A Simplified Model of the Effect of a Fire Sprinkler Spray on a Buoyant Fire Plume

Abstract

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 However, in the application of active fire suppression by water droplets, the equations are no longer valid.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.

A review on fire suppression by fire sprinklers

“…The study concluded from its findings that a solid cone water spray pattern and fine water droplet sizes increase the suppression efficiency, while emphasizing that high flow rates will only lead to more expensive operating costs. A modified buoyancy equation model of Morton's was proposed by Schwille and Lueptow 43 to include a fire sprinkler spray, and by adding a term in the momentum equation to reflect the momentum of a uniform-disperse droplet field of a sprinkler spray, the adjusted momentum equation was obtained. This was done by including the effect of homogeneous, uniform velocity droplet field on the momentum of the field.…”

“…58 The mean flame height is defined as the elevation above the source of the fire on the central axis, where the flames appear 50% of the time. 43 A series of tests was carried out to investigate the influence of sprinkler actuation times in preventing flame spread for varied fire sizes in a tunnel fire test by Marke. 59 They observed that as fire size increases, the chances of preventing flame spread (and extinction of ignition source) decrease.…”

Numerical Study on the Interaction of Water Mist with a Fire Plume

“…  is diffusion coefficient, S  is source term and S p is relative amount of liquid terms to gas terms. Water mist model: The motion equation of water mist droplet can be described as: (2) where F x is source term formed by a variety of force, u is fluid velocity, u p is droplet velocity,  is fluid viscosity coefficient,  is fluid density, p  is droplet density, D p is droplet diameter, and C D is drag coefficient which can be expressed as:…”

“…The variation regularities of the interaction of water mist with a fire plume is an effective method to reveal the mechanism of fire extinguishing by water mist [1] . The research on numerical simulation on the interaction of water spray with a fire plume has been carried out for many years, and the recent studies focus on numerical modeling of the interaction of water spray with a fire plume and its similarity criterion [2,3] . The previous results show that there is a balance between drag force of water droplet and buoyancy of fire plume under a particular water flow conditions.…”