Powder discharging from a silo provokes an emission of dust. To understand and prevent this source of danger,3D simulations of a silo dischargewere performed using an Euler-Euler approach. The impact of the coupling between the flow inside the silo and the granular jet in free-fall is analyzed. Results show that the solid mass flow rate is correctly predicted and that gas back-flowing at the hopper exhaust appears responsible for the formation of a fluctuating and radially expanding jet. However, the radial expansion of the free-falling jet is underestimated. Stochastic fluctuations of the particles velocity at the hopper exhaust are introduced to evaluate their effect on the downstream development of the free-falling jet. These fluctuations are found capable of generating a development of the jet similar to that observed experimentally. This suggests that the granular flow conditions at the hopper exhaust are responsible for the further dispersion of powder.