Virtual origin correction for a fire plume in a room under displacement ventilation regime

The paper examines experimentally and theoretically the virtual origin position of a fire plume in the so-called simultaneous filling and emptying box problem. Small-scale experiments are carried out with a pool fire placed into a rectangular box with an opening vent located at the ceiling. At steady state, a balance is achieved between the smoke mass flow rate supplied by the fire plume and the mass flow rate of smoke that escapes through the ceiling vent. A theoretical model for the simultaneous filling and emptying of a box is proposed, to predict the thickness and the temperature of the smoke layer. The model involves the conservation of mass and energy for the smoke layer as well as the calculation of the heat transfer through the walls. The characteristics of the fire plume at the layer interface are evaluated using the self-similar solutions including a correction of the virtual origin position. A new correction is suggested for the virtual origin position. The comparison of the model including the new virtual origin correction with the experimental data shows a good agreement.