Liquid column

 


Establishment of a model for the water bombing from an aircraft


The design objective of an aerial delivery system is to guarantee an efficient ground coverage under adverse meteorological conditions, to delay the fire progress and give time to the firemen to act.

Due to the action of the aerodynamic forces, the liquid breaks up into a cascade of fluid structures that form a spray region with the characteristic cloud shape, as shown in the following figure :

 
 
Schematic representation of the cascade of fluid structures originated by the breakup of a liquid jet into a crossflow of air
 
The balance of aerodynamic drag, liquid inertia, gravity, surface tension, and viscous forces induces both deflection and deformation of the jet column. Deflection leads to a curved liquid-jet profile that will break and fragment the column into large segments near the point of curvature due to the growth of wave instabilities. Small droplets are entrained in the near-wall region owing to the wake flow that develops behind the liquid column. During the process, deformation increases the frontal cross section of the jet column and increases the drag, which leads to surface stripping of smaller ligaments and fragments directly from the column.
 
The volume of liquid released from the airtanker is then subjected to two sorts of physical instabilities that control the atomization process of the air-liquid interface and the resulting droplet population.
The Rayleigh-Taylor instability is an instability of an interface between two fluids of different densities, which occurs when the lighter fluid is pushing the heavier fluid. As for the Kelvin-Helmholtz instability, it can occur when velocity shear is present within a continuous fluid, or when there is sufficient velocity difference across the interface between two fluids.
During the drop phase, these two instabilities are both observed resulting in a very complex process of primary and secondary atomization mechanisms.
 
As a first approximation, we have chosen not to take into account those instabilities, since their study is quite complicated. The assumptions we have made are listed on the page dedicated to the establishment of the jet trajectory equations.