Factors affecting the migration velocity of the outburst coal powder
The transport of outburst coal is one of the main forms of the gas internal energy dissipation in coal seams. Through experimental observations, the outburst coal particles experience various forms of transformation during their migration in the roadway, with a non-constant migration velocity, making the process relatively complicated. In previous studies31, the migration of the outburst coal powder particles was regarded as free suspension movement. To facilitate analysis, only the average velocity of the gas flow along the axis of the roadway was taken into consideration, ignoring its fluctuations, the fluctuation of the gas flow rate perpendicular to the axis of the roadway, and the radial component of the flow velocity of ejected coal particles. Based on the suspension movement mechanism of the solid particles in two phase flow and the law of energy conservation, a one-dimensional mathematical model of the migration of the outburst coal particles in the roadway was established. This model can be divided into a particle group acceleration stage and a gas–solid equilibrium movement deceleration stage.
$$ \begin{gathered} L{ = }L_{{\text{a}}} { + }L_{d} \hfill \\ L_{a} \left\{ \begin{gathered} \left( {\frac{v – u}{{v_{n} }}} \right)^{2 – K} – \frac{{v_{n} }}{v} – \frac{{\lambda_{s} u^{2} }}{2gD} = \frac{u}{{\text{g}}}\frac{du}{{dL}} \hfill \\ \left( {1 – \lambda_{g} \frac{\Delta L}{D}} \right)v_{c}^{2} + n\left( {1 – \lambda_{s} \frac{\Delta L}{D}} \right)u_{c}^{2} = v^{2} + nu^{2} \hfill \\ \end{gathered} \right. \hfill \\ L_{d} \left\{ \begin{gathered} \left( {\frac{v}{{v_{n} }}} \right)^{2 – K} \left[ {1 – \left( \frac{u}{v} \right)^{2 – K} } \right] – \frac{{v_{n} }}{v} – \frac{{\lambda_{s} u^{2} }}{2gD}\left( \frac{u}{v} \right)^{2} = 0 \hfill \\ \Delta L = \frac{{\left[ {\left( {v_{c}^{2} – v^{2} } \right) + n\left( {u_{c}^{2} – u^{2} } \right)} \right]D}}{{\lambda_{g} v_{c}^{2} + n\lambda_{s} u_{c}^{2} }} \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered} $$
(2)
where L is the total migration distance of outburst coal, m; La is the migration distance of the outburst coal acceleration stage, m; Ld is the migration distance of deceleration stage, m; ∆L is the distance value of each calculation step, m; u and v are outburst coal particle and gas flow velocity, m/s; uc and vc are respectively the initial velocity of outburst coal and gas flow in the calculation stage, m/s; vn is suspension velocity, m/s; g is the acceleration of gravity, N/kg; D is roadway diameter, m; λg is the pressure loss coefficient along the flow path; λs is the resistance coefficient of particles group; n is solid–gas mass ratio; the value of K is 0 or 1, when the diameter of outburst coal particles is large and Newton’s resistance formula is obeyed, K = 0; when the diameter of coal particles is small and the Stokes resistance formula is obeyed, K = 1, Reynolds number can be used to evaluate the motion state of particles, as shown in Table 3.
It is known that at the outburst port, L = 0 and the initial coal particle velocity uc = 0; and at the end of the coal powder migration, the gas velocity v = vn. The initial velocity of the outburst gas flow can be calculated as follows47:
$$ u_{c} = \sqrt {\frac{2k}{{k – 1}}\frac{{p_{0} }}{\rho }\left[ {1 – \left( {\frac{{p_{c} }}{{p_{0} }}} \right)^{{\frac{k – 1}{k}}} } \right]} $$
(3)
where k is the thermodynamic coefficient of gas. The relationship between the total migration distance L, the maximum movement velocity vmax and the initial gas flow velocity vc can be obtained by step calculation.
Relationship between migration velocity and time of outburst coal powder
According to Table 3, the calculated critical particle size of the Newtonian resistance zone and the Stokes resistance zone under the experimental conditions was 850 µm, and the corresponding suspension rate was 4.72 m/s. From the above experimental results, at the experimental gas pressures, about 60–68% of the outburst coal powder particles were smaller than the critical particle size.
Taking the migration of the 850 µm coal powder particles under gas pressure of 0.3 MPa as a calculation example, the relationship between the migration velocity, distance, and time of the outburst coal powder were obtained, as shown in Fig. 9. The gas velocity gradually decreased as the outburst developed, and the movement of the coal powder particles initially increased rapidly and then decreased. The migration velocity of the coal powder particles increased rapidly to a peak value of…
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