A mathematical model for predicting liquid release and spraying characteristics of fixed-wing airtankers

Airtankers are one of the most effective methods for combating forest fires. To investigate the firefighting performance of fixed-wing airtankers, a mathematical model for predicting the liquid release and spraying characteristics of aerial firefighting aircraft is proposed in this study. The present model utilizes nozzle flow equations to describe liquid discharge and integrates equations for Kelvin–Helmholtz and Rayleigh–Taylor instabilities for primary breakup, along with a simplified diffusion sub-model for droplet spreading. A tailor-made decoupled algorithm is developed to solve the model. The model is validated through drop tests with the DC-10 aircraft and experiments in the low-speed wind tunnel, demonstrating its accuracy in capturing primary spray pattern features. The influences of dropping conditions on firefighting efficiency are further investigated, including drop height, ground speed, discharge mass flow rate, and crosswind velocity. The computation results indicate that increasing drop height decreases core coverage level with minimal impact on effective pattern width, while higher ground speeds reduce coverage level and pattern width; increased discharge mass flow rate enhances coverage level and effective width but shortens retardant line length; crosswind effects introduce asymmetry in the pattern profile and affect coverage thickness.