## 3 Results and Discussion
### Pareto Front Points
#### 3.1.1 Mean Flow Field  
The contour plots of the normalized mean static pressure, mean axial velocity, and mean tangential velocity of all the models are represented in the first, second, and third rows of Figure 5, respectively, and the corresponding radial profiles are represented in Figure 6. From the first row, it becomes apparent that the pattern of the pressure distribution is similar in all models--the pressure is at its maximum near the walls and lowest near the rotational axis of the inner core. This is due to the strong swirling nature of the flow. The mean pressure value is highest near the walls in model C and lowest in A, with a comparable value in Std as well as the B model that takes intermediate values. The same can be seen in the radial profiles at all the axial stations, such as \(z/D=1.0\), 2.0, and 3.0 (from left to right, respectively) in Figure 6. The magnitude of the pressure field relates to the pressure drop values--the greater the wall static pressure, the more pressure losses are expected. Near the geometrical axis, the lowest pressure is observed in model C and the highest in model A, with models B and Std having intermediate values. Large pressure gradients exist in the core region of model C, and this regime is very narrow. This contrasts with the pressure distribution in model A, where the (relative) variations are very few.  
The second row in Figure 5 elucidates the contour plots of mean axial velocity, and the second row in Figure 6 represents its radial profiles at different axial stations. It becomes apparent that the axial velocity is directed in the downward direction near the solid walls (also termed the outer vortex region) and in the upward direction in the core region. The flow reversal takes place once the downwardly directed swirling flow touches the bottom plate of the cyclone. In the outer vortex region, the axial velocity magnitude is seemingly the same in all models. However, the difference is observed in the inner vortex regime--its magnitude is maximum in model C, followed by models B, Std, and A (in ascending order). The same is reflected in the radial profiles at all stations.  
The last row in Figures 5 and 6 represents the contour plots and radial profiles of mean tangential velocity, respectively. The tangential velocity magnitude is maximum in model C and lowest in model A, with intermediate values for Std and B models that have nearly similar values. Clear information is available in the radial profiles. The mean tangential velocity magnitude increases linearly in the core region till it reaches the outer region of the inner vortex. Thereafter, it reduces nonlinearly until it reaches the cyclone walls, where it takes the lowest value. The slope of the tangential velocity has the maximum values for model C, which indicates a much faster-rotating vortex core than other models. A minimum value is observed in model A, and its slope indicates the slowest rotation of the inner vortex. It is important to note that due to the high rotational rate of the inner vortex in model C, the dip in the static pressure profile is prominent, followed by the narrowest zone compared to the other models.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline _Sl. No._ & \(D_{\text{s}}/D\) & \(D_{\text{e}}/D\) & \(H_{\text{f}}/D\) & \(B_{\text{e}}/D\) &  
Figure 5: Contour plots on \(Y=0\) plane. From left to right: cyclone models Std, A, B, and C. From top to bottom: mean static pressure, mean axial velocity, and mean tangential velocity, respectively.