A mathematical model on interaction of smoke layer with sprinkler spray
A mathematical model was developed for predicting the downward descending behavior of the buoyant smoke layer under sprinkler spray. The behavior of the smoke layer was determined by considering the interaction between the drag force of the sprinkler spray and the buoyancy force of the hot smoke layer itself in the spray region. The smoke layer may be pulled down with its thickness increased at the center of the spray region due to the cooling and drag effects of the sprinkler spray, thus to form a downward “smoke logging” plume. In the mathematical model developed in this paper, the critical condition under which the smoke layer lost its stability, as a serious concern, was predicted. Additionally, the length of the downward plume, which was rarely investigated before, was also further calculated. Full-scale experiments were carried out to validate the model. Results showed that the predictions, including the critical condition and the length of the plume, by the mathematical model agreed well with that observed and measured in the experiments. The length of the downward plume was shown to increase with the sprinkler operating pressure by an approximately linear correlation.