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Diesel spray breakup and evaporation determine the characteristics of the fuel-air mixing for mixture-fraction based combustion models. An accurate spray breakup model is a key point for their predictability, especially primary breakup. Different from the popular droplet-particle based Langragian models, we resolve the liquid phase in Eulerian frame. In addition, a level-set method is employed to capture the two-phase flow interface, including surface tension force. The phase transition is taken into account by introducing surface regression velocity into the level-set transport equation. Through 3D direct numerical simulation (DNS), we can have insight in the formation of ligaments and droplets for diesel direct injection. As experimental results are still difficult to obtain for dense spray, the simulation result reveals the spray primary breakup with the help of modern supercomputers in first principle