Study on unsteady characteristics of the reactor coolant pump under non-uniform inflow

The primary circuit of a nuclear power plant contains a steam generator (SG) and two vertical reactor coolant pumps (RCPs). Two RCPs are installed at the bottom of the SG. The structure of the channel-head of the SG is special, which leads to uneven flow from the RCP inlet and affects the operation performance of the pump. Taking the RCP of the third-generation reactor as the research object, the unsteady characteristics of the third-generation RCP under non-uniform inflow conditions were investigated using CFD, and the pressure pulsation characteristics inside the RCP were mainly studied. A series of monitoring points were set at the channel of the channel-head, impeller, diffuser and casing section respectively to study the influence of non-uniform flow on the pressure fluctuation and radial force distribution of the RCP. The results show that non-uniform inflow can cause instability in pressure fluctuations in the “throat” region of the channel-head. The interaction between the impeller and diffuser can cause pressure pulsation from the impeller outlet to the diffuser inlet, potentially impacting the safe and stable operation of the RCP. This research provides certain theoretical support for the design of RCPs under the condition of non-uniform inflow.


Introduction
The energy demand is high due to scientific and societal advances.Nuclear power has gained attention for its development and safe usage.The advanced large-scale pressurized water reactor (NPP) Generation III nuclear power plant has two main cooling loops to transfer the heat generated in the reactor core to the SG.The safety design and reliability assessment of the RCP generally assumes that the pump operates under uniform inlet flow conditions.However, in the NPP Generation III, the direct connection between the channel-head and the RCP results in non-uniform inlet flow, impacting pump efficiency and operation stability [1].Due to the asymmetric structure of the channel-head and the sudden contraction of the section of the pump inlet section, the inlet flow of the RCP is uneven, and the uneven flow destroys the symmetry of the pump inlet flow field, reduces pump performance and increases the risk of impeller fatigue failure.Yi-bin Li [2]mainly used CFD numerical simulation to study the effects of the hydraulic performance of the discharge inlet flow on the RCP and conducted experimental verification, and it was found that there was an obvious vortex at the entrance of the impeller.The quality flow velocity speed and the generation and evolution of the vortex in the radial shooting and the impeller channel show strong unevenness, thereby enhancing the pulse of pressure and increasing the impeller load.Heng Zhang [3] employed CFD numerical simulation to investigate the mechanics of non-uniform flow within the channel-head of the SG and discovered that the channel-head's asymmetric structure and the abrupt contraction of the connection between the channel-head and the inlet pipeline caused flow separation, resulting in non-uniform inflow.The RCP's performance is significantly reduced under the non-uniform flow, with clear speed distortion observed at the impeller inlet on both sides.However, the swirl distortion characteristics differ significantly.
The primary energy transmission medium of the RCP in the first circuit is mainly the coolant.In the first circuit, it is used to drive the cooling fluid for phase change, and then the energy is passed to the second circuit through the SG.In normal RCP operation, the blades of the impeller and the diffuser periodically intersect.This causes interaction between the medium flow in the impeller internal flow channel and the medium flow in the diffuser flow channel, impacting the mutual fluid velocity, pressure distribution, and velocity distribution [4].This interaction is referred to as dynamic and stationary interference [5].The mutual influence between dynamic and stationary forces creates pressure fluctuations within the fluid domain of the pump.These fluctuations occur within a certain range and are characterized by short durations.Specifically, a single fluctuation is referred to as a pressure pulsation [6].Pressure pulsation is an important factor causing unstable phenomena such as vibration and noise in reactor coolant pumps, and severe pulsation can lead to the occurrence of nuclear accidents [7].Xu Zhang et al. [8] employed Fluent to numerically calculate the unsteady threedimensional flow of the RCP and found that the amplitude of pressure pulsation reached its maximum value between the impeller and the diffuser, and the dissipation rate of pressure pulsation waves in the impeller channel was greater than that in the diffuser channel.Jiarong Gu [9] used numerical simulation to analyze the relationship between unsteady vortices and pressure pulsation in a high-temperature molten salt pump (MSP) and found consistency between the high-pressure pulsation zone and the areas where vortices develop, move, and detach.
In terms of experimental research on RCPs, Qiang Zhou [10] conducted experimental research on the pressure pulsation and vibration characteristics of RCPs at different speeds and operating temperatures.The root mean square method (RMS) and fast Fourier transform method (FFT) were used for data processing, and it was found that the intensity of pressure pulsation increased as the speed increased; as the temperature gradually increased, the intensity of pressure fluctuations first decreases and then increases.Yuchen Song [11] employed time-resolved tomography particle image velocimetry (tomo-PIV) technology to conduct experimental analysis on the non-uniform inflow of the RCP and combined it with MART technology to reconstruct the non-uniform flow field inside the RCP.
Many scholars, both domestic and international, typically employ experiments and numerical simulations in tandem to examine pressure pulsation properties within pumps under non-uniform flow conditions.Yun Long [6,12] conducted experimental and numerical simulations on the flow and pressure pulsation characteristics of RCPs under non-uniform inflow at different flow rates and speeds.Song Huang [13] compared and explored the time-domain and frequency-domain characteristics of pressure pulsation of RCPs under different inflow conditions through experimental and numerical research, and conducted pressure spectrum analysis using FFT and wavelet coherence.Xu Rui [14] used numerical simulation methods to treat pressure pulsation using Fourier transform and root mean square (RMS) methods.They conducted pressure pulsation analysis on the pump casing and outlet pipeline, providing a certain basis for studying the non-uniform flow in RCPs, as well as pump fault diagnosis and vibration analysis.Song Huang [15] carried out numerical and experimental research to investigate the pressure pulsation features of the RCP in the hump zone and found that when the RCP enters the hump zone, it encounters strong flow separation and rotational stall phenomena.This leads to a rise in the low-frequency signal inside the pump and intensifies the pressure pulsation phenomenon.The lowfrequency rotational stall is primarily responsible for this effect.In summary, the study of pressure pulsation in RCPs is extremely important for maintaining the secure and steady performance of RCPs.The main causes of pressure pulsation include distortion of the inlet flow of the RCP, secondary reflux, cavitation, and dynamic and stationary interference between the impeller and the diffuser.The vast majority of scholars use theoretical analysis, experimental design, CFD simulation, and other methods to explore the pressure pulsation inside the pump.

Hydraulic model
The basic geometric parameters of the impeller and diffuser were modelled using the software CFturbo based on the design parameters of the RCP, and the domains of the channel-head, casing and outlet sections were established by using 3D software.The calculation domain of the established coupling model of the channel-head and the RCP mainly includes four parts: the channel-head, impeller, diffuser, casing and outlet section, as shown in Figure 1.

Grid division
According to the coupling model of the channel-head and the RCP, the four domains are divided into grids.Among them, the impeller and the diffuser are divided into structured grids using Turbogrid, while the rest are divided into unstructured grids using Workbench Mesh, as shown in Figure 2. As for the verification of grid independence, it has been completed in [16].The final selection includes 1.13 million impeller grids, 1.92 million diffuser grids, 1.97 million channel-head grids, 1.28 million casing and outlet section grids, and a total of 6.3 million grids.

Boundary conditions
The primary numerical calculation parameters for the channel-head and RCP coupling model are presented in Table 1.ANSYS CFX commercial software was utilized to perform the numerical simulation of the channel-head and RCP coupling model.During the simulation, the liquid phase consisted of water at 25℃, with a density of 997 kg/m 3 and a dynamic viscosity of 8.899×10

Monitoring point settings
In order to explore the pressure fluctuation in different hydraulic components of the RCP caused by nonuniform incoming flow, a series of monitoring points are set in the channel of the channel-head, impeller, diffuser, casing and outlet section, as shown in Figure 3.

Performance curve
Figure 4 shows the steady-state Q-H curve and Q-η curve of the channel-head and the RCP coupling model at flow rates between 0.3Q and 1.2Q.The results indicate a gradual decrease in head as flow rate increases, while efficiency first shows an increase followed by a decline.The design operating point is the optimal efficiency point.Figure 5 shows the constructed model pump experimental bench, which was experimented using a straight-pipe model.The reliability of the numerical simulation method was verified through the obtained experimental results [6].

Pressure pulsation in the channel of the channel-head
Figure 6 illustrates the root mean square (RMS) of monitoring points C1~C5 at the central axis of the channel-head under different flow rates.The pressure change trend remains consistent when the fluid passes through the contraction section of the channel head under different flow conditions.The pressure at C5 is the lowest, and as the pressure point gradually approaches C1, the pressure slowly increases and tends to stabilize.Figure 7 shows the root mean square (RMS) of monitoring points P1~P9 near the wall of the middle section of the contraction section of the channel-head under different flow rates.From the results, it is evident that a substantial pressure drop occurs in the region around the "throat", leading to a noticeable decline in pressure at P9 compared to P1~P8.Where, p is the transient pressure, Pa; p is the average pressure of the impeller in the rotation cycle, Pa; 2 u is the impeller outlet circumferential velocity, m/s; ρ is the density of the liquid medium; 2 D is the impeller outlet diameter.Figure 8 shows the frequency domain diagram of P10~P12 at varied flow rates.It is observed that there is no significant difference in pressure at the three monitoring points under different flow rates.Under different flow rates at the same monitoring point, the pressure fluctuation under low flow rate (0.5Q) and high flow rate (1.2Q) conditions is more unstable than that near the standard operating point and is more significant under high flow rate conditions.

Pressure pulsation in the channel of the impeller
To further explore the instantaneous flow pattern inside the impeller, the pressure pulsation at the monitoring points in the impeller flow channel is analyzed.Figure 9 shows the frequency domain diagram of Y1~Y3 at different flow rates.The shaft frequency of the RCP is fn = n/60 = 24.67Hz; and the blade frequency is the product of the number of blades and the rotational frequency, which is 5fn = 123.33Hz.
It can be seen from Figure 9 that the pressure pulsation phenomenon in the impeller passage is obvious, and the value of pressure pulsation shows a significant increasing trend from the impeller inlet to the impeller outlet, which is mainly due to the dynamic and stationary interference between the impeller and the diffuser.The pressure fluctuations at Y1, Y2, and Y3 are all concentrated in the lowfrequency region, and the pressure fluctuations in the high-frequency region are almost undetectable.It is speculated that the reason may be that when there is no cavitation phenomenon in the RCP, the lowfrequency signal of pressure pulsation may be caused by the dynamic and stationary interference between the impeller and the diffuser, and flow separation may occur when the impeller blades rotate at high speeds.
At the Y1 monitoring point, when the frequency is 246.67 Hz, the corresponding pressure coefficient value is the maximum at different flow rates, and the frequency value at this time is just twice the blade frequency, and the frequency corresponding to the wave crest in the frequency domain diagram is an integral multiple of the blade frequency.At the same time, it was found that when the frequency is an integer multiple of the blade frequency (multiple frequency), a peak will appear on the frequency domain diagram.
At monitoring points Y2 and Y3, when the frequency is 271.33 Hz, the pressure fluctuation is the most intense.When the frequency is 271.33 Hz, 542.66 Hz, 813.99 Hz, 1085.33 Hz, or 1356.66Hz, the peak value will appear on the frequency domain diagram.Under standard operating conditions, the amplitude of pressure fluctuation at the main frequency of the three monitoring points is much higher than that at the harmonic.Therefore, it can be considered that the blade frequency plays a leading role in the vibration induced by pressure fluctuation under design operating conditions.Figure 10 shows the polar coordinate diagram of radial force resultant of the impeller at different flow rates.In order to explore the influence of non-uniform flow caused by the special structure of the channel-head on the radial force of the impeller during the high-speed rotation of the RCP, edit the force formula of the impeller in the x direction and y direction through the formula editor in CFX, use the edited formula to monitor the radial force received by the impeller, and finally obtain the transient radial force distribution of the impeller of the RCP.
It can be seen from the figure that under all working conditions of the pump body, the flow rate and pressure distribution of each flow channel of the pump impeller are symmetrically distributed, and at the same time conform to the number of blades of the impeller.The difference is the magnitude of the radial force, which can be found to have the largest radial force of the impeller at 1.2Q and the highest value of 600 N. Then it decreases as the flow rate decreases, and reaches the minimum value at 0.9Q, after which the radial force gradually expands, which means that at 0.9Q, the force at the impeller outlet is the least and the pump runs the most stable.
And the radial force change from 0.5Q to 1.0Q still shows some regularity, while at 1.2Q, there is a different change, especially at the peak.At 1.2Q, the force is 600 N, the gradual alternation changes, while the rest of the flow rate is the opposite of 1.2Q.At 0.5Q, from a transient point of view, the radial force of the impeller is more evenly distributed in all directions, and it is possible that due to the poor hydraulic stability of the pump body under the working conditions of small flow, the radial force that should be in the flow channel fluctuates greatly, and reaches the radial force value of the impeller, and the radial force value of the impeller is in line with the normal law under the rest of the flow, and the radial force at the impeller is more obvious.

Conclusions
In this paper, a CFD numerical simulation was conducted to simulate the pressure fluctuations in each hydraulic component of the RCP in the third generation reactor under non-uniform flow.The analysis focused on the influence of non-uniform flow on the pressure fluctuation and radial force distribution in the RCP, by setting a series of monitoring points in the model pump.It was found that non-uniform incoming flow can cause instability in pressure fluctuations in the "throat" region of the channel-head.
The interaction between the impeller and diffuser can cause pressure pulsation from the impeller outlet to the diffuser inlet, potentially impacting the safe and stable operation of the RCP.

Figure 1 .
Figure 1.Coupling model of the channel-head and the RCP.

Figure 2 .
Figure 2. Grid division of the channel-head and the RCP.
−4 kg/(m•s).This paper discusses Long's[17] choice of turbulence models.Specifically, it focuses on turbulence models that consider turbulent shear stress transport and utilizes SST k-ω turbulence models for closing the RANS equation.SST k-ω turbulence models have proven to accurately predict flow separation under backpressure gradients.Extensive studies have verified their effectiveness in incompressible flow prediction.When conducting unsteady calculations, the dynamic-stationary interface is the Transient Rotor Stator and the steady results at the corresponding operating points are used as the initial field for this unsteady calculation.The rotation time of the impeller during a single cycle is T=60/1480=0.04054054s, calculated every 0.5° rotation of the impeller, with a time step of t=T/720=5.63063×10−5 s.The operating conditions are calculated over a period of 10 weeks, and the final result is based on the calculation for the 10th week.

Figure 3 (Figure 3 .
Figure 3. Setting of monitoring points for hydraulic components of the RCP.

Figure 7 .
Figure 7. RMS values of P1~P9 at different flow rates.In order to analyze the unsteady pressure fluctuation in the 'throat' of the channel-head, the pressure coefficient Cp is introduced.The commonly used expression of the pressure coefficient is：

Figure 8 .
Figure 8. Frequency domain diagram of P10~P12 at different flow rates.

Figure 9 .
Figure 9. Frequency domain diagram of Y1~Y3 at different flow rates.

Figure 10 .
Figure 10.Polar coordinate diagram of radial force resultant of the impeller.

Figure 12 .
Figure 12.Frequency domain diagram of WK1 at different flow rates.

Table 1 .
Main numerical calculation settings of the channel-head and the RCP coupling model.