# Evaluating the Ceiling Gas Temperature in a Branched Tunnel Fire with a Sloped Mainline Region under Natural Ventilation

^{1}

^{2}

^{*}

## Abstract

**:**

^{*2/3}, but the effect of the mainline slope on temperature longitudinal decay is worth considering. Finally, a normalized expression for longitudinal temperature decay in an inclined mainline is proposed by taking the fire power and mainline slope into account.

## 1. Introduction

_{max}is the maximum ceiling temperature rise in K, Q is the heat release rate in kW, v is the ventilation velocity in m/s, r is the radius of the fire source in m, H

_{ef}is the effective tunnel height in m, U’ is the non-dimensional ventilation velocity, w* is the characteristic plume velocity in m/s, and g is the gravitational acceleration in m/s

^{2}; ρ

_{a}is the ambient density in kg/m

^{3}, c

_{p}is the specific heat of air kJ/kg·K, and T

_{a}is the ambient temperature in K.

## 2. Theoretical Analysis

_{stack}= ΔρgH, where ΔP

_{stack}is the stack pressure difference in Pa, Δρ is the density difference in kg/m

^{3}, and H is the height in m. Under the circumstances, the stack pressure is only induced at the upstream mainline before shunting. Thus, the stack pressure in the upstream region is expressed as follows:

_{u}is the smoke back-layering length upstream in m, β is the tunnel slope angle in degree, and h and L are the height difference and length between the inclined mainline two ends in m.

_{u}is the temperature exponential decay coefficient. Substituted Equation (4) into Equation (3) and integrals as follows:

_{stack,u}induced by the stack effect between smoke stagnation and joint node. Thus, the pressure difference induced by buoyancy is given as follows:

_{buo}is the airflow velocity induced by buoyancy in m/s.

_{smoke}is the density of the smoke layer in kg/m

^{2}, v

_{e}is the induced velocity in m/s, and P

_{a}, P

_{b}, and P

_{c}are the kinetic energy in mainline before shunting, mainline after shunting, and ramp in Pa, respectively; ΔP

_{e}is the pressure difference induced by asymmetric entrainment in Pa. The kinetic energy in the tunnel could be expressed as follows:

_{i}is the dynamic pressure of smoke movement in different tunnel regions in Pa, and u

_{i}is the smoke movement velocity in a tunnel in m/s.

_{r}is the coefficient induced by the branched structure, λ is the friction coefficient, and D

_{s}is the hydraulic diameter of the smoke layer in m. From ideal gas law with density and temperature, the dynamic pressure in each tunnel region induced by smoke movement is given as follows:

_{i}is the length of the relative tunnel region in m.

_{a}> P

_{b}+ P

_{c}cosθ, v

_{e}is a positive value in the same direction as v

_{buo}, otherwise v

_{e}is negative.

_{ef}

^{*}

^{2/3}, and k

_{r}relates to sinθ. Therefore, the ventilation velocity in the branched tunnel with an inclined mainline before shunting can be given as follows:

^{*}, and the left-hand side of the expression is normalized using (gH)

^{1/2}. The dimensionless formula for induced ventilation velocity is given as follows:

_{T}is the coefficient accounting for bifurcation structure, and V’ is the dimensionless induced velocity.

## 3. Numerical Method

#### 3.1. Physical Model Set-Up

#### 3.2. Grid Sensitivity Analysis

_{x}= 6. The minimum fire power in the present work was 3 MW, and the corresponding D* was 1.49. Hence, the grid size of 0.25 m was adopted under D*/δ

_{x}= 6. Therefore, in order to save time and obtain accurate results, the grid size near the fire source 55 m was set as 0.25 m, and the mesh away from the fire source was 0.5 m. The boundary of the mesh is set as “Open” to connect with the outside.

## 4. Results and Discussion

#### 4.1. Induced Velocity in Sloped Mainline

#### 4.2. Maximum Temperature in Branched Tunnel

_{max}declined with the mainline slope. For Q < 15 MW, the effect of the mainline slope on the maximum ceiling temperature rise is limited. But in the inclined single-line tunnel, Zhong et al. [54] and Zhang et al. [31] found that the maximum temperature decreased with the larger tunnel slope regardless of fire power. The downstream and upstream in the previous ordinary tunnel are also inclined so that the fire plume can easily deflect downstream. The induced airflow enhances the heat convection between smoke and fresh air, resulting in a cooling effect. At the same time, the distance from the fire source to the ceiling increased with the tunnel slope. The more heat is lost due to convection and radiation before the plume impinges on the ceiling, the maximum temperature decreases with a greater tunnel slope in an ordinary inclined tunnel.

_{ef}

^{*2/3}, as shown in Figure 10. Overall, the dimensionless ceiling maximum excess temperature can be well collapsed by Q

_{ef}

^{*2/3}exponentially, expressed as Equation (22).

#### 4.3. Temperature Longitudinal Decay in Sloped Mainline

_{1}and A

_{2}are constant coefficients, B

_{1}and B

_{2}are the coefficients varied with different branched tunnel regions, x is the axis distance in m, x

_{max}is the position of maximum temperature, and H is the tunnel height in m.

^{*}, given as follows:

_{1}, A

_{2}, and B

_{1}have a very small difference between each condition. Therefore, the average value is used to correct the coefficients, where A

_{1}= 0.6, A

_{2}= 0.4 and B

_{1}= 2.5. The exponential power index coefficient of B

_{2}increases with the mainline slope and can be correlated by h/L, as shown in Figure 14. The coefficient of B

_{2}can be given as follows:

## 5. Conclusions

- (1)
- The unidirectional airflow velocity in the inclined mainline region is induced during a slope larger than 1% due to the stack effect. The induced velocity increased with the upstream mainline slope that prevents the smoke reverse flow. A dimensionless expression is proposed to correlate the induced airflow velocity that shows a good linearly increasing for the mainline slope larger than 1%.
- (2)
- The effect of the mainline slope on the maximum temperature beneath the tunnel ceiling is limited, especially for relatively small fire power. The dimensionless maximum temperature can be well collapsed using Q
_{ef}^{*2/3}but is independent on a mainline slope. The growth rate of maximum temperature is divided into two parts by a slope of 1%. A two-piecewise formula is developed for the maximum temperature beneath the ceiling in the branched tunnel with an inclined upstream mainline. - (3)
- The mainline slope before shunting significantly affects the temperature longitudinal decay in the inclined mainline region, which can be well correlated using the sum of two exponential functions. The attenuation coefficients relate to heat release rate under a 1% slope, but it is independent of fire power during a slope larger than 1%. The empirical model is proposed to predict the longitudinal ceiling temperature in the sloped mainline region. This study contributes to the understanding of smoke temperature profiles in naturally branched tunnels with negative mainlines and guides extraction design.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

A_{1,} A_{2} | constant coefficient | ΔT_{(x)} | ceiling excess temperature (K) |

B_{1}, B_{2} | coefficients varied with different branched tunnel region | ΔT_{max} | maximum ceiling temperature rise (K) |

c_{p} | specific heat of air (kJ/kg·K) | u_{i} | smoke movement velocity in tunnel (m/s) |

C_{T} | coefficient account for bifurcation structure | U’ | non-dimensional ventilation velocity |

d | thickness of smoke layer (m) | v_{e} | induced velocity (m/s) |

D^{*} | characteristic fire diameter | v_{buo} | airflow velocity induced by buoyancy (m/s) |

D_{s} | hydraulic diameter of smoke layer (m) | v | ventilation velocity (m/s) |

f | full size parameter | V’ | dimensionless induced velocity |

g | gravitational acceleration (m/s^{2}) | w* | characteristic plume velocity (m/s) |

h | height difference between inclined mainline two ends (m) | x | axis distance (m) |

H_{ef} | effective tunnel height (m) | x_{max} | position of maximum temperature (m) |

H | tunnel height (m) | ||

k_{r} | coefficient induced by branched structure | Greek symbols | |

K_{u} | temperature exponential decay coefficient | △ | difference |

l_{u} | smoke back-layering length at upstream (m) | θ | bifurcation angle (°) |

l_{i} | length of relative tunnel region (m) | ρ_{a} | ambient density (kg/m^{3}) |

L | length between inclined mainline two ends (m) | ρ_{smoke} | density of smoke layer (kg/m^{2}) |

P_{a,} P_{b,} P_{c} | kinetic energy in mainline before shunting, mainline after shunting, and ramp (Pa) | Δρ | density difference (kg/m^{3}) |

P_{i} | dynamic pressure of smoke movement in difference tunnel region (Pa) | β | tunnel slope angle in degree |

ΔP_{e} | pressure difference induced by asymmetric entrainment (Pa) | λ | friction coefficient |

ΔP_{buo} | pressure difference induced by buoyancy (Pa) | ||

ΔP_{stack} | stack pressure difference (Pa) | Subscripts and Superscripts | |

ΔP_{stack, u} | pressure difference induced by stack effect between smoke stagnation and joint node (Pa) | a | ambient |

Q | heat release rate (kW) | buo | buoyancy |

Q_{ef} | heat release rate for effective tunnel height | e | entrainment |

Q* | dimensionless heat release rate | ef | effective |

Q_{ef}* | dimensionless heat release rate based on the effective tunnel height | i | relative tunnel region |

r | radius of fire source (m) | s | smoke |

T_{a} | ambient temperature (K) | stack, u | stack effect at upstream |

ΔT | longitudinal temperature rise (K) | u | upstream |

## References

- Deng, Y.W.; Chen, C.; Li, Q.; Hu, Q.Q.; Yuan, H.T.; Li, J.M.; Li, Y. Measurements of real-world vehicle CO and NOx fleet average emissions in urban tunnels of two cities in China. Atmos. Environ.
**2015**, 122, 417–426. [Google Scholar] [CrossRef] - Meng, N.; Shu, Y.M.; Zhang, S.H. Study on smoke temperature induced by two fires in a naturally ventilated tunnel. Tunn. Undergr. Space Technol.
**2023**, 131, 104774. [Google Scholar] [CrossRef] - Wan, H.X.; Jiang, Y.J.; Jiang, J.P. A survey of fire accidents during the process of highway tunnel operation in China from 2010 to 2021: Characteristics and countermeasures. Tunn. Undergr. Space Technol.
**2023**, 139, 105237. [Google Scholar] [CrossRef] - Caliendo, C.; Genovese, G.; Russo, I. A 3D CFD modeling for assessing the effects of both longitudinal slope and traffic volume on user safety within a naturally ventilated road tunnel in the event of a fire accident. IATSS Res.
**2022**, 46, 547–558. [Google Scholar] [CrossRef] - Yang, D.; Liu, Y.L.; Zhao, C.M.; Mao, S.H. Multiple steady states of fire smoke transport in a multi-branch tunnel: Theoretical and numerical studies. Tunn. Undergr. Space Technol.
**2017**, 61, 189–197. [Google Scholar] [CrossRef] - Li, Q.; Chen, C.; Deng, Y.W.; Li, J.M.; Xie, G.Y.; Li, Y.; Hu, Q.Q. Influence of traffic force on pollutant dispersion of CO, NO and particle matter (PM2.5) measured in an urban tunnel in Changsha, China. Tunn. Undergr. Space Technol.
**2015**, 49, 400–407. [Google Scholar] [CrossRef] - Du, T.; Yang, D.; Peng, S.N.; Xiao, Y.M. A method for design of smoke control of urban traffic link tunnel (UTLT) using longitudinal ventilation. Tunn. Undergr. Space Technol.
**2015**, 48, 35–42. [Google Scholar] [CrossRef] - Li, Q.; Chen, C.; Yuan, H.T.; Wang, L.Y.; Xu, S.H.; Li, Y.R. Prediction of pollutant concentration and ventilation control in urban bifurcate tunnel, China. Tunn. Undergr. Space Technol.
**2018**, 82, 406–415. [Google Scholar] [CrossRef] - Liu, C.; Zhong, M.H.; Tian, X.L.; Zhang, P.H.; Xiao, Y.; Mei, Q. Experimental and numerical study on fire-induced smoke temperature in connected area of metro tunnel under natural ventilation. Int. J. Therm. Sci.
**2019**, 138, 84–97. [Google Scholar] [CrossRef] - Jiang, L.; Creyssels, M.; Hunt, G.R.; Salizzoni, P. Control of light gas releases in ventilated tunnels. J. Fluid Mech.
**2019**, 872, 515–531. [Google Scholar] [CrossRef] - Alpert, R.L. Calculation of response time of ceiling-mounted fire detectors. Fire Technol.
**1972**, 8, 181–195. [Google Scholar] [CrossRef] - Alpert, R.L. Turbulent ceiling-jet induced by large-scale fires. Combust. Sci. Technol.
**1975**, 11, 197–213. [Google Scholar] [CrossRef] - Kurioka, H.; Oka, Y.; Satoh, H.; Sugawa, O. Fire properties in near field of square fire source with longitudinal ventilation in tunnels. Fire Saf. J.
**2003**, 38, 319–340. [Google Scholar] [CrossRef] - Hu, L.H.; Huo, R.; Peng, W.; Chow, W.K.; Yang, R.X. On the maximum smoke temperature under the ceiling in tunnel fires. Tunn. Undergr. Space Technol.
**2006**, 21, 650–655. [Google Scholar] [CrossRef] - Li, Y.Z.; Lei, B.; Ingason, H. The maximum temperature of buoyancy-driven smoke flow beneath the ceiling in tunnel fires. Fire Saf. J.
**2011**, 46, 204–210. [Google Scholar] [CrossRef] - Salizzoni, P.; Peruzzi, C.; Marro, M.; Cingi, P.; Angeli, D.; Kubwimana, T.; Mos, A. Measurements and scaling of buoyancy-induced flows in ventilated tunnels. Flow
**2023**, 3, E15. [Google Scholar] [CrossRef] - Tang, F.; Mei, F.Z.; Wang, Q.; He, Z.; Fan, C.G.; Tao, C.F. Maximum temperature beneath the ceiling in tunnel fires with combination of ceiling mechanical smoke extraction and longitudinal ventilation. Tunn. Undergr. Space Technol.
**2017**, 68, 231–237. [Google Scholar] [CrossRef] - Zhou, T.N.; He, Y.P.; Lin, X.; Wang, X.H.; Wang, J. Influence of constraint effect of sidewall on maximum smoke temperature distribution under a tunnel ceiling. Appl. Therm. Eng.
**2017**, 112, 932–941. [Google Scholar] [CrossRef] - Zhou, T.N.; Li, H.H.; Chen, Q.P.; Wei, R.C.; Wang, J. Understanding sidewall constraint involving ventilation effects on temperature distribution of fire-induced thermal flow under a tunnel ceiling. Int. J. Therm. Sci.
**2018**, 129, 290–300. [Google Scholar] [CrossRef] - Hu, L.H.; Huo, R.; Li, Y.Z.; Wang, H.B.; Chow, W.K. Full-scale burning tests on studying smoke temperature and velocity along a corridor. Tunn. Undergr. Space Technol.
**2005**, 20, 223–229. [Google Scholar] [CrossRef] - Tang, F.; Cao, Z.L.; Chen, Q.; Meng, N.; Wang, Q.; Fan, C.G. Effect of blockage-heat source distance on maximum temperature of buoyancy-induced smoke flow beneath ceiling in a longitudinal ventilated tunnel. Int. J. Heat Mass Transf.
**2017**, 109, 683–688. [Google Scholar] [CrossRef] - Chen, C.K.; Zhu, C.X.; Liu, X.Y.; Yu, N.H. Experimental investigation on the effect of asymmetrical sealing on tunnel fire behavior. Int. J. Heat Mass Transf.
**2016**, 92, 55–65. [Google Scholar] [CrossRef] - Yao, Y.Z.; He, K.; Peng, M.; Shi, L.; Cheng, X.D.; Zhang, H.P. Maximum gas temperature rise beneath the ceiling in a portals-sealed tunnel fire. Tunn. Undergr. Space Technol.
**2018**, 80, 10–15. [Google Scholar] [CrossRef] - Huang, Y.B.; Li, Y.F.; Dong, B.Y.; Li, J.M.; Liang, Q. Numerical investigation on the maximum ceiling temperature and longitudinal decay in a sealing tunnel fire. Tunn. Undergr. Space Technol.
**2018**, 72, 120–130. [Google Scholar] [CrossRef] - Shi, J.K.; Zuo, C.; Xiong, Y.; Zhou, M.; Lin, P. Experimental study of different sealing ratios on the self-extinction of tunnel fires. Tunn. Undergr. Space Technol.
**2021**, 112, 103894. [Google Scholar] [CrossRef] - Tang, F.; Cao, Z.L.; Palacios, A.; Wang, Q. A study on the maximum temperature of ceiling jet induced by rectangular-source fires in a tunnel using ceiling smoke extraction. Int. J. Therm. Sci.
**2018**, 127, 329–334. [Google Scholar] [CrossRef] - Takeuchi, S.; Aoki, T.; Tanaka, F.; Moinuddin, K.A.M. Modeling for predicting the temperature distribution of smoke during a fire in an underground road tunnel with vertical shafts. Fire Saf. J.
**2017**, 91, 312–319. [Google Scholar] [CrossRef] - Cong, H.Y.; Bi, M.S.; Bi, Y.B.; Jiang, H.P.; Li, Y.C.; Gao, W. Experimental and theoretical studies on the smoke temperature distribution along the tunnel ceiling with natural ventilation by the board-coupled shafts. Int. J. Therm. Sci.
**2021**, 159, 106639. [Google Scholar] [CrossRef] - Oka, Y.; Imazeki, O. Temperature distribution within a ceiling jet propagating in an inclined flat-ceilinged tunnel with natural ventilation. Fire Saf. J.
**2015**, 71, 20–33. [Google Scholar] [CrossRef] - Huo, Y.; Gao, Y.; Chow, W.K. A study on ceiling jet characteristics in an inclined tunnel. Tunn. Undergr. Space Technol.
**2015**, 50, 32–46. [Google Scholar] [CrossRef] - Zhang, X.L.; Lin, Y.J.; Shi, C.L.; Zhang, J.P. Numerical simulation on the maximum temperature and smoke back-layering length in a tilted tunnel under natural ventilation. Tunn. Undergr. Space Technol.
**2021**, 107, 103661. [Google Scholar] [CrossRef] - Hu, L.H.; Chen, L.F.; Wu, L.; Li, Y.F.; Zhang, J.Y.; Meng, N. An experimental investigation and correlation on buoyant gas temperature below ceiling in a slopping tunnel fire. Appl. Therm. Eng.
**2013**, 51, 246–254. [Google Scholar] [CrossRef] - Ji, J.; Wang, Z.Y.; Ding, L.; Yu, L.X.; Gao, Z.H.; Wan, H.X. Effects of ambient pressure on smoke movement and temperature distribution in inclined tunnel fires. Int. J. Therm. Sci.
**2019**, 145, 106006. [Google Scholar] [CrossRef] - Han, J.Q.; Liu, F.; Wang, F.; Weng, M.C.; Wang, J. Study on the smoke movement and downstream temperature distribution in a sloping tunnel with one closed portal. Int. J. Therm. Sci.
**2020**, 149, 106165. [Google Scholar] [CrossRef] - Chen, C.K.; Nie, Y.L.; Zhang, Y.L.; Lei, P.; Fan, C.G.; Wang, Z.Y. Experimental investigation on the influence of ramp slope on fire behaviors in a bifurcated tunnel. Tunn. Undergr. Sp. Technol.
**2020**, 104, 103522. [Google Scholar] [CrossRef] - Huang, Y.B.; Li, Y.F.; Li, J.M.; Li, J.X.; Wu, K.; Zhu, K.; Li, H.H. Experimental investigation on maximum gas temperature beneath the ceiling in a branched tunnel fire. Int. J. Therm. Sci.
**2019**, 145, 105997. [Google Scholar] [CrossRef] - Huang, Y.B.; Li, Y.F.; Li, J.X.; Wu, K.; Li, H.H.; Zhu, K. Experimental study on the temperature longitudinal distribution induced by a branched tunnel fire. Int. J. Therm. Sci.
**2021**, 170, 107175. [Google Scholar] [CrossRef] - Lei, P.; Chen, C.K.; Zhang, Y.L.; Xu, T.; Sun, H.K. Experimental study on temperature profile in a branched tunnel fire under natural ventilation considering different fire locations. Int. J. Therm. Sci.
**2021**, 159, 106631. [Google Scholar] [CrossRef] - Lei, P.; Chen, C.K.; Zhao, D.Y.; Zhang, Y.L.; Xu, T.; Jiao, W.B. Study on heat allocation and temperature profile in a T-shaped branched tunnel fire with different branch slopes under natural ventilation. Tunn. Undergr. Space Technol.
**2022**, 126, 104508. [Google Scholar] [CrossRef] - Liu, C.; Zhong, M.H.; Shi, C.L.; Zhang, P.H.; Tian, X.L. Temperature profile of fire-induced smoke in node area of a full-scale mine shaft tunnel under natural ventilation. Appl. Therm. Eng.
**2017**, 110, 382–389. [Google Scholar] [CrossRef] - Li, Z.S.; Gao, Y.J.; Li, X.S.; Mao, P.F.; Zhang, Y.C.; Jin, K.Y.; Li, T.; Chen, L.F. Effects of transverse fire locations on flame length and temperature distribution in a bifurcated tunnel fire. Tunn. Undergr. Space Technol.
**2021**, 112, 103893. [Google Scholar] [CrossRef] - Liang, K.; Hao, X.F.; An, W.G.; Tang, Y.H.; Cong, Y.Z. Study on cable fire spread and smoke temperature distribution in T-shaped utility tunnel. Case Stud. Therm. Eng.
**2019**, 14, 100433. [Google Scholar] [CrossRef] - Cheng, H.H.; Liu, C.; Chen, J.F.; Wu, L.; Zhao, Y.T.; Zhong, M.H. Full-scale experimental study on fire under natural ventilation in the T-shaped and curved tunnel groups. Tunn. Undergr. Space Technol.
**2022**, 123, 104442. [Google Scholar] [CrossRef] - Huang, Y.B.; Liu, X.; Dong, B.Y.; Zhong, H.; Wang, B.; Dong, Q.W. Effect of inclined mainline on smoke back-layering length in a naturally branched tunnel fire. Tunn. Undergr. Space Technol.
**2023**, 134, 104985. [Google Scholar] [CrossRef] - Gao, Z.H.; Liu, Z.X.; Ji, J.; Fan, C.G.; Li, L.J.; Sun, J.H. Experimental study of tunnel sidewall effect on flame characteristics and air entrainment factor of methanol pool fires. Appl. Therm. Eng.
**2016**, 102, 1314–1319. [Google Scholar] [CrossRef] - Huang, Y.B.; Li, Y.F.; Li, J.X.; Wu, K.; Li, H.H.; Zhu, K.; Li, J.M. Experimental investigation of the thermal back-layering length in a branched tunnel fire under longitudinal ventilation. Int. J. Therm. Sci.
**2022**, 173, 107415. [Google Scholar] [CrossRef] - Blanchard, E.; Boulet, P.; Desanghère, S.; Carlotti, P. Energy balance in a tunnel fire: Midscale tests and CFD simulations. ISAT
**2011**, 14, 349–362. [Google Scholar] - Yao, Y.Z.; Li, Y.Z.; Ingason, H.; Cheng, X.D. Numerical study on overall smoke control using naturally ventilated shafts during fires in a road tunnel. Int. J. Therm. Sci.
**2019**, 140, 491–504. [Google Scholar] [CrossRef] - Deng, T.; Norris, S.; Sharma, R.N. Numerical study of the flame geometry of pool fires in longitudinally ventilated tunnels. Tunn. Undergr. Space Technol.
**2023**, 132, 104882. [Google Scholar] [CrossRef] - Wang, Z.Y.; Ding, L.; Wan, H.X.; Ji, J.; Gao, Z.H.; Yu, L.X. Numerical investigation on the effect of tunnel width and slope on ceiling gas temperature in inclined tunnels. Int. J. Therm. Sci.
**2020**, 152, 106272. [Google Scholar] [CrossRef] - Gao, Z.H.; Li, L.J.; Sun, C.P.; Zhong, W.; Yan, C.B. Effect of longitudinal slope on the smoke propagation and ceiling temperature characterization in sloping tunnel fires under natural ventilation. Tunn. Undergr. Space Technol.
**2022**, 123, 104396. [Google Scholar] [CrossRef] - Yang, Y.X.; Long, Z.; Cheng, H.H.; Chen, J.F.; Liu, C.; Zhong, M.H. Experimental and numerical study of smoke temperature distribution characteristics in a sloped tunnel. Sustain. Cities Soc.
**2021**, 73, 103091. [Google Scholar] [CrossRef] - Zhou, Y.; Yang, Y.; Mao, Z.L.; Bu, R.W.; Gong, J.H.; Wang, Y.X.; Yi, L. Analytical and numerical study on natural ventilation performance in single- and gable-slope city tunnels. Sustain. Cities Soc.
**2019**, 45, 258–270. [Google Scholar] [CrossRef] - Zhong, W.; Liu, L.; Han, N.; Gao, Z.H. Investigation on the maximum ceiling temperature of the weak plume impingement flow in tunnel fires under longitudinal ventilation. Tunn. Undergr. Sp. Technol.
**2022**, 123, 104396. [Google Scholar] [CrossRef]

**Figure 1.**Schematic diagram of smoke movement in branched tunnel with sloped mainline before shunting. The blue arrows represent the direction of flow of the ambient wind and the orange represents the direction of flow of the high temperature flue gases.

**Figure 3.**Schematic of the branched tunnel with slope mainline, (

**a**) Skeleton branched tunnel, (

**b**) Tunnel cross-section.

**Figure 4.**Validation of numerical results by comparing with experimental data, (

**a**) Picture of experimental setup, (

**b**) Temperature at quasi-steady state, and (

**c**) Longitudinal temperature.

**Figure 6.**Schematic of smoke movement in the bifurcated tunnel with different mainline slope, (

**a**) Smoke exhaust through upstream portal, slope ≤ 1%, (

**b**) Smoke exhaust only through downstream end, slope > 1%.

**Figure 11.**Typical temperature longitudinal decay in sloped mainline, (

**a**) Different heat release rate with a slope of 4%, (

**b**) Different mainline slope with HRR 10 MW. The blue arrow represents the direction of ambient air flow and the orange arrow represents the direction of high temperature flue gas flow, which is easy to understand.

**Figure 12.**Dimensionless temperature longitudinal distribution in sloped mainline, (

**a**) Mainline slope of 1%, (

**b**) Mainline slope of 2%, (

**c**) Mainline slope of 3%, (

**d**) Mainline slope of 4%, (

**e**) Mainline slope of 5%, (

**f**) Mainline slope of 6%, and (

**g**) Mainline slope of 7%.

**Figure 13.**Correlation of decay coefficient with heat release rate for ceiling temperature, 1% slope.

No. | Heat Release Rate (MW) | Slope (%) |
---|---|---|

1–7 | 3 | 1, 2, 3, 4, 5, 6, 7 |

8–14 | 5 | |

15–21 | 10 | |

22–28 | 15 | |

29–35 | 20 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lu, N.; Yao, X.; Yang, J.; Huang, Y.
Evaluating the Ceiling Gas Temperature in a Branched Tunnel Fire with a Sloped Mainline Region under Natural Ventilation. *Fire* **2024**, *7*, 152.
https://doi.org/10.3390/fire7050152

**AMA Style**

Lu N, Yao X, Yang J, Huang Y.
Evaluating the Ceiling Gas Temperature in a Branched Tunnel Fire with a Sloped Mainline Region under Natural Ventilation. *Fire*. 2024; 7(5):152.
https://doi.org/10.3390/fire7050152

**Chicago/Turabian Style**

Lu, Ning, Xiaolin Yao, Jinming Yang, and Youbo Huang.
2024. "Evaluating the Ceiling Gas Temperature in a Branched Tunnel Fire with a Sloped Mainline Region under Natural Ventilation" *Fire* 7, no. 5: 152.
https://doi.org/10.3390/fire7050152