Research on the internal pressure pulsation characteristics of reactor coolant pump under non-uniform inflow

In the third generation of nuclear power technology, the first circuit of the nuclear power plant consists of a steam generator and two vertical reactor coolant pumps (RCPs). The two vertical nuclear pumps are installed upside down at the bottom of the steam generator, resulting in uneven flow at the inlet of the reactor coolant pump due to the special structure of the lower chamber of the steam generator. The RCPs is the sole high-speed rotating machinery in the primary circuit, operating under non-uniform flow conditions for extended periods. The resulting effects on pump performance remain ambiguous. In this study, we focused on the pressure pulsation of the non-uniform flow of a third-generation RCP. To analyze this, we utilized high-precision numerical simulation methods to obtain information regarding the internal pressure pulsation characteristics of the non-uniform inflow. Additionally, we investigated the impact that non-uniform inflow has on the radial force characteristics of the RCP. This study aims to enhance the comprehension of pressure pulsation characteristics in reactor coolant pumps under non-uniform inflows. It will offer valuable insights for research on vibration control in these pumps, and support the development of third-generation nuclear power technology.


Introduction
The energy transfer medium in the reactor coolant pump's first circuit is primarily a coolant, which drives the first circuit's coolant for phase change and then transfers energy to the second circuit via the steam generator.During normal operation of the reactor coolant pump, the vanes and guide vanes meet periodically.The flow of the medium within the impeller's internal flow channel interacts with the medium flow in the guide vane flow channel, affecting the mutual fluid velocity, pressure distribution, and velocity distribution.This interaction between the vane flow channel and the medium flow in the guide vane flow channel is known as dynamic and static interference.This mutual influence of dynamic and static components generates pressure pulsations in the pump's fluid domain, resulting in a specific range of fluctuations.Each fluctuation lasts only briefly, and is labelled as a single pressure pulsation [1].Previous studies at both domestic and foreign levels [2] indicate that the turbulent pressure pulsation and pump noise within the nuclear primary pump predominantly stem from the non-homogeneous flow of the impeller inlet and output, as well as the dynamic and static disturbance of the impeller stream channel and guide vane stream channel.The interaction between the impeller and guide vane generates both dynamic and static interference, ultimately leading to pressure pulsation within the pump.This pressure pulsation propagates throughout the water body of the reactor coolant pump and can result in fatigue damage to certain hydraulic overflow components, as well as abnormal radial vibration within the pump shaft and interior.Long-term exposure to pressure pulsation must be avoided to prevent potential damage.Under certain working conditions, the pressure pulsation may approach the natural frequency of the pump body, which promotes the resonance of the pressure pulsation and the pump body.
This generates significant mechanical structural damage due to the vibration effect of resonance, thus posing a serious threat to the safety of nuclear power plants during operation and maintenance.Miyabe et al. [3] investigated the reactor coolant pump using high-speed photography technology and a pressure pulsation measuring instrument.Their findings revealed that during internal rotational stall, a significant amount of backflow occurs at the impeller outlet and guide vane inlet.This causes an unstable flow field within the pump, resulting in severe vibration and pressure pulsation.Such instability has a negative impact on the pump's operational and maintenance safety.The Korea Institute of Atomic Energy (KAERI) [4] conducted an evaluation of a self-designed reactor coolant pump for a 1400MW nuclear reactor with an adaptive reactor type.The performance was tested in both cold and hot conditions, revealing that pressure pulsation in a specific temperature range is directly proportional to the natural frequency of the main pump as a whole.The blade frequency and harmonics within this temperature range are also proportional to the natural frequency of the main pump, leading to an abnormal increase in amplitude.BAUMGERTEN et al. [5] conducted an experiment using numerical simulation to investigate the reactor coolant pump.The research involved a 3D unsteady simulation of the internal flow field, specifically to study pressure pulsation and discover the resulting changes.The findings were compared and proved to be consistently feasible, making it a viable method for studying the internal pressure pulsation change of the reactor coolant pump through numerical simulation.Zhu Rongsheng et al. [6] utilized CFD numerical simulation technology to examine the performance of the nuclear primary pump.Through internal flow field analysis, it was determined that significant pressure pulsation occurs within the pump during low flow conditions.This is attributed to dynamic and static interference generated by the impeller and guide vane.Blade frequency induction is identified as the primary contributing factor to the pressure pulsation inside the pump.Furthermore, a considerable backflow phenomenon occurs at the impeller outlet flow channel and guide vane inlet.The pressure pulsation of the main nuclear pump fluctuates periodically and violently under conditions of low flow.Zhu Rongsheng et al. found that climate change has severe implications for the natural environment.Their research indicates that rising global temperatures lead to a decrease in biodiversity and an increase in extreme weather events.Furthermore, the study highlights the need for urgent action to mitigate the impact of climate change on ecosystems and human societies.The authors argue that increased public awareness and policy changes are key to achieving this goal.They suggest that policymakers should focus on reducing greenhouse gas emissions and implementing sustainable development practices.The numerical calculation method was utilized to examine pressure pulsation at the outlet of the pressurized water chamber under varying working conditions.This research focused on the reactor coolant pump, and the results indicated that the pressure pulsation signal fluctuated in accordance with the inlet flow.
Additionally, the pressure pulsation was found to become stronger as the deviation from the design working conditions increased.The study found that the spherical design of the reactor coolant pump resulted in the generation of a large return flow between the impeller and the guide vane, thereby impacting the internal pressure pulsation.Technical terms were explained when first used, and the language was kept objective and clear with no biased evaluations or ornamental language.Common academic structure was maintained, and the formatting adhered to style guides.Li Jing et al. [8] conducted an independent investigation on the non-uniform distribution of guide vanes and their associated machines, using the 1400MW reactor coolant pump as their foundation.By employing a numerical simulation method, the research analyzed the internal pressure pulsation and found that the non-uniform distribution of guide vanes had minimal impact on external characteristics.However, it substantially enhanced the internal pressurized water flow, decreasing the hydraulic kinetic energy and reducing the amplitude of pressure pulsation at the blade frequency and its frequency doubled.LONG et al. [1] employed numerical simulation to investigate pressure pulsations of the reactor coolant pump under different flow conditions.The main objective of the study was to provide certain design concepts for reactor coolant pump under non-uniform flow conditions.To analyze the pressure pulsations, the authors used various methods, including but not limited to Fourier transform, root mean square and peak-to-peak.

Non-uniform flow hydraulic model
In order to advance the examination of the lower chamber-reactor coolant pump's distinctive direct connection structure's impact on the small reactor main pump's inlet flow and the front section vane inlet flow, we reconstructed the coupling model of the lower chamber-reactor coolant pump and analyzed and compared the flow disparities between them.Please refer to Figure 1:

Grid division
The lower chamber uses a non-structured the model consists of four bodies of water: channelhead, impeller, diffuser, volute, and outlet section water body, as illustrated in Figure 2 for the non-structural grid of the lower chamber:

Non-uniform flow is not an unsteady calculation settings
When carrying out unsteady calculations, the Frozen Rotor method is utilised at the interface of motion and static.The corresponding working point's constant result is then used as the initial field for this unsteady calculation.The impeller's single-cycle rotation time is T=60/1480=0.04054054s,and the impeller is calculated every 3° rotation, with a time step of t=4T/480=3.378378×10-4s.Each working condition is calculated for a total of 10 weeks, and the final calculation result is obtained during weeks 7-10.Two monitoring points are positioned at the impeller's inlet and the volute's outlet, as demonstrated in Figure 3, for pressure pulsation detection.P1 and P2 denote the monitoring points on the inlet surface of the impeller, while PO1 and PO2 indicate the pump outlet monitoring points:

Pressure pulsation analysis
The analysis considers the obtained calculation results.Figures 4 and 5    From the above figure, it is apparent that the pressure varies periodically over time, with the cycle time aligned with T, and the number of rotations equivalent to the chosen number of cycles.In order to perform an in-depth analysis of the impact of pressure pulsation at various operating conditions, FFT Fourier transforms were carried out on the pressure pulsation time domain characteristics at four monitoring points under different working conditions.A waterfall diagram was produced, as illustrated by Figure 6  The frequency of the pump shaft is fn=n/60=24.67Hz,while that of the blade is calculated by multiplying the number of blades with the conversion frequency of 5fn to give 123.33Hz.The figure's x-axis represents the frequency, the y-axis represents the magnitude, and the z-axis represents the various operating points.It is evident that the maximal amplitude will arise at the axial frequency that corresponds to the leaf frequency, with each leaf frequency matching a cycle.The maximum number of peaks is five, the same as the number of blades, aligning with the law of frequency domain traits, specifically that the pinnacle value of pulsation amplitude is in tandem with the axial frequency and multiple integer values of both blade and leaf frequency.The presentation is generally low-frequency, with high-amplitude frequencies concentrated within 2 times the leaf frequency.The amplitude of highfrequency pulsation is small, as the difference in magnitude is not significant.

Radial force analysis
During the high-speed rotation of the pump, centrifugal force acts on the impeller, resulting in a radial force.Under normal flow conditions, the radial force of each impeller rotation is evenly distributed along the circumference, thus cancelling each other out and enabling the pump to operate smoothly.In order to examine the impact of the unique structure of the lower chamber of the primary pump in the small reactor on radial force, we have generated a time domain diagram of radial force and a polar coordinate diagram indicating radial force, as depicted in Figure 7 and Figure 8, respectively.Figure 8 indicates the radial force polar coordinates in the X and Y directions (a and b, respectively), and the resultant radial force polar coordinates (c).In pre-treatment, we can obtain the components FX and FY in two radial directions.However, the magnitude of the radial force is not directly detectable in CFX, necessitating its inclusion in output-control by editing the formula.The following formula is then applied to achieve the desired result: FX=(force_x@blade + force_x@hub + force_x@shroud) FY=(force_y@blade + force_y@hub + force_y@shroud)  Analysis of Figure 7 demonstrates that the change trend of the impeller when rotating for one week is essentially identical to the previous week with no discernible periodicity observed in its internal radial force.The radial force distribution of the impeller under standard working conditions differs from that which can be eliminated by conventional pumps, and it is irregular and impossible to eliminate.By analyzing the radial force in the X and Y directions, it is evident that the unique vortex formed by the lower chamber's specialized structure creates two symmetrical concentrated vortex structures on the X axis at the impeller inlet.This results in a transverse pressure difference, causing the X and Y radial forces to exhibit mirror symmetry instead of central symmetry on its axis of symmetry, which is intersected at a 90° angle.Consequently, the resultant force of the radial force does not align with that of the conventional pump.This uneven radial force distribution will significantly impact the shaft power of the pump, leading to changes in external factors such as pump efficiency.Additionally, it will negatively affect pump body vibration, thus highlighting an urgent issue that requires resolution.

Experimental validation
The layout of the test circuit adopts straight pipe inlet for testing.Figure 9 shows a photograph of the test site.Test equipment and instruments mainly include: pumps, motors, pipelines, torque meters, Under the design parameters, the numerical simulation has produced results of 16.0m whilst the test results have yielded a head of 15.5m, confirming that they meet the design requirements.The simulation value is 3.2% higher compared to the test value, with an error below 5%, further attesting to the accuracy of the numerical simulation.The numerical simulation results demonstrate an efficiency of 82.5%, whereas the test results achieve an efficiency of 81.2% which satisfies the design parameters.Notably, numerical simulation is 1.3% more efficient than the test data.An analysis error is evident as the numerical simulation disregards the roughness of the pipeline's inner wall, and neglects the loss and wall effect during transportation.The reactor coolant pump's pump body is spherical in shape, resulting in complex flow that is constrained by its structure.The inlet and outlet pressure measurements were somewhat impacted by the testing conditions, affecting measurement accuracy and position.External characteristic curve trends were similar to the design condition.All in all, numerical simulation can be used to analyse the small reactor's reactor coolant pump's internal flow.

Conclusion
In this paper, CFD numerical simulations are carried out to simulate the pressure fluctuations of various hydraulic components of small modular reactor coolant pump (SMRCP) under non-uniform inflow.The effects of non-uniform inflow on pressure fluctuations and radial force distributions in the SMRCP are analysed by focusing on the effects of non-uniform flow through a series of monitoring points in the model pump.It was found that non-uniform inflow leads to unstable pressure fluctuations in the inlet and outlet regions.This may affect the safe and stable operation of the SMRCP.

Figure 2 .
Figure 2. Grid division of the Channel-head and the RCP.
display the time domain characteristic curve under standard working conditions.Figure4illustrates the pressure pulsation of the inlet monitoring point, with Figure (a) representing the P1 time domain characteristic curve and Figure (b) reflecting the P2 time domain characteristic curve.Further, Figure 5 presents the pressure pulsation of the outlet monitoring point, whereby Figure (a) shows the PO1 time domain characteristic curve, and Figure (b) elucidates the PO2 time domain characteristic curve.(P1) time domain characteristic plot.(b)P2 time domain characteristic plot.

Figure 4 .
Time-domain characteristic curve of inlet monitoring point.(a)PO1 time domain characteristic plot.(b)PO2 time domain characteristic plot.

Figure 5 .
Time domain characteristic curve of exit monitoring point.

Figure 9 .
Figure 9. Test site photos.By testing the performance of the pump at different flow rates, the test data and the simulation data are plotted and compared in a graph, as shown in Figure 10, where Figure 10(a) is the Q-H curve and Figure 10(b) is the Q-η curve: