A numerical model is developed to examine laminar flame spread and extinction over a thin solid fuel in lowspeed concurrent flows. The model provides a more precise fluid-mechanical description of the flame by incorporating an elliptic treatment of the upstream flame stabilization zone near the fuel burnout point. Parabolic equations are used to treat the downstream flame, which has a higher flow Reynolds number. The parabolic and elliptic regions are coupled smoothly by an appropriate matching of boundary conditions. The solid phase consists of an energy equation with surface radiative loss and a surface pyrolysis relation. 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 with the flame spread rate being an eigen value. Calculations are performed in purely forced flow in a range of velocities which are lower than those induced in a normal gravity buoyant environment. Both quenching and blowoff extinction are observed. The results show that as flow velocity or oxygen percentage is reduced, the flame spread rate, the pyrolysis length, and the flame length all decrease, as expected. 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, diffuse 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 quenching extinction limit. Low velocity quenching occurs as a result of heat loss. At low velocities, surface radiative loss becomes a significant fraction of the total combustion heat release. In addition, the shorter flame length causes an increase in the fraction of conduction downstream compared to conduction to the fuel. The...

A detailed three-dimensional model for steady flame spread over thin solids in concurrent flows is used to compare with existing experiments in both buoyant and forced flows. This work includes (1) several improvements in the quantitatively predictive capability of the model, (2) a sensitivity study of flame spread rate on input parameters, (3) introduction of flame radiation into the buoyant-flow computations and (4) quantitative comparisons with two sets of buoyant upward spread experiments using cellulosic samples and a comparison with forced downwind spread tests using wider cellulosic samples. In additional to sample width and thickness, the model computation and experimental comparison cover a substantial range of environmental parameters such as oxygen percentage, pressure, velocity and gravity that are of interest to the applications to space exploration. In the buoyant-flow comparison, the computed upward spread rates quite favorably agree with the experimental data. The computed extinction limits are somewhat wider than the experimental limits based on only one set of older test data (the only one available). Comparison of the flame thermal structure (also with this set of older data) shows that the computed flame is longer and there is structure difference in the flame base zone. This is attributed to the sample cracking phenomenon near the fuel burnout, a mechanism not treated in the model. Comparison in forced concurrent flows shows that the predicted spread rates are lower than the experimental ones if the flames are short but higher than the experimental ones if the flames are long. It is believed that the experimental flames may have not fully reached the steady states at the end of 5-second drop. The effect of gas-phase kinetic rate on concurrent flame spread rates is investigated through the variation of the pre-exponential factor. It is found that flames in forced flow are less sensitive to the change of kinetics than flames in buoyant flow; and narrow samples are more sensitive to the change of kinetics compared with wide samples. The rate of chemical kinetics affects the flame spread rates primarily through two mechanisms: the amount of un-burnt fuel vapors escaping the reaction zone and the induced velocity variation through flame temperature change in the case of the buoyant flames.