Predictions of the primary breakup of fuel in realistic fuel spray nozzles for aero-enginecombustors by means of the SPH method are presented. Based on simulations in 2D, novel insightsinto the fundamental effects of primary breakup are established by analyzing the dynamics ofLagrangian-coherent structures (LCSs). An in-house visualization and data exploration platformis used in order to retrieve fields of the finite-time Lyapunov exponent (FTLE) derived from theSPH predictions aiming at the identification of time resolved LCSs. The main focus of this paperis demonstrating the suitability of FTLE fields to capture and visualize the interaction between thegas and the fuel flow leading to liquid disintegration. Aiming for a convenient illustration at a highspatial resolution, the analysis is presented based on 2D datasets. However, the method and theconclusions can analoguosly be transferred to 3D. The FTLE fields of modified nozzle geometriesare compared in order to highlight the influence of the nozzle geometry on primary breakup, whichis a novel and unique approach for this industrial application. Modifications of the geometry areproposed which are capable of suppressing the formation of certain LCSs, leading to less fluctuationof the fuel flow emerging from the spray nozzle.