Fragmentation of fuel injection has a fundamental influence on engine performance. The influence factors for the breakup of the spray process, including near nozzle fields, are still unclear. The Primary and secondary breakup of fuel sprays occurring with turbulence perturbation is devoted to simulation. And the evolutionary processes of Newtonian and power-law fuels atomization affected by turbulence are investigated in present models. A validated single-phase fully developed turbulent flow is generated first to store time-varying outlet velocity database. Then, the database is mapped as the two-phase model inlet velocities boundary. A modified VOF (Volume of Fluid) coupled with DNS (direct numerical simulation) method is applied to study the deformation and breakup of fuel spray. Wavy surface, ligaments, and droplets with various scales and shapes turn up gradually in jet evolution process. Meanwhile, after being sheared, distorted and stretched, different ligaments separation patterns are captured. Larger Reynolds number and higher gas densities accelerate the jet break-up process. Higher injection velocities and lower power-law indexes (n<1) result in better atomization effects while it's too viscous to fragment for shear-thickening (n>1) fuel jet. What's more, similar breakup patterns are detected in shear-thinning fluid (n<1) jets compared to Newtonian fuel jet (n=1). However, the disintegration is considerable easier and more violent, especially in the later stage. When it comes to the secondary breakup, in internal combustion engines for instance, the flow is complex and rapidly varying. Also, there are rarely canonical flows in reality. As for the breakup process, apart from critical Weber number, critical Reynolds number should also be taken into consideration. Besides, the breakup patterns are different from uniform velocity field when a drop is exposed to a turbulent velocity field.