Froude-modeling-based general scaling relationships for fire suppression by water sprays

Based on the Froude modeling concept, Heskestad proposed a set of scaling relationships for the spray–plume interaction for high droplet Reynolds number conditions (10≤Red≤500). The droplet Reynolds number is defined as the ratio of the product of droplet diameter and the absolute value of the droplet velocity relative to the gas velocity over the gas kinematic viscosity. The aforementioned scaling relationships have been used widely for scale-modeling of water-based fire protection under conditions within or beyond 10≤Red≤500. Recently, it was shown that the same scaling relationships can be extended to low droplet Reynolds number conditions of Red≤1 except that the droplet size is scaled with the 1/4-power of the scale ratio, instead of the 1/2-power for 10≤Red≤500. The conditions of 10≤Red≤500 in general prevail in sprinkler applications and the conditions of Red≤1 usually take place in water mist applications. With the above difference in mind, the Froude modeling is revisited in this paper to establish a set of general scaling relationships not limited to specific droplet-Reynolds-number regimes. The derived general relationships not only reproduce those for Red≤1 and 10≤Red≤500, but also reaffirm the previous finding that the scaling relationships are independent of the scale ratio except for the droplet size, whose scaling requirement varies with the range of Red values in which the scale-modeling is performed. The published experimental results to date show that the Froude-modeling-based scaling relationships for spray–plume interaction are a viable tool for scale-modeling of the fire suppression or extinguishment by water sprays.