Conditions of the Water–Coal Fuel Drop Dispersion at Their Ignition in the Conditions of High-Temperature Heating

ABSTRACT

The results of a numerical analysis of the conditions and characteristics of the dispersion of the water–coal particles during ignition under the conditions of an intense radiation-convective heating have been presented in the article. A comparative analysis of the theoretical and experimental values of ignition delay times of the fuel particles has showed their good correlation. Also, a comparative analysis of the characteristic dispersion times, obtained theoretically and established in the experiments, has showed a good correlation between them. According to the results of the numerical simulation, it has been established that dispersion of the water–coal particles during their heating before their ignition can occur as a result of the occurrence of the filtration stresses in the porous structure of the fuel. It has been found that the dispersion of the particles occurs before a complete evaporation within the pore moisture.

The theoretical analysis has shown that the permeability of a dry coal structure has a significant effect on the characteristics and dispersion conditions. The influence of the values of the dimensionless Darcy criterion (Da) on the dispersion conditions has also been analyzed. It has been established that as the value of Da increases, the dispersion time decreases substantially. This is due to a decrease in the permeability of the porous structure of the fuel.

KEYWORDS:

• Water–coal fuel particle
• heating
• dispersion
• ignition
• ignition delay time

Conventional designations

Dimensions:

T—	=	temperature, К;
$\mathrm{\Delta }T=T_{eva}-T_0$ —	=	heating temperature before the steam formation process, К;
Teva—	=	maximum possible evaporation temperature$\cong$373 К;
T0—	=	temperature at the initial time.
σ—	=	the Stefan-Boltzmann constant, W/(m2 · K4);
ε(T)—	=	integral degree of blackness depending on temperature;
p—	=	pressure, Pa;
${\alpha }^t$—	=	a linear coefficient of thermal expansion of coal, 1/K;
E—	=	Young’s modulus of elasticity on tension and compression of coal, Pa;
υ—	=	Poisson’s ratio;
η—	=	degree of fuel pyrolysis;
Φ—	=	angular coordinate;
k—	=	the pre-exponent of a heterogeneous (m/s) or homogeneous (1/s) reaction;
u—	=	speed of movement of the mixture of water vapor and gaseous pyrolysis products in fuel pores in the radial direction, m/s;
v—	=	speed of movement of the mixture of water vapor and gaseous pyrolysis products in the pores in the azimuthal direction, m/s;
Mdaf—	=	volatiles content;
Kp—	=	coal permeability coefficient, m2;
ω—	=	dynamic viscosity, PA∙s;
Q—	=	thermal effect, J/kg;
λ—	=	thermal conductivity coefficient W/(m· K);
c—	=	heat capacity, j/(kg· K);
$\chi =\frac{K_p}{\omega \beta m\ast }$—	=	piezo conductivity coefficient, m2/s;
ρ—	=	density, kg/m3;
$a=\frac{\lambda }{c\rho }$—	=	coefficient of thermal diffusivity, m2/s;
r—	=	radius, m;
Δ—	=	transformation parameter of the evaporation front, m;
s—	=	the typical size of the pore m;
$m\ast$—	=	porosity;
t—	=	time, s;
$t_{hw}=\frac{{\left(r\ast \right)}^2}{a\ast }$—	=	a characteristic time of the heat wave propagation over the radius r*, s.

Dimensionless quantities:

$\theta =\frac{T-T_0}{\mathrm{\Delta }T}$—	=	temperature;
τ = t/t*—	=	time;
C = c/c*—	=	heat capacity;
P = ρ/ρ*—	=	density;
Λ = λ/λ*—	=	coefficient of thermal conductivity;
U = u/u*—	=	speed in the radial direction;
V = v/u*—	=	speed in the azimuthal direction;
R = r/r*—	=	radius;
Π = m/m*—	=	porosity;
Η = p/p*—	=	pressure of the vapor–gas mixture in the porous structure of the particle;
Χ = χ/χ*—	=	coefficient of piezoconductivity;
Di = di/di*—	=	diffusion coefficient;
Yi—	=	mass concentration of the i-th component of the gas mixture (CH4, H2O, H2, CO);
Ψ—	=	Heaviside function;
δ—	=	Dirac function;

Dimensionless complexes and criteria:

$\mathrm{A}rr=K_{td}\mathrm{\Delta }exp\left(-\frac{E}{RT}\right)$—	=	criterion of Arrhenius;
$\mathrm{{\rm Y}}=\frac{\omega u\ast }{p\ast r\ast }$—	=	braking parameter;
$Da=\frac{\omega r\ast u\ast }{K_{p}p\ast }$—	=	Darcy criterion;
$Ku=\frac{Q_{eva}}{\mathrm{\Delta }Tc\ast }$—	=	Kutateladze criterion;
$K_{td}=\frac{k}{t\ast }$—	=	constant of the thermal decomposition process;
$K_{\lambda }=\frac{{\lambda }_g}{{\lambda }_{wcf}}$—	=	complex characterizing the intensity of the heat transfer from the boundary layer of the particle to the fuel layer;
$Fo=\frac{a\ast t\ast }{{\left(r\ast \right)}^2}$—	=	Fourier criterion;
$F{o}_H=\frac{\chi t\ast }{{\left(r\ast \right)}^2}$—	=	analog of Fourier criterion in the piezoconductivity Equation (4);
$Pe=\frac{u\ast r\ast }{a\ast }$—	=	Peclet criterion;
$Po=\frac{Q_i{W}_i{\left(r\ast \right)}^2}{\lambda \ast \mathrm{\Delta }T}$—	=	Pomerantsev criterion for the ith chemical reaction;
$P{o}_i^H=\frac{W_i{\left(r\ast \right)}^2\omega }{{\rho }_{gm}p\ast K_p\ast }$—	=	analog of Pomerantsev criterion (equation of piezoconductivity (4)) for the chemical reactions (thermal decomposition, interaction of water vapor and carbon of coke);
$P{o}_{eva}^i=\frac{W_{eva}{\left(r\ast \right)}^2\omega }{s{\rho }_{gm}p\ast K_p\ast }$—	=	analog of Pomerantsev criterion (the equation of piezoconductivity (4)) for the evaporation process;
$P{o}_i^{dif}=\frac{W_i{\left(r\ast \right)}^2}{{\rho }_{g}d\ast }$—	=	analog of Pomerantsev criterion (diffusion Equation (16));
$K{i}_{C+O_2}=\frac{Q_{C+O_2}{W}_{C+O_2}r\ast }{\lambda \ast \mathrm{\Delta }T}$—	=	Kirpichev criterion for the combustion reaction of carbon;
$Sk\left(\theta \right)=\frac{\epsilon \left(T\right)\sigma \mathrm{\Delta }{T}^3}{\lambda \ast }$—	=	Stark criterion;
$\mathrm{\Omega }=\frac{V_F}{\mathrm{\Delta }}{t}_{hw}$—	=	the rate of water evaporation;
$N=\frac{\rho \ast u\ast r\ast }{d\ast {\rho }_g}$	=	;
$\zeta =\frac{{\left(r\ast \right)}^2}{K_P}$	=	.

Subscript indices:

0—	=	the initial moment of time;
1—	=	area of the initial (water-saturated) fuel;
2—	=	area of dry fuel;
f—	=	water condition at freezing temperature;
F—	=	evaporation front;
g—	=	high-temperature gas;
gm—	=	mixture of water vapor and gaseous products of pyrolysis.
c—	=	coal;
i—	=	reaction number;
eva—	=	the boundary of the system “wet fuel—dry carbon frame”;
td—	=	end of the thermal decomposition process;
ign—	=	ignition;
out—	=	outer radius of a particle;
oxi—	=	oxidizer (air);
std—	=	beginning of thermal decomposition;
sur—	=	particle surface;
td—	=	thermal decomposition process;
wcf—	=	water–coal slurry;
wat—	=	water.

Superscripts:

*—	=	scale of magnitudes:
T* =	=	Toxi;
t* =	=	1c;
c* =	=	c1;
ρ* = ρ1—	=	for Equation (1);
ρ* = ρoxi—	=	for Equations (7) and (16);
λ* =	=	λ1;
u* =	=	uoxi;
r* =	=	rout;
m* =	=	m0;
p* =	=	p0;
χ* =	=	χ1;
d*i→oxi =	=	di→oxi.

Additional information

Funding

This research has been performed within the framework of the strategic plan for the development of National Research Tomsk Polytechnic University as one of the world-leading universities (project VIU-ISHE-300/2018).