Solution of analytical model for fuel spray penetration via homotopy perturbation method

The present paper attempts to solve equations in the initial stage and the two-phase flow regime of fuel spray penetration using the HPM-Padé technique, which is a combination of the homotopy perturbation method (HPM) and Padé approximation. At the initial stage, the effects of the droplet drag and the air entrainment were explained while in the two-phase flow stage, the spray droplets had the same velocities as the entrained air. The results for various injection pressures and ambient densities are presented graphically and then discussed upon. The obtained results for these two stages show a good agreement with previously obtained expressions via successive approximations in the available literature. The numerical result indicates that the proposed method is straight forward to implement, efficient and accurate for solving nonlinear equations of fuel spray.