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An extensive numerical study of two-phase flow inside the nozzle holes and the issuing jets for a multi-hole direct injection gasoline injector is presented. The injector geometry is representative of the Spray G nozzle, an eight-hole counter-bored injector, from the Engine Combustion Network (ECN). Homogeneous Relaxation Model (HRM) coupled with the mixture multiphase approach in the Eulerian framework has been utilized to capture the phase change phenomena inside the nozzle holes. Our previous studies have demonstrated that this approach is capable of capturing the effect of injection transients and thermodynamic conditions in the combustion chamber, by predicting phenomenon such as flash boiling. However, these simulations were expensive, especially if there is significant interest in predicting the spray behavior as well.