Gravity Effects on the Minimum Explosive Concentrations in 1-D Dust Explosion

ABSTRACT

Theoretical predictions of dust-explosion characteristics, such as the minimum explosive concentration (MEC), can help improve the accuracy of quantitative risk assessment. This paper presents a continuum model to simulate one-dimensional dust-cloud combustion. It is found that the dilution of dust by thermal expansion reduces the propagation speed of a combustion wave through a dust cloud. At the same time, the delay in the increase of particle velocity due to relaxation time counteracts the dilution effect. Therefore, neglecting the relaxation time results in the underestimation of propagation speed. In the absence of heat loss, extinction occurs when the adiabatic combustion temperature decreases to the ignition temperature; MEC is independent of particle size in such cases. With the presence of heat loss, on the other hand, extinction occurs at a higher dust concentration; MEC increases with particle size. Accurate evaluation of ignition temperature is key to the quantitative prediction of MEC. A particular focus is given to gravity effects, reflecting recent experimental efforts to obtain fundamental insights into propagation mechanisms without being affected by gravity. In upward propagation, particles fall toward the reaction front, enhancing combustion and increasing the propagation speed. The situation in downward propagation is the opposite, and extinction occurs when the gravity level is beyond a critical value. In upward propagation, MEC can decrease with an increase in particle size, owing to the influence of gravity.

KEYWORDS:

• Dust explosion
• continuum modeling
• minimum explosive concentration (MEC)
• relaxation time
• gravity

Acknowledgements

This work was partly supported by JSPS KAKENHI Grant Numbers JP18H03822, JP19H01807, JP21H04593, and JP21K14379 and partly by the front-loading research project of the Japan Aerospace Exploration Agency (JAXA).

Disclosure statement

No potential conflict of interest was reported by the authors.

Nomenclature

$C_{\mathrm{p}}$	=	dust concentration [kg·m−3]
$c$	=	specific heat [J·kg−1·K−1]
$d_{\mathrm{p}}$	=	particle diameter [m]
$g$	=	acceleration of gravity [m·s−2]
$H$	=	Heaviside step function
$K$	=	heat-loss coefficient [W·m−3·K−1]
$k$	=	reaction rate constant [m2·s−1]
$l_{\mathrm{p}}$	=	inter-particle spacing [m]
$N_{\mathrm{p}}$	=	particle number density [m−3]
$Q$	=	heat of combustion [J·kg−1]
$\mathrm{R}{\mathrm{e}}_{\mathrm{p}}$	=	particle Reynolds number [–]
$T$	=	temperature [K]
$T_{\mathrm{i}\mathrm{g}}$	=	ignition temperature [K]
$v$	=	velocity [m·s−1]
$x$	=	moving coordinate [m]
Greek symbols	=
$\epsilon$	=	emissivity [–]
$\lambda$	=	thermal conductivity [W·m−1·K−1]
$\mu$	=	viscosity [Pa·s]
$\rho$	=	density [kg·m−3]
$\sigma$	=	thermal expansion ratio, $T_{\mathrm{a}\mathrm{d}}/T_0$, [–]
${\sigma }_{\mathrm{S}\mathrm{B}}$	=	Stefan-Boltzmann constant [W·m−2·K−4]
${\tau }_{\mathrm{r}}$	=	relaxation time [s]
Subscripts	=
0	=	unburnt state
c	=	convection
g	=	gas phase
p	=	particle
r	=	radiation

Additional information

Funding

The work was supported by the Japan Society for the Promotion of Science [JP18H03822,JP19H01807,JP21H04593,JP21K14379]; Japan Aerospace Exploration Agency [Front-loading Research Project]