Cyclone separators are widely used for gas–solid separation due to their robustness and low operating cost. This study focuses on the experimental validation of a single cyclone configuration and the development of a MATLAB-based numerical framework. The model employs a Euler–Lagrange approach to capture centrifugal, drag, and gravitational forces acting on spherical polyethylene particles (D = 5 mm). Laboratory-scale measurements of airflow, pressure drop, and separation efficiency showed strong agreement with the numerical model (deviation < 6%), confirming its reliability for the single cyclone case. Beyond this validated framework, exploratory simulations were carried out for series and parallel cyclone configurations to provide predictive insights into possible design trade-offs. Unlike high-fidelity CFD–DEM models, which are computationally intensive and allow detailed turbulence and particle–particle interactions, the present MATLAB model is simplified but transparent and fast to implement. Its originality lies in demonstrating a low-cost, experimentally calibrated tool that can support preliminary design decisions. The multi-cyclone results should be interpreted as predictive trends, as no direct experimental validation was possible within the present setup. These findings offer preliminary guidance for balancing efficiency, energy demand, and throughput in applied mechanics of multiphase flow systems.

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.

Reverse-flow cyclone preselection is often performed with nominal semi-empirical closure values, although swirl and turbulence corrections are family-dependent. This study develops a scenario-based robust geometric screening framework for fixed-throughput reverse-flow cyclones using a family-calibrated reduced-order model for cut size and grade efficiency, combined with a fixed-Eu pressure drop. The design variables are the inlet-area ratio, vortex-finder diameter ratio, and effective residence-height ratio. Closure uncertainty is represented by 27 combinations of the swirl-intensity coefficient, turbulence-correction coefficient, and turbulence intensity. Deterministic and robust Pareto fronts are compared in the pressure-drop–corrected-cut-size plane (Δp,d_50,t), and worst-case grade-efficiency indicators are evaluated for 2 and 5 μm particles. The results show that closure uncertainty substantially penalizes nominal fine-particle predictions: across the robust Pareto set, the worst-case corrected cut size is 1.79–1.93 times the nominal value. Within the original design window, the reduced-order screen identifies a balanced candidate near ϕ_in ≈ 0.10, D_e/D = 0.40, and H_eff/D = 6, with lower predicted nominal and worst-case corrected cut sizes than the baseline at unchanged fixed-Eu pressure drop estimate. The selected geometries are not independently validated in the present study and should be treated as candidates for subsequent high-fidelity assessment. Design-grid refinement and extended-bounds, hydraulic, and logistic-slope sensitivity audits show that the numerical screening results are stable within the adopted formulation but remain conditioned by its closure assumptions.