The primary break-up of an injection system results in the formation of non-spherical droplets and liquid ligaments. Depending on the Weber number, a secondary break-up may occur, resulting in the formation of smaller, spherical droplets. The droplet size distribution (DSD) is measured after the completion of the secondary break-up to obtain a high sphericity validation rate. Numerical simulation of both break-ups using an Interface Capturing Method (ICM) is challenging due to the computational demands. The scale of the smallest droplets is typically 2 to 3 orders of magnitude smaller than the numerical domain, requiring a large number of computational elements. However, the ligaments and droplets formed during the primary break-up process contain valuable information about the final spray size distribution. Research by Palanti [1] proposed an analysis based on the curvature and surface area of the early atomization process to calculate the final DSD. This analysis was further extended by Ferrando [2] adding the capability to calculate the velocity of the droplets. The curvature-surface analysis has been applied to a commercial simplex swirl atomizer [3] using Large-Eddy Simulation (LES) where the DSD was well captured in comparison with experiments [4]. However, the numerical simulation overestimated the joint velocity distribution of the droplets. This particular injector has a complex geometry and several physical processes are involved. The model and discretization schemes chosen play a role in solving the flow, therefore, the overestimation of the droplet velocity may be due to the flow downstream, and not the curvature analysis itself. To further study this analysis, this work uses a simpler academic case with a simpler geometry. A Direct Numerical Simulation is performed using the ARCHER code, in order to avoid using any turbulence model that may affect the final results. Unlike previous works which used the interFoam solver (volume of fluid-based solver), this study uses a more precise ICM called the level-set method. The curvature-surface analysis method is applied to evaluate its effectiveness.