1. Introduction
Smoke generated during a fire is a complex mixture of carbon particles, condensable tar, and volatile organic compounds. Among the physical and chemical properties of such smoke, the particle size distribution (PSD) has a crucial impact on visibility reduction, smoke detector performance, and particle transport and deposition behavior, making it a key element in fire safety engineering[1-3]. In particular, the particle size directly affects visibility in a fire environment by dominating light scattering and absorption characteristics, making it a key factor that determines the available safe egress time (ASET). As smoke detectors are optimized for a specific particle size range (usually from sub-micron to several micrometers) in the design process, alarm delays or malfunctions may occur if the PSD of actual smoke is not consistent with the sensing characteristics of the detector.
Recent studies have emphasized that smoke particle size variation significantly affect smoke detection and visibility reduction during a fire. Hong et al.[4] verified that the smoke generated during the combustion of acrylonitrile-butadiene-styrene (ABS) has an approximately 41% higher mass-specific extinction coefficient compared to other polymers, such as unplasticized polyvinyl chloride (UPVC). This difference results from differences in particle size and chemical composition, where a high mass-specific extinction coefficient may lead to faster visibility reduction and early detection. Although widely used, computational fluid dynamics (CFD)-based fire simulation tools cannot fully reflect the PSD variability and heterogeneity of smoke observed from actual fires, as they use a fixed average particle size (approximately 1 μm) as input.
Changes in smoke particle size significantly affect both aerodynamic behavior and optical characteristics. Smoke particles initially form as nanometer-level primary particles at the early stage through nucleation and condensation processes and gradually grow into large agglomerates through coagulation and aggregation while ascending. Floyd et al.[5] reported that an aerodynamic diameter of approximately 10 μm must be considered to accurately predict soot concentration in fire dynamics simulator (FDS) simulation, and that consistency with experiment results significantly improves when gravitational settling and deposition mechanisms are included. They also pointed out that most of the soot mass exists in particles smaller than 1 μm; however, approximately 5% of it or higher is distributed in a size range of 5 μm or larger, thereby significantly affecting the deposition rate and the speed of visibility reduction.
Meanwhile, changes in the size and geometry of smoke particles also directly affect their optical characteristics. The mass-specific extinction coefficient (Km) indicates light reduction due to the light absorption and scattering by smoke particles, and is determined by the particles’ geometry and chemical properties. Km is expressed as the sum of the scattering coefficient and the absorption coefficient. The absorption coefficient is primarily affected by the carbon structure and chemical composition, whereas the scattering coefficient varies depending on physical properties, such as the number of particles, particle size, and geometry. Therefore, changes in particle size and aggregation structure directly affect the Km value, which plays a crucial role in visibility reduction and the response characteristics of optical smoke detectors.
In current computational analysis, smoke concentration is calculated by entering a fixed value for Km. This may reflect smoke transport characteristics due to ventilation flow, but cannot fully consider changes in aerodynamic drag or deposition behavior depending on the particle size. Conversely, when smoke particle size information is provided in FDS, a representative fire simulation tool developed by NIST, it enables the simulation of deposition behavior caused by flow-induced aerodynamic drag, gravitational settling, thermophoresis, and viscous effects. As deposited smoke particles adhere to walls and ceilings, affecting both visibility and detection performance, accurate particle size information is essential.
Against this research background, recent studies have emphasized that accurate reflection of PSD variation is essentially required to improve the accuracy of smoke simulation. Liu et al.[6] confirmed the phenomenon that the particle median diameter rapidly grows from approximately 0.1 μm to several micrometers in the biomass combustion plume through aerosol spectrometer measurements, and revealed that high-concentration organic aerosols are the main cause. Li et al.[7] also reported that the spatial variability of soot particles was evident in the indoor solid fuel combustion environment, and the mass mean aerodynamic diameter (MMAD) increased from approximately 0.8 μm near the flame to the level that exceeded 10 μm near the ceiling. These results indicate that an approach that precisely reflects spatial and temporal PSD variation is required to enhance the accuracy of smoke behavior and fire safety predictions.
Despite widespread recognition, experimental data on PSD variation during polymer combustion remain limited. In particular, quantitative analysis for polymers, such as ABS, are insufficient. For advances in fire safety engineering, it is essential to quantitatively identify the formation of sub-micron-sized primary particles and their growth into several micrometer-sized agglomerates. Such data are important for more reliable fire safety design as they contribute to enhancing the accuracy of smoke detector calibration, visibility reduction modeling, CFD-based smoke transport simulation, and surface deposition predictions.
ABS was selected as a sample for smoke behavior analysis in this study due to its widespread use in various industries (e.g., architecture, electronic devices, and automotive interior) and its tendency to emit large amount of smoke and toxic gases in the event of a fire. As such, this study aims to comprehensively analyze PSD during the combustion of ABS in the near-flame region (chemical region) and the upper plume region (aerodynamic region). To this end, key PSD indicators, such as the count mean diameter (CMD), mass median diameter (MMD), and MMAD, were measured for each region using a high-performance aerosol spectrometer and a particle counter. The measured MMAD values for each region were input into the FDS simulation to model the structure of the gravimetric and simultaneous light extinction (GSLE) experimental device. Deposition characteristics by particle size and changes in smoke concentration distribution were compared and analyzed in both the near-flame and the upper plume regions.
Because the particle size data measured near the flame reflect the characteristics of the section where primary particles are generated during smoke formation, their use enables analysis of the sensitivity of transport and deposition characteristics. Conversely, the particle size data measured in the upper plume region reflect the aggregation and growth processes, thereby representing the typical characteristics of the smoke particles observed from the actual fire. Therefore, this study quantitatively identified the impact of particle size variation on smoke behavior by applying the MMAD values measured from the two regions to the FDS model, respectively, and comparing and analyzing changes in concentration distribution and soot deposition under the same conditions. This approach offers a practical analytical basis for enhancing the accuracy of smoke transport and visibility predictions.
2. Experimental and Numerical Setup
2.1. Measurement of Smoke Particle Size Distribution
The smoke particle formation mechanism is described in Figure 1. Precursors generated from the pyrolysis of combustibles form initial nuclei through nucleation, and primary particles are subsequently formed through growth and condensation. The primary particles then grow into partially coalesced agglomerates and agglomerates through the coagulation, breakage, aggregation, and coalescence processes.
This particle growth process varies depending on the upward flow and residence time of smoke. Relatively small particles are present in the near-flame region, while aggregation and growth occur more actively as particles move to the upper plume region. Therefore, in this study, experiments were performed for both the near-flame and the upper plume regions to analyze differences in deposition characteristics and concentration distribution caused by particle size variation.
PSD was quantitatively evaluated through experiments performed using GRIMM 11-D (GRIMM Aerosol Technik GmbH, Germany), a high-performance particle counter. Measurements were taken during the combustion of ABS.
Particle size measurements were performed at two locations: approximately 5 cm above the flame in the buoyant flow direction (near-flame region) and approximately 50 cm above the flame (upper plume region). PSD was measured five times at each location, with each measurement based on a 30-s sampling interval. The locations were set to precisely analyze the size distribution characteristics according to the formation stage and growth of smoke particles. The 5 cm location corresponds to the region dominated by the nucleation and initial condensation stages based on the particle formation mechanisms reported in previous studies[8-10]. The 50 cm location was set to the plume region where aerodynamic characteristics are dominant due to the sufficient growth of particles. Based on this, the impact of particle size variation on smoke transport and deposition behavior could be compared and analyzed for each region.
The particle count distribution as a function of particle size is expressed by the following particle distribution function (PSD):
where dN represents the number of particles per unit volume between the initial particle size D and the next particle size D + d for particle size classification, and dD denote the particle size section. fN(D) denotes a distribution function that represents the number of particles per unit diameter, and it is used to precisely identify the size characteristics of smoke particles. The cumulative number of classified particles can be converted into concentration by calculating each moment of PSD, which is expressed as follows:
Cumulative PSD is calculated as follows:
In Eq. (2), i = 0 is the zero-order moment, which represents the total number concentration per unit volume. i = 1 is interpreted as unit volume-based diameter concentration and i = 3 as mass concentration.
The number of particles according to the particle diameter is classified based on the zero-order moment, and the count median diameter (or geometric mean diameter, Dp,g) is calculated as follows:
where ni denotes the number of particles corresponding to the distribution section Di and Nt denotes the total number of particles.
CMD (Dp,c) and the mass mean diameter (Dp,m) are calculated by applying the Hatch-Choate transformation law[11] as follows:
where σ represents the standard deviation of the distribution, and p denotes the dimensional weighting factor for Dp. The values presented in Table 1 for Hatch-Choate transformation were used.
Generally, when the count median diameter (Dp,g) exceeds 0.5 μm, aerodynamic diameter characteristics should be also considered[12]. The aerodynamic diameter is defined as the diameter of spherical particles with the same settling velocity based on a density of 1.0 g/cm³ regardless of the shape and density of the particles. It is set to settle at the same velocity as the particles in the airflow. MMAD (Dp,ma) is calculated as follows:
where ρp denotes the density of smoke particles (1.74 g/cm³) and ρ0 the density of reference spherical particles (1.0 g/cm³).
Figure 2 shows the PSD experiment results measured approximately 5 cm above the flame in the buoyancy direction, following the ignition of ABS, a combustible, at the bottom. Measured CMD was converted into a percentage based on the total number of particles. The mass mean diameter was also converted into a percentage by dividing it by the total mass concentration. They were then visualized according to the aerodynamic particle diameter. The conversion into a percentage was performed to clearly identify the relative proportions of different diameter sections, and to facilitate intuitive interpretation of the relatively important size ranges. In the analysis results, small particles exhibited a relatively high frequency in the near-flame region, indicating that smoke particles mainly exist as primary particles corresponding to nucleation and condensation stages in the region.
Figure 3 shows the PSD results measured from the near-flame region (5 cm) and the upper plume region (50 cm) in a single graph. In the schematic at the top, the formation and growth mechanism of smoke particles is visualized by dividing it into the near-flame region and the upper plume region. In the graph at the bottom, the aerodynamic diameter distribution characteristics of the two regions are expressed for comparison. In the near-flame region, primary particles were dominant based on the count concentration, and MMAD was 1.03 μm. Conversely, in the upper plume region, agglomerates were actively formed and MMAD increased to 10.04 μm. This is likely due to the increased coagulation and aggregation between particles toward the upper plume region and the combination of the increase in residence time and the turbulent mixing effect in the upward flow. As these differences in PSD depending on the region significantly affect smoke transport and deposition behavior, the input of MMAD that reflects regional characteristics is also required in follow-up FDS simulation.
2.2. Numerical Modeling with FDS
In this study, the transport and wall deposition behavior of smoke particles were numerically analyzed using FDS (version 6.7.9), based on the MMAD values measured from each region during ABS combustion. FDS applies a Large Eddy Simulation (LES)-based numerical analysis technique, which resolves large eddies while modeling small eddies of the sub-grid scale (SGS) in turbulent flow analysis[13].
In LES-based FDS, physical quantities are separated into the grid scale (GS) and SGS components through spatial filtering of the three-dimensional incompressible governing equations. The Deardorff model is used as a turbulence model. This approach enables LES to precisely predict smoke flow, turbulence, and heat transfer characteristics that vary over time, as well as to calculate the movement and deposition behavior of aerosols.
In the transport and deposition process of smoke particles, various physical forces are combined around the particles. Figure 4 shows the major forces acting on a spherical smoke particle in FDS. Forces, such as gravity, thermophoresis, drag, and buoyancy, act on the particle. The interaction of these forces determines the transport path and wall deposition behavior of the particle. Gravity induces motion in the settling direction according to the mass of the particle. When a temperature gradient exists between the wall and fluid, the particle moves from the high-temperature region to the low-temperature wall due to thermophoresis. The relative speed between the gas and the particle in the flow field causes drag, attenuating the relative motion of the particle. The buoyancy generated by the velocity gradient in the flow has a certain level of influence under turbulent conditions.
FDS has constructed a deposition model by reflecting these physical mechanisms. The mass flux (m ˙ d e p . s ′ ′
In this instance, the mass of the smoke particles deposited per unit area is calculated by multiplying the smoke concentration on the wall (ρYs) by the deposition rate per unit area (udep). The deposition rate per unit area is the sum of the gravitational setting rate (ug), deposition rate by thermophoresis (uth), and deposition rate by diffusion and turbulence (udt), as shown in Eq. (7)[15].
This study focused on the analyzing deposition behavior according to the smoke particle size by region. While ug is strongly affected by the particle size, uth and udt are less affected by the particle size[5]. Therefore, the gravitational settling rate (ug) is calculated using Eq. (8)[16].
where g denotes the gravitational acceleration, ms the smoke particle mass, χd the particle shape factor, μ the kinematic viscosity of air, rs the smoke particle radius, and Cn the slippage correction factor of Cunningham, which is calculated using Eq. (9)[16].
where Kn represents the Knudsen number, which is calculated as the ratio of the average free path (Cs) to the particle radius (λs), as shown in Eq. (10)[17].
In this study, based on the above deposition model, 7.8 m2/g reported from a previous study[18] was input for the mass-specific extinction coefficient (Km) of ABS smoke used in the GSLE experiment, and the MMAD values of each region measured in Section 2.1 were applied for smoke particle size information. The differences in smoke transport and deposition characteristics between the regions were analyzed by applying MMAD 1.03 μm in the near-flame region (5 cm) and MMAD 10.04 μm in the upper plume region (50 cm).
FDS modeling was implemented by referring to the structure of the transmission cell (TC), a key component of the GSLE experimental device. The internal geometry of TC was modeled as a 0.8 m × 0.08 m × 0.08 m cuboid. The inflow rate was set to 6.6 L/min based on the airflow, and ABS smoke particles were injected in the form of a mixture with a mass ratio (Yₛ)[4]. Consequently, the analysis focuses on the transport and deposition behavior of the smoke particles introduced at a constant flow velocity without simulating flame or heat release characteristics. Therefore, characteristics length (D*)-based grid settings used in typical fire simulation are not applied in this study.
Accordingly, the grid size was determined at a level that can stably capture the transport and deposition behavior of smoke particles. When the grid size was changed from 5 to 10 and 20 mm for comparison, temporal changes in smoke concentration and soot deposition at the corresponding locations showed no significant difference. Therefore, in this study, the grid size (dx) was set to 10 mm considering numerical stability and computational efficiency.
In addition, the wall temperature was fixed at 25 ℃ to minimize the thermophoretic effect caused by the temperature gradient between the wall and the fluid, and deposition behavior was analyzed with focus on gravitational settling. The smoke particle mass deposited on the bottom wall of TC was set as the analysis target, and changes in soot deposition by region during the simulation time were compared and analyzed. Based on this, changes in deposition characteristics and smoke concentration distribution due to the particle size difference by region were compared and analyzed with FDS simulation results.
3. Results and Discussion
3.1. Comparison of FDS Results on Mass Concentration of Soot with Different Particle Sizes
Based on the MMAD measurement results described above, FDS simulations were performed in this study by inputting the MMAD values measured from the near-flame region and the upper plume region, respectively. Changes in smoke concentration distribution in each region were then analyzed.
In FDS, the mass concentration of smoke (ρYs) is calculated as the product of the smoke particle mass fraction (Ys) and the fluid density (ρ). The fluid density is used instead of the density of smoke particles because smoke particles are assumed to be aerosols completely mixed with the gaseous fluid in the FDS aerosol model.
In the simulation, MMAD 1.03 μm measured from the near-flame region (5 cm) and MMAD 10.04 μm measured from the upper plume region (50 cm) were applied, respectively. In both cases, the air/smoke mixture inflow rate was set to 6.6 L/min under the same conditions. Therefore, the mass fraction (Ys) represents the relative mass ratio of smoke particles in the entire fluid. By multiplying it by the fluid density (ρ), the actual mass concentration of smoke particles per unit volume (kg/m3) was calculated.
Figure 5 shows the changes in the average smoke concentration inside the TC (ρYs) during the simulation time under the MMAD condition by region. In the initial inflow stage, both conditions formed a stable smoke inflow state while showing similar concentration rise curves. This is because smoke was evenly distributed inside the TC, as the air/smoke mixture flow rate remained constant and the flow field in the FDS model stabilized rapidly.
As the simulation progressed, however, the average smoke concentration was formed near a relatively low position of 0.08 g/m3 under the MMAD 10.04 μm condition. Under the MMAD 1.03 μm condition, however, concentration variation at a relatively high position of 0.18 g/m3 was maintained. In particular, the peak concentrations under the two conditions differed by approximately 2.2 times.
This difference in concentration variation results from differences in smoke transport and loss mechanisms that depend on particle size. Large particles have a shorter residence time inside the TC due to the greater influence of gravitational settling and wall interactions, making it difficult to maintain the average concentration. In contrast, small particles maintain a more stable concentration distribution because the binding effect with the flow field is dominant. In addition, as the relative influence of thermophoresis and diffusion effects is not large for small particles, they exhibit different concentration maintenance characteristics from large particles for which gravitational settling is dominant as the main loss mechanism.
3.2. Comparison of Deposition Characteristics of Soot Particles with Different Particle Sizes
The smoke concentration results presented in the previous section confirmed that the average smoke concentration decreased relatively rapidly under the MMAD 10.04 μm condition. This concentration variation results from the gravitational settling of smoke particles and the loss caused by wall deposition. Therefore, in this section, the temporal change in the mass of the smoke particles deposited at the bottom of TC is compared and analyzed to investigate the difference in deposition characteristics depending on the particle size more quantitatively.
Figure 6 shows changes in the cumulative mass of the smoke particles deposited on the bottom wall of TC during the simulation time under the MMAD 1.03 μm and 10.04 μm conditions.
At the beginning of the simulation, soot deposition was insignificant for both conditions. Over time, however, cumulative soot deposition tended to rapidly increase under the MMAD 10.04 μm condition. Under the MMAD 1.03 μm condition, however, a gentle deposition increase curve was observed.
At the end of the simulation, cumulative soot deposition under the MMAD 10.04 μm condition was approximately 5.28 mg, which was approximately 38 times higher than cumulative soot deposition under the MMAD 1.03 μm condition (approximately 0.14 mg). These results quantitatively show that particles were rapidly deposited on the bottom wall of TC as the particle size increased due to the increased gravitational settling effect.
To further investigate differences in spatial deposition characteristics, the bottom wall of TC was uniformly divided into eight sections in the flow direction, and the distribution of soot deposition was analyzed for each section. Based on this analysis, the impact of particle size variation on deposition distribution at each location inside TC can be identified.
Figure 7 shows the distribution of soot deposition across each section at the end of the simulation. Under the MMAD 10.04 μm condition, Sections 1 and 2 (near the inlet) exhibited the highest soot deposition, and soot deposition tended to decrease as the section number increased. In particular, approximately 1 mg was deposited in Section 1, decreasing to approximately 0.1 mg in Section 8. This indicates that large particles rapidly settled immediately after introduction, and they tended to be deposited near the inlet.
Under the MMAD 1.03 μm condition, however, a relatively uniform deposition distribution was observed over all sections. The difference in soot deposition between the sections was not significant (approximately 0.002 mg), indicating that small particles were more uniformly spread due to the binding effect with the flow field and they are deposited over a broad area due to the increased residence time.
These quantitative results align with the smoke concentration variation tendency observed in the previous section, confirming that smoke concentration and deposition characteristics are closely related to the particle size. In particular, large particles rapidly settle, thereby sharply decreasing the average concentration inside TC and causing concentrated deposition near the bottom inlet. Small particles exhibit relatively excellent concentration maintenance and evenly distributed deposition.
3.3. Discussion of Particle Size Effects on Smoke Transport and Deposition
In this study, FDS simulation was performed by applying the MMAD measured for each region, and smoke concentration variation and deposition characteristics were quantitatively compared. The smoke concentration variation results confirmed in Section 3.1 showed that the average concentration tended to decrease more rapidly under the condition with larger MMAD. This tendency is consistent with the deposited mass results at the bottom of TC analyzed in Section 3.2. Under the MMAD 10.04 μm condition, the deposited mass significantly increased compared to the MMAD 1.03 μm condition, indicating that the deposition loss by gravitational settling is the main cause of the smoke concentration reduction.
In FDS, smoke concentration is calculated as the mass concentration of smoke (ρYs), which is the product of the smoke particle mass fraction (Ys) and the fluid density (ρ). As confirmed in Section 3.1, similar concentration increases occurred in the initial inflow stage under the same air/smoke mixture flow rate and Ys conditions. However, as the simulation progressed, the concentration reduction effect by deposition was evident when MMAD was large. This tendency aligns with the result of previous studies[5-7], which show that the gravitational settling effect significantly increases alongside the increase in smoke particle size.
In addition, the soot deposition under the MMAD 10.04 μm condition was approximately 38 times higher than that under the MMAD 1.03 μm condition. Accordingly, when the deposited mass distribution results were examined for each section inside TC, deposition concentration increased at the bottom and in the area near the outlet under the condition with large MMAD. This is likely because the residence time is short for large particles as they settle relatively rapidly in the flow field and the possibility of interactions with the walls is high for them. Conversely, small particles were evenly distributed because the binding effect with the airflow was dominant, and they exhibited more uniform distribution characteristics even in the deposition patterns by section.
This difference in deposition significantly affects the accuracy of smoke behavior predictions in fire simulation. In particular, the change in soot deposition caused by a change in MMAD is directly linked to smoke concentration variation, visibility, and sensor response performance beyond simple wall contamination. Therefore, reflecting PSD is required during the input of initial conditions for simulation.
The results of the FDS simulation performed in this study are consistent with the concentration and deposition behavior characteristics according to the particle size observed in previous studies, confirming that the deposition model of FDS properly reflects physical mechanisms. In particular, the findings of this study reconfirmed that the impact of a change in MMAD in indoor environment or enclosed space on smoke concentration predictions and visibility evaluation is an element that must be considered more precisely in the practical design and verification stages.
4. Conclusion
This study quantitatively analyzed the impact of the PSD generated during the combustion of ABS on smoke transport and wall deposition behavior through FDS-based simulation. To this end, PSD was measured in the near-flame region (5 cm) and the upper plume region (50 cm) using a GRIMM 11-D particle counter and the MMAD values by region were entered into FDS simulation.
In addition, the TC was modeled by referring to the structure of the GSLE experimental device, and the air/smoke mixture flow rate was set to 6.6 L/min. The thermophoretic effect was excluded by fixing the wall temperature at 25 ℃, and deposition behavior was analyzed with focus on gravitational settling. FDS simulated the flow field and smoke transport through LES-based analysis. For wall deposition, cumulative soot deposition over time was calculated using the deposition model in FDS.
The main results of this study are as follows:
(1) During ABS combustion, smoke particles grew to MMAD 1.03 μm in the near-flame region and MMAD 10.04 μm in the upper plume region. This confirmed that particles grew to large agglomerates through coagulation and aggregation processes as they ascended.
(2) In the results of FDS simulation performed under the same inflow conditions, the average smoke concentration (ρYs) rapidly decreased over the simulation time under the MMAD 10.04 μm condition, whereas a relatively stable concentration distribution was maintained under the MMAD 1.03 μm condition. This is likely because the residence time decreased and the loss increased due to the gravitational settling of large particles.
(3) The cumulative mass of the smoke particles deposited on the bottom wall of TC was 5.28 mg under the MMAD 10.04 μm condition, which was significantly higher compared to 0.14 mg under the MMAD 1.03 μm condition. When the bottom wall of TC was divided into eight sections for analysis, Sections 1 and 2 near the inlet exhibited the highest soot deposition for both conditions. Under the MMAD 10.04 μm condition, the non-uniformity of the deposition distribution was higher. This is likely due to the rapid settling of large particles and their increased interactions with the walls.
This study is a case of quantitatively analyzing the impact of particle size variation on FDS-based smoke transport and wall deposition prediction results for each region, and emphasizes the need to reflect PSD in fire simulation in the future.
Future research is required on PSD variation and deposition behavior under various fuel, combustion, and ventilation conditions, and the predictive accuracy of the model will be further improved through validation with actual experiment results.
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