Similarity solutions and applications to turbulent upward flame spread on noncharring materials

Abstract

The primary achievement in this work has been the discovery that turbulent upward flame spread on noncharring materials (for pyrolysis lengths less than 1.8 m) can be directly predicted by using measurable flammability parameters. These parameters are: a characteristic length scale which is proportional to a turbulent combustion and mixing related length scale parameter ( q ̇ ″ net ( ΔH c ΔH v )) 2, a pyrolysis or ignition time τ p , and a parameter which determines the transient pyrolysis history of a non-charring material: 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, q ̇ ″ 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 c 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, q ̇ ″ fw . The present discovery was made possible by using both a numerical simulation, developed earlier, and exact similarity solutions, which are developed in this work. The predictions of the analysis have been 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 a function of the height normalized by the flame height ( Z Z f ) having a maximum value that is nearly constant for many materials; this profile is approximated in the work by a uniform profile of constant heat flux over the flame length, without loss of generality or violation of the physical situation. As the pyrolysis length increases (> ∼ 1.8 m), radiation dominates and a different total wall heat flux distribution applies. For this case a numerical simulation, such as FMRC's upward Flame Spread and Growth (FSG) code, can be used to predict upward flame spread rates while the present correlations can provide an upper bound for the flame spread rate.