Flame spread predictions over linear discrete fuel arrays using an empirical B-number model and stagnation point flow

Abstract

A stagnation-point flow model based in part on the mass transfer B-number was adapted to approximate the heat flux and time to ignition of dowel arrays subject to forced convection flame spread. Previous work on forced flow flame spread along a dowel array has characterized the existence of discretized flame behavior. In deployment-scale wildland fire models, small fuels are smaller than the grid resolution. Sub-grid modeling then relies on empirical relationships, such as Nusselt number–Reynolds number (Nu-Re) models, to estimate the fire spread. Current Nu-Re models utilized to calculate the heat flux and ignition times predict higher heat transfer and faster ignition times with increasing flow speeds. However, analysis of the flame spread revealed that the ignition time has a parabolic relationship with the flow speed, with the fastest ignition time occurring around the onset of the discrete flame behavior. Nu-Re models cannot capture the upward inflection of ignition times beyond the onset of the discrete flame spread, where the ignition times increase with greater flow speeds. A boundary layer solution to the plume heat flux impinging on the next unignited dowel was employed to develop a B-number empirical model. The B-number model captures the changes to mass and heat transfer induced by differences in the flow speed and array spacing. The proposed empirical B-number model together with heat flux approximation generates more accurate predictions for ignition times than the existing approach.