Scaling the transport of firebrands by wind-blown plumes

The possibility of using a reduced-scale model based on the Froude-scaling technique to study the transport of spherical, cylindrical and disk-shaped firebrands by a wind-blown plume was investigated theoretically. The cases of hot particles produced by arcing copper power lines and burning sparks produced by arcing aluminium power lines were also considered. In each case, scaling relationships were derived for mass, linear-momentum, angular momentum and energy transport equations of the firebrands, using well-established models. The analysis shows that, in the case of cylindrical firebrands, incompatible conditions on brand diameter are obtained to scale both the linear-momentum equation and the mass and energy equations. It also shows that all physical processes scale correctly for hot copper particles as well as spherical and disk-shaped burning embers with the exception of the conservation of angular momentum in the case of disks. Despite this drawback, numerical results, obtained using an integral model representing a wind-blown plume, show that the mass and spatial distributions for both types of firebrands can be satisfactorily reproduced down to a scale of 1:5.