## 4 Conclusions  
The objective of this study was to enhance the effectiveness of the Stairmand cyclone separator through the optimization of its geometry. The Muschelknautz method of modeling (MM)--a well-known mathematical model used for predicting pressure losses and cut-off diameter of the particulate phase--was utilized for optimization using genetic algorithms. All geometrical parameters, which include inlet dimensions, vortex finder diameter and its insertion length, cyclone main body diameter, cone tip diameter, and conical section height, were taken into consideration for optimization. A few cases from the Pareto front points were selected, and numerical simulations were performed using advanced closure LES to assess the relative performance with respect to the baseline model. The investigation defines the importance of considering the cyclone main body diameter (\(D_{\mathrm{c}}/D\)) for optimization, and the optimized diameter was observed to take a larger value than the original size. Conclusive results indicate the following:  
* In cyclone model A, the pressure losses decreased significantly by 43.22%, with a marginal reduction of 2.16% in the overall collection efficiency and an increase in the cut-off size by 12.3%.  
Figure 14: Particle traces (colored with particle diameters) in cyclone model A and model C (top to bottom) at different time intervals.  
* In model B, with a reduction in the pressure drop by 4.67%, cut-off sizes decreased by 15.71%, with a 19.05% enhancement in the collection efficiency.
* In Model C, with an increase in the pressure drop by 36.62%, the cut-off size decreased by 41.94%, and the collection efficiency increased by 24.69%.  
Overall, the results of the study imply that the optimized geometries were significantly better than the standard model regarding particle separation efficiency and pressure drop. The research underscores the importance of considering all geometrical parameters to achieve optimal performance in the cyclone separators. With the large number of optimized datasets provided in the manuscript, the designers will have a wide choice of appropriate ones to select. Since all the geometric entities are normalized with the original diameter of the cyclone, there is flexibility when applying them to any cyclone size. As an extension to the present study, the future plan is to also optimize the cyclone performance based on the particle loading condition.  
Conceptualization, L.S.B.; methodology, L.S.B.; software, S.P., L.S.B., A.M., O.P., A.A. and M.W.; validation, S.P. and M.W.; formal analysis, M.W.; A.M. and O.P. investigation, S.P., L.S.B. and M.W.; resources, S.P. and O.P.; data curation, S.P., L.S.B., A.M., O.P., A.A. and M.W.; writing--original draft preparation, S.P. and L.S.B.; writing--review and editing, S.P., L.S.B., A.M., O.P., A.A. and M.W.; visualization, S.P. and L.S.B.; supervision, L.S.B.; project administration, L.S.B. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare no conflict of interest.