A simplified model of the effect of a fire sprinkler spray on a buoyant fire plume

Equations describing the fluid motion in buoyant plumes have been applied to fire plumes by researchers and engineers since Morton et al. developed them in the 1950s. However, in the application of active fire suppression by water droplets, the equations are no longer valid. The equations have been modified to include the effect of a homogeneous, uniform velocity droplet field on the momentum of the fluid. Solving the resulting ordinary differential equations shows that the plume widens and the upward velocity of the plume slows significantly due to the presence of droplets. Results from this simple model appear to match the results of more sophisticated numerical simulations. The model further demonstrates that the interaction between the upward momentum of the plume and the downward momentum of the droplet spray can be critical for fire suppression.