Granular flows through converging sections such as conical hoppers have been reported to be submitted to instationarities, which in certain circumstances can appear to be organized and periodic. In this paper, we explore this phenomenon by conducting discrete element modelling simulations of a 3D gravity-driven hopper flow and varying a large number of parameters such as hopper geometry and granular sample properties. Dedicated postprocessing techniques are developed and used to investigate the spatial and temporal patterns of these instationarities and to bring some understanding on the physics of this spontaneous phenomenon. Numerical results show that a clear structure appears for these instationarities, under the form of rapidly propagating waves relating variations in velocity magnitude and coordination number. While very faint, periodic variations of the sample density are also detected. The parametric study reveals that the self-organization of these variations requires a narrow set of conditions in terms of hopper geometry and intergranular contact friction coefficient.