Modeling the trajectory of window flames with regard to flow attachment to the adjacent wall

A model for predicting the trajectory of window flame ejected from a fire compartment was formulated incorporating the effect of wall above the opening. Based on the observation in the reduced scale experiments, window flames were divided into the following categories with regard to its trajectory configuration: the flow which ascends almost vertically up after ejection maintaining a certain separation from the wall; and the flow which ascends upward after ejection and gradually approaches to the wall in the downstream. In the model, trajectories of these flows were approximated by cubic polynomials whose coefficients were given as functions of a dimensionless parameter F*. The parameter F* was derived from the conservation equation of momentum which incorporates the effect of pressure gradient across the ascending flows. Critical condition for the occurrence of flow attachment was described as a proportion of the maximum separation from the wall versus the opening width. Trajectories predicted by the proposed model were then compared with the measurement data which indicated reasonable agreements.