Similarity solutions and applications to turbulent upward flame spread on non-charring materials

Turbulent upward flame spread on non-charring materials (for pyrolysis lengths less than 1.8 m) is shown to be directly predicted by using measurable flammability parameters. The controlling parameters are: a combustion related length scale which is proportional to (dq″_net ΔH_c/ΔH_v)², a pyrolysis or ignition time τ_p, and a transient pyrolysis parameter: λ = L/c ΔT_p = ratio of the latent heat to the sensible heat of the pyrolysis temperature of the material. In the length scale parameter, dq″_net is the total net heat flux from the flames to the wall (i.e. total heat flux minus reradiation losses), ΔH_c is the heat of combustion and ΔH_v is an effective heat of gasification for the material. The pyrolysis or ignition time depends (for thermally thick conditions) on the material thermal inertia, the pyrolysis temperature and the total heat flux from the flames to the wall, dq″_fw. The controlling parameters were developed by using a numerical simulation, developed earlier, and new exact similarity solutions which complement existing similarity solutions. The predictions of the analysis are validated by comparison with upward flame spread experiments on PMMA. The present results are directly applicable for pyrolysis lengths less than 1.8 m over which experiments in practical materials show that the total (radiative and convective) heat flux to the wall from the flames is constant and nearly uniform over the flame length. As the pyrolysis length increases (>approx. 1.8 m), radiation dominates and a different total wall heat flux distribution applies.