A Methodology for Predicting Temperature Distribution inside Concrete Pavement under A Pool Fire

ABSTRACT

Understanding the internal temperature distribution of concrete is critical to further determine the variation characteristics of its thermo-mechanical properties. Due to the complexity of heat transfer during the combustion of pool fires, the internal temperature distribution of concrete under its influence is much different from that under uniform high-temperature field. In this work, a systematic mathematical model was proposed to predict the temperature distribution inside concrete pavement under the action of pool fire, and a series of corresponding experiments were conducted to validate the prediction results. Heat transfer process during pool fire combustion and heat dissipation process of high-temperature concrete after pool fire extinction were both analyzed in detail. A comprehensive heat transfer coefficient was used to predict the temperature distribution in combustible liquid. Temperature control discretization equations inside the concrete in both the processes of pool fire combustion and extinction were derived. The established mathematical model was implemented by MATLAB programming. Finally, corresponding experiments were conducted to verify the model prediction results, and the results showed that the two were in good agreement. The results obtained in this work can facilitate a better understanding of the design and maintenance of concrete pavement.

KEYWORDS:

• Concrete pavement
• pool fire
• temperature distribution
• mathematical model
• experimental validation

Nomenclature

$A_F$	=	Flame surface area (m2)
$C$	=	Constant
$C_0$	=	Constant, ranging from 2 to 6
$C_2$	=	Planck’s second coefficient, 1.4388$\times$10−2 m·K
$C_C$	=	Specific heat capacity of concrete (J/(kg·K))
$C_{\rho L}$	=	Specific heat capacity of liquid (J/(kg·K))
$F$	=	View factor from flame to liquid surface
$F_0$	=	Fourier number
$f_v$	=	Volume fraction of carbon black particles
g	=	Gravity acceleration (m/s2)
Gr	=	Grashof number
h	=	Distance between the point on the center line of fire source and liquid surface (m)
$h_1$	=	Convective heat transfer coefficient between liquid and concrete (W/(m2·K))
$h_2$	=	Convective heat transfer coefficient between concrete and air (W/(m2·K))
$h_L$	=	Liquid internal heat convection coefficient (W/(m2·K))
$h_r$	=	Distance between liquid surface and upper edge of oil pan (m)
$H_F$	=	Flame height (m)
$K$	=	Effective emission coefficient
$K_1$	=	Comprehensive thermal conductivity (W/(m·K))
$K_2$	=	Surface heat transfer coefficient (W/(m2·K))
$K_F$	=	Constant
$L$	=	Average optical length of flame body (m)
$L_V$	=	Latent heat of evaporation of liquid (J/kg)
Pr	=	Prandtl number
${\dot{Q}}_c$	=	Heat release rate (kW)
${\dot{Q}}_{cond}$	=	Heat conduction from pool wall to liquid layer (W)
${\dot{Q}}_{conv}$	=	Convection heat between flame and fuel layer (W)
${\dot{Q}}_{evap}$	=	Liquid evaporation heat (W)
${\dot{Q}}_F$	=	Total net heat directly used to evaporate (W)
${\dot{Q}}_{heat}$	=	Heat conduction from boiling layer to temperature gradient layer (W)
${\dot{Q}}_{rad}$	=	Radiant heat from flame to liquid (W)
${\dot{Q}}_{re-rad}$	=	Heat feedback from liquid to flame (W)
t	=	Time (s)
$T_0$	=	Ambient temperature (K)
$T_F$	=	Instantaneous flame temperature (K)
$T_{F,m}$	=	Maximum Flame Temperature (K)
$T_L$	=	Liquid surface temperature (K)
$T_B^t$	=	Liquid bottom temperature at time t (K)
$T_i^n$	=	Temperature of the i-th point at time n
$V_{\mathrm{F}}$	=	Flame volume (m3)
$V_L$	=	Burning line speed (m/s)

Greek symbols

$\alpha$	=	Thermal diffusivity (m2/s)
${\alpha }_c$	=	Thermal diffusivity of concrete (m2/s)
${\alpha }_v$	=	Liquid volume expansion coefficient
$\delta$	=	Characteristic scale (m)
$\mathrm{\Delta }{T}_{C-0}$	=	Temperature difference between flame centerline and ambient (K)
$\mathrm{\Delta }t$	=	Time step (s)
$\mathrm{\Delta }z$	=	Space step (m)
${\epsilon }_1$	=	Liquid surface reflectivity
${\epsilon }_F$	=	Flame radiation emissivity
${\epsilon }_L$	=	Liquid radiation emissivity
$\eta$	=	Constant
$\lambda$	=	Comprehensive heat transfer coefficient (W/(m·K))
${\lambda }_c$	=	Thermal conductivity of concrete (W/(m·K))
${\lambda }_L$	=	Liquid heat conduction coefficient (W/(m·K))
${\lambda }_D$	=	Liquid heat convection conversion coefficient (W/(m·K))
$\nu$	=	Kinematic viscosity coefficient
${\rho }_c$	=	Density of concrete (kg/m3)
${\rho }_L$	=	Liquid density (kg/m3)
$\sigma$	=	Black body radiation constant, 5.67$\times$10−8 W/(m2·K4)

Declaration of interest statement

The authors declared no potential conflicts of interest with respect to the research, authorship, and publication of this article.

Supplementary material

Supplemental data for this article can be accessed on the publisher’s website.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Nos. 51804338, 51406241).