Fire Technology

, Volume 55, Issue 1, pp 129–148 | Cite as

A Model Considering the Flame Volume for Prediction of Thermal Radiation from Pool Fire

  • Gansu Shen
  • Kuibin ZhouEmail author
  • Fan Wu
  • Juncheng JiangEmail author
  • Zhan Dou


Thermal radiation is an important parameter to evaluate the hazard of pool fires. In the conventional solid flame model for the radiant heat flux calculation, the burning flame is often assumed to be of a cylinder or a cylinder–cone combined shape whose height and diameter equal the flame height and pool diameter, respectively. Obviously, the conventional model does not take into account the actual flame volume. Thus, this paper presents a revised solid flame model by correcting the flame diameter with the flame height and flame volume. The heat release rate per unit flame volume is approximately 1100 kW/m3 for hydrocarbon pool fires, by which the flame volume can be calculated with the known heat release rate. By theoretical analysis on experimental data in literature, correlations of centerline temperature and flame emissivity are proposed to calculate the flame surface emissive power of heptane pool fires. The obstruction effect of smoke around the burning flame on the thermal radiation is also considered by correcting the transmissivity of thermal radiation in the surrounding medium. Comparisons in prediction between the new and conventional models are conducted against the experimental measurements of 0.3 m, 0.5 m, 0.7 m, 1 m, 6 m heptane pool fires. It is found that the new model with the cylinder–cone combined shape assumption can better predict the thermal radiation from heptane pool fires in both near and far fields.


Pool fire Radiant heat flux Flame volume Radiation model Model validation 

List of Symbol

\( c_{p} \)

Specific heat of air at constant pressure (kJ/kg k)

\( c_{s} \)

Mass concentration of smoke in the flame gases (kg smoke/m3)

CT, f

A constant (Eq. 10)


Pool diameter (m)


Flame surface emissive power (kW/m2)


Emissive power of clear burning flame, 140 kW/m2 (Eq. 6)


Emissive power of flame surrounded by smoke, 20 kW/m2 (Eq. 6)


Geometrical view factor


View factor of part 1 to the target


View factor of part 2 to the target


Gravitational acceleration (m/s2)


Mean flame height (m)


Continuous flame height (m)


Intermittent flame height (m)

\( {{\Delta h_{c} } \mathord{\left/ {\vphantom {{\Delta h_{c} } {S_{a} }}} \right. \kern-0pt} {S_{a} }} \)

Energy produced by consuming unit mass of oxygen (Eq. 10)


\( {\text{Coefficient}} = \left( {{r \mathord{\left/ {\vphantom {r {\left( {H_{i} - H_{c} } \right)}}} \right. \kern-0pt} {\left( {H_{i} - H_{c} } \right)}}} \right)^{2} \)


Horizontal distance from the center of the pool fire to the target edge (m)


Mean beam length (m)

\( \dot{m}^{\prime\prime} \)

Mass burning rate per area (kg/m2 s)

\( \dot{m}^{\prime\prime}_{\infty } \)

Mass burning rate per area of a pool fire with infinite diameter (kg/m2 s)

\( \dot{q}^{\prime\prime} \)

Radiant heat flux (kW/m2)

\( \dot{q}^{\prime\prime}_{1 - v} \)

Radiant heat fluxes received by the target from part 1 (kW/m2)

\( \dot{q}^{\prime\prime}_{2 - v} \)

Radiant heat fluxes received by the target from part 2 (kW/m2)

\( \dot{Q} \)

Heat release rate (kW)


Flame radius (m)


The distance from the point source to the target (m)


Extinction coefficient, 0.12 m−1 (Eq. 6)


Flame temperature (K)


Ambient air temperature (K)


Flame temperature in continuous flame zone (K)


Flame temperature in intermittent flame zone (K)

\( \Delta T \)

Excess temperature (K)

\( \Delta T_{McC} \)

Excess temperature calculated by McCaffrey formula (K)


Height above the burner surface (m)

Greek Symbols

\( \alpha ,\gamma \)

Diameter correction coefficient

\( \beta \)

Mean-beam-length corrector

\( \varepsilon \)

Flame emissivity

\( \kappa \)

Absorption coefficient (m−1)

\( \kappa_{m} \)

Specific soot extinction area (m2/kg)

\( \rho_{a} \)

Ambient air density (kg/m3)

\( \sigma \)

Stefan-Boltzmann constant, \( 5.67 \times 10^{ - 8} \) W/(m2 K4)

\( \tau \)


\( \tau_{a} \)

Transmissivity of atmosphere

\( \tau_{s} \)

Transmissivity of smoke

\( \phi \)

Correction coefficient (Eq. 14)

\( \chi_{r} \)

Radiation fraction



Body 1, body2


Vertical object



This work was sponsored by the National Key Research and Development Plan (No. 2016YFC0800100), the National Natural Science Foundation of China under Grant Nos. 51876088 and 51506082, and Jiangsu Province Graduate Student Training Innovation Project (No. KYCX17_0918).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Safety Science and EngineeringNanjing Tech UniversityNanjingPeople’s Republic of China
  2. 2.Institute of Measurement and Electronic Technology, Department of AutomationTsinghua UniversityBeijingPeople’s Republic of China

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