## 5 Results and Discussion
### Flow Analysis in Design and Off-Design Conditions
In pumps with a regenerative impeller, such as the 'S-shape' impeller, the flow inside the pump can be one of two types, tangential flow surrounded by the impeller and recirculating flow formed inside the impeller [6]. The recirculating flow, including axial, radial, and tangential components, are responsible for the energy transport, which causes violent mixing between the internal flow inside the impeller and the channel flow. Figure 14: Velocity and tangential velocity vectors on the mid-width plane of the pump impeller. (**a**) \(\emptyset\)= 0.31; (**b**) \(\emptyset\)= 0.39; (**c**) \(\emptyset\)= 0.47. Figure 13: Turbulent kinetic energy and tangential velocity vectors on the normal planes near the inlet region. (**a**) \(\emptyset\) = 0.31; (**b**) \(\emptyset\) = 0.39; (**c**) \(\emptyset\) = 0.47. In the design flow condition with a flow coefficient of 0.39, a relatively large circulating flow is observed compared to the other flow conditions. It is noted that a larger recirculation flow increases momentum exchange due to the higher tangential velocity, thus resulting in the high pump efficiency shown in Figure 9. The recirculation flow formed in the concave region of the impeller blade is not sufficiently developed at the inlet of the pump (Plane 1), so it shows eccentricity. It develops a full circular shape at Plane 2 and decreases somewhat due to increased rotational force by high pressure near the pump outlet (Plane 3). On the other hand, in off-design flow conditions, the formation of recirculating flow is relatively small compared to the design flow condition, the low-speed flow region increases at lower flow conditions. At the same time, the intensity of the rotational speed around the recirculation flow also decreases in the high-flow condition. It is no use to say that the increase in the magnitude and intensity of the circulation flow generated inside the blades contributes to the increase in pump efficiency by increasing the momentum energy. Figure 16 shows the pressure comparisons along the solute casing of the pump for the design and off-design operating conditions. The measuring position is indicated by a solid purple line, as shown in Figure 16b. It is known that pressure along the pump casing is composed of an 'acceleration-linear-deceleration' pattern. It was found that there is an acceleration and a linear region of the pump in the three flow conditions, which shows the distinctive nature of the regenerative impeller. As shown in the figure, the pressure gradient increases as the flow rate increases in the linear region along the rotational direction of the impeller. Although the gradient of pressure-rise is almost similar for three flow conditions, flow characteristics such as velocity patterns and vortex generation are quite different, as shown in Figures 14 and 15. [PERSON] et al. [4] also reported similar findings related to such impellers. Figure 17 shows the pressure at the 90 percent span of the impeller for the design and off-design operating conditions. As shown in the figure, pressure increases with the rotation of the pump impeller, while relatively high pressure is observed as the flowrate decreases. The negative (suction) pressure at the inlet due to the rotation of the pump impeller increases as the flowrate increases, and the pressure at the pump outlet side increases as the flow rate decreases. Figure 15: Tangential velocity vectors on the mid-width plane of the pump impeller shown in Figure 11a. (**a**) \(\oslashash\) = 0.31; (**b**) \(\oslash\) = 0.39; (**c**) \(\oslash\) = 0.47.