Reliability Investigation of a Pump-Turbine System at Various Operating Conditions

2.1 Pump-turbine Model

The plan view of the pump-turbine system can be seen in Fig. 1. For this study there are 7 blades, 19 stay vanes and 20 guide vanes in total. The pump- turbine has H = 32 m, Q = 0.336 m³/s and N = 1200 min^-1.

Pump-turbine components are categorized in two parts, pressurized static parts and movable stressed parts. The fixed parts include the spiral casing, top and bottom cover, stay vane and draft tube. The movable parts include guide vanes and impeller blades. The operating condition and requirements for pumpturbine impeller includes high velocity, two operating modes, prone to cavitation, corrosion and sand erosion. Therefore, it is recommended to use martensite low carbon stainless steel (13Cr4Ni)⁽³⁾. Material properties are shown in Table 1.

2.2 Numerical methods

The result of Computational Fluid Dynamics (CFD) analysis shows the internal flow on the pump-turbine fluid domain, giving a description of hydrodynamic characteristic of the pump-turbine system. The static structural analysis is carried out by using the CFD results as the input load condition, which when combined is known as Fluid Structure Interaction analysis (FSI). Similar methods have been referred that were conducted by Xiao⁽⁴⁾ and Rama⁽⁵⁾ et al. The FSI analysis were performed by combining the CFD analysis results in ANSYS CFX and structure analysis in ANSYS static structural⁽⁶⁾.

Table 2.

Operating conditions for simulation

Table 3.

Numerical methods and conditions

Fig. 2

Numerical grid for CFD analysis

Fig. 3

Numerical grid of the pump-turbine system for static structural analysis

Table 2 shows the varying operating conditions for the simulations and Table 3 presents the numerical methods. In addition, the numerical grid and boundary conditions also further explained with Figs. 2 to 4. The impeller is the only rotating component in both directions, whereas all other components are fixed. The natural gravitational force is also applied.

Fine hexahedral numerical grids were used for CFD calculation and fine tetrahedral grids were used for structural analysis with imported load solution mapping greater than 90 %. Mesh dependence test and turbulence model dependence tests were also carried out as shown in Fig. 5. Shear stress transport (SST) model was utilized for all final calculations and input condition for FSI analysis.

A single impeller was selected randomly to study the stress and deformation in detail. Four measuring locations were identified as shown in Fig. 6. Measuring point 1 consisting of 32 measuring points set on the impeller edge at the hub. Measuring point 2 consisting of 32 measuring points set on the impeller edge at the shroud. Measuring point 3 consisting of 20 measuring points set on the impeller blade high pressure side from hub to shroud. Measuring point 4 consisting of 20 measuring points set on the impeller blade low pressure side from hub to shroud.

Fig. 4

Boundary condition for FSI analysis

Fig. 5

CFD validation test according to different element numbers and turbulence models

Fig. 6

Measuring points 1 to 4 on the impeller blade

3.1 Overall stress and deformation on pump-turbine system

The maximum equivalent stress and total deformation of impeller and guide vane at different operation condition are summarized in Fig. 7. It indicates that the maximum equivalent stress are much smaller than the material yield stress, and the maximum equivalent stress shows a increase tendency with the changing of operating condition from partial to excessive at both modes. In addition, the total deformation of all the operating condition shown in a quite small magnitude which have quite small influence on the structural stability.

The result of overall structure FSI analysis at the normal operating condition are presented by equivalent stress and total deformation in Figs. 8 and 9. The large stress appears in the connection of guide vane and casing, and also the impeller blade. The stress distribution indicates the relatively weak region is guide vane shaft and impeller blade tip. In addition, the distribution of stress and deformation shown in both modes are in a similar area.

Fig. 7

The maximum stress and deformation on the impeller and guide vane according to different operating conditions for both pump and turbine modes

3.2 Investigation of stress and deformation distribution on the impeller

The maximum stress on impeller appears at the connection of impeller blade and hub, at every operating condition of both modes. The maximum deformation of pump mode appears at the medium of blade low pressure side in partial loading condition, and moves to the shroud of impeller high pressure side in normal and excessive loading condition. For turbine mode, the maximum deformation also appears at the medium of blade high pressure side in partial loading condition, and moves to the shroud of impeller high pressure side in normal and excessive loading condition. The maximum stress and deformation for both modes are presented in Figs. 10 and 11, both appearing in the excessive loading.

Fig. 8

The overall stress and deformation distribution for Case 2 in pump mode

Fig. 9

The overall stress and deformation distribution for Case 5 in turbine mode

Fig. 10

Maximum stress and deformation on impeller for Case 3 in pump mode

Fig. 11

Maximum stress and deformation on impeller for Case 6 in turbine mode

Fig. 12

The investigation of stress on impeller blade in pump mode

3.3 Comprehensive investigation of stress and deformation on a single impeller blade and guide vanes

Figs. 12 to 15 show more detail presentation of stress and deformation at the four measuring locations of the impeller blade in the operating conditions of partial, normal and excessive loading. The figures show the periodic jump of stress and deformation in the impeller edge of hub and shroud, which are caused by the periodic distribution of impeller blade. In addition, the value of stress and deformation present a similar trend that the maximum value appears in the operating condition of excessive loading in contrast to normal and partial loading.

It can be observed that measuring points 1 and 2 show similar trends and do not show significant changes in contrast to measuring points 3 and 4, which show a rising trend at the ends and falling trend at the center. As shown in Figs. 12(c) and 13(c), the stress in the two ends (location No. 1, 19 and 20 of measuring point 3) of impeller blade high pressure side are higher than the central locations. However, the stress distribution on the blade lower pressure side shows a different tendency, a peak appears near three-quarters of the abscissa(location No. 14 to 16 of measuring point 4), as shown in Figs. 12(d) and 13(d). The deformation on the high and low pressure side of impeller blade shows a similar tendency that the deformation have a peak in the center of the blade side, as the curves shown in Figs. 14(c) and 15(c).

As shown in Fig. 16, the maximum stress on the guide vane are located in almost the same position, the shaft used for connecting the guide vane. Figure 17 shows that the deformation of guide vane is not uniform in every guide vane of pump mode, especially the normal and excessive loading. In contrast, the deformation in every guide vane of turbine mode is almost same among the three operating conditions.

Fig. 13

The investigation of stress on impeller blade in turbine mode

Fig. 14

The investigation of deformation on impeller blade in pump mode

Fig. 15

The investigation of deformation on impeller blade in turbine mode

Fig. 16

The investigation of stress on impeller blade

Fig. 17

The investigation of deformation on impeller blade