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Position of Maximum Ceiling Temperature in a Tunnel Fire

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Abstract

The position of the maximum ceiling gas temperature indicates how far the fire plum could be blown away by a ventilation flow. It could be applied to estimate the activation of a detection system or a sprinkler system, or to estimate the range of damage to the tunnel structure. An equation for predicting the position of the maximum ceiling gas temperature in a tunnel fire is proposed based on a theoretical analysis and validated using both laboratory test data and full scale test data. A flame angle has been defined based on the position of the maximum ceiling temperature in a tunnel fire. The flame angle is directly related to the dimensionless ventilation velocity, and it becomes insensitive to the heat release rate for a large tunnel fire. Further, it is found that a constant critical flame angle exists, defined as the flame angle under the critical condition when the backlayering just disappears. For a given tunnel and fire source, the flame angle under critical conditions is the same value, independent of heat release rate, and the maximum ceiling temperature under critical conditions always corresponds to the same position. Generally the horizontal distance between the position of the maximum ceiling temperature and the fire source centre is around 1.5 times the effective tunnel height under the critical condition.

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Abbreviations

\( A_{f} \) :

Fuel area (m2)

\( b \) :

Tunnel width (m)

\( b_{fo} \) :

Radius of fire source (m)

\( c_{p} \) :

Heat capacity of air (kJ/kg K)

\( Fr \) :

Froude number

\( g \) :

Gravity acceleration (m/s2)

\( H \) :

Tunnel height (m)

\( H_{ef} \) :

Effective tunnel height (m)

\( L_{b} \) :

Backlayering length (m)

\( L_{MT} \) :

Horizontal distance between position of the maximum ceiling temperature and the fire source centre (m)

\( L_{traj} \) :

Distance between the position of the maximum ceiling temperature and the fire source centre (m)

\( m_{p} \) :

Plume mass flow rate in Eq. (5) (kg/s)

\( m^{\prime}_{p} \) :

Plume mass flow rate in Eq. (6) (kg/s)

\( Q \) :

Total heat release rate (kW)

\( Q_{c} \) :

Convective heat release rate (kW)

\( Q^{*} \) :

Dimensionless heat release rate defined in Eq. (11)

\( Q^{\prime} \) :

Dimensionless heat release rate defined in Eq. (4)

\( Ri^{\prime} \) :

Modified Richardson number

\( Ri^{\prime}_{c} \) :

Critical modified Richardson number

\( T_{o} \) :

Ambient temperature (K)

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

Maximum ceiling temperature (K)

\( u \) :

Plume velocity (m/s)

\( V \) :

Longitudinal velocity (m/s)

\( V_{c} \) :

Critical velocity (m/s)

\( V^{\prime} \) :

Dimensionless ventilation velocity defined in Eq. (1)

\( V_{c}^{\prime } \) :

Dimensionless critical ventilation velocity

\( z \) :

Distance above fire source (m)

\( \rho_{o} \) :

Ambient density (kg/m3)

\( \varphi \) :

Flame angle (o)

\( \varphi_{c} \) :

Critical flame angle (o)

\( \alpha \) :

Coefficient defined in Eq. (2)

\( \beta \) :

Coefficient defined in Eq. (2)

\( \eta \) :

Coefficient defined in Eq. (2)

cal :

Calculated

meas :

Measured

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Acknowledgments

This study was sponsored by the Swedish Road Administration (SRA) and SP Tunnel and Underground Safety Centre. We would like to acknowledge Mr Bernt Freiholtz at SRA for his advice and encouragement in this project and Dr Margaret McNamee for her valuable comments. The authors would also like to thank Prof. Bo Lei, associate Prof. Zhihao Xu and associate Prof. Zhihui Deng at Southwest Jiaotong University for their help in the tests.

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Authors and Affiliations

  1. SP Technical Research Institute of Sweden, Borås, Sweden

    Ying Zhen Li & Haukur Ingason

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  1. Ying Zhen Li
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  2. Haukur Ingason
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Correspondence to Ying Zhen Li.

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Li, Y.Z., Ingason, H. Position of Maximum Ceiling Temperature in a Tunnel Fire. Fire Technol 50, 889–905 (2014). https://doi.org/10.1007/s10694-012-0309-2

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