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Int J Fire Sci Eng > Volume 38(3); 2024 > Article
Im, Kim, Jeong, and Lee: Error Rates of Tunnel Fire Simulations According to Model Scale

Research Paper

International Journal of Fire Science and Engineering 2024;38(3):1-7.

Published online: September 30, 2024

DOI: https://doi.org/10.7731/KIFSE.6f31474d

Error Rates of Tunnel Fire Simulations According to Model Scale

Hajun Im, Wonchang Kim, Keesin Jeong, Taegyu Lee†

Department of Fire and Disaster Prevention, Semyung University, Choongbuk 27136, Republic of Korea

†Corresponding Author, TEL: +82-43-649-1315, FAX: +82-43-649-1787, E-Mail: ltg777@semyung.ac.kr

Received August 1, 2024       Revised August 12, 2024       Accepted August 12, 2024

Copyright © 2024 Korean Institute of Fire Science and Engineering

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Many experiments, including firefighting experiments, have been performed through simulations to observe representative trends. Numerous experiments have also been conducted by making scale models because of space limitations. Simulations and scale model experiments, however, have large errors compared with real-world full-scale experiments. In this study, we used the PyroSim software to calculate the error rate of simulations performed at reduced scales. The simulation was designed using Froude scaling from 1:1 to 1:2, 1:10, and 1:20 ratios considering a tunnel bus fire scenario. In the simulation results, the smoke arrival time at a certain location showed an increasing error rate as the scale reduced, and the temperature showed a similar tendency. The results of this study are expected to contribute to the efficient design of simulations and scale model experiments considering the a tradeoff between experiment costs and error rates.

Keywords: Tunnel fire; Smoke flow; Simulation; Scale model; Error rate

1. Introduction

Advances in technology have allowed to increase the height and size of buildings, resulting in an increased risk of fire. Accordingly, there is growing interest in building safety. In addition, buildings in complex and diverse forms are becoming increasingly common as a wider range of types can be constructed. As a result, safety and firefighting are essential aspects that have been widely studied [1].
Among the deaths caused by fire accidents in South Korea over the past 5 years, suffocation caused by smoke and toxic gas inhalation accounted for more than 30.8% of the cases, and the mortality rate increased to 42.1% when accompanied by the inhalation burn caused by smoke, indicating that numerous deaths are closely related to smoke [2]. Accordingly, studies have been conducted worldwide, including Korea, to identify the flow and characteristics of smoke during fires.
Research on firefighting and safety has a relatively limited environment to perform experiments. As completely accurate characteristics can be identified only through observation by causing a fire or through experiments performed in spaces that are actually used or completed, experiments are limited, and perfectly accurate data are difficult to collect [3]. Thus, scale model and computer simulation experiments that identify tendencies by making small models have been performed in various fields, including firefighting, where experiments are constrained [4,5].
Scale model experiments are similar to computer simulations but differ in various aspects. Scale models can be easily constructed compared with actual experiments, but material selection and model construction are limited. For instance, when a scale model fire experiment is performed, reusing an already tested model is difficult, and even a small error may cause the collapse of the experiment. In addition, even replicating the same model may lead to different results from the expected error depending on the model scale. Many researchers, however, suitably predicted trends from scale model experiments and analyzed fire characteristics before the appearance of computer simulations [6].
In this study, we aimed to analyze the error rate of small-scale simulation experiments to secure quality data from fire experiments by complementing the shortcomings of scale model experiments and computer simulations. An appropriate scale with respect to the human and physical resources required for experimentation was considered by performing simulations at various scales. Our findings are expected to contribute to the acquisition of quality research data in firefighting and other fields.

2. Simulation Setup

2.1 Simulation design

Figure 1 shows the design of this simulation using Pyrosim. The simulation was designed considering a bus fire in a tunnel of 1,000 × 10 × 5 m. The mesh was opened at both ends of the tunnel, and flames were set to occur continuously on the top of the bus. The maximum fire intensity was set to 20 MW in accordance with the NFPA 502 standard, and the simulation was performed for 1,200 s [7]. Heptane was used as the material of the fire source, and parameters CO_YIELD = 0.010 and SOOT_YIELD = 0.015 were considered. The vehicle had a size of 2.5 × 4.0 × 13.0 m in accordance with KDS 44 10 00: 2023 [8]. To compare the behavior of smoke between short and long sections, we assumed the bus fire onset was at 200 m from the 1,000 m tunnel entrance at the 1:1 scale.
Table 1 lists the values set according to the simulation scales considered in this study. The size of the tunnel was reduced in a dimension proportional to the scale ratio, and the cell size was reduced accordingly [9]. The peak heat release rate (HRR) was 20 MW at the 1:1 scale, and HRR was calculated according to the scale reduction by applying the Froude scaling law. The HRR per unit area was calculated by dividing the HRR by the area of the top surface of the bus. Room temperature was set to 20 ℃. Gas detectors were simulated to be installed at heights of 5 and 1.8 m for the 1:1 scale considering the maximum tunnel height and human breathing height, respectively, and temperature sensors were simulated to be installed at 5 and 1.5 m for the 1:1 scale.

2.2 Simulation equations

The PyroSim software is based on fire dynamics simulation (FDS). In this study, simulation was performed by applying a large eddy simulation, and FDS calculations were performed using the following four governing equations [10,11]:
(1)
∂ρ∂t+∂(ρuj)∂xj=0
(2)
(∂∂t(ρuj)+∂∂xi(ρujui))=∂∂xi(μeff(∂ui∂xi+∂uj∂xi))−∂ρ∂xi+ρgi
(3)
∂∂t(ρ∅)+∂∂xj(ρuj∅)=∂∂xj(Γeff∂∅∂xj)+S∅
(4)
P=ρRT
These equations represent the mass conservation, momentum conservation, scalar modeling, and equation of state, respectively. The behavior of heat and smoke in simulations was calculated based on the formulas for FDS.
Eqs. (5)-(7) represent the Froude scaling law. In this study, the length of the tunnel was adjusted using a primary function, but the constants related to HRR, smoke flow velocity, and time could not be one-dimensionally reduced in the same manner as the length. Thus, the Froude scaling law was used.
(5)
VMVP=(LMLP)1/2=α
(6)
TMTP=(LM/VMLP/VP)1/2=α
(7)
QMQP=(LMLP)5/2=α5
where Q is the HRR, V is the flow velocity, L is the length, M represents the model, P represents the prototype, and α is the length scale. Eqs. (5) and (6) show that the velocity ratio between the model and prototype is proportional to the square root of the length ratio, and the time ratio is also proportional to the square root of the length because it is related to the velocity ratio. On the other hand, according to Eq. (7), the HRR is proportional to the length ratio to the power of 5/2.

3. Simulation Results

3.1 Simulated temperature characteristics

Figure 2 shows the simulation temperature results at scales of 1:1, 1:2, 1:10, and 1:20. The results of the temperature sensor at 150 m from the entrance, 50 m from the bus, and a height of 5 m are shown. After sufficient smoke arrival and temperature increase at the sensor location, the temperature was found to be approximately 182 ℃ at the 1:1 scale, 159 ℃ at the 1:2 scale, 115 ℃ at the 1:10 scale, and 78 ℃ at the 1:20 scale. Compared with the 1:1 scale, differences of approximately 12.6%, 36.8%, and 57.1% (at 1:2, 1:10, and 1:20 scales, respectively) were observed. In addition, the times to reach a stable section after a sharp temperature increase were 232, 220, 230, and 228 s for the 1:1, 1:2, 1:10, and 1:20 scales, respectively, indicating a sufficient temperature increase over a similar period.

3.2 Smoke arrival time and error rate results

Figure 3 shows the smoke arrival time at each gas detector according to the simulation scale. The smoke arrival time was analyzed at heights 5.0 and 1.8 m separately. The smoke arrival time showed a similar pattern at all scales, with only slight differences depending on the scale. Figure 3(a) shows the smoke arrival time at the gas detector located at the human breathing height of 1.8 m. Smoke was not measured at gas detector locations 20 and 21 due to the presence of the bus. Figure 3(b) shows the smoke arrival time at 5.0 m. The smoke flow graph showed a form similar to that of a primary function divided around the bus location. In the two graphs, the smoke flow at the 1:20 scale was different from the smoke flow at different scales, possibly owing to excessive scale reduction.
Figure 4 shows the absolute error rate of the smoke arrival time compared with that at the 1:1 scale. At a gas detector location of 1.8 m, the difference from the model of the 1:1 scale increased as the scale of the simulation model decreased. The error rate increased according to the reduction ratio towards the location of the fire source. When smoke was more than 100 m away from the fire source, however, the error according to the scale reduction was not constant. At a gas detector location of 5.0 m, different patterns from those at 1.8 m were observed. Consequently, analysis was limited as the scale decreased.
Figure 5 shows the average absolute error rate of smoke arrival time with respect to the time at the 1:1 scale. At a gas detector height of 5.0 m, the error rate was 12.9% at the 1:2 scale, 16.6% at the 1:10 scale, and 13.1% at the 1:20 scale, showing that the error rate increase was not inversely proportional to the scale reduction. At a gas detector height of 1.8 m, however, error rates of 11.1%, 19.01%, and 27.1% were observed at the 1:2, 1:10, and 1:20 scales, respectively. The error rate with respect to the smoke arrival time at the 1:1 scale increased as the model became smaller. Overall, additional calculations may be helpful in reducing the error rate.

4. Conclusion

In this study, simulations were performed by designing a tunnel bus fire scenario at various scales. The following conclusions were drawn:
1) When the simulation temperature was analyzed according to the scale, the temperature was found to be approximately 182 ℃ at the 1:1 scale, 159 ℃ at the 1:2 scale, 115 ℃ at the 1:10 scale, and 78 ℃ at the 1:20 scale. Hence, as the scale decreased, the temperature at the same location also decreased. Compared with the 1:1 scale, the differences were approximately 12.6%, 36.8%, and 57.1% for the 1:2, 1:10, and 1:20 scales, respectively. Consequently, as the scale decreased, the error rate with respect to the results at the 1:1 scale increased.
2) Smoke flow was expected to spread in the shape of an inverted trapezoid with respect to the fire source, but the simulation results for smoke flow showed a different trend. This appeared to be because a thick smoke layer was formed from the time when smoke flow was generated and spread. In addition, the exit of the tunnel was not reached over the simulation period of 1,200 s. In particular, the smallest flow was observed at the 1:20 scale, which was the smallest scale.
3) Smoke flow showed a similar pattern at all scales, resulting in slight differences depending on the scale. In addition, the flow velocity of smoke was relatively constant, and the smoke arrival times followed the shape of primary functions on both sides of the bus.
4) When the smoke arrival time error between a simulation scale of 1:1 and the reduced scales was calculated, the gas detectors at 5.0 and 1.8 m showed different patterns. The trigger time error rate of the gas detector at 5.0 m was not proportional to the scale, whereas the error rate increased as the model scale was reduced for the gas detector at 1.8 m, which is the human breathing height.
In this study, simulations were designed assuming that the error rate increased as the scale increased. Different results, however, were observed depending on the detector location. This appeared to be due to the smoke occurrence height at the fire source and different smoke flow characteristics depending on the height. Therefore, the calculation of correction values according to the scale is required in future work considering various conditions. This is expected to contribute to improve the accuracy of scale model and simulation experiments as well as reducing experiment costs.

Notes

Author Contributions

Conceptualization, W.K. and T.L.; methodology, W.K.; software, W.K and K.J.; validation, W.K. and T.L.; formal analysis, H.I.; investigation, H.I.; resources, W.K.; data curation, H.I.; writing―original draft preparation, H.I.; writing―review and editing, W.K.; visualization, T.L.; supervision, W.K.; project administration, T.L.; funding acquisition, K.J. All authors have read and agreed to the published version of the manuscript.

Conflicts of Interest

The authors declare no conflict of interest.

Acknowledgments

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2022R1F1A1073333).

Figure 1.
Experimental design of tunnel and bus in PyroSim.
KIFSE-6f31474df1.jpg
Figure 2.
Temperature results according to simulation scale.
KIFSE-6f31474df2.jpg
Figure 3.
Smoke arrival time at gas detectors according to scale.
KIFSE-6f31474df3.jpg
Figure 4.
Absolute error rate of smoke arrival time with respect to smoke arrival time at 1:1 scale.
KIFSE-6f31474df4.jpg
Figure 5.
Average absolute error rate of smoke arrival time with respect to smoke arrival time at 1:1 scale.
KIFSE-6f31474df5.jpg
Table 1.
Simulation Conditions Considered in This Study
Parameter Scale
1:1 1:2 1:10 1:20
Tunnel size (L × W × H) [m] 1,000 × 10 × 5 500 × 5 × 2.5 100 × 1 × 0.5 50 × 0.5 × 0.25
Cell size [m] 0.5 0.25 0.05 0.025
Peak HRR [kW] 20,000 3535.5 63.2 11.2
HRR per unit area [kW] 615.4 435.1 194.6 137.6
Ambient temperature [℃] 20
Gas detector location (H) [m] 5 1.8 2.5 0.9 0.5 0.18 0.25 0.09
Temperature sensor location (H) [m] 5 1.5 2.5 0.75 0.5 0.15 0.25 0.075

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