## 2.1 Idling process of reactor coolant pump

In order to better predict the change of the performance characteristics of RCP during idling, the influence of the change of guide vane angle was analyzed, and the idling process is divided into three period, nonlinear transient period (*T**i* = 0 ~ 8s, *T**i* = 0 indicates that the RCP starts idling, and *T**i* = 8s is the middle time of this period, nonlinear transition period(*T**i* = 16 ~ 32s, *T**i* = 32s is t / 4, *T**i* = 24s is the middle time of this period, *T**i* = 16 ~ 24s is defined as nonlinear transient period I, and *T**i* = 25 ~ 32s is defined as nonlinear transient period II), linear transient period (*T**i* = 33s ~ 130s), as shown in Fig. 5. Compared with the linear transient period, the hydraulic parameters in the first two period s change sharply, which has a more important impact on the safe and stable operation of the RCP. Therefore, this paper focuses on the nonlinear transient period and transition period of the RCP idling process.

## 2.2 External characteristic analysis

## 2.2.1 Analysis of head change

Figure 6 is the head curve of RCP with different guide vanes in nonlinear transient period and the nonlinear transition period during the idling process, it can be found that with the progress of idling, the head drop rate gradually decreases, and the head drop in nonlinear transient period I is the fastest, and the head drop in 8s is close to 60% of the rated head. It is found from Fig. 6(a) and Fig. 6(b) that in the nonlinear transient period, the pump head of DY4 model is always the highest. The head of DY2 and DY3 is slightly lower than that of DY4. The head of DY2 and DY3 are similar and the rate of decline is basically the same. Within 7 seconds before idling, the head of DY1 is the lowest. With the development of idling, the head of DY1 decreases gradually. Compared with other model pumps, the head drop rate of DY5 is the largest, and the head is always the lowest after 7s, which is quite different from the head under constant flow condition, which indicates that DY5 is greatly affected by the change of transient flow field and speed under idling condition. The head drop amount and drop rate in the nonlinear transition period are much smaller than those in the nonlinear transient period, and the head of DY5 is still at the lowest level in this period as shown in Fig. 6 (c) and Fig. 6 (d). There is a sudden drop in the head of DY4 after the half flow time point. When idling for 21s, the head of DY4 is lower than DY2 and DY3, and then the head drop rate decreases, and the head is gradually higher than other models.

## 2.2.2 Analysis of impeller torque variation

Figure 7 is the torque change curve of the RCP impeller at different guide vanes in the nonlinear transient period and the nonlinear transition period during the idling process. It is found from Fig. 7 that the torque of each model pump impeller in the nonlinear transient period and the nonlinear transition period is DY5 > DY4 > DY3 > DY2 > DY1, which indicates that the hydraulic torque gradually increases when the change law of guide vane angle changes from convexity to concavity. In the nonlinear transient period I, the transfer torque of DY5 is significantly higher than that of other models, and the torques of the other four models are similar. With the development of idling, the torque of DY5 is gradually close to that of other models, which indicates that in the initial period of idling, more energy loss is caused by impact loss and friction loss in the guide vane of DY5, which increases the impeller torque and operating power of the unit. Under the same stored energy, the idling time of DY5 decreases, and the flow decreases, it is not conducive to improving the idling characteristics of RCP. Therefore, in order to improve the idling characteristics of RCP, when the guide vane blade is designed according to the distribution law of the installation angle, the concavity degree of the installation angle should be appropriately reduced, the length of the guide vane blade should be reduced, and the width of the guide vane channel should be increased.

## 2.3 Analysis of radial force characteristics

Radial force is an important dynamic characteristic of the RCP. During idling, the radial force of the RCP will change significantly, which will adversely affect the reliable operation of the RCP. Therefore, the radial force of RCP during idling was analyze. Variation of the radial force of impeller of RCP at different guide vanes in the non-linear transient period and the non-linear transition period during the idling process shown as Fig. 8. The variation law of the radial force of the impeller is different in different idling periods, but it changes around point(0, 0) as a whole. The regularity of the non-linear transient period I is the most obvious. After the half flow time(*T**i* = 15s), the radial force of the impeller fluctuates more disorderly, and the reduction rate of the radial force in the Y direction is smaller than that in the X direction. This is mainly because the Y direction is parallel to the outlet of the pump casing, which is greatly affected by the disturbance of the volute outlet, resulting in a small reduction rate of the radial force of the impeller in the Y direction. Comparing the model pumps with different guide vane guide vane angles, it is found that the radial force of the impeller varies greatly during idling. In different idling periods, the radial force on DY5 impeller is relatively small and the fluctuation range is weak, while the radial force on DY1, DY2 and DY3 impeller is relatively high and the fluctuation range is strong. Before idling, the radial force of DY4 impeller is the largest. With the development of idling, the radial force of DY4 is gradually smaller than that of other models. In the nonlinear transition period II, the radial force magnitude and fluctuation amplitude are similar with that of DY5. When idling for 32s, the total radial force of DY4 is 235N which is nearly 30 times lower than that before idling, and the decrease amplitude is larger than that of other models.

The radial force change of the guide vane of the RCP at different guide vanes in the nonlinear transient period and the nonlinear transition period during the idling process shown as Fig. 9. It is found that the radial force borne by the guide vane gradually decreases with the occurrence of idling, but its magnitude is obviously higher than that of the impeller, and the change law is quite different from that of the impeller. The radial force fluctuation of the guide vane does not change around the point(0, 0), and the radial force fluctuation centers of different guide vane models are different, which is mainly caused by the different guide vane structures and the asymmetric structure of the volute. In different idling periods, the radial force of DY2 guide vane is smaller than that of other model pumps, and its radial force mainly fluctuates in the first and fourth quadrants, and gradually shifts to the first quadrant with progress of idling. The radial force of guide vane of DY5 is larger than that of other model pumps, and its fluctuation quadrant range is similar with that of DY2. The radial force of guide vane gradually shifts to the fourth quadrant from nonlinear transient period I to nonlinear transition period II. The radial force of DY3 guide vane is mainly distributed in the first and third quadrants. The fluctuation amplitude of radial force in the Y direction is much larger than that in the X direction, and the overall fluctuation amplitude is second only to DY5. After the half flow time point, the radial force of DY3 guide vane gradually moves from the second quadrant to the third quadrant. The radial force gradient of DY1 guide vane in the Y direction is large. When the idling enters the nonlinear transient period II, the radial force amplitude is much smaller than that of other guide vanes. As the idling enters the nonlinear transient period, the radial force in the Y direction gradually increases in this period, which indicates that when the guide vane angle changes upward, the corresponding guide vane model is most affected by the fluid medium flow at the volute outlet after the idling half flow time point. The radial force of guide vane of DY4 during idling is similar with that of its impeller. From the initial point of nonlinear transient period, I to the end point of nonlinear transition period II, the variation amplitude of radial force of guide vane is much higher than that of other model pumps.

## 2.4 Blade load characteristic analysis

The blade load is difference between the static pressure value of pressure surface and the static pressure value of suction surface at the same streamline on the blade, and its value is related to the partial derivative of the velocity moment on the axial streamline. Duaring idling, the surface load of the impeller and guide vane of the RCP changes complex. Analyzing the change law plays an important role in reducing the fatigue damage of the blades and improving the operation stability of RCP.

Figure 10 is the load distribution of the impeller blades of RCP with different guide vanes at different idling times (*T**i* = 0s, 1s, 8s, 15s, 32s). With the development of idling, the pressure on the pressure surface and suction surface of the impeller blade increases as a whole, and the load on the impeller blade decreases gradually. The changes of blade surface pressure of different model pumps at different idling time have similar laws. At the same idling time, the suction surface pressure increases gradually from the inlet to the outlet of impeller blade, and the pressure surface pressure decreases first, then increases and then decreases. There is a tendency of sudden pressure drop near the inlet and outlet of the blade pressure surface, and the static pressure of the working surface near the trailing edge of the impeller blade is gradually smaller than suction surface, which is mainly because the surface pressure of the impeller blade is greatly affected by the fluid impact and the dynamic and static interference of the impeller guide vane. At different idling times, the load curves of impeller blades of different models are similar. At the inlet of the impeller blade, the load of the impeller blade drops suddenly. From the inlet to the outlet, the blade load increases first and then decrease. When the relative position of the impeller blade along the flow line is 0.6, the load reaches the maximum, and the load of the impeller blade near the blade outlet is 0, and then increases inversely. Comparing the impeller blade loads of different model pumps at different idling times, it is found that the difference load of model pump impeller blades with different guide vane angles gradually decreases with the idling. Before Idling (*T**i* = 0s), when the relative position of the impeller blades along the streamline changes from 0 to 0.6, the load of the impeller blades of DY4 is the largest and DY1 is the smallest. The load of the impeller blades of other model pumps gradually increases with the change of the guide vane installation angle from convexity to concavity. When the relative position is greater than 0.6, the rule is broken, which is mainly due to the difference in the dynamic and static interference strength between different guide vane models and impellers, resulting in a large fluctuation in the surface pressure at the trailing edge of impellers. After idling for 1s, the pressure load of DY5 impeller blade is significantly higher than that of other models, which indicates that at the initial period of idling, the DY5 impeller blade is subject to the highest alternating load intensity with the sharp decrease of flow and speed. When idling enters the half flow time point (*T**i* = 0s), the guide vane angle of DY4 and DY5 is concavity. After the relative position of the impeller blade along the flow line is 0.6, the load change of the impeller blade is similar, and is significantly larger than that of other model pumps. When the idling time is *T**i* = 32s, there is a sudden increase in the load of DY5 impeller blades when the relative position of streamline is 0.8, and the load change curves of impeller blades of different model pumps at other positions basically coincide.

Load distribution of guide vane blades of reactor coolant pumps with different guide vanes at different idling times shown as Fig. 11. It is found that before idling, there is a large difference in the surface pressure of different guide vane models along the streamline direction of the guide vane. From the inlet to the outlet of the blade, the static pressure value of the guide vane pressure surface of DY1, DY2 and DY3 decreases gradually as a whole, and the static pressure value of the guide vane suction surface decreases first and then increases slowly. The static pressure values of the pressure surface and suction surface of the guide vanes of DY4 and DY5 are both small at first and then increase along the streamline direction. The turning point of increase of the static pressure value of the pressure surface appears near the blade inlet, while the turning point of the increase of the static pressure value of the suction surface appears near the blade outlet. With the idling, for the same guide vane model, the shape of the surface pressure curve from the inlet to the outlet of the guide vane is similar at different idling times. Under the influence of inflow impact and dynamic and static interference, the pressure on the blade surface near the guide vane inlet drops abruptly. This phenomenon gradually weakens with the development of idling. Compared with different guide vane models, it is found that the sudden drop amplitude from DY1 to DY5 decreases at first and then increases. The sudden drop amplitude of the inlet pressure of the guide vane of DY4 is the smallest and that of DY5 is the largest. The sudden drop of the pressure of both models occurs on the suction surface of the guide vane. It can be seen from the load change curve of the guide vane blade that the load change law of the guide vane blade along the streamline direction at different idling times of the same model pump is similar. Among them, the average pressure load of the guide vane blade of DY3 is the smallest, followed by DY2 and DY4, and the average load of the guide vane blade of DY5 is the largest, and the sudden load drop at the blade inlet is the most obvious. The load of the guide vane of each model pump is the closest at the relative position of 0.5 along the streamline direction, and the load value gradually tends to 0 with the idling. When the relative position along the streamline direction is less than 0.5, the load of the guide vane of each model pump fluctuates greatly, and the fluctuation amplitude gradually decreases with the development of idling. In the nonlinear transient period and nonlinear transition period, the load fluctuation of the guide vane of DY5 is the largest, and the maximum fluctuation is about 0.8MPa, which is about 4 times of the maximum fluctuation of DY3. When the relative position along the streamline direction is greater than 0.5, the load on the guide vane of each model pump is relatively small and tends to increase first and then decrease. The average load on the guide vane of DY2 is close to 0, and the absolute value of the average load on the guide vane of other model pumps gradually increases from DY1 to DY5.