In this article Eulerian-Lagrangian 2D computer simulations of consequences of primary dust explosions in two vessels connected by a duct are described. After an explosion in the primary vessel a propagation of hot pressurised gases to the secondary vessel, initially uniformly filled with dust particles, is simulated. The gas phase is described by the standard equations and it is coupled with the particulate phase through the drag force and the convective heat transfer. No chemical reaction is considered in the model since the objective was to model the system up to the time of ignition. The computation was performed for different lengths and diameters (heights) of the linking duct. Having analysed the results, it was concluded that the simulations agree with experimental observations in that the probability of transmission of an explosion from the primary to the secondary vessel decreases with decreasing diameter (height) and increasing length of the connecting pipeline. Snapshots of particle positions for different times are presented. The work illustrates the behaviour of the mixture in the secondary vessel: the particles tend to concentrate in clouds, and domains with no particles are observed. This may influence the explosion characteristics of the system.