Powder discharging from a silo provokes an emission of dust. To understand and prevent this source of danger, 3D simulations of a silo discharge were 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. (C) 2020 Elsevier B.V. All rights reserved.