## 5 Evaluation of Hydraulic Losses
The fluid exhibited chaotic behavior in the impeller region, which accounts for the losses discovered earlier. The turbulent behavior of the fluid at the second stage impeller was, however, not carried over to the next stage. The diffuser and return vane at the second stage corrected the flow instabilities and prepared the fluid incidence angle tangent to the next stage blade angle. Figure 11: Blade loading at the mid-span of the impeller at each stage for water at the design point. Figure 10.0 Contours at the meridional plane of the second stage impeller for (**a**) pressure and (**b**) velocity in a stationary frame. The disparity between the fluid incidence angle and the blade angle at the second stage impeller was due to the incoming flow from the solute. The fluid entering the solute from the first stage impeller split into the two arms of the 180 deg staggered twin solute, flowed along the solute surfaces and rejoined toward the solute exit. The fluid at the solute exit was observed to have a larger radial force than the axial force and, as a result, created a pre-swirl at the inlet of the second stage impeller. This pre-swirl of the fluid was responsible for the imbalance in the flow angles and the losses associated with it. The velocity triangle diagram of the flow at the inlet of the impellers is shown in Figure 10.1 Theoretically, at the design flow rate, the fluid reached the impeller radially without any swirl. The absolute fluid velocity at the inlet creates an angle of \(\alpha=90\lx@math@degree\) with the direction of the blade rotation in an ideal case. However, these assumptions are not likely to conform to an actual centrifugal pump [30]. The absolute flow angle decreased sharply to 12.68 deg, and the relative flow angle increased to form an obtuse angle of 121.6 deg at the second stage impeller. This was due to the high absolute velocity at the impeller inlet caused by the large circumferential velocity component of the flow exiting the solute. Figure 15 shows the 3D velocity streamlines at the solute-impeller interface, indicating a significant shift in the flow direction. As mentioned above, it can be seen that the circumferential velocity increased excessively due to the outlet shape of the first stage solute. The absolute flow angle at the inlet of the Stage 3 impeller was 25% lower than the ideal case due to the swirl velocity observed at the inlet, which was formed by the return vanes of the second stage. Here, the second stage return vanes acted as an inlet guide vane to the third stage impeller. The velocity triangle diagrams of Stage 4 and 5 impellers are similar to the Stage 3 impeller. Figure 10.2 (**a**) Theoretical, (**b**) Stage 2 and (**c**) Stage 3 velocity triangles at the impeller inlet. Figure 10.3 Blade-to-blade views of the velocity streamlines at the midspan of the impellers at each stage. The left and right impellers at the first stage indicate the double-suction impeller. The cause of the losses at the second stage was identified as the sudden change in the flow angle at the volute-impeller interface due to a high radial force from the volute. The effect of this was visualized by identifying the vortex core region formed inside the impeller. The velocity streamlines and the vortex core with a swirling strength of 0.004 are shown in Figure 10.4 The majority of the vortices were formed at the pressure side of the impeller, causing blockage to the incoming flow. They were formed due to the flow separation at the leading edge. These vortices could be suppressed by regulating the incoming flow from the volute. Figure 10.5 Velocity streamlines and vortex core region (swirling strength = 0.004). Figure 10.6 3D velocity streamlines at the volute-impeller interface (Stage 1–Stage 2 interface). To address the losses at the second stage, we provide certain design recommendations to pump manufacturers:  
1. The pre-swirl observed at the volute exit must be suppressed by reducing the large radial forces of the fluid flowing through the twin volute.