The numerical model was presented for the coal combustion in the packed bed. The bifurcation characteristic of the ignition-extinction of solid-phase smoldering and tran- sition to flaming was studied for the packed bed of coal.One of the Frank-Kamenetskii parameter β_1 was selected as the control parameter.The computed results show that the bifurcation curve is obviously divided into two zones of solid-phase reaction and gas- phase reaction,and the total process of ignition-extinction presents twice bifurcation cha- racteristic.Moreover,the vanishing of critical state of ignition-extinction is studied.One of the transition points,ε_2=0.05,is numerically solved for the vanishing of critical state.The larger the value of ε_2 is,the easier the gas-phase can react.However,the combustion temperature will decrease with increasing ε_2.The other transition point α_2=0.53 is also ob- tained.With increasing the value of α_2,the combustion temperature of gas-phase reaction is close to the smoldering temperature of coal.When α_2 is infinite,the only reaction occur- ring is the smoldering combustion of solid-phase,and the gas-phase cannot react.
