An Explicit Semi-Empirical Model for Cyclone Separator Cut Size with Swirl and Turbulence Corrections

Cyclone separators remain widely used for gas–solid separation, yet analytical prediction of cut size and pressure drop remains challenging. This study presents an explicit semi-empirical model for the cut size (d50) of reverse-flow cyclones based on the radial particle equation of motion in cylindrical coordinates, with d50 obtained by equating radial migration time and residence time. A closed-form solution is derived in the Stokes regime, whereas non-Stokes behavior is handled numerically through the Schiller–Naumann drag correction. Turbulence is incorporated through a phenomenological correction, and the grade–efficiency curve is represented by a logistic relation. The model was implemented in MATLAB R2025a and applied in a parametric study covering inlet velocity, particle density, cyclone diameter, and gas viscosity. A Euler-type pressure drop relation was included to examine the separation–energy trade-off. Validation on the Kim et al. benchmark using one calibration point per cyclone family and six independent verification cases yielded a mean absolute percentage error of 13.5% and a root mean square error of 0.22 μm for d50; the paired pressure drop check gave a 2.8% mean absolute percentage error. A complementary benchmark based on Wang et al. using 15 cm 1D3D and 2D2D cyclones under actual-air and standard-air conditions further supported the family-calibrated use of the model. A separate scale-up test showed that constant swirl intensity similarity is not transferable across large diameter changes. The formulation provides a transparent reduced-order tool for preliminary design and sensitivity analysis.