Description and application of an analytical model to quantify downward smoke displacement caused by a water spray

Abstract

An analytical model is developed from basic principles to quantify the downward smoke displacement as caused by a water spray from e.g., a sprinkler head. The underlying assumptions are identified and the global balance is described between downward drag force, potentially downward buoyancy due to a cooling effect within the water spray envelope in the smoke layer, and the upward buoyant force in the ambient air below the smoke layer. From this balance, the downward smoke displacement is quantified. It is explained that the classical Bullen theory to define a criterion for smoke layer stability is in general not valid. There is always downward smoke displacement, although potentially small, depending on the circumstances. The tracking of individual water droplets leads to the evolution of the spray envelope radius and provides the total downward drag force on the smoke. An extensive sensitivity study is presented, varying the water spray angle at the nozzle, the water droplet diameter, the smoke layer temperature, and inclusion or not of the cooling effect by water and air entrainment in the downward smoke displacement. It is highlighted that the downward smoke displacement is more pronounced for smaller droplets (for fixed water mass flow rate), and for lower smoke layer temperatures. For larger water spray angle at the nozzle, the downward displacement also increases monotonically with initial smoke layer thickness. A smaller spray angle at the nozzle leads to stronger downward smoke displacement and the variation of downward smoke displacement with initial smoke layer thickness is non-monotonic: stronger descent of smoke for thinner smoke layer, but beyond a critical smoke layer thickness also again a stronger descent with increasing smoke layer thickness. The accuracy of the model as presented is illustrated by means of an experimental data set.