## 3 Results and Discussion
### CFD Analysis
#### 3.1.1 Performance Augmentation of the Fan Due to Hub Geometry Treatment at Design Mass Flow Rate  
As demonstrated in Figure 7A,B, air tends to experience a stalling effect on the backside shroud plate while moving along the suction tube. It depicts the type of flow at the fan's inlet eye area for the hub-less base model. It has been revealed that the presence of low-pressure stall disturbances causes a significantly disturbed flow field of velocity when fluid enters the rotating impeller. A proper geometric intervention in the eye region is required to decrease this. Hub designs with spheroidal and ellipsoidal hub ratios varying from 0.30 to 0.80 and 0.30 to 1.30, respectively, are investigated to establish the optimal hub model geometry that will result in minimum flow distortions at the fan inlet and finally re-align it with the main stream. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Hemispherical Hub**} & \multicolumn{2}{c}{**Ellipsoidal Hub**} \\ \hline
**Model** & **Spheroidal Hub Ratio** & **Model** & **Ellipsoidal Hub Ratio** \\ \hline Hub-less base & 0.00 & Hub-less base & 0.00 \\ \hline S1 & 0.30 & E1 & 0.30 \\ \hline S2 & 0.40 & E2 & 0.50 \\ \hline S3 & 0.50 & E3 & 0.70 \\ \hline S4 & 0.60 & E4 & 0.90 \\ \hline S5 & 0.70 & E5 & 1.10 \\ \hline S6 & 0.80 & E6 & 1.30 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Ellipsoidal and spheroidal hub ratios used for CFD analysis. Figures 8 and 9 show the trend of the effectiveness of the hub for various hemispherical and ellipsoidal hub geometry configurations at the design point volume coefficient of 0.051. The research reveals that, compared to the hub-less base model, improved hub effectiveness is attained for all the configurations of hemispherical and ellipsoidal hub geometries. For configurations S3 and E5, respectively, a hub effectiveness improvement of 1% and 1.7% above the hub-less basic model is noted. Figure 8: Effectiveness of the hub for different hemispherical hub designs. Figure 7: Visualization of the velocity for the hub-less base arrangement. (**A**) Side view, (**B**) Enlarged view of Sections AA and BB. This is explained by the fact that the hub's hemispherical or ellipsoidal shape eliminates the stalling effect seen in the hub-less base model and improves flow direction into the impeller's meridian inlet route. Here, it must be emphasized that the main causes of flow losses are stalling at the hub wall and turbulent flow at the impeller's entrance brought on by the swirling of incoming fluid. This can be explained by stating that for these configurations, the flow losses brought on by turbulence are decreased, improving the fan's overall performance. Additionally, it appears that hub effectiveness is at its highest for configurations S3 (corresponding to a spheroidal hub ratio of 0.5) and E5 (corresponding to an ellipsoidal hub ratio of 1.1). This is attributed to the fact that for configurations S3 and E5, in addition to the streamlined through flow that was previously described, useful acceleration was also attained, which tends to flush the swirling eddies, thereby efficiently guiding the flow. Because of this, it can be seen that these geometric configurations, as depicted in Figure 10A and 10B, respectively, significantly lower flow-related losses, particularly stalling losses, in the vicinity of the impeller's inlet when compared to the hub-less base model. Therefore, it is clear that among the combinations examined for higher static pressure recovery, these geometric configurations appear to be the best hub designs. Contrarily, it can be seen from Figure 8 that the hub effectiveness significantly decreases for hemispherical hub topologies with spheroidal hub ratios higher than 0.50. As shown in Figure 9, the useful hub effectiveness of ellipsoidal hub configurations likewise exhibits a decreasing trend for hub ratios above 1.10.