A Model of Low-Speed Concurrent Flow Flame Spread Over a Thin Fuel

Abstract

Abstract A numerical model is developed to examine steady, laminar flame spread and extinction over a thin solid fuel in low-speed concurrent flow. The model incorporates an elliptic treatment of the upstream flame stabilization zone near the fuel burnout point, and a parabolic treatment of the downstream flame, which has a higher flow Reynolds number. This provides a more precise fluid-mechanical description of the flame than using parabolic equations throughout, and is the first time such an approach has been used in concurrent flame spread modeling. The parabolic and elliptic regions are coupled smoothly by matching boundary conditions. The solid phase consists of an energy equation with surface radiative loss and a surface pyrolysis relation. Calculations (with the flame spread rate being an eigenvalue) are performed for forced flow without gravitational influences in a range of velocities which are lower than those induced in a normal gravity buoyant environment. Steady spread with constant flame and pyrolysis lengths is found possible for thin fuels and this facilitates the adoption of a moving coordinate system attached to the flame. Both quenching and blowoffextinction are observed. As flow velocity or oxygen percentage is reduced, the flame spread rate, the pyrolysis length, and the flame length all decrease. The flame standoff distance from the solid and the reaction zone thickness, however, first increase with decreasing flow velocity, but eventually decrease very near the quenching extinction limit. The short, weak flames observed at low flow velocities and oxygen levels are consistent with available experimental data. The maximum flame temperature decreases slowly at first as flow velocity is reduced, then falls more steeply close to the extinction limit. At low velocities, surface radiative loss becomes a significant fraction of the total combustion reactions’ heat release. In addition, the shorter flame length causes an increase in the fraction of conduction downstream (into the gas phase) compared to conduction to the fuel. These heat losses lead to lower flame temperatures, and ultimately, a quenching extinction. This extinction mechanism differs from that of blowoff, where the flame is unable to be stabilized due to the high flow velocity.