A three-dimensional model of flame spread over a thin solid in low-speed concurrent flow

A three-dimensional model of concurrent flame spread over a thin solid in a low-speed flow tunnel in microgravity has been formulated and numerically solved. The gas-phase combustion model includes the full Navier-Stokes equations for the conservation of mass, momentum, energy and species. The solid is assumed to be a thermally-thin, noncharring cellulosic sheet and the solid model consists of continuity and energy equations whose solution provides boundary condition for the gas phase. The gas-phase reaction is represented by a one-step, second-order finite-rate Arrhenius kinetics and the solid pyrolysis is approximated by a one-step, zeroth-order decomposition obeying an Arrhenius law. Gas phase radiation is neglected but the solid radiative loss is included in the model. Selected results are presented showing detailed three-dimensional flame structures and flame spread characteristics.; In a parametric study varying the flow velocity, oxygen level and the tunnel and solid fuel widths, two distinctive types of flame behavior are observed and two important three-dimensional effects are found, namely wall heat loss and oxygen side diffusion. The lateral heat loss shortens the flame and retards flame spread. On the other hand, oxygen side diffusion enhances the flame and also pushes it closer to the solid surface, which increases the flame heat feedback to solid and the flame spread rate. In higher oxygen and/or higher speed flows, the flames are long and are far away from the quenching limit. In such cases, three-dimensional effects are dominated by heat loss to the side walls in the downstream portion of the flame and flame spread rate increases with fuel width. In low oxygen and low speed flows, the flames are short and are close to the quenching limit. Oxygen side diffusion then becomes a dominant mechanism exhibiting large effects on the narrow three-dimensional flames. Flame spreads faster as the solid width is made narrower. Due to the oxygen side diffusion, the low-oxygen flammability limit is extended beyond the two-dimensional limit for moderately narrow samples.