A Free-Surface Model of a Jet Impinging On a Sprinkler Head

Understanding the atomization of fire sprinkler sprays fills a critical gap in the modeling of fire suppression systems. Previous research by the authors has shown an instability model coupled with a stochastic transport model can paint most of the sprinkler spray picture, but requires input in the form of thickness and velocity of unstable fluid sheets. The model outlined describes a water jet impinging on a perforated deflector plate as a velocity potential. The free surface separating the jet from the surrounding air takes the form of a vortex sheet with the air assumed to be at rest. Through the use of the Green's function, the fluid velocity potential can be posed as a boundary value problem. Any solution obtained is an exact solution to the inviscid flow equations and the interior flow a solution to the Navier-Stokes equations. The resulting model allows for the determination of the complete flow field over a sprinkler head of arbitrary geometry and input conditions. Knowledge of this flow field provides insight into the impact of sprinkler head geometry and fluid velocity as well as providing the above mentioned inputs for a complete model of fire sprinkler sprays.