K.Y. Li

A Mathematical Model on Interaction of Smoke Layer with Sprinkler Spray

Abstract 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.

Experimental investigation on drag effect of sprinkler spray to adjacent horizontal natural smoke venting

Discharge rate of a horizontal adjacent smoke vent under sprinkler spray is experimentally investigated. Temperature of smoke layer and velocity of smoke venting were measured, under different sprinkler operating pressures and smoke venting areas. CO concentration at the smoke vent center and velocity of vent flow with fresh air outside were recorded in tests under different smoke venting conditions. Experimental results have shown that efficiency of smoke venting is controlled by a combination of smoke buoyancy and drag force of sprinkler spray. Only when buoyancy is greater than drag force the smoke could be extracted by venting. Velocity of smoke venting has shown to decrease as the operating pressure increases. Smoke venting logging, which represents the failure of smoke venting, was experimentally found from certain operating pressure called initial logging pressure. The CO concentration was found to increase after sprinkler was operated as the smoke is constrained in the spray region with horizontal momentum decreased. Negative pressure difference is caused at the vent when there is smoke venting logging, which might practically bring the exterior fresh air into the fire building. Additionally, experiments results have shown that the venting area has little influence on smoke flow under smoke venting logging.

Evaluation of simplified calculation methods for determining heat transfer between a smoke flow and a sprinkler spray

Empirical equations determining heat transfer between a smoke layer and a sprinkler spray have been assessed by using data from several experiments available in the literature. The comparison of the heat loss and temperature of the smoke layer under sprinkler spray shows that the equations developed by Williams for 15 mm pendent conventional sprinklers agree reasonably well with the experimental results. Equations from Spearpoint et al. (Spearpoint MJ, Williams C and Morgan HP. Engineering relationships for calculating the heat transfer from a horizontally-moving Buoyant smoke layer to a sprinkler spray, Fire Research Station, Borehamwood, Herts, UK, 1993 (unpublished)) perform fairly well compared to upright sprinkler experiments especially for a spray sprinkler case but need more validation due to the lack of experimental data. Predictions from the equation given by Heselden are close to the values for a pendent conventional sprinkler with a depth below ceiling less than 0.3 m but values are lower than those given by Williams (Williams C. The Downward Movement of Smoke due to a Sprinkler Spray, PhD dissertation, South Bank University, London, UK, 1993) and by Li et al. (Li SC, Chen Y, Wei D, Yang D, Sun XQ, Huo R and Hu LH. A Mathematical Model for Cooling Effect of Sprinkler on Smoke Layer. In: Proceeding ASME 2009 Heat Transfer Summer Conference, San Francisco, California, USA, Vol. 3, 2009, pp. 7–13). If the effect of smoke downdrag is taken into account, then the Heselden equation performs well whereas the other equations give relatively higher predictions. For a conservative assessment, the predictions from the equation given by Li et al. multiplied by a factor of 1½ are sufficiently in excess of the maximum heat loss values predicted by other equations. However, the heat loss must be compared to the total convective heat flow to avoid getting unreasonable results. The study has been limited by data regarding smoke temperature, layer depth, sprinkler types, and operating pressures. As a result, the conclusions should only be applied to 15-mm nominal sprinklers for a smoke flow with an average temperature of less than 100°C, a depth less than 1.6 m, and water flow rates below 133 L/min. The equations should be used with care for any other conditions.

A Mathematical Model of the Drag Component of a Sprinkler Spray Adjacent to Horizontal Smoke Vents

A mathematical model has been developed to investigate the effect of a sprinkler spray on adjacent horizontal smoke venting and in particular the water droplet drag component. The pressure difference across a roof vent and the volumetric flow of smoke vented are determined by considering the interaction between the drag force of the sprinkler spray and the buoyancy of the smoke layer in the spray region. Smoke venting may become progressively more inefficient as the sprinkler operating pressure increases due to the cooling and drag effect of the sprinkler spray. Full scale experiments were carried out to validate the model. Results show that the mathematical model can predict the observed trend of a decrease in vented volumetric flow with an increase in sprinkler operating pressure, which eventually leads to ineffective smoke venting. Experiments with different smoke venting areas show that vent area has little influence on smoke flow once sprinkler pressure causes a loss in smoke flow efficiency or vent function.

Studies of Cooling Effects of Sprinkler Spray on Smoke Layer

An experimental study was performed to measure the cooling of a smoke layer by water sprays. This was followed by the development of a mathematical model based on the theory of Chow and Tang. The predictions of the model agree well with the experimental measurements. Water sprays investigated in the present work provided significant cooling of the smoke layer. We observed little effect of increasing the water pressure from 50 to 100 kPa on the cooling of the smoke layer.