significant variations in the peak size and time between repeated experiments. This is because PVC forms a charring residue along with non-flammable gases (such as HCl) during pyrolysis. This residue has low thermal conductivity, which blocks or delays radiative and convective heat transfer from the surface, thereby non-linearly delaying the increase in the internal fuel temperature and the pyrolysis reaction. The shape and distribution of the residue can be highly sensitive to subtle experimental conditions such as the initial uniformity of the specimen surface and the location of flame contact, which can induce differences in the HRR time-series curves between repeated experiments. This decrease in repeatability is due to material properties, indicating that the combustion reproducibility of PVC is lower than that of ABS.
Figure 6 presents a comparison between the THR values calculated by integrating the HRR curves. For ABS, the experimental average THR is 3.98 MJ, with a standard deviation of ±0.125 MJ (±3.2%), whereas the FDS-predicted value is 4.00 MJ, indicating an error of only 2.7%. By contrast, for PVC, the experimental average THR is 0.50 MJ, with a standard deviation of ±0.18 MJ (±36.5%), indicating significant variation between experiments; the FDS-predicted value is 1.05 MJ, representing an overestimation of approximately 111%. This is because the combustion suppression effect caused by HCl and the charring residue generated during combustion are not fully implemented in the FDS model.
Figure 7 displays a comparison between the obtained MLR values. ABS shows a rapid increase in the MLR at the start of combustion, followed by a peak around 60 s, and then a gradual decrease. The simulation reproduces this pattern relatively well. Because ABS mostly transforms into a gaseous state after pyrolysis, leaving little residue, the accuracy of FDS predictions based on the MLR indicators is high. In the case of PVC, the MLR predicted from the FDS is relatively similar to the experimental results, unlike the predictions for the HRR and THR. Although the combustion suppression effect of PVC significantly impacts heat release, it is partially reflected in the mass loss itself. This suggests that the numerical model, by considering the residue fraction, achieves a limited degree of realism in terms of the mass loss.
Figure 8 shows the surface thickness change over time calculated using the FDS. ABS exhibits a tendency to decrease in thickness gradually as combustion progresses and then maintain a constant thickness after reaching the residue fraction (νs). This is the result of modeling that shows the residue remaining on the fuel surface after pyrolysis is complete, preventing further combustion. By contrast, PVC shows a tendency to increase in thickness over time because the solid residue generated after pyrolysis accumulates on the surface and increases the thickness owing to the charring residue setting within the FDS. In actual experiments, the accumulation of these residues reduces heat transfer and combustion. However, the FDS model overestimates combustion persistence by treating this simply as an increase in thickness without considering the physical suppression effects.
These comparison results indicate that the FDS can yield prediction results similar to experimental results for some indicators, such as the HRR and MLR, during the early stages of combustion. However, for materials with complex combustion suppression mechanisms, such as PVC, the effects of reduced heat transfer due to residue accumulation, reaction delay, and suppressed fuel exposure are not fully reflected, causing overestimation of the THR and combustion duration. Therefore, the reliability of numerical analyses should be evaluated by considering both the fuel properties and the limitations of the numerical model. In the future, improvements to physics-based models are needed to accurately reflect combustion inhibition mechanisms and residual effects.
4. Conclusion
In this study, the effects of pyrolysis characteristics and residue formation mechanisms on heat and mass transfer prediction were compared and analyzed by conducting cone calorimeter experiments and FDS-based numerical simulations on ABS and PVC, which are polymer fuels. The HRR, THR, and MLR were measured three times each in the experiment, and the effective heat of combustion, soot and CO yields, and residue fraction were incorporated into the FDS model for quantitative comparison with the numerical analysis.
In the case of ABS, a single pyrolysis pathway and a low residue formation rate were observed, indicating generally good agreement between the numerical analysis and experiments. By contrast, PVC showed the characteristics of suppressed heat transfer and combustion reactions because charring residues generated during combustion accumulated on the surface and non-flammable gases (such as HCl) generated as pyrolysis products diluted the oxygen concentration. These complex inhibition mechanisms were not fully reflected in the FDS basic model, leading to overestimation of the HRR and THR. However, the FDS-predicted MLR was relatively similar to the experimental value, suggesting that the setting considering the residue fraction was valid to a certain extent.
These results suggest that when a combustion analysis of polymer fuels is conducted, the FDS can provide accurate predictions for simple fuels (ABS) but may have limited reliability for fuels with complex inhibitory properties (PVC). Specifically, single-metric consistency evaluations based on the HRR may not reflect suppression characteristics; thus, an approach for evaluating model reliability by concurrently using multiple evaluation metrics, such as the MLR, is required.
Furthermore, the results of this study were interpreted based on data obtained under small-scale forced heat-flux conditions using a cone calorimeter. Owing to the nature of the experimental conditions, certain limitations exist: radiative and convective heat-transfer boundaries are restricted, and the effects of the high-temperature gas layer and changes in the oxygen concentration are not reflected. Therefore, caution is needed when directly applying the results interpreted under these single conditions to real-scale spaces or various environmental conditions. In future work, advanced pyrolysis models incorporating multi-step reaction models, oxygen dilution reaction inhibition mechanisms, and dynamic residue coverage effects should be developed.
In conclusion, the limitations and possibilities of FDS analyses were quantitatively compared based on the combustion and pyrolysis characteristics of polymer fuels through experimental validation, providing directions for future fire-based combustion analyses and prediction accuracy improvements.
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