Numerical Investigation on the Mechanism of Double ...

The radial hydraulic forces on the impeller and volute within one cycle of impeller rotation for different flow rates (0.8and 1.2) are shown in Figure 11 and Figure 12 using the force coefficient. Radial hydraulic forces on the impeller regularly develop and revolve around the origin in the coordinate system. The variations of these forces are exhibited in obvious periodicity, affected by impeller structure because of blade number. The force pulsations excite the pump casing to vibrations [ 20 ]. The fluid flows from the rotating impeller uniformly and impacts on the asymmetric structure of the volute. The impeller-volute interference produces some radial hydraulic forces. The bigger the pulsation amplitude is, the more severely the pump vibrates. On the normal condition of, radial hydraulic force on the pump with single-volute is apparently smaller than that on the double-volute pump. However, bigger force on the pump with single-volute arises at 0.8and 1.2, which illustrates positive effects of double-volute on the force pulsation variation for abnormal conditions. The existence of second volute tongue is in favor of homogeneous flows in the pump because of the double-volute structure superior to the asymmetric structure of the single volute. As shown in Figure 13 , some unsteady flows developing severely on abnormal conditions can be improved, such as flow recirculation and stall. These simulated force characteristics and unsteady flows correspond to published literatures [ 8 10 ]. Smaller force amplitude contributes to mitigating the pump-casing vibration, and then makes the pump run more reliably. Meanwhile, these forces on the volute are trapped in the fourth quadrant, which indicates the direction of pump-case vibration inducing by radial hydraulic force.

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The vector of radial hydraulic force on the pump can be decomposed into two orthogonal component forces,and, which are lay on the radial section of pump. The force vector orientation is referenced from the first cross-section of volute in the rotating coordinate direction, and positive in the direction of impeller rotation. The force is normalized by the force coefficientbased on the impeller outlet tip velocity:whereis the radial hydraulic force (N),is the impeller diameter (m),is the impeller width (m), andis the circumferential velocity in the largest base circle of the impeller (m/s).

Performance characteristics of pumps with single-volute and double-volute were tested, and tested results in comparison are presented in Figure 9 . The head values of single-volute pump and double-volute pump at the rated flow are 18.9 m and 18.1 m, respectively, reaching the design requirement (18 m). Despite the decrease in pump efficiency, the double-volute model is still an effective technique applied in the engineering. Single-volute pump has a little higher head than double-volute pump in the whole flow range. This head difference gradually increases when the flow rate goes up to 35 m/h from pump startup, as shown in Figure 10 . The maximum difference is about 1.2 m when the flow rate reaches 35 m/h. The head difference on the large-flow condition is obviously higher than that of the low-flow condition. Meanwhile, operation efficiencies of pumps encounter similar situation. The efficiency of single-volute pump is higher than that of double-volute pump on the large-flow condition. The maximum difference between pump efficiencies is about 5% when the flow rate increases to 35 m/h. Tested performance results illustrate that the double-volute structure has a big effect on pump performance on the large-flow condition, both pump head and operation efficiency decline obviously.

3.2. Steady-State Pressure Field

Because of asymmetric structure of pump volute, pressure difference in flow field is generated between both cross-sections (seen in Figure 2 ) in the collinear radial direction, such as volute cross-sections 1&#;5, 2&#;6, 3&#;7, or 4&#;8. This pressure difference can induce radial hydraulic force acting upon impeller or volute.

Q

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N,

Q

N and 1.2

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N). From the impeller inlet to the volute outlet, the pressure energies of water gradually increase in both pumps. The working fluids flowing from impeller to volute are well homogeneous for two pumps. However, along volute cross cross-sections 1&#;8, there is a trend of water pressure increasing in the flow field which verifies the generation of radial hydraulic force. Moreover, some flow disturbances are observed around blade tip and volute tongue, due to wake flow in the outlet of blade passage and flow impact on the tongue. Obviously, the area of this flow-disturbance region in double-volute pump is bigger than that in single-volute pump. This change of the flow can affect flow structure in the pump and then cause the hydraulic force variation. This phenomenon is caused by the interaction between the blade tip and the second volute tongue.Figure 14 shows pressure contours at the mean rotational planes of pumps with single-volute and double-volute for different flow rates (0.8and 1.2). From the impeller inlet to the volute outlet, the pressure energies of water gradually increase in both pumps. The working fluids flowing from impeller to volute are well homogeneous for two pumps. However, along volute cross cross-sections 1&#;8, there is a trend of water pressure increasing in the flow field which verifies the generation of radial hydraulic force. Moreover, some flow disturbances are observed around blade tip and volute tongue, due to wake flow in the outlet of blade passage and flow impact on the tongue. Obviously, the area of this flow-disturbance region in double-volute pump is bigger than that in single-volute pump. This change of the flow can affect flow structure in the pump and then cause the hydraulic force variation. This phenomenon is caused by the interaction between the blade tip and the second volute tongue.

The isolation plate of double-volute can cause some friction loss, which induces that the pump works at the rated flow with small decline. This phenomenon results in a few drops in the pressure field of impeller inlet. However, considering both head curves and internal pressure fields of these two pumps, this pressure drop has less effects on the pump performance and cavitation.

For different operation conditions in Figure 14 , comparisons of inner flow characteristics in the pumps with single-volute and double-volute are close, so the normal flow rate was selected as the research subject for exploring pressure distributions in the volute cross-sections in Figure 15 . The water distributes high pressure to low pressure from top to bottom in the section, which shows that the high pressure region locates at the outside surface of the volute-chamber inner wall. For the double-volute, the difference between downside pressure and upside pressure of the plate produces some energy expenditure due to the existence of the metal plate. This could ultimately lead to the decreasing of pump efficiency and radial hydraulic force.

Meanwhile, these two volutes have the same shape and size for cross-sections 1&#;4, but higher pressure exists in the flow field of the pump with double-volute. The double-volute facilitates the fluid energy transformation from kinetic energy to pressure energy. After the fourth section, an annular volute was separated from the spiral passage in the double-volute. The high pressure fluid flows past the annular volute according to pressure contours in the cross-sections 5&#;8. The high pressure energy is concentrated in the upper volute separated from the tongue, while the fluid energy transformation in the under volute is not sufficient due to the comparatively shortened volute passage. Therefore, the fluid entering the volute passage with the double-volute carries a large portion of unconverted kinetic energy, which results in a considerable amount of friction loss and various hydraulic losses. This explains that the head and operation efficiency of double-volute pump is lower than that of the single-volute pump. Moreover, the integration between the increase of pressure energy in cross-sections 1&#;4 and the loss of kinetic energy in cross-sections 5&#;8 may cause the decrease of pressure difference in flow field along the radial direction, which takes positive effect of balancing radial hydraulic force.

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