Water droplet changes its movement direction and velocity when it bypasses an aircraft component with the surrounding airflow or gets blown by air injection from the inner part. When the deflected droplet impacts on the downstream surface, its impingement characteristics would be different from those without the frontal effects. In this article, a Lagrangian method was developed to include those upstream effects on the droplet collection efficiency. Validation cases were carried out for a cylinder and an MS (1)-0317 airfoil, whereas a multielement airfoil and an engine cone with a hot air film-heating anti-icing system were computed to investigate the effects of the upstream component and air injection on the impingement characteristics of downstream surfaces. It is found that the present collection efficiencies are in good agreement with the experimental data and the simulation results obtained by the Eulerian and traditional Lagrangian methods when not affected by those upstream factors. The droplet deflections and trajectory crossings are observed clearly under the influence of the upstream component, and the Lagrangian results of downstream surfaces differ from those of the Eulerian method. In addition, due to the air injection from the inner engine cone, the peak collection efficiency on the cone surface increases with the decrease of the droplet diameter and the value even exceeds one when the droplet is small. This work is helpful for the understanding of the droplet motion and the accuracy of aircraft icing simulation.