Research on the Influence of Density, Length and External Air Flow Rate on the Smoldering Limit of Paper Scraps by a Cylindrical Rod Heater

Abstract

This study investigates the minimum ignition temperature of smoldering paper scraps with varying bulk densities and lengths under different external airflow rates. Paper scraps of different lengths were compressed to modify the bulk density within the smoldering fuel bed. The ignition tests were performed using a rod-heater with a controlled temperature range of 340–460 °C. Once the rod-heater reached the preset temperature, the current was turned off, and the rod-heater was inserted into the center of the vertically oriented combustion chamber filled with paper scraps. By recording the temperature variations at different locations within the combustion chamber, the ignition limits of smoldering paper scraps with varying bulk densities under different external airflow rates were determined. The results showed that in the absence of external airflow and with a fixed paper scrap length, the ignition limit of smoldering paper scrap exhibits a clear U-shaped trend as bulk density increases. Furthermore, we found that in the absence of external airflow, the length of paper scraps had no significant effect on the ignition limit in the low bulk density range. However, in the high bulk density range, the ignition limit increased with scrap length. As for cases with external air flows, the ignition limit of paper scrap smoldering combustion once again exhibits a U-shaped trend with varying bulk density. Compared with the condition without forced airflow, however, the inflection point of the U-shaped curve shifts toward the higher-density region. Moreover, within the range of externally forced airflow rates examined in the present study, the length of paper scraps had no significant effect on the smoldering ignition limit.

1. Introduction

Smoldering combustion is a low-temperature, slow, and flameless combustion phenomenon [1,2] that occurs as an oxidation reaction on the surface of porous fuels. This process relies on the heat generated from its own heterogeneous reactions to sustain its propagation. Smoldering combustion can be initiated by heat sources that are insufficient to produce a flame, and once initiated, it is difficult to extinguish. This characteristic is particularly evident in forest subterranean fires, which can burn for extended periods, ranging from days to months or even longer [3,4]. Furthermore, under certain conditions, smoldering combustion can transition into fully developed fires, resulting in significant economic losses. The burning process of smoldering combustion produces a substantial amount of toxic and harmful gases, which pose serious threats to both the social environment and human health.

Due to the critical importance of smoldering combustion in fire safety [5], the fundamental characteristics of smoldering combustion have been extensively studied. Rein et al. [6] studied the effect of bulk density on smoldering combustion using polyurethane foam as an experimental sample. It was shown that the rate of smoldering propagation decreased with increasing density. Moussa et al. [7] proposed a two-step reaction mechanism for cellulosic materials, where the fuel is first pyrolyzed and then oxidized. The process of smoldering combustion is a complex process that consists of a combination of heat and mass transfer. The ignition point is determined by a delicate balance between the heat supplied by the reaction front, heat loss, and the heat generated by the chemical reaction [8]. Therefore, there are many factors affecting the ignition of smoldering combustion. Hagen et al. [9] found that bulk density has a tremendous effect on the ignition temperature and weight loss of smoldering combustion. Hadden et al. [10] experimentally found that the critical heat flux of smoldering combustion increases with increasing sample size, and further that the increase in sample size increases the ignition limit of smoldering combustion. Xie et al. [11] investigated the effect of high bulk density, and the effect of wind velocity on the ignition characteristics of cotton bales and found that the ignition diffusion rate and peak temperature increased almost linearly with wind velocity due to the increase in oxygen supply. In addition, Walther et al. [12] found that the minimum energy required for ignition decreased as the oxygen mass fraction increased. Thus, bulk density, sample size, and air flow rate are important parameters affecting ignition.

The smoldering of municipal solid waste, often triggered by discarded cigarettes or other smoking-related materials, has consistently been identified as a leading contributor to the fire pathways through which urban spot fires are initiated. According to the CTIF Report No. 29 (2024) [13], which provides a comprehensive analysis of global fire statistics for 2022, there were 640,093,000 residential fires, accounting for 23.1% of the total number of fires. Additionally, 51,564,000 fires were attributed to smoking-related factors, representing the third highest cause of fires among all contributing factors.

Despite extensive investigations into the smoldering behavior of various materials, limited information exists regarding the specific conditions required for smoldering to be initiated in paper scraps by a discarded cigarette. The ignition mechanism of fuel by a discarded cigarette butt fundamentally differs from that of flames or radiation [14,15]. When a cigarette butt comes into contact with a fuel, energy is transferred from the cigarette to the fuel and its surrounding environment. However, as the cigarette no longer receives a continuous energy supply, its temperature decreases, thereby creating distinct boundary conditions for the heat source. If the cigarette butt remains sufficiently hot, carbon oxidation or oxidative pyrolysis reactions within the fuel bed can sustain the propagation of the smoldering front, potentially leading to smoldering or the generation of flames [16]. The ignition threshold of the fuel bed under these unique boundary conditions is influenced by various factors [17]. Given that paper is a ubiquitous combustible material, this study employs common paper scraps as the experimental material to investigate the ignition process. In this study, we used a rod-heater to simulate the process of cigarette ignition of paper scraps. A series of experiments were conducted to vary the rod-heater temperature, paper scraps bulk density, length, and wind speed conditions to investigate the propagation characteristics of paper scraps smoldering and the effect on the ignition limit of paper scraps.

2. Materials and Methods

2.1. Experimental Samples

In the present research, shredded paper scraps (Figure 1) derived from commonly used cellulose paper were selected as experimental samples. The physical properties of these paper scraps are summarized in

Table 1. Physical Properties of Paper Scraps.

Length (mm)	Width (mm)	Thickness (mm)	Intrinsic Density(kg/m3)
30	3	8.7 × 10−2	301.1
45
60
75

. The samples were prepared in lengths of 30 mm, 45 mm, 60 mm, and 75 mm to investigate the influence of length variations on their combustion characteristics. The width of the paper scraps was maintained at 3 mm to ensure a controlled variable, while the thickness was measured as 8.7 × 10⁻² mm.

The bulk density of the paper scraps was regulated within the range of 5 kg/m³ to 50 kg/m³. Specifically, when the bulk density was lower than 5 kg/m³, it became challenging to achieve a uniform sample within the combustion chamber. On the other hand, when the bulk density exceeded 50 kg/m³, it became difficult to compress and stabilize the sample within the combustion chamber.

2.2. Experimental Setup and Experimental Conditions

The experimental investigation of smoldering ignition in paper scraps was carried out using the apparatus illustrated in Figure 2. The system comprises a combustion chamber, a base, a heating unit, a gas supply system, a temperature acquisition system, and a digital camera. The combustion chamber is a transparent cylindrical container with a height of 200 mm and an internal diameter of 150 mm, mounted above a stainless-steel base. The chamber is open at the top, allowing combustion gases to be discharged vertically. A fume collection hood is positioned above the chamber to guide the exhaust gases away from the experimental setup. To prevent displacement of the fuel bed under thermal stress during high bulk density conditions, a rigid perforated metal plate was installed horizontally at the top of the chamber. This plate served as a mechanical constraint to suppress any upward expansion of the paper scraps while still allowing exhaust gases to pass freely through the perforations. The lower section of the stainless-steel base incorporates a cylindrical air diffuser positioned at its bottom, measuring 200 mm in diameter and 100 mm in height. This diffuser is uniformly perforated to distribute incoming air evenly into the combustion chamber.

To monitor the temperature distribution within the porous fuel bed, six K-type thermocouples (1 mm in diameter and 75 mm in length) were mounted along the vertical center axis of the combustion chamber. TC1 was positioned 50 mm below the top edge of the chamber, and the remaining thermocouples (TC2–TC6) were installed at uniform 20 mm intervals downward. Temperature data were recorded at 5-second intervals. A rod-heater, controlled by an external ignition controller, was inserted horizontally through a sidewall opening and extended 75 mm into the chamber. Its tip was aligned with the vertical centerline and positioned at the mid-height of the fuel bed, equidistant from the top and bottom boundaries. The relative positions of the thermocouples and the rod-heater are illustrated in Figure 2. The physical specifications of the rod-heater are listed in

Table 2. Properties of heater.

Diameter (mm)	Length (mm)	Heat Capacity(J/K)	Specific Heat (J/(kg·K))
9.42	88.9	12.49	460

.

To minimize the influence of environmental factors, the ambient temperature was kept within 15–20 °C, while humidity levels were kept within 30% to 40% for the entire duration of the test. A specified length of paper scraps was placed inside the combustion chamber and compacting them to a prescribed bulk density, compressed to a predetermined bulk density. Air was introduced at a controlled flow rate through the stainless-steel base, which functioned as a cylindrical air diffuser with a diameter of 200 mm and a height of 100 mm. The diffuser was designed to ensure uniform upward airflow into the combustion chamber. To ensure consistent sample packing across different bulk densities, a standardized loading protocol was implemented. Paper scraps were gently poured into the chamber and evenly distributed using a flat tool to eliminate large voids and prevent uneven layering. To avoid crumpling, folding, or artificially spaced arrangements that may arise under low-density conditions, a flat-top pressing surface was then applied to lightly compact the material. This process allowed the fuel bed to reach the target bulk density while maintaining a stable and uniform porous structure throughout the chamber.

Experiments were performed at discrete rod-heater setpoints ranging from 340 to 460 °C in 10 °C intervals, with each condition tested independently under a fixed initial temperature. For each experiment, the rod-heater was preheated outside the combustion chamber to the target initial temperature. After the target temperature had been achieved, the power supply was shut off and the rod heater was promptly inserted into the combustion chamber. Thus, each run used a single initial temperature, and the rod-heater temperature was not ramped during any single test. The ignition limit of the paper-scrap fuel bed was then recorded as a function of the initial temperature, the bulk density of the fuel bed, the paper-scrap length, and the airflow rate. In the present study, ignition was defined as the onset of a self-sustained smoldering front that continued after the heater was removed and propagated across the fuel bed, indicated by a sequential and sustained temperature rise exceeding 350 °C at all thermocouples.

In this experimental setup, the length of the paper scraps was varied between 30 and 70 mm, the bulk density ranged from 5 to 50 kg/m³, and the airflow rate varied from 0 to 30 NL/min. To ensure the reliability and reproducibility of the results, each set of conditions was repeated three times.

3. Results and Discussion

3.1. Ignition Limit of Paper Scraps at Different Bulk Densities Without an External Air Flow

This section focuses on the influence of paper scrap bulk density within the fuel bed on the ignition limit under conditions without externally forced airflow.

Figure 3 illustrates the trend of the smoldering ignition limit of paper scraps as the bulk density increases. Initially, the ignition limit decreases with increasing bulk density, but it subsequently increases with further increments in bulk density. At a bulk density of 12 kg/m³ and a rod-heater temperature of 420 °C, only one out of the three replicate experiments failed to ignite, while the other two successfully ignited. This condition was therefore recorded as the ignition limit. Consistent results were obtained across all three replicates for all other conditions.

As shown in Figure 3, the ignition limit of paper scraps exhibits a U-shaped trend with increasing bulk density at a fixed paper scrap length. This behavior is attributed to the competitive effects of porosity, heat capacity, and oxygen supply. To qualitatively describe this U-shaped trend, a simple model is presented in this paper. When the rod-heater is inserted into the porous fuel bed, the power supply is cut off, leading to a gradual drop in its temperature. This thermal decay is primarily due to two mechanisms: the transfer of energy from the rod-heater to the adjacent fuel material and thermal losses through convective and radiative mechanisms to the surrounding environment. The governing energy balance models for both the rod-heater and the sample are expressed in Equations (1) and (2), respectively:

• Energy balance for the rod-heater:

$$V_h{\rho }_h{c}_h\left(\mathit{\partial }{T}_h/\mathit{\partial }t\right)=-S_1{\lambda }_{ts,eff}(T_h-T_{ts})/d+Q_{loss,h}$$

(1)

• Energy balance for the test sample:

$$V_{ts}{\rho }_{ts}{c}_{ts}\left(\mathit{\partial }{T}_{ts}/\mathit{\partial }t\right)=S_1{\lambda }_{ts,eff}(T_h-T_{ts})/d+Q_{loss,ts}+{\omega }_{hr}{H}_{hr}$$

(2)

In Equation (1), the first term denotes the transient thermal response of the rod-heater, the second quantifies conduction between the heater and the test sample, and the final term represents convective and radiative heat losses to the surrounding atmosphere (note: $Q_{loss,h}$ < 0).

In Equation (2), the first and second terms correspond to internal energy accumulation and heat conduction from the heater, respectively. The third term captures ambient losses ($Q_{loss,ts}$ < 0), and the last reflects the heat released by chemical reaction within the fuel.

Porosity plays a crucial role in thermal conduction. As bulk density rises, the reduction in void fraction enhances the sample’s effective thermal conductivity, modeled by: (${\lambda }_{ts,intrinsic}\left(1-{\varphi }_{ts}\right)+{\lambda }_{air}{\varphi }_{ts}+{\varphi }_{ts}4\epsilon \sigma T_{ts}^3{D}_p$) At lower densities, diminished conductivity leads to poor heat transfer from the heater (2nd term in Equations (1) and (2)). due to the low effective thermal conductivity of the sample. Meanwhile, there was a large heat loss from the heater to ambient air. (3rd term in Equation (1)) The energy lost from the rod-heater is defined as the ratio of $Q_{loss,h}$ and $S_1{\lambda }_{ts,eff}(T_h-T_{ts})/d$, then as the bulk density increases, this ratio decreases and the rod-heater gives off less heat to the environment, making ignition relatively easy

Regarding the heat capacity effect, as the bulk density of the paper scrap fuel bed increases, the heat capacity of the paper scraps also increases. This leads to a higher ignition limit for the paper scraps (1st term in Equation (2)).

Regarding oxygen availability, denser packing reduces the total internal oxygen volume, impairing its ability to reach high-temperature zones. This restriction affects the energy source term in Equation (2), governed by: ${\omega }_{hr}={\displaystyle \frac{C_{o_2,\mathrm{\infty }}}{(1/k+1/h_{o_2})}}$, where $C_{o_2,\mathrm{\infty }}$ is the oxygen concentration in the ambient, $k$ represents the chemical control effect, and $h_{o_2}$ illustrates the diffusion control effect.

Through the analysis of the experiments, we have gained a better understanding of the U-shaped trend shown in Figure 4. In low-density configurations (e.g., 12 kg/m³), porosity dominates heat transport properties. Larger pore volumes yield weaker conduction, limiting energy delivery to the fuel. However, interstitial oxygen remains abundant due to large pore sizes compared to the paper thickness. As density increases, the dominance of oxygen limitation and thermal capacity becomes more apparent, raising the ignition threshold and forming the observed U-shaped trend.

As the bulk density increases, the influence of oxygen supply and heat capacity becomes more significant in the ignition process. A denser fuel bed contains more material per unit volume, leading to higher thermal inertia, and the reduced porosity inhibits oxygen diffusion into the interior of the bed. Consequently, this results in a gradual increase in the ignition limit at higher bulk densities. It should be noted that oxygen availability plays a critical role in shaping the observed ignition limit trends. While our current explanation remains qualitative, future work will focus on direct in situ measurements of oxygen concentration—such as using oxygen sensors or gas sampling techniques—to quantitatively assess oxygen availability within the fuel bed. These efforts will improve our understanding of how bulk density and porosity influence local oxygen levels during smoldering ignition.

3.2. The Influence of Paper Scrap Length Within the Fuel Bed on the Ignition Limit Without External Forced Air Flow

This section primarily discusses the effects of paper scrap length within the fuel bed on the ignition limit, in the absence of externally forced air flow.

As shown in Figure 5, the ignition limits of the paper scraps fuel bed across all tested sizes follow a U-shaped curve, which supports the accuracy of our previous analysis. The natural stacking density of small-sized paper scraps is approximately 15 kg/m³, while that of large-sized paper scraps is around 5 kg/m³. Within the low bulk density range (10–15 kg/m³), the lowest ignition temperatures for paper scraps with lengths of 45, 60, and 75 mm are 420 °C, 400 °C, and 420 °C, respectively. In this range, the effect of paper scrap length on the ignition limit is minimal. In the high bulk density range (15–25 kg/m³), for instance, at a bulk density of 16.98 kg/m³, the lowest ignition temperatures are 400 °C, 400 °C, 420 °C, and 420 °C for 30, 45, 60, and 75 mm paper scraps, respectively. At a bulk density of 19.81 kg/m³, the lowest ignition temperatures are 400 °C, 420 °C, 420 °C, and 440 °C for 30, 45, 60, and 75 mm paper scraps, respectively. At a bulk density of 22.5 kg/m³, the lowest ignition temperatures are 420 °C, 420 °C, 440 °C, and 460 °C for 30, 45, 60, and 75 mm paper scraps, respectively. Compared with low-density regions, the size of paper scraps has a more pronounced effect on the smoldering ignition limit of the fuel bed in high-density regions.

Based on the analysis of the U-shaped trend from the previous section, the smoldering ignition limit of the fuel bed in high-density regions is characterized by a larger heat capacity and limited oxygen availability in the fuel bed. This is most likely because, in high-density regions, the size of paper scraps influences the oxygen supply conditions within the fuel bed, while the heat capacity remains constant at a given bulk density. This is evidenced by the temperature distributions shown in Figure 6.

Figure 6 illustrates the temperature distribution within the paper scraps fuel bed for two individual cases. The temperature profiles within the test sample, obtained at initial rod-heater temperatures of 400 °C and 440 °C, with paper scrap lengths of 30 mm and 75 mm at a bulk density of 14.15 kg/m³, are presented.

Figure 6a shows the temperature distribution for a paper scrap length of 30 mm, while Figure 6b corresponds to a length of 75 mm. In both non-ignition cases, the temperatures recorded by all thermocouples remained below 100 °C. Nevertheless, a significant difference is observed between the two paper scrap lengths. For the 30 mm case, the temperatures in the upper part of the combustion chamber (TC-1 to TC-3) were higher than those in the lower part (TC-4 to TC-6). Notably, the local temperatures at TC-1 and TC-2 even exceeded that at TC-4, despite TC-4 being located closer to the rod-heater. A similar phenomenon was also reported in our previous research [18]. This behavior can be attributed to the heat transfer characteristics within the porous medium: in addition to conductive and radiative energy transfer from the rod-heater to the surrounding fuel, the upper section of the chamber experienced notable heating due to buoyancy-induced convective airflow. This upward convection significantly contributed to elevating the temperature of the paper layer positioned in the upper zone. However, when the paper scrap length increased to 75 mm, this buoyancy-driven convection effect was strongly suppressed, resulting in a substantial reduction in convective heat transfer. Consequently, heat transfer was dominated by radiation and conduction, leading to higher temperatures near the heaters (TC-3 and TC-4) compared to locations farther away (TC-1, TC-2, TC-5, and TC-6). The suppression of natural convection in the fuel bed deteriorates oxygen supply, making the effect of paper scrap size on the smoldering ignition limit of the fuel bed more pronounced in high-density regions.

3.3. Ignition Limit of Paper Scraps with External Air Flow

This section explores how varying externally supplied airflow—introduced beneath the fuel bed—affects the ignition threshold and smoldering spread behavior of the paper scrap samples. Given that the ignition limit in the high-density region is primarily governed by oxygen transport within the fuel bed, this part of the study focuses exclusively on the effect of air flow rate on the ignition limit of paper scraps in the high-density region.

Figure 7 shows the ignition limits of paper scraps without external airflow (Figure 7a), with 10 NL/min external airflow rate (Figure 7b). As discussed before, in the absence of an external air flow, raising the bulk density from 17 kg/m³ to 25 kg/m³ leads to a rise in the ignition threshold. However, at external airflow rates of 10 NL/min, the ignition behavior exhibits a non-monotonic trend: the threshold initially declines with increasing density, followed by a subsequent increase as density continues to rise. Specifically, at a bulk density of 19.81 kg/m³, the minimum initial rod-temperature required for ignition of the paper scraps without external airflow is 420 °C (Figure 7a). In contrast, when an external airflow rate of 10 NL/min is applied, the minimum ignition temperature is significantly reduced to 380 °C (Figure 7b). This enhanced ignition tendency with external airflow can be attributed to the increased oxygen supply to the fuel bed facilitated by the externally induced airflow.

In the presence of externally forced airflow, the ignition limit of paper scrap smoldering combustion once again exhibits a U-shaped trend with varying bulk density. Compared with the condition without forced airflow, however, the inflection point of the U-shaped curve shifts toward the higher-density region.

The effect of airflow on the temperature profiles in the vertical combustion chamber is presented in Figure 8. In the absence of external airflow (Figure 8a), the smoldering front was first detected at the bottom thermocouple (TC-6) and subsequently propagated upward, a behavior that has been previously identified and explained in detail in our earlier study [18]. When an airflow of 30 NL/min was introduced (Figure 8b), the smoldering front followed the same pattern but propagated at a substantially higher rate. This acceleration was attributed to the oxygen-diffusion-limited nature of the smoldering process, whereby the additional airflow enhanced oxygen availability [19], leading to higher sample temperatures and faster front propagation.

The effect of paper scrap length on the ignition limit of smoldering combustion under external airflow is presented in Figure 9. Figure 9a,b show the minimum temperatures required for smoldering at different bulk densities for paper scraps of 30 mm and 60 mm in length, respectively. The results indicate that increasing the paper scrap length had no significant influence on the ignition limit with the presence of external forced airflow. In particular, no appreciable rise in the minimum ignition temperature was observed with longer paper scraps under the 30 NL/min airflow conditions. This can be explained by the fact that, under forced airflow, the convective heat transfer from the rod-heater to the test sample was not hindered by the increase in scrap length.

It should be noted that in this study, the influence of longer paper scrap lengths on the ignition limit was not comprehensively examined under external airflow conditions. It is hypothesized that at greater lengths, convective heat transfer from the rod-heater to the sample may be reduced, potentially requiring higher ignition temperatures or stronger airflow to sustain smoldering. Further investigations will be carried out to clarify the effect of extended paper scrap lengths on smoldering ignition limits under forced airflow.

4. Summary and Conclusions

This paper investigates the ignition temperature and smoldering propagation characteristics of paper scrap under varying conditions, including paper scrap length, bulk density, and externally forced airflow rate. The effects of these factors on the ignition limit of the paper scrap fuel bed have been discussed. The main findings are as follows:

(1)

In the absence of external airflow and with a fixed paper scrap length, the ignition limit of smoldering paper scrap exhibits a clear U-shaped trend as bulk density increases. This trend is attributed to the complex interplay between porosity, heat capacity, and oxygen supply within the fuel bed.

(2)

In the absence of external airflow, the length of paper scraps had no significant effect on the ignition limit in the low bulk density range. However, in the high bulk density range, the ignition limit increased with scrap length. This phenomenon can be attributed to the suppression of natural convection within the fuel bed, which reduces oxygen supply and thereby makes the influence of scrap size on the smoldering ignition limit more pronounced under high-density conditions.

(3)

In the presence of externally forced airflow, the ignition limit of paper scrap smoldering combustion once again exhibits a U-shaped trend with varying bulk density. Compared with the condition without forced airflow, however, the inflection point of the U-shaped curve shifts toward the higher-density region.

(4)

Within the range of externally forced airflow rates examined in the present study, the length of paper scraps had no significant effect on the smoldering ignition limit.

In future research, efforts will be directed toward developing numerical simulations of the smoldering combustion process of paper scraps, which are expected to extend the insights obtained from the present experiments and enable predictions under a broader range of physical and boundary conditions. Additionally, future studies should investigate smoldering ignition and propagation under more varied scenarios, such as different moisture contents and paper material compositions, to further advance the understanding established in this work.