The flow field of cyclone separators was simulated with different vortex finder diameters and inlet dimensions using the Reynolds Stress Model to determine the mechanism of stagnation of axial velocity. Two flow patterns of axial velocity in cyclone were observed with changing vortex finder diameter and inlet dimension. As vortex finder diameter and inlet dimension increased, stagnation worsened. If the pressure gradient at the centerline of cyclone separator is positive, stagnation of axial velocity appears in the separation space of cyclone. The variation of the dimensionless critical vortex finder diameter of stagnation with inlet dimension was attributed to the proportion distribution of energy loss in cyclone. Finally, response surface methodology and Muschelknautz method of modeling (MM) were applied and yielded parameters with significant effects on stagnation. The variance analysis confirmed a larger quantitative contribution from inlet dimension on stagnation compared to that of vortex finder diameter, which will be useful for the structural optimization of cyclone. Display omitted •Give the effect of Der and Ka on stagnation in detail for the first time.•Acquire the condition for stagnation just appearing in the separation space.•The mechanism of axial velocity stagnation is revealed.•Provide quantitative contribution from Der and Ka on stagnation by RSM.•Reveal the variation of Dcer with Ka.