Liquid–gas–solid three-phase flows in hydrocyclones are studied numerically in this paper by employing a coupled method of the volume of fluid (VOF) and discrete element model (DEM) with Reynolds stress model (RSM) turbulence model. The numerical method is validated by comparing the calculated results to those of experiments published in the literature about the separation of particle flows in hydrocyclones. Since VOF-DEM model could capture the gas–liquid interface of particle flows, the three-dimensional formation process of the air-core together with the formation of the spiral trajectory of particles are depicted for the first time. In addition, the effects of the particle concentration ω (less than 12%) on the air-core formation time Tf and diameter Da are studied systematically, which has not been reported in the literature. The increase of ω has both positive and negative actions on the change of Tf and Da, and the compromises of two kinds of actions generate the valley or peak of the curves of Tf versus ω and Da versus ω, respectively. Moreover, the results for three hydrocyclones with different cone angles are also compared to study the effects of the cylindrical and conical section on the air-core formation and the separation performance of the hydrocyclones. By analyzing the flow fields and the pressure changes inside the hydrocyclones, qualitative explanations of the relevant discoveries are given in this paper. The results will be helpful in the investigation of the multiphase flow behaviors in the hydrocyclone and in the selection of the appropriate hydrocyclone.