The common design of cyclone separators is the cylinder-on-cone design, and the conical shape has a strong effect on the behavior of the vortex core low in the cyclone. The "vortex length" is the distance between the lip of the gas outlet tube and the position at which the core of the vortex attaches to the wall of the cyclone separation space. This occurs spontaneously at an axial position that, at present, cannot be predicted, although it has a profound effect on the cyclone operation, since, if the vortex is too short, it can lead to plugging and wear. In this paper numerical CFD simulations, using advanced turbulence modeling (LES), are the basis for the formulation of models for the vortex length taking into account the geometrical and operational variables influencing it. The work leads to useful models for the vortex length and reveals important information about which variables determine it and the nature of their effects.