Dynamics of coal dust flame acceleration: A feedback control model for unsteady flow

Several modeling concepts borrowed from control theory are employed to develop an algebraic and ordinary differential equations model for the dynamics of unsteady coal dust flame acceleration in a constant area duct closed at one end, e.g., in a coal mine tunnel. We are particularly concerned with modeling the feedback mechanisms which cause a coal dust flame to accelerate, leading to detonation. Previous experimental studies have been conducted on both coal dust flame propagation and on individual coal particle combustion. Based on the results, a physical model is proposed in which coal dust flame acceleration is entirely controlled, in a feedback fashion, by volatiles emission and their reaction. A control system model is developed that employs five well-stirred reactor subsystems with three feedback interaction mechanisms. The model consists of a leading shock wave, followed by a variable length volatiles emission region ahead of the flame, a fixed length burning region immediately behind the flame front, and a variable length exhaust region extending back to the closed end of the duct. The feedback mechanisms incorporated into the model include heat transfer and pressurization from the burning region to the volatiles emission region, and pressurization from the volatiles emission region to the turbulent mixing region behind the shock wave. Each well-stirred reactor is described by a system of algebraic and ordinary differential equations for the rate of change of conditions inside the reactor. Numerical simulation results reveal that, despite far-reaching simplifications (ordinary instead of partial differential equations, ideal gases insteady of two-phase flow, separation of volatiles emission and combustion, neglection of char burning), the model exhibits the fundamental dynamic properties of the flame propagation process. The model agrees with qualitative photographic experimental results and is applicable to both the case where the flame accelerates to detonation and to the case where the combustion process dies out.