Comparing Ignition of Fuel Beds to Firebrand Showers to Ignition of Fuel Beds by Non-Reacting Heaters

Figures & data

Figure 1. A comparison to fuel bed ignition by a non-reacting heater and firebrand showers.

Figure 2. Experimental setting for (a) Ignition with a cartridge heater and (b) Ignition with firebrand showers.

Figure 3. Smoldering ignition (SI) delay time vs heat flux from a cartridge heater.

Figure 4. Sensitivity analysis on Equation (5)(5) $t_{\mathit{ig}}=\frac{{\mathit{\rho }}_{\mathit{fuel}}{c}_{\mathit{fuel}}\mathit{V}\left(T_{\mathit{ig}}-T_0\right)}{\dot{q}{A}_{\mathit{ch}}}$(5) .

Figure 5. Intervals of arrival time of firebrands vs smoldering ignition delay time, for given SI spot.

Table 1. Data for Equation (5)(5) $t_{\mathit{ig}}=\frac{{\mathit{\rho }}_{\mathit{fuel}}{c}_{\mathit{fuel}}\mathit{V}\left(T_{\mathit{ig}}-T_0\right)}{\dot{q}{A}_{\mathit{ch}}}$(5) .

	$c_{\mathit{fuel}}$	$T_{\mathit{ig}}$	$T_0$	$\mathit{V}$
	1.11 (J/g)	753 (K)	273 (K)	6890 (mm^3)
Ref.	Peters and Bruch (2003)	Boonmee and Quintiere (2002)	*	*

*indicates experimental condition or observation.

Figure 6. Calculated heat contribution from a firebrand to the fuel bed.

Figure 7. Calculated heat loss from fuel beds to the air.

Table 2. R² value for regression model for Figure 6.

Burnout time	25 seconds	30 seconds	35 seconds
Number-based approach (Eq. (16))(16) ${\rho }_{\mathit{fuel}}{c}_{\mathit{fuel}}\mathit{V}\left(T_{\mathit{ig}}-T_0\right)=\mathit{n}\left\{\mathrm{\Delta H}\times \mathrm{\Delta }{m}_{\mathit{fb}}-\left[\mathit{h}{ }_{\mathit{fb}}\left(T_{\mathit{fb}}-T_0\right)+\mathit{\epsilon \sigma }\left({{\mathit{T}}_{\mathit{fb}}}^4-T_0^4\right)\right]t_b{A}_{\mathit{fb},\mathit{ex}}\right\}-\left(t_{\mathit{ig}}-t_{\mathit{eff}}\right)A_{\mathit{fuel},\mathit{ex}}\mathit{B}$(16)	0.36	0.31	0.27
Effective heating time approach (Eq. (18))(18) ${\rho }_{\mathit{fuel}}{c}_{\mathit{fuel}}\mathit{V}\left(T_{\mathit{ig}}-T_0\right)=t_{\mathit{eff}}\left\{\frac{\mathrm{\Delta H}\times \mathrm{\Delta }{\mathit{m}}_{\mathit{fb}}}{t_b}-\left[\mathit{h}{ }_{\mathit{fb}}\left(T_{\mathit{fb}}-T_0\right)+\mathit{\epsilon \sigma }\left({{\mathit{T}}_{\mathit{fb}}}^4-T_0^4\right)\right]A_{\mathit{fb},\mathit{ex}}\right\}-\left(t_{\mathit{ig}}-t_{\mathit{eff}}\right)A_{\mathit{fuel},\mathit{ex}}\mathit{B}$(18)	0.60	0.49	0.41

Figure 8. Comparison of smoldering ignition delay time vs heat flux between ignition from a non-reacting cartridge heater to firebrand showers.

Table

$A_{\mathit{ch}}$	[m^2]	surface area of the cartridge heater in contact with the fuel bed
$A_{\mathit{fb},\mathit{ex}}$	[m^2]	firebrand area exposed to the wind
$A_{\mathit{fuel},\mathit{ex}}$	[m^2]	fuel bed area exposed to wind
$c_{\mathit{fuel}}$	[J/g K]	specific heat capacity of fuel beds (wood)
$\mathit{F}$	[-]	view factor
$\mathit{h}{ }_{\mathit{fb}}$	[W/m^2K]	convection coefficient of a firebrand
$h_{\mathit{fuel}}$	[W/m^2K]	convective heat transfer coefficient of the fuel bed
$\mathrm{\Delta H}$	[J/g]	heat of combustion of a firebrand
$\dot{q}$	[W/m^2]	heat flux from a cartridge heater
$Q_{\mathit{ch}}$	[kJ]	heat from a cartridge heater
$Q_{\mathit{fb},\mathit{comb}}$	[kJ]	heat generated from the combustion of firebrands
$Q_{\mathit{fb},\mathit{loss}}$	[kJ]	heat loss to the ambient atmosphere
$Q_{\mathit{fb},\mathit{i}}$	[kJ]	heat contribution from i-th firebrand landing on the fuel bed
$Q_{\mathit{fb},\mathit{s},\mathit{t}}$	[kJ]	heat contribution from a single firebrand at time $\mathit{t}$
$Q_{\mathit{fb},\mathit{s}}$	[kJ]	heat contribution from a single firebrand
$Q_{\mathit{fb},\mathit{t}}$	[kJ]	heat contributed to the fuel bed at time $\mathit{t}$ ($0\le \mathit{t}\le t_{\mathit{ig}}$) from firebrands
$Q_{\mathit{fb},\mathit{total}}$	[kJ]	net heat contributed to the fuel beds from the firebrands
$Q_{\mathit{fuel},\mathit{conv}}$	[kJ]	convective heat transfer (cooling) to the fuel beds
$Q_{\mathit{fuel},\mathit{loss}}$	[kJ]	total heat loss from fuel beds to the air
$Q_{\mathit{fuel},\mathit{rad}}$	[kJ]	radiative heat loss from fuel beds to the air
$Q_{\mathit{fuel},\mathit{total}}$	[kJ]	total heat in the fuel bed system
$Q_{\mathit{ig}}$	[kJ]	energy required for fuel bed ignition
$\mathrm{\Delta }{m}_{\mathit{fb}}$	[g]	mass loss of a firebrand
$m_{\mathit{fb},\mathit{t}}$	[g]	mass of a given firebrand at time $\mathit{t}$
$T_0$	[K]	initial temperature of the fuel bed (room temperature)
$T_h$	[K]	measured temperature of the cartridge heater
$T_{\mathit{fb}}$	[K]	temperature of a firebrand
$T_{\mathit{fuel}}$	[K]	temperature of the fuel bed
$T_{\mathit{ig}}$	[K]	ignition temperature
n	[-]	number of firebrands involved with ignition
$\mathit{t}$	[s]	Time
$t_b$	[s]	burnout time
$\mathit{AccessisdeniedAccessisdenied}$	[s]	effective heating time
$t_{\mathit{ig}}$	[s]	time to fuel bed ignition
V	[m^3]	volume of the fuel bed involved with the ignition
${\rho }_{\mathit{fuel}}$	[g/m^3]	bulk density of the fuel beds
$\mathit{\sigma }$	[W/m^2K^4]	Stefan-Boltzmann constant
$\mathit{\epsilon }$	[-]	Emissivity

Peters, B., and C. Bruch. 2003. Drying and pyrolysis of wood particles: Experiments and simulation. J. Analytical Appl. Pyrolysis 70 (2):233–50. doi:10.1016/S0165-2370(02)00134-1.

 Web of Science ®Google Scholar

Boonmee, N., and J. Quintiere. 2002. Glowing and flaming autoignition of wood. Proc. Combust. Inst. 29 (1):289–96. doi:10.1016/S1540-7489(02)80039-6.

 Google Scholar