Highly-resolved numerical simulations have been performed for a coaxial, twin-fluid nozzle, which is designed for fundamental research of the atomization process in entrained flow gasification (EFG). Objective of the work is to reveal specifically the influence of the relative injection angle $\alpha$ between the central liquid jet and the annular airflow (external-mixing) on the primary atomization. A glycerol/water mixture with a dynamic viscosity of 200 mPa·s is atomized at atmospheric condition and with a gas-toliquid ratio of 0.6. The angle of attack between liquid and airflow has been varied from $\alpha$ = 0° to 60°. The computational grid consists of approx. 10 million cells, using a smallest resolution of 25 µm. In agreement with the corresponding experiment, the calculated breakup morphology is characterized by a pulsating mode destabilization, accompanied by disintegration of membrane-type ligaments. The breakup of the liquid jet is found to be enhanced from $\alpha$ = 0° to 30°, which leads to a decrease of the liquid core length $L_C$. This is attributable to a reinforced aerodynamic interaction or an enhanced multiphase momentum transfer from the gas to the liquid phase, respectively. ... mehrThe gas flow velocity close to the liquid jet is increased in this case, which is in accordance with results obtained from the PIV measurement. The reason for the increase of local flow velocity is shown to be caused by an increased local static pressure at the base of the liquid jet with increased $\alpha$, which results in a favorable pressure gradient in main flow direction. However, further increase of $\alpha$ from 30° to 60° leads to a decreased flow velocity around the liquid jet, so that $L_C$ increases and the atomization performance decreases with $\alpha$. The behavior is further elucidated by means of the multiphase momentum exchange or the liquid phase kinetic energy, which increase from $\alpha$ = 0° to 30° and decreases with further increased $\alpha$. The result reveals the essential impact of the nozzle design parameters on the atomization process in addition to the general operating parameters. In summary, there exists an optimal relative injection angle between the liquid and air streams in the range of 30°<$\alpha$<45° for a best atomization performance.