A new mathematical tool for modelling the processes in fuel sprays

New concepts of positively (negatively) invariant manifolds for non-linear systems with non-Lipschitzian nonlinearities have been introduced. It is pointed out that the order reduction of these systems can be performed, using these new concepts. It is shown that the singularly perturbed system of three equations (droplet radii, gas temperature and fuel vapour concentration) describing evaporation and ignition of monodispersed sprays possesses the attractive positively invariant manifold. This allows us to reduce this system to the system of two equations describing gas temperature and fuel concentration when the droplet evaporation process has been completed. An additional equation describes the reduction of droplet radii when the variations of gas temperature and fuel vapour concentration can be considered small.