Effects of guide vane angle on internal flows and vortex characteristic of reactor coolant pump passage under flow coastdown

In order to explore the effects of guide vane angle on internal flows of reactor coolant pump during flow coastdown, the law of vortex evolution and vortex intensity change in the impeller and guide vanes was analyzed. Based on the second generation vortex identification method: Q criterion, the unsteady evolution law and vortex intensity change of impeller guide vane during flow coastdown were analyzed by numerical simulation. The results show with the flow coastdown, fluctuation law of pressure and velocity in the impeller keeps consistent, while the pressure gradually approaches the outlet pressure and the speed decreases. When the vortex identification’s threshold value is Q=24000 s-2, the vortex area in impeller is small and vortex structure is clear. In a rotation period, the shape and area of vortex structure at the inlet with different guide vane angles are the same. The outlet’s vortex structure is affected by dynamic-static interference, resulting the vortex structure is the same but the vortex area is different. The law of guide vane placement angle changes from “convex-vortex” to “concave -vortex”, and vortex area decreases gradually. In the guide vane, horseshoe vortex is dominant, and structure of blocked vortex and shear layer decreases during flow coastdown.


Introduction
The nuclear reactor coolant main circulation pump, abbreviated as the "reactor coolant pump", is the only high-speed rotating power equipment in the primary circuit of the reactor.It drives the circulation of high-temperature and high-pressure working media in the nuclear island, transfers the heat energy of the reactor core to the steam generator to generate steam, drives the turbine to generate electricity, and ensures the normal circulation of the primary coolant to cool the core.When a power failure occurs in a nuclear power plant due to an accident, the reactor coolant pump(RCP) will lose its external power and idle under the inertia of the flywheel in a short time.This process is called the flow coastdown process of the RCP.In the process of flow coastdown, the internal flow of the RCP is very complicated, and the vortex in the channel will seriously affect its internal flow field and flow coastdown characteristics, thus affecting the stable operation of the RCP.For the analysis of the flow field in the RCP, the traditional method is to analyze the velocity and pressure changes in the runner, but it can't fully reveal the real flow state inside.The vortex dynamics research method can effectively diagnose the vortex structure inside the RCP, identify the position, strength and change law of the vortex, and play an important role in analyzing the change of the flow field in the flow coastdown process of the RCP.
Xu et al [1] carried out transient characteristics and internal flow characteristics of RCP under power failure were studied by numerical simulation method and the flow field analysis model of RCP was established, which revealed the flow characteristics in the RCP.Zhang et al [2] research and analysis of transient power-off accidents and numerical simulation characteristics of internal flow field of RCP under different moment of inertia, the influence of moment of inertia on idling of RCP is obtained.The calculation results show that the greater the moment of inertia of unit pump, the more favorable it is to reduce the consequences of the accident and improve the safety performance of the RCP.Gao et al [3] studied the moment balance relation of the RCP force derives the transient equation under the condition of idling and the transient speed is determined by the ratio of steady kinetic energy, which is verified by experimental data.Wang [4] studied the numerical simulation method is used to study the pressure and velocity pulsation, the impeller force pulsation and vibration in different multiphase flow conditions under the idling condition of the main pump of the mixed-flow core.Scholars at home and abroad have done a lot of research on the transient changes of RCP after power failure and flow coastdown [5], but little research on vortex dynamics.Hunt et al [6] carried ou the method of velocity gradient tensor method is used to study the change of the rotating part in the vortex region, and it is concluded that the region with Q>0 is defined as the vortex.Wang and Du et al [7] studied the Q criterion to capture the vortex structure, through the analysis of unsteady characteristics, it is found that the vortex structure in the impeller and guide vane channel will show periodic splitting, which will lead to the change of vortex structure at the inlet of guide vane and the blockage at the inlet.LI S [8] studied the variation of vorticity and distribution area of blade tip clearance of mixed-flow pump was observed by Q criterion.Ye et al [9] studied the quintic polynomial was used to fit the mathematical model of the flowrate and rotation speed of the RCP during idling, and the variation law of hydraulic parameters during idling was studied.At the same time, the vortex dynamic characteristics of the RCP blades were analyzed by Q criterion vortex identification method and surface flow spectrum morphology analysis method.It was found that a strong vortex formed in the guide vane channel and distributed periodically along the blade direction, and the vortex area of the fluid in the guide vane decreased with the increase of idling time.
From the above research, it can be seen that the research on guide vane angle mainly focuses on the inlet and outlet of guide vane, and there is a lack of systematic research on vortex law by the variation law of guide vane angle along blade streamline.However, as the connecting components between the guide vanes and the impeller, the medium flowing into the guide vane inlet from the impeller outlet will have a higher velocity, causing a significant impact on the guide vane and forming vortices in the guide vane channel, resulting in energy loss.Therefore, Choosing an appropriate guide vane placement angle variation pattern will improve the flow loss in the nuclear main pump Therefore, this paper studies the influence of different setting angles on the internal flow of the RCP under the flow coastdown condition, analyzes the vortex dynamics characteristics in the flow coastdown process, reveals the internal flow law of the RCP, and improves the theoretical reference for the optimal design and stable operation of the RCP.

Research objects
As shown in figure 1, the RCP hydraulic model mainly includes five areas: inlet basin, impeller, space guide vane, spherical volute and outlet basin.In order to ensure that the calculation results are close to the real flow situation, the inlet and outlet basins of the nuclear main pump should be appropriately extended (in the actual calculation model, the inlet section is extended by 3 times the inlet diameter and the outlet section by 5 times the outlet diameter).

Calculation domain meshing of reactor coolant pump
Import the water model of reactor coolant pump into ICEM software for grid division, as shown in figure 2 The near wall, blade inlet-outlet and pressurized water chamber tongue of the fluid domain are encrypted, and the grid quality is above 0.3 and the minimum angle is above 18°.The y+ in most areas of the impeller and guide vane basins is controlled within 10~20, and in some areas within 20~35.By setting different grid sizes, five sets of grids are divided and the grid independence is verified.When the grid is about 4.48 million, the calculated lift and efficiency are basically unchanged.In order to verify the reliability of numerical calculation, the head(H) and efficiency (ƞ) obtained by numerical simulation of DY3 reactor coolant pump model are compared with the experimental results, and the performance curve of nuclear main pump is shown in figure 2. The results show that the simulation results are in good agreement with the test results.The deviations of the lift and efficiency under the design flow condition are 3.10% and 1.38% respectively, and the deviations of other flow conditions are all within 5%.

Figure 2.
Grid details of water model.

Boundary conditions and numerical verification
Based on the software ANSYS CFX, the full three-dimensional numerical simulation of the internal flow field of the reactor coolant pump is carried out.The inlet of the main pump adopts the mass flow inlet condition, the outlet adopts the pressure outlet condition, and the idling speed adopts the data of reference [1].The frozen rotor model is used for data transmission at the dynamic-static interface, and the non-slip wall is used for the wall.In order to meet the calculation requirements of SST K-Ω model, an Automatic wall treatment model is adopted near the wall.The wall roughness is 0.025mm, and the numerical accuracy of convection term and turbulence term is high-order solution accuracy.In order to verify the reliability of numerical calculation, the head(H) and efficiency(ƞ) obtained by numerical simulation of DY3 reactor coolant pump model are compared with the experimental results, and the performance curve of reactor coolant pump is shown in figure 3. The results show that the simulation results are in good agreement with the test results.The deviations of the lift and efficiency under the design flow condition are 3.10% and 1.38% respectively, and the deviations of other flow conditions are all within 5%.
Where λ1, λ2 and λ3 are the three eigenvalues of the equation, then P, Q and R can be expressed by Where P, Q and R are the three Galileo invariants of ▽V, and tr and det represent the trace value and determinant value of the matrix respectively.The Q criterion defines the region where the second matrix invariant Q is greater than 0 as a vortex, and requires that the pressure of the vortex region is less than that of the surrounding fluid region.Its formula 3: Where ∥ ∥F is the F-norm of the matrix, A and B are respectively represented as the symmetric part and anti-symmetric part of ▽V, and represent the deformation and rotation in the flow field respectively.Q criterion is an accurate vortex identification method, which effectively eliminates the influence of wall shear layer on the vortex in the channel, and has good identification ability.It is suitable for the three-dimensional complex spatial flow state in the reactor coolant pump.

Characteristics of internal flow change under flow coastdown
During idling, the pressure and speed change of RCP is instantaneous.Studying the pressure and speed change in impeller and guide vane at different idling times has an important influence on mastering the pressure and speed change law and energy conversion characteristics of RCP during idling.Figure 5 shows the characteristic curves of the pressure and speed of the impeller runner of the RCP with different guide vanes at different idling times (Ti =0s, 1s, 8s, 15s, 32s) during idling.Before idling, the pressure and speed of different model pumps have the same variation law and similar values, which indicates that the average pressure and speed in the impeller runner are less affected by changing the variation law of guide vane angle.With the idling, the fluctuation law of pressure and speed in the impeller runner keeps similar changes, while the pressure gradually approaches to the outlet pressure and the speed gradually decreases.At the same idling moment, when the relative position of the impeller along the streamline is between 0 and 0.4, the average pressure and average speed in the impeller runner change gently.When the relative position is greater than 0.4, the gradient of pressure and velocity increases.When the relative position is 0.6-0.8, the pressure rises fastest and the speed decreases rapidly in this range.Near the outlet of the impeller, the pressure in the impeller increases slowly, and there is a small sudden drop, while the speed rises sharply, and the outlet speed increases by nearly 25%.When Ti =0s, the pressure in DY1 impeller is relatively large, and the pressure increase rate of DY5 is high near the impeller outlet.The speed of each model is basically the same before the relative position along the streamline is 0.8.After that, the average speed of the impeller passage of DY5 is gradually smaller than that of other model RCP, and DY5 has the same change phenomenon at other idling moments.When idling enters the halfflow time point (Ti =15s), the average pressure in the impeller passage of DY5 is the highest, and DY4 is the lowest, and the pressure of other models is similar.This trend is most obvious when the relative positions along the impeller streamline are 0~0.4 and 0.8~1.0.DY4-DY5 showed a trend of increasing first and then decreasing, and the average speed from DY1 to DY5 gradually increased.Among the five groups of models, the gradient of average pressure and average velocity in the guide vane channel of DY5 is the largest.When the relative position of the guide vane along the streamline is 0.4, the pressure value of DY5 is the smallest, which is close to 15.8MPa, which is 0.25MPa different from that of DY1.With the idling, the average pressure difference in the guide vane channel of the two groups of model gradually decreases, and the difference is less than 0.05MPa when Ti=32s, and the pressure difference at the outlet of the guide vane also decreases.At different flow coastdown moments, the average pressure and velocity in the guide vane channel of the same model pump are similar, and the gradient of pressure and velocity decreases gradually.In Ti=0-8s, the pressure in the channel fluctuates in a small range except DY5, and the speed of each model pump decreases at the highest rate in this stage.

Spatio-temporal evolution of vortex structure during flow coastdown
According to a large number of research literatures, the Q criterion vortex identification method is greatly affected by the threshold.Because the flow field in the nuclear main pump is complicated, in order to better capture the vortex structure, it is necessary to determine the threshold of idling process analysis.Taking the DY1 model as an example, since the vortex area is the largest when Ti=1s, the vortex structure in the impeller and guide vane when Ti=1s is selected for analysis.
Figure 7 shows the vortex structure of flow field in the impeller of RCP obtained by Q criterion vortex identification method when different thresholds are taken.It can be seen from the figure that the vortex structure of impeller flow field is quite different under different thresholds.When the threshold is large, the vortex area in the impeller flow field is large, but it is seriously polluted by shear, so it is difficult to clearly identify the vortex structure in the flow field.When Q=12000s -2 , the shroud and hub of the impeller and the wall of the blade are all identified as vortex areas.When Q=18000 s -2 , the vortex area on the wall of the trailing edge of the blade decreases, but the vortex structure at the blade inlet and the hub increases, and the larger vortex area basically blocks the inlet area, which is inconsistent with the actual operating conditions.With the decrease of the threshold, the shear pollution on the blade surface is improved, but too small is not conducive to the identification of the vortex structure in the impeller.When Q=32000s -2 , the vortex area in the impeller is greatly reduced, and the capture integrity of the vortex structure is poor.When Q =24000s -2 , the vortex structure in the impeller inlet, impeller channel and blade trailing edge is clear.Therefore, when Q=24000s -2 is selected as the regional threshold of impeller flow field, it can be considered that the vortex structure can be truly reflected.Figure 8 shows the vortex structure of the flow field in the guide vane of the RCP obtained by the Q criterion vortex identification method under different threshold values.It can be seen from the figure that with the increasing of Q value, the vortex area in the guide vane gradually decreases, and the wall shear pollution is gradually eliminated, but the pollution degree is less than that in the impeller area.When Q=12000 s -2 , the vortex structure in the guide vane is rich, the shear layer of the shroud is mistaken for the vortex structure.The vortex structure in the guide vane is concentrated and various vortex clusters intersect with each other, forming obvious blocking effect in the flow channel.At the same time, it is difficult to capture the specific form of each vortex due to the large number of vortex structures.When Q=18000 s -2 , the intersection of vortex clusters decreases, but the vortex clusters are still concentrated, and the definition of vortex structure identification is insufficient.When it is increased to 24000 s -2 , the hairpin vortex at the guide vane inlet and the horseshoe vortex in the guide vane channel can be clearly displayed, and the identification of vortex structures in other areas is also high.When Q=32000 s -2 , the vortex structure in the guide vane channel forms broken vortex, hairpin vortex breaks, horseshoe vortex area decreases, and the smaller vortex structure in the region basically disappears.According to the above analysis, the display effect is better when Q=24000 s -2 is selected as the threshold of guide vane flow field.Figure 9 is a schematic diagram of the evolution law of the vortex structure of the RCP blades with different guide vanes in the flow coastdown process and the selection of thresholds at different idling moments is consistent.It can be seen from the figure that the vortex structure in the impellers of different models gradually decreases with the idling, and the area of vortex at the inlet disk, vortex at the outlet trailing edge and vortex at the shear layer of the impeller decreases obviously.When Ti=1s the number of vortex in the inlet disk increases sharply, and the area of vortex belt at the inlet rim increases, which may be caused by the rapid decrease of flowrate at the initial stage of idling, resulting in the backflow at the impeller inlet.Comparing the model pumps with different guide vane angles, it can be found that the shape and area of vortex structure in the impeller inlet area of different model pumps are basically the same at different idling moments.However, in the impeller passage and the impeller trailing edge near the outlet, the vortex shape is roughly the same, but the vortex area is different due to the dynamic and static interference between the impeller and the guide vane.Before idling, the trailing edge vortex area of DY4 model pump impeller blades is the smallest, while that of DY5 model pump impeller blades is the largest.The trailing edge vortex areas of other model pump impellers are the same, but the breaking degree of trailing edge is different, and the breaking degree of DY1 trailing edge vortex is larger.When Ti=1s, the vortex at the trailing edge of each model pump has little change, and a "spherical" vortex structure appears in the impeller channel, with a small vortex area.When the idling reaches Ti =8s, a "thin-bar" vortex structure appears in the impeller channel of each model pump.With the change law of guide vane placement angle gradually changing from DY1, which is "convex-vortex", to DY4, which is "concave-vortex", the area of the vortex structure gradually decreases, and when the concave-convex degree further increases to DY5, the area of the "thin-bar" vortex structure increases.When Ti=15s, there is still a "thin-strip" vortex structure in each model pump, and its variation law is the same as that when Ti=8s.When idling reaches Ti=32s, the vortex at the inlet disk and the vortex band at the inlet rim of each model pump impeller basically disappear, and there is still a small "pointed airfoil" vortex structure at the trailing edge of the impeller blade.The broken vortex area on this vortex structure gradually decreases from DY1 to DY4, and DY5 has the largest vortex structure area compared with other models.To sum up, in the process of idling, DY4 vortex has the smallest area, the smallest number and the most stable vortex evolution.Figure 10 is a schematic diagram of the evolution law of the flow field vortex structure of the guide vane of the RCP during flow coastdown.It can be seen that the flow field vortex structure in the guide vane is more complex than that of the impeller, and the channel vortex is dominant, mainly composed of horseshoe vortex.With the development of idling, the vortex structure forming blockage in the guide vane gradually becomes smaller and the shear layer vortex structure gradually weakens.At Ti =1s, the area of the inner vortex structure of the guide vane increases, but the increase is smaller than that of the impeller inlet area.Comparing the internal vortex structures of different model pump guide vanes, it can be found that the shapes of internal vortex structures of different guide vanes are obviously different.Before idling, the horseshoe vortex at the inlet of the guide vane and in the guide vane channel gradually lengthens as the change law of the guide vane placement angle changes from DY1, which is "convexvortex", to DY5, which is "concave-vortex".In DY1 and DY2, the guide vane inlet horseshoe is shorter and has a regular shape, and the number of vortex structures in them is equal.The horseshoe vortex area in DY2 guide vane channel is larger than that in DY1.One end of the horseshoe vortex at the guide vane inlet of DY3 is elongated, and the other end is shorter and squeezed into the guide vane channel.However, the number of vortices is less than that of DY1 and DY2, and the horseshoe vortex in the guide vane channel is also elongated, but its structural area is basically the same as that of DY2.The horseshoe vortex at the inlet of DY4 inner guide vane basically disappears and is elongated into a "strip-shaped" vortex belt.The horseshoe vortex in the channel is thin ellipsoid and attached to the pressure surface of guide vane, and its vortex area is smaller than that of other guide vane models.The internal passage vortex of DY5 is basically composed of a strip vortex belt, and its internal vortex area is the widest compared with other model pumps.When Ti=1s, the distribution of vortex core in guide vanes of each model pump is similar to that before idling, and the shape of vortex structure in guide vanes changes little.When the idling reaches Ti=8s, the vortex structure area of each model pump guide vane decreases nearly twice, and DY4 decreases the most.The vortex structures of DY1, DY2, DY3 at the shroud and hub of the guide vane and near the outlet are obviously reduced, but there is still a large horseshoe vortex at the inlet.The length of the vortex band in the channel of DY5 guide vane decreases, but the vortex structure area is still the largest in all models.When Ti=15s, the horseshoe vortex at the inlet of the guide vanes of DY1 and DY2 basically disappeared, while the large vortex clusters in the guide vanes of other model pumps decreased and the slender broken vortex increased.When the idling reaches Ti=32s, the large vortex clusters in the guide vanes of each model pump basically disappear, leaving only the small slender vortex and broken vortex, which gradually shift to the wall, and the vortex evolution in the guide vanes of DY5 is the most obvious.

Impeller and Guide vane vortex distribution characteristics
Figure 11 show the Q value distribution map of the middle section of the RCP impeller at different idle rotation times.The threshold range of the Q criterion has a great influence on the identification of the strong vortex region.Therefore, the Q value range is determined to be [ -3000,3000 ].Before the idling, the strong vortex area in the middle section of each model pump impeller is evenly distributed, mainly around the suction surface of the blade inlet, the middle part of the suction surface and the trailing edge of the blade suction surface.The vortex structure strength of each model pump impeller is similar at the suction surface and the middle part of the blade suction surface, but the vortex strength of different model pump impellers is different at the trailing edge of the blade suction surface.Among them, DY4 strong vortex area is the narrowest, and the number of elongated vortex structures is the smallest.From DY1 to DY3, the vortex strength near the trailing edge of the impeller blade gradually weakens, and the vortex strength of DY5 guide vane trailing edge is obviously higher than that of other models.However, before idling, the Q value area of the strong vortex area decreases continuously.When Ti=1s, the strong vortex area near the trailing edge of the impeller blade increases, and when idling reaches Ti=8s, the area of the strong vortex area decreases significantly.When Ti=32s, the strong vortex area at the inlet suction surface and the trailing edge of the suction surface of the blade basically disappears.At this time, the Q value of each model pump impeller is evenly distributed, and the Q value in the flow passage approaches to 0. In the whole idling process, the area of strong vortex in DY4 impeller is always the smallest, which indicates that the flow stability of DY4 pump impeller is higher than that of other models.Figure 12 shows the distribution of Q value in the middle section of the guide vane of the RCP at different idle time, and the range of Q value is consistent with the impeller.Before the idling, the distribution uniformity of the strong vortex area in the middle section of the guide vane of each model pump is weak, and the distribution position of the strong vortex area in the guide vane with different guide vane angle is different.The area of DY1 vortex is strong, the strong vortex area is mainly distributed in the middle of the flow channel, and some flow channels have medium vortex area.The distribution of DY2 and DY3 strong vortex areas is similar, mainly distributed near the trailing edge and the convex side of the blades.In DY4 and DY5, the vortices are elongated near the pressure surface of the blade, and there is also a small range of strong vortices in the trailing edge of the blade.The area of DY4 strong vortex area in the five guide vane models before idling is small, and the vortex intensity in DY1 is significantly higher than that in DY2 and DY3.The vortex intensity in DY5 is the largest, and the vortex area with high Q value is wide.With the development of idling, the number of vortex structures in the strong vortex region of the guide vane of each model pump decreases continuously, and the vortex intensity decreases continuously.When Ti = 1s, due to the rapid decrease of flowrate and rotation speed, the interference between impeller and guide vane is severe, which makes the vortex intensity in guide vane increase.At this time, the vortex intensity of DY3 and DY4 increases the least compared with that before idling, while DY5 is greatly affected and the vortex intensity increases obviously.From Ti = 1s to Ti = 8s, the range of Q value in the guide vane of each model gradually decreases from −3000 s -2 ~ 3000 s -2 to −2000 s -2 ~ 2000 s -2 , and the range of strong vortex area decreases by about 33 %.When Ti = 8s, the vortex structure in DY5 is still relatively complex, and the vortex intensity is the highest, followed by DY1, and the area of strong vortex in DY4 is the smallest.When Ti = 15 s, the Q value range of the main flow area of different guide vanes gradually narrowed to −1000 s - 2 ~ 1000 s -2 , and the medium vortex area was dominant.When Ti = 32 s, the strong vortex area basically disappeared and a small number of vortices exist near the impeller outlet.

Conclusions
In this paper, the numerical simulation method is used to study the influence law of the guide vane placement angle of the RCP on the flow state in the idling state, and the Q criterion is used to study the evolution law and the change of vortex intensity in the impeller guide vane.The main conclusions are as follows: (1) The variation law of guide vane angle has little influence on the pressure and velocity in the guide vane runner, but has great influence on the pressure and velocity in the guide vane runner.The average pressure of guide vane is similar to that of guide vane angle, but the average velocity of guide vane is opposite to that of guide vane, in which the average pressure and velocity of DY1 fluctuate the least and DY5 fluctuates the most.The maximum average pressure difference between DY1 and DY5 can reach 0.25Mpa.As the idling progresses, the average pressure difference in the guide vane channel of the two model pumps gradually decreases.With the development of idling, the fluctuation law of pressure and velocity in impeller and guide vane of model pump with different guide vanes is similar to that before idling.
(2) On the whole, with the idling, the vortex structure and vortex intensity in the impeller and guide vane of the model pump with different guide vane placement angles gradually decreased, but when Ti=1s, the vortex structure in impeller and guide vane increased and the area of strong vortex increased.At different idling moments, the shape and area of vortex structure at the inlet of different model pump impellers are basically the same, but the vortex structure area and intensity in the impeller passage and the blade trailing edge are different.With the change law of guide vane placement angle changing from "convex-vortex" DY1 to "concave-vortex" DY4, the vortex structure area and intensity gradually decrease, but the vortex structure area and intensity in DY5 impeller with a larger "concave-vortex" degree are the largest.
(3) The structure of the guide vane inner vortex is more complex than that of the impeller, and the horseshoe vortex dominates, mainly distributed in the guide vane inlet and guide vane channel.The shape and strength of the guide vane inner vortex with different guide vane placement angles are different, and the evolution law of the vortex at different idling moments is also different.At the same idling time, the number of vortex and the area of strong vortex in the guide vane first decreased and then increased from DY1 to DY5, among which DY4 vortex has the smallest structural strength and area and DY5 has the largest.
However, due to the use of numerical simulation methods for analysis in this article, there is no corresponding experimental data to support the conclusion.Therefore, in the future, experimental comparisons will be conducted when conditions are met to verify the correctness of the theory, provide theoretical reference for the optimization design and stable operation of the reactor coolant pump, and leverage the characteristics of combining theory and practice to meet the needs of complex and comprehensive equipment manufacturing of the reactor coolant pump.

3. 2
. Q criterion study the vortex dynamics characteristics in the reactor coolant pump idling, the second generation vortex identification method Q criterion was proposed by Hunt et al in 1988, which was obtained based on the eigenvalue of the velocity gradient tensor ▽V[8].For incompressible fluid, the characteristic equation of ▽V explained by formula 1：  3 +  3 +  +  = 0

Figure 5 .
Figure 5. Pressure and velocity variation characteristics of impeller passage during flow coastdown transient process.Figure6is the characteristic curve of pressure and speed change in the guide vane channel of RCP with different guide vanes at different idling moments.The average pressure curve in the guide vane flow channel from DY1 to DY4 increases linearly.The average pressure in the DY5 flow channel decreases first and then increases, while the average pressure from DY1 to DY5 gradually decreases.DY4-DY5 showed a trend of increasing first and then decreasing, and the average speed from DY1 to DY5 gradually increased.Among the five groups of models, the gradient of average pressure and average velocity in the guide vane channel of DY5 is the largest.When the relative position of the guide vane along the streamline is 0.4, the pressure value of DY5 is the smallest, which is close to 15.8MPa, which is 0.25MPa different from that of DY1.With the idling, the average pressure difference in the guide vane channel of the two groups of model gradually decreases, and the difference is less than 0.05MPa when Ti=32s, and the pressure difference at the outlet of the guide vane also decreases.At different flow coastdown moments, the average pressure and velocity in the guide vane channel of the same model pump are similar, and the gradient of pressure and velocity decreases gradually.In Ti=0-8s, the pressure in the channel fluctuates in a small range except DY5, and the speed of each model pump

Figure 6 .
Figure 6.Characteristics of pressure and velocity variation in diffuser flow channel during Flow coastdown transient process.

Figure 7 .
Figure 7. Vortex identification results of Q-criterion for flow field in impeller under different thresholds.Figure8shows the vortex structure of the flow field in the guide vane of the RCP obtained by the Q criterion vortex identification method under different threshold values.It can be seen from the figure that with the increasing of Q value, the vortex area in the guide vane gradually decreases, and the wall shear pollution is gradually eliminated, but the pollution degree is less than that in the impeller area.When Q=12000 s -2 , the vortex structure in the guide vane is rich, the shear layer of the shroud is mistaken for the vortex structure.The vortex structure in the guide vane is concentrated and various vortex clusters intersect with each other, forming obvious blocking effect in the flow channel.At the same time, it is difficult to capture the specific form of each vortex due to the large number of vortex structures.When Q=18000 s -2 , the intersection of vortex clusters decreases, but the vortex clusters are still concentrated, and the definition of vortex structure identification is insufficient.When it is increased to 24000 s -2 , the hairpin vortex at the guide vane inlet and the horseshoe vortex in the guide vane channel can be clearly displayed, and the identification of vortex structures in other areas is also high.When Q=32000 s -2 , the vortex structure in the guide vane channel forms broken vortex, hairpin vortex breaks, horseshoe vortex area decreases, and the smaller vortex structure in the region basically disappears.According to the above analysis, the display effect is better when Q=24000 s -2 is selected as the threshold of guide vane flow field.

Figure 8 .
Figure 8. Vortex identification results of Q-criterion for flow field in diffuser under different thresholds.

Figure 9 .
Figure 9. Vortex evolution law of turbine flow field at different idle time.Figure10is a schematic diagram of the evolution law of the flow field vortex structure of the guide vane of the RCP during flow coastdown.It can be seen that the flow field vortex structure in the guide vane is more complex than that of the impeller, and the channel vortex is dominant, mainly composed of horseshoe vortex.With the development of idling, the vortex structure forming blockage in the guide vane gradually becomes smaller and the shear layer vortex structure gradually weakens.At Ti =1s, the area of the inner vortex structure of the guide vane increases, but the increase is smaller than that of the impeller inlet area.Comparing the internal vortex structures of different model pump guide vanes, it can be found that the shapes of internal vortex structures of different guide vanes are obviously different.Before idling, the horseshoe vortex at the inlet of the guide vane and in the guide vane channel gradually lengthens as the change law of the guide vane placement angle changes from DY1, which is "convexvortex", to DY5, which is "concave-vortex".In DY1 and DY2, the guide vane inlet horseshoe is shorter and has a regular shape, and the number of vortex structures in them is equal.The horseshoe vortex area in DY2 guide vane channel is larger than that in DY1.One end of the horseshoe vortex at the guide vane inlet of DY3 is elongated, and the other end is shorter and squeezed into the guide vane channel.However, the number of vortices is less than that of DY1 and DY2, and the horseshoe vortex in the guide vane channel is also elongated, but its structural area is basically the same as that of DY2.The horseshoe vortex at the inlet of DY4 inner guide vane basically disappears and is elongated into a "strip-

Figure 10 .
Figure 10.Vortex evolution law of flow field in diffuser at different idle moment.

Figure 11 .
Figure 11.The distribution of Q value in the middle section of impeller at different idle moments.Figure12shows the distribution of Q value in the middle section of the guide vane of the RCP at different idle time, and the range of Q value is consistent with the impeller.Before the idling, the distribution uniformity of the strong vortex area in the middle section of the guide vane of each model pump is weak, and the distribution position of the strong vortex area in the guide vane with different guide vane angle is different.The area of DY1 vortex is strong, the strong vortex area is mainly distributed in the middle of the flow channel, and some flow channels have medium vortex area.The distribution of DY2 and DY3 strong vortex areas is similar, mainly distributed near the trailing edge and the convex side of the blades.In DY4 and DY5, the vortices are elongated near the pressure surface of the blade, and there is also a small range of strong vortices in the trailing edge of the blade.The area of DY4 strong vortex area in the five guide vane models before idling is small, and the vortex intensity in DY1 is significantly higher than that in DY2 and DY3.The vortex intensity in DY5 is the largest, and the vortex area with high Q value is wide.With the development of idling, the number of vortex

Figure 12 .
Figure 12.The distribution nephogram of Q value in the middle section of diffuser at different idle moments.

Table 1 .
Main geometric parameters and performance parameters of reactor coolant pump.