Study on performance and flow loss of reactor coolant pump with different laws of guide vane angle

To study the influence of different laws of guide vane angle on the performance of reactor coolant pump (RCP), five models of RCP with different guide vane were designed, and the three‐dimensional numerical calculation was carried out. Based on the entropy production theory, analysis of flow loss at part‐load, design, and the over‐load flow rate was investigated. The results show that under the design flow and over‐load flow condition, the head, and efficiency of the DY4 (RCP model of the fourth guide vane variation) model are the highest, and the best efficiency occurs at the design flow rate. Compared with the DY1 (RCP model of the first guide vane variation) model, the efficiency of RCP is increased by 3.68%. At design flow and over‐load flow, the distribution of pressure and velocity streamlines of the DY4 model pump is uniform and stable, the flow loss ratio in the guide vane and volute is the lowest, and the high‐value area is small. Under the condition of part‐load flow rate, the pump head and efficiency of DY5 (RCP model of the fifth guide vane variation) model are the highest, and the highest efficiency appears at 0.8Qd which is 1.69% higher than the best efficiency value of DY4. At the part‐load flow rate, the static pressure values in the guide vane and volute of the DY5 model pump are significantly higher than that of other models. The velocity change in the flow channel is uniform, and the flow loss in the guide vane and volute is the lowest. Compared with the part‐load flow rate condition, the hydraulic performance of the DY5 model pump under design flow rate and over‐load flow condition is lower than that of other models.


| INTRODUCTION
The reactor coolant pump (RCP) is the heart of the nuclear island and the only high-speed rotating device. Continuous and stable operation has an important impact on the safe and reliable performance of nuclear power plants. 1 For extremely harsh working conditions, the operating performance of RCP under the condition cannot be ignored. For ensuring that the RCP work normally under extreme conditions such as power outage, accidents and disasters (earthquakes, fires), High hydraulic performance was required. 2 The guide vane is one of the components of RCP, and it is the key component of energy conversion. 3 The optimal parameter and structural design are essential to improve the operation efficiency and safety design of the RCP.
At present, a lot of research has been done on the influence of guide vane geometry parameters or structure on the performance of RCP. Jie and Shiming 4 studied the influence of guide vane with twisted vanes and guide vane vanes on the performance of RCP. It was found that both guide vane models could make the velocity distribution in the pump uniform, but the static pressure distribution of the twisted guide vane was more uniform than that of the diffusion guide vane. Jing et al. 5 studied the influence of nonuniform guide vane on the performance of the RCP by numerical simulation. The results show that the flow loss at the volute tongue and the multioperating performance of the RCP can be improved by using a specific form of nonuniform guide vane. Minguan et al. 6 used fluent to study the influence of different guide vane numbers and guide vane inlet positions on the mixed flow RCP. It was found that when the guide vane number is 16, the calculated head and hydraulic efficiency of the pump were the highest. When θ = 14°, the model pump has the best performance. Based on the RNG k-ε turbulence model, Xin et al. 7 analyzed the influence of the circumferential arrangement position of the guide vane on the external characteristics and internal flow field structure of RCP. It was found that the head and efficiency of the pump changed greatly when the circumferential arrangement position of the guide vane was changed at the part-load flow rate but changed greatly at the over-load flow rate. Xiuyong et al. 8 studied the influence of the guide vane on the hydraulic performance of the RCP by computational fluid dynamics (CFD) analysis and experiment, and the efficiency of the RCP was the highest when the guide vane was 0.025, and the hydraulic loss in the guide vane and volute was the smallest. Thus, the above studies lack systematic studies on the influence of guide vane setting angle on the performance of RCP. The angle of guide vane's one of the important geometric parameters of a guide vane. If it is not properly selected, it will lead to large bending and effective over-current of the guide vane.
To deeply study the performance of the pump, the flow loss in the pump is usually analyzed. The traditional analysis uses the pressure drop method [9][10][11] to study the hydraulic loss in the pump, but this method cannot characterize the position and size of the hydraulic loss of each flow component. In recent years, more and more researchers use entropy production theory to analyze flow loss in fluid machinery. Shen et al. 12 introduced the entropy production theory and studied the energy dissipation under different flow rate and tip clearance of axial flow pump intuitively by numerical simulation. Wang et al. 13 to study the hydraulic characteristics of a liquefied natural gas cryogenic submersible pump, the size and position of hydraulic loss in the pump are obtained based on entropy production theory, and then the performance of the pump is optimized. Yuan et al. 14 conducted the vortex simulation of the centrifugal pump, and analyzed the irreversible loss combined with the entropy production method. Kaiyao et al. 15 quantitatively analyzed the flow loss of each water-passing component based on the entropy production theory. The above research confirms the feasibility of entropy production theory in fluid mechanical flow loss analysis.
Based on the above research, this paper takes the angle of the guide vane as a variable. The external characteristics and internal flow characteristics of RCP with different laws of guide vane angle are compared and analyzed. Based on the entropy production theory, the flow loss distribution characteristics of each flow component are analyzed to explore the influence of the change of angle of the guide vane on the hydraulic performance of the RCP and provide a theoretical reference for the optimization design of the RCP.

| RCP and grid
The density of the fluid medium is 742 kg/m 3 , and temperature is 293°C, and the kinematic viscosity is 9.4 × 10 −8 m 2 /s, and other design parameters are shown in Table 1, and the hydraulic model of the pump is shown in Figure 1. To ensure that the calculation results are close to the real flow situation, the inlet and outlet basins of RCP are appropriately extended.
Grid quality is the key factor to determine the accuracy and convergence of CFD calculation. The commercial software ANSYS-ICEM is used, and the structured grid with fast generation speed, good quality, and better calculation convergence is used. As shown in Figure 2, local encryption is carried out at the inlet and outlet of the impeller and guide vane and near the blade. At the same time, the mesh quality is guaranteed to be above 0.3 and the minimum angle is above 18°. In most areas of the impeller and guide vane basin, y+ is controlled within 10-20, and the local area is within 20-35.
To make the simulation results more accurate and improve the running speed of the program, the DY3 RCP model is taken as an example to set up six sets of grids with different densities to verify the independence of the grids. The grid parameters and calculation results are shown in Figure 3. It can be seen from Figure 3 that with the increase in the number of grids, the head and efficiency gradually increase. According to the calculation, when the number of grids increases from 4.49 to 4.85 million, the change range of head is 0.05% and the change range of efficiency is 0.3%. It can be seen that the change rate of head and efficiency is very small. Considering the computer configuration and calculation efficiency, the grid of the whole calculation basin is finally determined to be 4.49 million.

| Guide vane with different law
As shown in the left graph of Figure 4, keeping the inlet and outlet angle of the guide vane unchanged and controlling the wrap angle within a certain range, five guide vane models with different changing rules of guide vane along the blade inlet and outlet are designed, which are DY1 (the guide vane angle increases sharply first and then decreases gently, and the convexity is largest), DY2 model (the guide vane angle increases gently convex) and DY3 model (the guide vane blade angle increases linearly. The original model), DY4 model (guide vane angle increased gently concavity), DY5 model (guide vane angle decreased first and then increased, the concavity is largest). The inlet guide vane designed satisfies the linear relationship of α BLE3k = α 31 − 1.2°k

| Governing equations and validation
The fluid flow in the RCP follows the three laws of mass conservation, momentum conservation, and energy conservation, and the corresponding control equations are continuity equation, momentum equation, and energy equation. Assume that that coolant medium is compressible, the continuity equation is defined as The momentum equation is The SST k-ω is used. The inlet condition of the pump is mass flow rate, and the outlet condition is pressure outlet. The FROZEN-ROTOR model for data transmission between dynamic and static domains. Nonslip walls and the standard wall function are selected. The wall roughness is 0.025 mm, and the convergence residual is 10 −6 .
The head and efficiency obtained by numerical simulation of the DY3 RCP model were compared with the experimental results, and the performance curve of RCP was obtained, as shown in Figure 5. The results show that the simulation results are consistent with the experimental results. The deviation of head and efficiency under the design flow condition is 3.10% and 1.38%, and the deviation of the flow condition point is less than 5%. Thus, the numerical calculation method can accurately predict the external characteristics of the RCP, which provides a guarantee for further comparative analysis.

| External characteristics
The head and efficiency of the RCP are the most important performance parameters, and the expression of its efficiency and head is as follows: In the formula, P out is the average total exports pressure, Pa; P in is the average total imports pressure, Pa; ρ is the density of the fluid medium, kg/m 3 ; g gravity acceleration, m/s 2 ; Q is the RCP flow, m 3 /s; M is impeller torque, N·m; ω is the angular velocity of impeller rotation, rad/s. It is found from Figure 6 that as the flow rate changes from 0.6Q d to 1.4Q d , the change of head and efficiency of the DY5 model pump is the largest, and the change rate of the DY1 model is the smallest, indicating that compared with other models, DY1 model is less affected by flow rate, and DY5 model is greatly affected by flow rate. Under the designed flow condition, the head deviation of each model pump is relatively small, and the head of the DY1 model is the lowest. The schemes from the DY2 model to the DY5 model are 2.1%, 3.99%, 4.36%, and 1.46% higher than that of DY1, respectively. The head of the DY4 model is the highest, and the head is the largest from 1.0Q d to 1.4Q d . The variation law of efficiency and head is similar. At 1.0Q d , the efficiency of the DY4 model is the highest, and the efficiency value is 82.73%, which is 3.68% higher than that of the DY1 model pump with a large degree of convexity angle. When the design flow rate is biased toward part-load flow conditions, it can be found that with the decrease in flow rate, the DY5 head rises fastest, while the DY3 head rises most slowly. At 0.8Q d , the head and efficiency gradually increase from DY1 to DY5. The flow condition is the best efficiency point of DY5, and the maximum efficiency value is 84.42%. When the flow rate decreases to 0.6Q d , the head of DY2 is obviously larger than that of DY1 and DY3. At 1.4Q d , the head and efficiency of DY5 are significantly smaller than those of other models. It can be found from Figure 4 that this may be due to the

| Static pressure distribution
To analyze the influence of guide vane angle variation on static pressure distribution of flow field in impeller, guide vane, and volute of RCP, three typical working conditions (0.6Q d , 1.0Q d , and 1.4Q d ) with obvious efficiency change were selected for analysis. Figure 7 shows the pressure distribution nephogram on the middle section of the impeller and guide vane of RCP.
It can be seen from the diagram that the pressure increases gradually from the inlet of the impeller to the outlet of the guide vane at 1.0Q d but the pressure distribution of the impeller and guide vane of the RCP with different guide vanes is obviously different under the same flow condition, mainly in the outlet of the impeller and the guide vane flow channel. At 0.6Q d , there is a large area of the high-pressure area near the inlet of the guide vane and the pressure surface of the guide vane in each model pump, which is mainly caused by the impact of fluid on the inlet of the guide vane and the pressure surface of the vane, resulting in the sudden change of velocity. The static pressure value of the DY5 guide vane was significantly higher than that of other models, and the area of the high-pressure area near the pressure surface of the guide vane was wider. Although the high-pressure area of DY1 and DY3 is narrow, the outlet pressure is small, which indicates that the pressure gradient in the guide vane of DY1 and DY3 is small and the expansion capacity is weak at the part-load flow rate, which is the main reason for the low head and efficiency of the two models. At 1.0Q d , the pressure distribution trend of DY1-DY4 is consistent, the pressure change in the DY4 channel is relatively gentle, and there is less pressure mutation area, which indicates that the fluid flow in DY4 is relatively stable. The sudden change of pressure in the guide vane flow channel of DY5 is the most serious, which increases first and then decreases from inlet to outlet, and the flow is relatively disordered. When the operating flow increases to 1.4Q d , the pressure value in the impeller channel decreases significantly, and the pressure distribution uniformity from DY1 to DY4 increases, but the pressure value in the guide vane channel decreases gradually, and the low-pressure area in the DY5 channel is the most significant. Figure 8 is the pressure nephogram of the middle section of the spherical volute under different flow rates. It can be found the static pressure distribution of the volute matched by different guide vane models is obviously different, and the influence of the change law of guide vane angle on the pressure distribution is different. At 0.6Q d , the pressure distribution of the DY1 volute is the most uneven, the pressure amplitude is the smallest, and the low-pressure area of the outlet area is the largest, accounting for about 60% of the middle section of the volute. From the model pump DY1-DY5, the pressure changes in the volute first increase, then decreases, and finally increase, and the pressure distribution tends to be uniform. The pressure change is consistent with the variation law of head and efficiency at 0.6Q d . At 1.0Q d , the annular high-pressure area on the outer wall of the DY1 to DY4 volute gradually diffuses to the inside, the low-pressure area at the inlet of the volute gradually decreases, and the high-pressure area on the right side of the volute outlet gradually increases. When the flow rate increases to 1.4Q d , the pressure distribution uniformity of DY3 in DY1-DY4 is the worst, and the low-pressure area at the volute outlet is the widest. The farther the variation curve of the guide vane angle deviates from DY3, the smaller the low-pressure area at the volute inlet. The pressure values of DY5 at 1.0Q d and 1.4Q d were significantly lower than those of other models.  impeller, the velocity distribution is relatively uniform, and the velocity near the hub is relatively low. There are small vortex cores near the suction surface of the hub, and the vortex from the impeller inlet to the outlet is close to the blade pressure surface. Near the impeller outlet, the velocity streamline curvature is large and the distribution uniformity is poor. Due to the interaction between the impeller and the guide vane, the flow of liquid medium at the inlet of the guide vane is unstable, and the velocity variation at the inlet area is uneven. As the fluid continues to flow to the outlet direction of the guide vane, its constraint effect is enhanced by the guide vane blade, and the flow gradually becomes stable. In the guide vane outlet, fluid convection impact is strong, leading to a large area near the guide vane outlet's low-velocity zone. It is obvious that the flow in the spherical volute is extremely disordered, and the mainstream flow is spiral. There are two large vortices in the opposite direction, and there are also vortices near the outlet of the volute.

| Velocity distribution
It can also be found the change of guide vane blade angle has a great influence on the flow state, which is obviously different from Figure 9. At 0.6Q d , the number of vortices in the DY5 channel is the least, the vortex area is the smallest, the velocity change is uniform, and the flow of fluid medium in the guide vane is relatively stable, which shows that the DY5 has the best antirotation ability at a part-load flow rate. However, due to the strongest binding effect of the DY5, the strong impact from the guide vane occurs near the right side of the volute outlet, which makes the fluid flow direction shift to the left wall of the outlet. In the five groups of models, the outlet streamline of DY4 volute is the most uniform, the swirl flow in the left area of the volute outlet basically disappears, and the outlet situation of DY2 is close to that of DY4. DY1 has the densest vortex in the area far from the volute outlet, forming two large-area vortex core areas. Under the design flow condition, the velocity streamline distribution of each model pump is improved compared with 0.6Q d , but the flow in spherical volute is still chaotic and there is a large area of vortex core area. In the region away from the volute outlet, the larger vortex core evolves into several smaller vortices, and there is no vortex near the left side of the volute outlet. With the increase in flow rate, the vortexes in the DY5 impeller and guide vane decrease, and the streamline uniformity at the volute outlet improves. However, the number of vortexes increases far from the volute outlet and near the volute inlet, resulting in serious flow loss, which is the main reason for the low efficiency of DY5 at 1.0Q d .

| Entropy production theory
According to the principle of entropy increase, the fluid system is always accompanied by entropy generation. In the internal flow of the RCP, viscous stress of the fluid, the excitation force and phenomena of the vortex, backflow, separation of flow, and convective shock in the flow field can lead to energy dissipation, flow loss and increase the entropy production in RCP.
The transfer equation of entropy production is defined as, Based on the turbulent Reynolds-averaged Navier-Stokes equation, all quantities are divided into the timeaveraged part and wave-averaged part. The timeaveraged governing equations are as follows: This paper ignores the heat transfer effect and only considers the entropy production S DT caused by the dissipation term. The entropy production is obtained by integrating the entropy production rate. The total entropy production rate S pro,DT mainly includes three items: the unit volume entropy production rate S pro,D caused by the timeaveraged velocity, the unit volume entropy production rate S pro,D′ caused by the velocity pulsation, and the unit area entropy production rate S pro,W caused by the wall friction.
The entropy production caused by the sum of timeaveraged velocity and turbulent velocity is defined as F I G U R E 9 (A) Distribution of velocity (1. Impeller inlet, 2. Shroud, 3. Hub, 4. Impeller outlet and guide vane inlet, 5. Guide vane outlet, 6. Pressure surface of impeller blade). Q/Q d is (A) 0.6, (B) 1.0, and (C) 1.4 dissipation entropy production, and the dissipation entropy production rate per unit volume can be expressed as pro,DV pro,D pro,D′ In the formula, S pro,D′ can be obtained by numerical calculation, the expression is: S pro,D′ cannot be solved directly because the turbulent velocity field is difficult to obtain. According to the entropy production theory of Kock, 16 the fluctuating entropy production S pro,D′ and turbulence model have internal relations. In SST k-ω turbulence model, the entropy production rate caused by velocity fluctuation is defined as pro,D In the formula, α = 0.09; ω is turbulent vortex frequency; k is turbulent kinetic energy. Dissipation entropy production in the fluid domain of RCP can be obtained by volume fraction.
According to Xiang et al., 17 the entropy production caused by wall friction can be calculated. The entropy production per unit area S pro,W can be expressed as pro,W W W Then the wall entropy production corresponding to the wall friction loss can be expressed as The total entropy production (W/K) in the computational domain of RCP fluid is, Therefore, the total flow loss (W) of the RCP can be expressed as At the same time, to intuitively show the strength of the flow loss inside the RCP, the flow loss coefficient is defined Φ*: In the formula, u 2 is the impeller outlet circumferential velocity, m/s; ρ is fluid density, kg/m 3 ; Q is the flow rate under the design condition, m 3 /s.

| Change of flow loss
Flow losses variation of RCP under different flow rates are shown in Figure 10. It can be found that the dissipation loss in the internal flow loss of the RCP is much larger than the wall loss, indicating that the dissipation loss in the operation of the RCP is the main reason for irreversible flow loss. With the increase in flow rate, the wall loss increases gradually. Under the condition of part-load flow rate, the wall loss of each model pump is small, among which DY4 loss is the smallest and DY5 loss is the largest. The wall loss difference from DY1 to DY4 is still small at design and over-load flow rate, but the value of DY5 is larger than other models. The wall loss can be reduced when the blade length increases by appropriately changing the variation law of the guide vane blade angle, but the excessive increase will lead to a sharp increase in the wall friction loss, and the performance is the most obvious under-over-load flow rate. The variation law of dissipation loss with the flow is different from that of wall loss. With the increase in flow rate, dissipation loss decrease first and then increases. Dissipation loss of different pump models varies greatly. For DY1-DY4 models, the minimum dissipation loss is obtained when the dissipation loss changes from 0.6Q d to 1.4Q d at 1.0Q d in which the DY4 loss is the smallest, and the maximum deviation of the four models is 23.5%. The dissipation loss of DY5 reaches the minimum at 0.8Q d and the loss value is less than DY4 at 1.0Q d . The variation of total flow loss and dissipation loss is similar, indicating that the efficiency of DY4 and DY5 reaches the maximum at 1.0Q d and 0.8Q d , respectively, and the maximum efficiency of DY5 is higher than that of DY4, which is consistent with the previous conclusion.

| Proportion of flow loss
To further explore the internal flow loss of RCP under different flow conditions, the flow loss proportion of each flow component of RCP under different flow conditions was analyzed. It can be seen from Figure 11 that with the increase in flow rate, the proportion of flow loss in the inlet pipe, volute, and outlet pipe increases gradually, and the proportion of loss in the impeller and guide vane decrease. The influence of flow rate on the guide vane, volute, and outlet pipe is the most obvious. From 0.6Q d to 1.4Q d , the maximum difference in the loss proportion of guide vane, volute, and outlet pipe in each model pump is 40.42%, 24.35%, and 19.97%, respectively. Among them, the loss proportion of the guide vane changes the most. Under each flow condition, the flow loss ratio of the inlet pipe is the smallest, the maximum loss ratio is less than 2%, and the maximum change difference of the flow loss ratio is 1.08%. The flow loss ratio of the volute is always greater than 30%, and the maximum ratio is as high as 56.42%. Except 0.6Q d , the volute under the four flow rates is the largest area of flow loss in all flow components. The flow loss of the outlet pipe is the most obvious at 1.4Q d , which is closely related to the flow disorder of volute under an over-load flow rate.
Comparing different models, it can be found that the flow loss in the adjacent impeller and volute also changes when the guide vane structure changes due to the change of guide vane blade angle. At 0.6Q d and 0.8Q d , the proportion of flow loss in DY1-DY5 impeller passages showed an overall upward trend, and the proportion of flow loss in DY5 impeller passage was the highest, but the sum of losses in guide vane and volute was the smallest. The flow loss of DY1 guide vane and volute account for the largest proportion, which is an important reason for the lowest overall efficiency. When the flow rate increases to 1.0Q d , the proportion of flow loss in the impeller channel increases first and then decreases from DY1 to DY5, reaches the maximum at DY4, and the sum of loss proportions of guide vane and volute reaches the minimum at DY4. When the flow is running to an overload flow rate condition, the sum of the loss of the DY5 guide vane and the volute increases greatly, and the maximum proportion is 73.14%, which shows that under the over-load flow rate condition, the flow loss of the DY5 model guide vane and the volute is the highest, and shows that DY5 is not suitable for over-load condition.

| Flow loss distribution
The advantage of introducing the entropy generation method is that it can intuitively obtain the distribution of flow loss and the extreme area of flow loss, so as to analyze the causes of large flow loss. Three typical flow conditions (0.6Q d , 1.0Q d , and 1.4Q d ) are selected. Flow loss coefficient cloud chart based on entropy production is obtained, and the influence of guide vane blade angle variation on flow loss of each flow component of RCP is analyzed. Figure 12 shows the flow loss distribution of the RCP on the flow surface of the impeller and guide vane with different blade spans (such as span = 0.9, indicating the relative length of the impeller or guide vane from the rear cover plate is 0.9). It can be seen the flow loss distribution of the impeller and guide vane varies greatly at different blade spans, and it is the most obvious at part-load flow. From the shroud to the impeller hub, the flow loss in the impeller increases gradually, and the flow loss in the guide vane decreases gradually. Combined with Figure 9, it can be seen that the streamline near the shroud of the impeller is uniform, the streamline near the rear cover plate is disordered, and there is a vortex. The velocity near the shroud of the guide vane is large, the streamline distribution is uneven, and the turbulence loss is large. From the impeller inlet to the guide vane outlet, the main flow loss areas occur at the impeller blade inlet, the impeller blade suction surface, the dynamic static junction area, the impeller wake area, the pressure surface of the guide vane blade and the guide vane outlet area. The internal flow loss of the impeller is significantly greater than that of the guide vane. As shown in Figure 12A, at 0.6Q d , the variation law of different guide vane blade angles has a great influence on the flow loss distribution in the impeller and guide vane of the RCP. When span = 0.9, when the change law of the guide vane blade angle changes from DY1 to DY5, the flow loss in the impeller changes little, and the flow F I G U R E 13 Section division of volute loss in the guide vane decreases continuously. When the span is 0.5 and 0.1, the flow loss in the impeller passage is greatly affected by the guide vane, but the distribution of the flow loss in the impeller passage is relatively uniform, and the distribution regularity of flow loss in the guide vane is poor. When span = 0.9, the variation of flow loss in the guide vane is the same as that of 0.6Q d . When the span is 0.5 and 0.1, the overall internal flow loss of the guide vane from DY1 to DY5 decreases first and then increases, and the internal flow loss of DY4 is the smallest. There is a large area of flow loss area affected by the wake of the impeller in the guide vane channel, and the flow loss caused by the wake of the narrow channel (DY1-DY5) is gradually weakened. It can be seen from Figure 12C that at 1.4Q d , the region with large flow loss caused by the impeller wake still exists. When span = 0.9, the flow loss caused by the wake is the clearest. The flow loss from DY1 to DY5 increases gradually, and the flow loss in DY5 is higher than that in other models. When Span is 0.5 and 0.1, the internal flow loss of the pump is small except for DY5, and the flow loss of the leading edge and trailing edge of the DY5 guide vane is obviously enhanced.
The volute of RCP is divided into eight sections, each of which is 45°apart, as shown in Figure 13. Flow loss distribution nephogram of different sections of the volute of the RCP as Figure 14 shows. The main flow loss occurs near the inlet of the volute, and the loss coefficient from the inlet to the outer wall of the volute gradually decreases. It can be seen from Figure 14A that the distribution of high flow loss area in the volute is relatively uniform at 0.6Q d . The flow loss in DY3 volute is the largest. From Section I to Section VII, the area of high flow loss area decreases gradually, but the extreme value of Φ* increases continuously. It can be found from Figure 14B that when the flow rate increases to 1.0Q d , the overall flow loss in the volute of different model pumps increases, and the inlet Φ* value of the volute decreases significantly, but the area of high flow loss area in section VIII increases significantly. The flow loss in DY4 volute is the smallest. The internal flow loss of DY5 volute is the largest, and there are high flow loss areas with an area of more than 50% in Sections I and Section II. There is a high flow loss in Section VIII of DY1. According to Figure 14C, under the condition of overload flow rate, the distribution regularity of flow loss in the volute of RCP is the worst, and the area of high flow loss area is the largest. The high Φ* value area in DY5 volute is the widest, and the flow loss of the inlet and outlet is the highest. The flow loss of Section I and Section II of DY5 is more serious than that of 1.0Q d . The flow loss of DY4 increased compared with 1.0Q d and the main growth position was the circumferential area of the volute inlet adjacent to the matching guide vane.

| CONCLUSIONS
In this paper, the influence of the change law of the guide vane blade angle on the external characteristics, pressure distribution, and flow field distribution of the RCP under different flow conditions is analyzed. Based on the entropy production theory, the distribution characteristics of flow loss of the RCP are analyzed. The conclusions are done as below.
(1) The head and efficiency of RCP with different change rules of guide vane are quite different. Under the design flow condition and over-load flow condition, the head and efficiency of DY4 with concavity guide vane blade angle are the highest. Under the condition of part-load flow rate, the DY5 with a large concavity guide vane has the best head and efficiency, and the best efficiency point appears at 0.8Q d . (2) Under the condition of part-load flow rate, the static pressure values of DY5 guide vane and volute are significantly higher than those of other models, the velocity changes in the flow channel are relatively uniform, and the number of vortexes in the volute is the least. The pressure gradient in the DY1 guide vane is small, the expansion capacity is weak, the pressure value in the volute is the smallest, the pressure distribution is the most uneven, and the vortex is the most intensive in the area far from the volute outlet. Under the design flow rate, the pressure change in the DY4 guide vane flow channel is relatively stable, and the inlet flow of volute is the most stable. The flow stability of the DY5 guide vane and volute is poor, and the pressure mutation is the most serious. The static pressure value in the volute is significantly lower than in other models. Under the condition of over-load flow rate, the pressure distribution in the DY4 impeller and guide vane is the most uniform, the pressure distribution uniformity of DY3 in DY1-DY4 is the worst, and the lowpressure area at the volute outlet is the widest. The farther the variation curve of the guide vane angle deviates from DY3, the smaller the low-pressure area at the volute inlet. The maximum streamline curvature of DY1 near the outlet of the volute in the five models. (3) The dissipation loss in the internal flow loss of the RCP is much larger than the wall loss. The wall loss can be reduced when the blade length increases by appropriately changing the variation law of the guide vane blade angle. With the increase in flow rate, the dissipation loss decreases first and then increases, and the dissipation loss of pumps in different models varies greatly. The guide vane and volute are the main flow loss areas of RCP. At the part-load flow rate, the flow loss proportion of DY5 guide vane and volute is the smallest, and that of DY1 is the largest. At the over-load flow rate, the loss proportion of DY5 increases significantly, indicating that DY5 is not suitable for operation under over-load flow conditions. In the design condition, the flow loss of the DY4 guide vane and volute account for the smallest proportion. (4) Under different flow conditions, the variation of the guide vane blade angle has different effects on the flow loss distribution in the impeller, guide vane, and volute of the RCP. At 0.6Q d , the flow loss in the DY5 guide vane and volute is the lowest, but the flow loss at the volute outlet is the largest. The flow loss in the volute mainly occurs near the inlet of the volute. With the increase of flow rate, the flow loss in the volute increases. At 1.0Q d , the internal flow loss of the DY4 channel is the lowest, and the internal flow loss of the DY5 channel is the largest. The location near Section I and Section II is the main area of flow loss. At 1.4Q d , the wake effect of the DY5 impeller is the strongest, and the flow loss of the inlet and outlet in volute is the highest.