Critical Condition for the Combustion Rate of a Carbon Particle to be Activated: Theory and Experimental Comparisons

ABSTRACT

Relevant to the activation of solid fuel particle, critical condition for the combustion rate has been obtained, above which particle combustion can successfully be accomplished. Use has been made of the asymptotics, with focusing on the temporal variation of the particle mass in the plateau stage, as well as that of the particle temperature. It has been confirmed that this critical condition is closely related to the heat loss, and that there exists a comprehensive parameter, consisting of the combustion rate, oxygen mass-fraction, and pressure ratio, which only depends on the ambient temperature. Appropriateness and/or usefulness of this critical condition has further been examined, by use of such experimental data in the literature as are reported to burn in the quiescent environment. Arrhenius plot of the comprehensive parameter has been used in experimental comparisons, in which it is indicated that the upper half region separated by the critical condition corresponds to that for the particle combustion with surface reactions activated. Experimental data used are those from semi-anthracite to low-rank coal char, as well as petroleum coke, including soot. A fair degree of agreement has been demonstrated, indicating that the larger particles that can burn in the diffusion controlled regime locate in the upper half region, and that the smaller ones that have failed to be activated in the surface reactions locate below the critical condition. By virtue of this critical condition, it is even suggested that prediction for the particle activation in the course of combustion can easily be made, by examining combustion rate measured in the quasi-steady state. Finally, it is confirmed again that the reduction in particle size, which also exerts influences on particle deactivation, does not necessarily favor the particle combustion.

KEY WORDS:

• Heterogeneous combustion
• Particle activation
• Char combustion
• Critical combustion rate
• Critical particle size

Nomenclature

A	=	reduced surface Damköhler number
B	=	frequency factor
c	=	specific heat
cp	=	specific heat of gas at constant pressure
D	=	diffusion coefficient
E	=	activation energy
m	=	mass consumption rate
$\dot{m}$	=	mass burning (or combustion) rate in dimensional form
q	=	heat of combustion
r	=	particle radius
T	=	temperature
Ta	=	activation temperature
t	=	time
W	=	molecular weight
Y	=	mass fraction

Greek Symbols

α	=	heat loss parameter
β	=	conventional transfer number
δ	=	product(CO2)-to-carbon mass ratio
ε	=	emissivity
θ	=	perturbed temperature
λ	=	thermal conductivity
ν	=	stoichiometric coefficient
ρ	=	density
σSB	=	Stefan-Boltzmann constant
τ	=	nondimensional time

Subscripts

C	=	carbon
cr	=	critical condition
O	=	oxygen or C–O2 surface reaction
P	=	carbon dioxide or C–CO2 surface reaction
s	=	surface
∞	=	ambience
0	=	reference

Superscripts

~

=

nondimensional or stoichiometrically weighted

Acknowledgment

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.