Effects of transient pyrolysis on wind-assisted and upward flame spread

Abstract

This article describes recent developments in modeling fire growth on vertical surfaces by using a numerical code for upward flame spread that accurately simulates transient pyrolysis and convective, q ̇ ″ c , and radiative heat flux, q ̇ ″ r , from the flames. The results show that transient pyrolysis significantly affects the rate of upward flame spread even for noncharring materials such as PMMA. To demonstrate this point, the present work focuses on upward flame spread on vertical walls for an extent of the pyrolysis region such that the buoyant flow is laminar (e.g., the pyrolysis length is less than 50 mm). For the laminar case, where the radiative heat flux can be negligible and the convective heat flux versus height can be approximated as q ̇ ″ c ∼ Z −1 4 , one can obtain similarity solutions for the flame spread in which the ratio of the flame height to the pyrolysis length, Z f Z p = γ , is constant. This ratio, which directly affects the flame spread rate, can be substantially overestimated with a quasi-steady pyrolysis assumption, especially when the transient pyrolysis process is slow which occurs when L (C pΔT p) is large. ( L is the latent heat of pyrolysis, C p the heat capacity and T p the pyrolysis temperature of the solid). γ is only a function of ΔH c (L + C pΔT p) in the case of quasi-steady pyrolysis ( ΔH c is the heat of combustion per unit mass of pyrolysis gases) but is also a function of λ = L (C pΔT p) when transient pyrolysis is taken into account. In the range of λ from 3 to 50 transient pyrolysis can reduce the rate of upward flame spread by as much as a factor of four. The numerical results are validated by comparison with an exact analytic solution that is valid for large values of λ ≥ 15. The present results can explain discrepancies between experimental results and earlier theoretical models which overpredict flame spread, having assumed quasi-steady pyrolysis during flame spread. Because of its importance, transient pyrolysis even for noncharring materials must be included in flame spread models for accurate prediction and interpretation of flame spread rates.