A mathematical model on lateral temperature profile of buoyant window spill plume from a compartment fire

Abstract

A Gaussian-based mathematical model is theoretically brought forward to describe the lateral temperature profile (in the direction normal to the façade wall) of a spill buoyant plume from window of a compartment fire. The model is built up physically based on that this buoyant plume is conceptually produced by a rectangular fire source with characteristic side dimensions of ℓ1 (beside wall, physical length scale related to the effective area of the outflow) and ℓ2 (normal to wall, physical length scale representing the length after which the outflow turns from horizontal to vertical due to buoyancy) sitting beside an adiabatic façade wall at the neutral plane height of the window. A deduced length scale, by accounting for the entrainment of air mass flow rate into the plume from the non-constrained sides, is brought forward to characterize the effective plume thickness in the direction normal to the façade wall, which will be used in the Gaussian profile function. Experiments are carried out in an experimental device to validate the model developed for six different windows. Results show that the length scale proposed for describing the effective plume thickness can successfully collapse the experimental data of different total heat release rates for various window geometries, and the proposed Gaussian-based model can predict the lateral temperature profile measurements. Furthermore, an exponential function is proposed for the parameter β in the Gaussian profile of such a spill plume in relation to the window aspect ratio (H/W).