A numerical simulation infrastructure capable of calculating the flow of gas and the trajectories of particles through an aerodynamic lens injector is presented. The simulations increase the fundamental understanding and predict optimized injection geometries and parameters. Our simulation results were compared to previous reports and also validated against experimental data for 500 nm polystyrene spheres from an aerosol-beam-characterization setup. The simulations yielded a detailed understanding of the radial phase-space distribution and highlighted weaknesses of current aerosol injectors for single-particle diffractive imaging. With the aid of these simulations we developed new experimental implementations to overcome current limitations.