The results of the experimental study are detailed in this section. The performance is carried out to obtain main and operating characteristics for different hub geometry configurations. Thus, the following discussion takes into account overall efficiency, head coefficient, and relative theoretical efficiency corresponding to chosen volume coefficients at the rated speed for hub-less base configuration as well as two-hub geometry configurations.

### Effect of hemi-spherical hub configurations on the fan performance

#### Effect on overall efficiency

Figure 9 shows the variation of overall efficiency of the fan for various hemi-spherical hub configurations shown in Table 2. It is found that the presence of the hub improves the performance of the fan in terms of its overall efficiency at all volume coefficients. This is obviously because of the fact that basically hub provides better guidance for the flow of air at fan inlet in comparison to the hub-less configuration at corresponding volume coefficients. In general, it is observed that, on an average, there is an improvement in overall efficiency of about 2.6% for various hemi-spherical hub configurations over the hub-less base configuration at design volume coefficient as can be seen from the plot.

However, it is discernable that the hemi-spherical hub configuration S3 yields comparatively a higher overall efficiency of the fan at all volume coefficients. It is reasoned that this configuration is facilitating in re-laminarising the flow at the fan inlet which reduces inlet flow losses significantly and leads to static pressure improvement. Hence, hemi-spherical hub configuration S3 is considered as a useful optimum configuration for enhanced performance as regards to overall efficiency.

Further, the configurations S4 and S5 yield a lower overall efficiency when compared to S3 configuration. This is because of the possible constricted entry at the inlet due to protruding hub that could cause an accelerated flow resulting in flow losses.

#### Effect on main characteristics

The main characteristics for hemi-spherical hub configurations vis-a-vis the hub-less base configuration are depicted in Fig. 10. It is found that as the volume coefficient increases head coefficient decreases corroborating the theoretical trend required for a typical backward curved impeller. It is found that, for any of the hub configurations when compared to hub-less base configuration, the head coefficient seems to be higher at all volume coefficients. In general, it is observed that there is relatively a higher value of head coefficient of about 0.6% over the hub-less base configuration, on an average, at design point volume coefficient.

It is interesting to observe that S3 configuration also has a higher head coefficient value at all volume coefficients as was the case for overall efficiency. It is clear that with this hemi-spherical configuration, flow admittance into the inlet region near the radial bend is smoother with little or no turbulence thereby improving the energy transfer process. An improvement of about 1.4% in head coefficient for the hemi-spherical hub configuration S3 vis-à-vis the hub-less base configuration for the range of volume coefficients is seen from Fig. 10.

This is due to the fact that the hemi-spherical hub contravenes the effect of stalling that is generally expected for the hub-less base model. This also ensures a relatively better guidance over the smoother surface of the hemi-spherical hub. As a consequence, a more streamlined flow of air enters the impeller and losses relatively minimized. This results in better head coefficient for the hub configuration S3 when compared with hub-less base model.

#### Effect on operating characteristics

To understand the operating behavior of the hub-less base model vis-à-vis various hub configurations, a relative theoretical efficiency is defined as given in Eq. (4). Figure 11 clearly shows the variation of relative theoretical efficiency for hub-less base model and other hub configurations at various values of volume coefficients. It is found that for all the hub configurations compared to hub-less base configuration there is an average improvement in relative theoretical efficiency by about 0.8% corresponding to the design point operation.

Not surprisingly, S3 configuration found to be the optimum hub configuration that has a higher relative theoretical efficiency of about 2.4% when compared to hub-less configuration. The reason for this being the same as was stated earlier in the “Effect on overall efficiency” and the “Effect on main characteristics” sections.

### Effect of ellipsoidal hub configurations on the fan performance

#### Effect on overall efficiency

The variation of overall efficiency of the fan for various ellipsoidal hub configurations is shown in Fig. 12. It is found from Fig. 12 that there is an improvement in overall efficiency for the ellipsoidal hub configurations over that of the hub-less base configuration at all volume coefficients considered in the experimental work. This is attributed to the fact that the presence of the hub prevents the sudden change of direction from axial to radial thereby minimizing the minor losses incurred due to this transition. Essentially the hub geometry leads to a streamlined through flow of air in the vicinity of eye of the impeller when compared with hub-less base configuration. An average improvement of about 7.3% is observed for various ellipsoidal hub configurations over the hub-less configuration at design point operation of the fan.

Interestingly, it is also seen from Fig. 12 that hub configuration E5 yields relatively higher overall efficiency of the fan at all volume coefficients used in the study. The reason for this improvement is stated as follows.

It is reasoned that for the configuration E5, the convergence of flow over the hub surface seems to be optimum. This helps in streamlining the flow in the constricted passage effectively. As a result, there could be an optimum gradual change in flow direction along the annular passage between the hub and inlet casing. The combined effect of optimum convergence and smoother flow transition relatively lowers the accountable incident losses; thereby, performance in terms of overall efficiency is comparatively higher for ellipsoidal hub configuration E5 over other configurations.

For ellipsoidal hub configurations built with lower axial hub length (configurations E1, E2, E3, and E4), there is a possibility of rapid rise in the velocity almost near the entrance region of the impeller due to converging annular passage. This results in streamlining of the flow in the vicinity of eye region. Also, the jet type of flow is emerging out of inlet region onto the impeller and hence there may not be scope for a gradual change in the direction of fluid flow. Hence, due to dominating effect of convergence over the flow guidance, performance in terms of overall efficiency improves but marginally.

Contrastingly, for the ellipsoidal hub with larger hub length (configuration E6), flow traverses a relatively longer annular distance and then takes a turn into the radial direction. Combined effect of this is that there is associated skin friction loss in the annular region. The flow also suffers a turning loss due to poor guidance at the inlet to the impeller because of the hub geometry. Thus, this configuration contributes to higher flow losses which render this configuration not suitable when compared to other configurations.

#### Effect on main characteristics

The main characteristics for ellipsoidal hub configurations in comparison with hub-less base configuration are shown in Fig. 13. It is discernable that hub configurations are found to yield relatively higher head coefficient values when compared with the hub-less base configuration at all volume coefficients. An average improvement of about 3.6% is observed for hub configurations over the hub-less base configuration at design point.

Again, configuration E5 is found to be the optimum configuration in terms of head coefficient. This may be reasoned as follows. Configuration E5 provides adequate convergence over the hub surface and enters the impeller with minimum incidence and friction losses. This helps in bettering the head coefficient by about 7.5% for configuration E5 over the hub-less base configuration as seen from Fig. 13.

#### Effect on operating characteristics

Relative theoretical efficiency is plotted for ellipsoidal hub configurations vis-à-vis hub-less base configuration to quantify the beneficial effects of hub and is depicted in Fig. 14. For various values of volume coefficients adopted in the analysis, it is revealed that all the hub configurations are found to deliver better operating characteristics for the fan. An average improvement of about 3.7% is observed in relative theoretical efficiency for hub configurations over the hub-less base model at design point.

However, configuration E5 seems to yield relatively higher relative theoretical efficiency when compared to other ellipsoidal hub configurations including hub-less base model. An average improvement of about 7.7% in relative theoretical efficiency is observed for configuration E5 over the hub-less base model at design point of the centrifugal fan. This improvement in relative theoretical efficiency clearly corroborates the improvements in overall efficiency as well as the main characteristics of the fan.

### Comparison of optimum hemi-spherical and ellipsoidal hub configurations

It is interesting to compare the performance of the fan corresponding to the optimum hub geometry of hemi-spherical and ellipsoidal configurations. The overall efficiency and the relative theoretical efficiency are used for performance comparison.

The overall efficiency is plotted in Fig. 15 for optimum hemi-spherical hub configuration (S3) as well as optimum ellipsoidal hub configuration (E5), along with hub-less base configuration as benchmark. It is found that optimum ellipsoidal configuration (E5) shows a consistent improvement of about 11% in overall efficiency over that of the optimum hemi-spherical hub model (S3) for the range of volume coefficients considered.

Similarly, Fig. 15 also depicts the variation of relative theoretical efficiency for optimum hemi-spherical (S3) and ellipsoidal hub (E5) configurations. Again, the optimum ellipsoidal configuration E5 shows a significant improvement of about 3.5% in relative theoretical efficiency over that of the optimum hemi-spherical hub model (S3) for various volume coefficients used.

It is clear from the comparative study that configuration with ellipsoidal hub geometry E5 produces a better performance in terms of both the performance parameters. This may be established from the fact that a more streamlined flow in the vicinity of impeller eye region is obtained for this configuration when compared to optimized hemi-spherical hub model as well as hub-less base model. Due to this, flow incidence losses are significantly reduced and the overall effect across the entire fan is an improvement in both overall efficiency and relative theoretical efficiency for this E5 configuration.

Hence, it is established in this study from a series of experiments on different hub configurations with parametric variation in geometry that as a design prescription a hub with ellipsoidal hub ratio of 1.1 corresponding to configuration E5 is found to be the best overall design that can be adopted with reasonable assurance of improved performance among the various configurations studied.

### Development of correlations for the optimized hub-shape configuration

The results discussed in the “Effect on main characteristics” and the “Effect on operating characteristics” sections show that the fan performance characteristics, i.e., head coefficient (*ψ*) and relative theoretical efficiency (*η*_{Rt}), are significantly influenced by both volume coefficient (*ϕ*) and ellipsoidal hub ratio (*R*_{E}) considered in the study. Therefore, *ψ* and *η*_{Rt} can be expressed as functions of *ϕ* and *R*_{E} as given in Eqs. (9) and (10) respectively.

$$ \psi =f\left(\phi, {R}_E\right)={C}_1\;{\phi}^a{R}_E^b $$

(9)

$$ {\eta}_{Rt}=f\left(\phi, {R}_E\right)={C}_2\;{\phi}^m{R}_E^n $$

(10)

where *C*_{1}, *C*_{2}, *a*, *b*, *m*, and *n* are empirical constants.

Regression analysis of the experimentally obtained values has been performed to determine the constants in Eqs. (9) and (10). This analysis provides the exact relationships for *ψ* and *η*_{Rt}using least square fit and the correlations thus obtained are as shown in Eqs. (11) and (12) respectively.

$$ \psi =0.42\;{\phi}^{-0.015}{R}_E^{0.034} $$

(11)

$$ {\eta}_{Rt}=39.85\;{\phi}^{-0.088}{R}_E^{0.026} $$

(12)

Figures 16 and 17 show comparison of experimental and predicted values of head coefficient and relative theoretical efficiency for ellipsoidal hub geometry configurations. It can be seen from these parity plots that 95% of the predicted values of head coefficient and relative theoretical efficiency (calculated using Eqs. (11) and (12)) lies within ±5% of the experimentally obtained values as depicted by Singh et al. (2011).

The regression data of head coefficient for the correlation obtained in Eq. (11) has regression coefficient of 0.93 and average absolute deviation of 0.8% whereas the regression data of relative theoretical efficiency for the correlation obtained in Eq. (12) has regression coefficient of 0.89 and average absolute deviation of 4.9%. This depicts good agreement between predicted data and experimental data.

In conclusion, for the range of parameters investigated in the experimental work, the values of head coefficient as well as relative theoretical efficiency can be predicted with reasonable accuracy using the correlations developed in Eqs. (11) and (12) respectively.