# CFD Investigations of Cyclone Separators with Different Cone Heights and Shapes
## 2 Materials and Methods
### Details of the Analyzed Geometric Variants and the Adopted Assumptions of CFD Study
#### 2.3.1 Details of the Cyclone Models  
The Stairmand high-efficiency cyclone model [46] is used as a baseline model to evaluate the performance of the proposed cyclone design. The cyclone Stairmand is a cylinder-on-cone structure to which the inlet of the two-phase mixture (solid-fluid) is tangentially attached at the top. The geometry of this separator includes the following sections: two-phase mixture inlet (defined by height \(a\) and width \(b\)); vortex finder diameter (\(D_{\rm c}\)) and length (\(L_{\rm o}\)); the diameter of the lower conical section (\(B_{\rm c}\)); the height of the cylindrical section (\(H\)), the height of the conical section (\(H_{\rm c}\)), the dipleg height (\(L_{\rm c}\)), and cyclone diameter (\(D\)), as shown in Figure 1a; the dimensions are given in Table 1.  
Figure 1: Geometrical details of the Stairmand high-efficiency cyclone model (\(D\) = 0.205 m) with (**a**) straight walls of the conical section (referred to as the ST), (**b**) convex profile (referred to as the CV variant), and (**c**) concave profile (referred to as the CC variant). Apart from the straight walls of the conical section (referred to as the ST (straight) variant), we also consider curved conical walls. For this, the two proposed curved geometries include a convex profile (referred to as the CV variant, cf. Figure 1b), and a concave profile (referred to as the CC variant, cf. Figure 1c)--the profile description is based on the observations external to the cyclone. The convex profile, as shown in Figure 1b, consists of a parabolic curve attached tangentially to the vertical line of the cylinder at the top, while the other end is attached to a short downcomer tube. On the other hand, in the concave profile (cf. Figure 1c), one end is attached tangentially to the downcomer tube, whereas the other end is attached to the cylindrical section at the top. After completion of (2-D) geometry on the y plane, the cyclone model was generated by revolving the profile about the (z-) axis of revolution. As a final step, a rectangular duct was attached to all models near the cyclone roof. In addition to the above, we further explore the impact of different heights of the cylindrical section on the cyclone performance--the height of the cylinder is changed while maintaining a constant total cyclone height (\(H+H_{c}\)). The reason for not permitting any change to the total height is to optimize the design for a compact size. Such an approach was considered earlier by authors [15; 39; 40]. The details of all the cyclone geometries are given in Table 1, and the final geometries of all the models are represented in Figure 2.  
To summarize, in the present study, we categorize the cyclone variants based on the profile of the conical wall viz. a straight profile (ST variant), convex profile (CV variant) and concave profile (CC variant). The different heights of the cylindrical section in each variant are then further categorized as the cyclone models that contain a numeric character after the variant description (cf. Figure 2).