Generalized dynamics on the penetration of two phase fuel spray using differential transform method

The penetration of fuel spray as a result of the mixture of fuel droplet and entrained air usually generate nonlinear models whose solutions are normally difficult to realize analytically. This present study presents general approximate analytical solution to such problem by employing Differential transform Method (DTM). At the level of two-phase flow, the spray droplets and the entrained air have the same flow velocity. In order to fully understand the process, the parameters present in the governing equations are carefully studied. The obtained solution employing DTM is verified with Numerical Runge-Kutta (RKF45) and also compared with similar past works. Furthermore, the acquired results for different ambient densities and injection velocities are depicted and discussed. The results illustrate that continuous increase in the initial velocity and orifice diameter cause a corresponding increase in spray penetration while an antonymous effect is noticed for an increased semi cone angle and density. This work will find vital applications in the optimization of systems whose operation are influence by the aforementioned spray penetration processes.