Fire Technology

, Volume 53, Issue 5, pp 1765–1793 | Cite as

Numerical Investigation of Back-Layering Length and Critical Velocity in Curved Subway Tunnels with Different Turning Radius

  • Shaogang Zhang
  • Hui Yang
  • Yongzheng Yao
  • Kai Zhu
  • Yong Zhou
  • Long Shi
  • Xudong ChengEmail author


Curved tunnels are inevitable subjected to the city underground geological conditions. Due to the catastrophic consequence of tunnel fires with high population density, the related researches on fire safety of curved tunnel are full of significance. Therefore, a series of curved subway tunnels with turning radius of 300–1000 m were investigated numerically by FDS 5.5.3 in terms of the smoke back-layering length and critical ventilation velocity under the heat release rate of 5–10 MW. Theoretical analysis shows that the curved tunnel with the local resistance has an advantage of preventing smoke spreading compared with straight tunnel. The simulation results also indicated that both the smoke back-layering length and the critical ventilation velocity increased with the rising turning radius, and the straight tunnel has the largest values. In fact, the local resistance impact factor for the smoke back-layering length in the curved tunnel, \( k_{f} \), was controlled by turning radius \( R \) and ventilation velocity \( V \). The dimensionless critical velocity increased slightly from \( 0.638Q^{*1/3} \) to \( 0.669Q^{*1/3} \) when the turning radius increased from 300 m to 1000 m. Without considering the influence of turning radius (local resistance), previous models cannot be applied to the curved tunnel. The improved prediction models about smoke back-layering length and critical velocity with the factor of turning radius could provide a technical guideline for the tunnel ventilation designs.


Curved subway tunnel Turning radius Smoke back-layering length Critical velocity FDS 

List of symbols

\( H \)

Tunnel height (m)

\( Fr \)

Froude number

\( T_{\hbox{max} } \)

Maximal temperature of smoke (K)

\( u \)

Velocity of smoke gas (m/s)

\( D^{*} \)

Dimensionless grid size (−)


Grid size of simulation mesh (m)

\( L \)

Back-layering length (m)

\( Q \)

Total heat release rate (kW)

\( \dot{Q}_{L} \)

Heat loss to the tunnel ceiling (kW)

\( k_{f} \)

Local resistance impact factor

\( Q^{*} \)

Dimensionless heat release rate (−)

\( V \)

Longitudinal ventilation velocity (m/s)

\( V^{*} \)

Dimensionless ventilation velocity (−)

\( \mathop H\limits^{\_\_} \)

Hydraulic diameter of tunnel (m)

\( A_{b} \)

Cross-sectional area of blockage (m2)

\( x \)

Location of smoke temperature (m)

\( C_{k} \)

A constant in Equation (16)

\( \rho_{0} \)

Ambient air density (kg/m3)

\( T_{0} \)

Ambient air temperature (K)

\( R \)

Turning radius of curved subway tunnel (m)

\( T_{f} \)

Smoke gas temperature (K)

\( c_{p} \)

Thermal capacity of air (J kg−1 K−1)

\( g \)

Gravitational acceleration (m/s2)

\( A \)

Tunnel cross-sectional area (m2)

\( \dot{Q}_{flocal} \)

Heat loss due to the local-resistance (kW)

\( \lambda_{1} \)

A coefficient in Equation (16)

\( l^{*} \)

Dimensionless smoke back-layering length (−)

\( V_{c} \)

Critical ventilation velocity (m/s)

\( L_{f - b} \)

Distance between fire source and blockage (m)

\( h \)

Thickness of back-flowed smoke gas (m)

\( R^{*} \)

Dimensionless turning radius of curved tunnel (-)

\( x_{fire} \)

Location of fire source (m)

\( L_{S}^{*} \)

Dimensionless smoke back-layering length in straight tunnel (−)

\( L_{C}^{*} \)

Dimensionless smoke back-layering length in curved tunnel (−)

\( V_{SC}^{*} \)

Dimensionless critical velocity in the straight tunnel (−)

\( P_{S} \)

Static pressure difference between the smoke gas front and ambient air (Pa)

\( P_{d} \)

Hydraulic pressure of the incoming air flow (Pa)

\( \Delta T \)

Temperature difference between smoke and ambient air (K)

\( \Delta T_{fire} \)

Temperature difference between smoke above fire source and ambient air (K)



This work was supported by National Natural Science Foundation of China (No. 51323010), National Key Research and Development Program of China (Project No. 2016YFC0800603) and Fundamental Research Funds for the Central Universities (No.WK2320000035). We deeply appreciate them.

Compliance with Ethical Standards

Conflict of interest

The authors do not have any possible conflicts of interest.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Shaogang Zhang
    • 1
  • Hui Yang
    • 1
  • Yongzheng Yao
    • 1
  • Kai Zhu
    • 1
  • Yong Zhou
    • 1
  • Long Shi
    • 2
  • Xudong Cheng
    • 1
    Email author
  1. 1.State Key Laboratory of Fire ScienceUniversity of Science and Technology of ChinaHefeiPeople’s Republic of China
  2. 2.Center for Environmental Safety and Risk EngineeringVictoria UniversityMelbourneAustralia

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