Experiment on Pressure Pulsation of Axial Flow Pump System with Different Runaway Head

: The runaway condition is a damage condition for pumps and turbines which can induce the wake vortex, reverse ﬂow, and severe pressure pulsation. This study aimed to research the characteristics of pressure pulsation of axial ﬂow pumps under different runaway conditions, and the runaway model test was performed with different blade angles and heads. Moreover, four pressure sensors were uniformly arranged at the impeller inlet section to eliminate the random error. The time domain and frequency domain analysis were the main methods to obtain the change regulations. Results showed that the pressure pulsation under the runaway condition are mainly inﬂuenced by the rotation frequency, blade passing frequency, and wake vortex frequency. The dimensionless pressure pulsation coefﬁcient of rotation frequency and wake vortex frequency increased obviously with the runaway head increasing, but changed little with different blade angles. In addition, the dimensionless pressure coefﬁcient of wake vortex frequency of the sensors around the impeller inlet section differed a lot, which means that the wake vortex core is not in center of the rotation axis. The average dimensionless pressure pulsation coefﬁcient of wake vortex frequency is higher than that of rotation frequency with the same runaway head, owing to the severer wake vortex.


Introduction
The runaway condition of pumps is an extreme turbine condition in which the flow and rotation direction are the same with those of turbine condition. When a pump or turbine suddenly loses power by incident, the water in the pipe system will flow back and the impeller will rotate in the opposite direction [1,2]. Under the influence of the water level difference between the upstream and the downstream, the rotation speed of the impeller continues to speed up until the maximum value, called runaway speed. Under the runaway condition, the centrifugal force in the impeller and the vortex rope in the inlet pipe are produced inevitably [3], which will cause harm to the rotation device and constraint components [4]. In addition, the unstable flow pattern will generate severe pressure pulsation, which may damage the pump device [5]. Therefore, studying the runaway condition is of great importance for the safety of pumps or turbines.
Model test and numerical simulation are the main methods to study hydraulic machinery during transient processes. For credibility and authenticity, some scholars studied the runaway condition through the model test. Fortin et al. [6,7] measured the pressure on the impeller blade surface during the runaway process to relate the pressure and the vortex rope. Trivedi et al. [8,9] compared the pressure pulsation frequency with different blade angles during the runaway process. The high amplitude of the pressure pulsation may decrease the service life of the impeller blade. Zhang et al. [10] found that pressure pulsations were mainly influenced by the guide vane opening under the turbine mode. With the development of computer technology, the computational fluid dynamics (CFD) is widely used in fluid machinery simulation. Trivedi et al. [11] adopted the scale-adaptive simulation (SAS) shear stress transport (SST) model to study the runaway condition. The simulation results were verified with the model test. Hosseinimanesh et al. [12] simulated the runaway process with different Wicket gate openings. Zhang et al. [13] researched the S-shaped characteristics of pump-turbines with different rotational inertia, which showed that a large rotational inertia is easier than a small one to induce abrupt increases in runner radial forces. Yang et al. [14] compared the flow pattern and pressure pulsation of the pump with different specific speeds, indicating that the lower specific speed turbines more easily enter the reverse pump mode. Zhang et al. [15,16] considered the influence of water compressibility on the transient process to combine the one-dimensional (1D) water conveyance system and three-dimensional (3D) pump-turbine.
When it comes to the selection of the turbulence model and grid number during the simulation, different simulation situations and research goals result in different choices. For guiding the project in reality, the researchers prefer the standard k-ε, Realized k-ε, and RNG k-ε turbulence models with a lower grid number and more robust simulation [12,17,18]. For studying the intricate flow pattern in the pipe, the scholars tend to adopt the SST k-ω and SAS-SST turbulence models, which can simulate the flow near the wall accurately [11,19]. As for hydraulic machinery with long-distance water pipelines, the one-dimensional method of characteristics (MOC) is an appropriate method for runaway simulation; of course, there is no need for the turbulence model and grid generation [20,21].
The external characteristics of different pump types in the runaway situation differ significantly. As for the centrifugal pump with high head, the runaway oscillation process is often accompanied by an S region, which means the rotation speed and flow rate cannot converge to a stable value [16,22,23]. When comes to the axial flow pump with low head, the impeller torque will converge to zero during the runaway process, and the stable rotation speed contributes to the vortex rope [6,7]. Since the runaway condition is a complex state, which involves unsteady rotation speed, reverse discharge, vortices evolution, and complex flow patterns, and scholars study the unstable state from different aspects. The pressure fluctuation amplitude under runaway process is widely researched, because the rotation speed is mainly influenced by the torque, and torque accounts from the integral of blade-surface pressure around the axis [24,25]. Besides, the vortex in the pipe is also the focus, which results in the entropy generation [22,26,27].
The objective of this paper was to investigate the influence of runaway head on the pressure pulsation. Although the research of pressure fluctuation is common during the runaway simulation, there are still few studies using the method of model test. The remainder of this paper is organized as follows. A brief experimental setup of the model test rig and monitoring points are introduced in Section 2. Section 3 mainly contains the time domain and frequency domain analysis of the pressure pulsation. Finally, Section 4 summarizes this work and details the potential research issues.

Experiment Setup
In this research, the pressure fluctuation of an axial flow pump was studied under different runaway conditions. The main characteristic parameters of the prototype pump and model pump are displayed in Table 1. The model pump tests were carried out on the closed hydraulic machinery test rig at the Jiangsu Aerospace Hydraulic Equipment Co., Ltd., Yangzhou, China. Additionally, the test rig meets the requirement of International Standard Organization (ISO) 9906. Figure 1 presents the model test rig for the axial flow pump with low head, including low pressure tank, inlet conduit, impeller, guide vanes, outlet conduit, high-pressure tank, and electric motor. During the runaway condition, the flow pattern fluctuates violently in the inlet conduit due to the backflow and the impeller rotating in the opposite direction. In order to research the characteristics of pressure fluctu-Processes 2021, 9, 1597 3 of 11 ation in the inlet conduit, the data acquisition system with 10 channels produced by the HELM company was selected for pressure-signal sampling. In addition, the monitoring points (MP) of the pressure transducers (EM96369M series) are shown in Figure 2, i.e., the MP1-4 were uniformly arranged at the interface of the impeller and the inlet conduit; MP5 and MP6 were fixed at the directly above and below the inlet conduit, respectively. The main specifications of the model test rig and the pressure sensor applied for pressure pulsation are presented in Table 2. All model tests were conducted in conformity with the International Electrotechnical Commission (IEC) Standard 60193. pump with low head, including low pressure tank, inlet conduit, impeller, guide vanes outlet conduit, high-pressure tank, and electric motor. During the runaway condition, th flow pattern fluctuates violently in the inlet conduit due to the backflow and the impelle rotating in the opposite direction. In order to research the characteristics of pressure fluc tuation in the inlet conduit, the data acquisition system with 10 channels produced by th HELM company was selected for pressure-signal sampling. In addition, the monitorin points (MP) of the pressure transducers (EM96369M series) are shown in Figure 2, i.e., th MP1-4 were uniformly arranged at the interface of the impeller and the inlet conduit; MP and MP6 were fixed at the directly above and below the inlet conduit, respectively. Th main specifications of the model test rig and the pressure sensor applied for pressure pu sation are presented in Table 2. All model tests were conducted in conformity with th International Electrotechnical Commission (IEC) Standard 60193.   tuation in the inlet conduit, the data acquisition system with 10 channels produce HELM company was selected for pressure-signal sampling. In addition, the mo points (MP) of the pressure transducers (EM96369M series) are shown in Figure 2 MP1-4 were uniformly arranged at the interface of the impeller and the inlet cond and MP6 were fixed at the directly above and below the inlet conduit, respectiv main specifications of the model test rig and the pressure sensor applied for press sation are presented in Table 2. All model tests were conducted in conformity International Electrotechnical Commission (IEC) Standard 60193.    ±0.02

Runaway Curves and Working Conditions
The runaway rotation speed curves at different blade angles are displayed in Figure 3. On the one hand, the rotation speed increased significantly with the runaway head, because the high runaway head brings about a large discharge, increasing the rotation speed. On the other hand, the rotation speed decreased slightly with the blade angles, which indicates the influence of the blade angle on the flow pattern. In order to compare the characteristics of pressure fluctuation under different runaway conditions, four different water heads and four different blade angles were adopted when sampling the pressure signal during the runaway process. Namely, the test runaway head contains 0.65 m, 1.28 m, 2.05 mm and 3.06 m; meanwhile, the test blade angle includes −4 • , −2 • , 0 • , and +2 • . The characteristic parameters at α = +2 • with different runaway head are shown in Table 3, and the equations of rotation frequency, blade passing frequency (BPF), and impeller rotation cycle time are as follows:

Unsteady Pressure Pulsation Analysis
In order to eliminate the influence of the runaway head on the amplitude of pressure pulsation, the dimensionless pressure coefficient Cp [28][29][30] is introduced as follows: pp  The runaway speed of the axial flow pump under different water heads.

Unsteady Pressure Pulsation Analysis
In order to eliminate the influence of the runaway head on the amplitude of pressure pulsation, the dimensionless pressure coefficient C p [28][29][30] is introduced as follows: Since the rotation cycle time varies with the rotation speed, the number of impeller rotation cycles was designed as follows: where t is the signal time [s]. The time domain pulsation coefficient curves of at α = +2 • with different runaway head are presented in Figure 4. Figure 4a shows the pulsation coefficient curves at H = 0.65 m. Figure 4b shows the pulsation coefficient curves at H = 1.28 m. Figure 4c shows the pulsation coefficient curves at H = 2.05 m. Figure  As for the time domain pulsation characteristics of MP5 and MP6, the number of signal pulses in six impeller rotation cycles and the trends in pressure changes were different from those among MP1-4. Obviously, the main factors affecting the characteristics of pressure fluctuation were different. The pulsation coefficient curves of the frequency domain at α = +2° with different runaway heads are presented in Figure 5. Figure 5a shows the pulsation coefficient curves at H = 0.65 m. Figure 5b shows the pulsation coefficient curves at H = 1.28 m. Figure 5c shows the pulsation coefficient curves at H = 2.05 m. Figure 5d shows the pulsation coefficient curves at H = 3.06 m. The rotation frequency times (f/fn) are introduced in order to uniform rotation frequency. Without considering the low frequency, i.e., f is less than fn, the characteristics of frequency domain pressure pulsation among MP1-4 were under the influence of rotation frequency. In Figure 5a, it is represented that the main frequency of pressure pulsation among MP1-4 was 5fn = 45.46 Hz, i.e., the blade passing frequency fBPF, and the sub-frequency was fn, 2fn and 3fn. Additionally, the main frequency fBPF among MP1-4 explains that there are five obvious signal pulses in an impeller rotation cycle (Figure 4a). As for the pressure spectra among MP1-4 with H = 1.28 m (Figure 5b), the 2fn is the domain among high-frequency harmonics of fn, whereas fn and fBPF are the secondary. With the situation of H = 3.06 m (Figure 5d), the main frequency was fn, and the sub-frequency was 2fn and fBPF. Moreover, the main frequency fn among MP1-4 makes it clear that there exists one obvious signal pulses per impeller rotation cycle (Figure 4d). In a word, without considering the super low frequency (i.e., f/fn is less than 1), the main frequency of pressure pulsation among MP1-4 transforms from fBPF to fn with the increase of the runaway head, which explains evolution of the number of signal pulses in per impeller rotation cycle. As for the pressure spectra characteristics of MP5 and MP6 (Figure 5), the main frequency is never fn or the high-frequency harmonics of fn under different conditions,  The pulsation coefficient curves of the frequency domain at α = +2 • with different runaway heads are presented in Figure 5. Figure 5a shows the pulsation coefficient curves at H = 0.65 m. Figure 5b shows the pulsation coefficient curves at H = 1.28 m. Figure 5c shows the pulsation coefficient curves at H = 2.05 m. Figure 5d shows the pulsation coefficient curves at H = 3.06 m. The rotation frequency times (f /f n ) are introduced in order to uniform rotation frequency. Without considering the low frequency, i.e., f is less than f n , the characteristics of frequency domain pressure pulsation among MP1-4 were under the influence of rotation frequency. In Figure 5a, it is represented that the main frequency of pressure pulsation among MP1-4 was 5f n = 45.46 Hz, i.e., the blade passing frequency f BPF , and the sub-frequency was f n , 2f n and 3f n . Additionally, the main frequency f BPF among MP1-4 explains that there are five obvious signal pulses in an impeller rotation cycle ( Figure 4a). As for the pressure spectra among MP1-4 with H = 1.28 m (Figure 5b), the 2f n is the domain among high-frequency harmonics of f n , whereas f n and f BPF are the secondary. With the situation of H = 3.06 m (Figure 5d), the main frequency was f n , and the sub-frequency was 2f n and f BPF . Moreover, the main frequency f n among MP1-4 makes it clear that there exists one obvious signal pulses per impeller rotation cycle (Figure 4d). In a word, without considering the super low frequency (i.e., f /f n is less than 1), the main frequency of pressure pulsation among MP1-4 transforms from f BPF to f n with the increase of the runaway head, which explains evolution of the number of signal pulses in per impeller rotation cycle. As for the pressure spectra characteristics of MP5 and MP6 (Figure 5), the main frequency is never f n or the high-frequency harmonics of f n under different conditions, which leads to the different signal pulses and pressure phase from those among MP1-4 ( Figure 4). The Cp values of fn and fBPF among MP1-6 at α = +2° with different runaway heads are displayed in Figure 6. It can be observed from Figure 6a that the Cp value of fn increased obviously with the runaway head, which indicates that the influence of the rotation speed is enhanced with the large runaway head. Additionally, the Cp value among MP1-4 is similar to each other, owing to the ring column arrangement. In addition, the Cp value of MP5 is slightly lower than that of MP4 with the same runaway head. However, the Cp value of MP6 is close to zero for the location away from the rotation axial.
Considering the Cp value of fBPF in Figure 6b, the low change of the Cp value is contrary to that of fn. The Cp value of fBPF decreased slightly with the runaway head, which means the effect of the rotor-stator interaction (RSI) [31,32] was weakened. Besides, the Cp value of MP5 and MP6 was close to zero, which indicates that the RSI was weakened with distance between MP and the impeller. Under normal pump and turbine conditions, the severe RSI always contributes to the high-frequency harmonics of fBPF, namely 2fBPF and 3fBPF. However, the values of 2fBPF and 3fBPF were close to zero among MP1-6 under the runaway condition. This means the RSI is obviously weakened during the runaway process, and thus such amplitude of the high-frequency harmonics of fBPF can be ignored. The C p values of f n and f BPF among MP1-6 at α = +2 • with different runaway heads are displayed in Figure 6. It can be observed from Figure 6a that the C p value of f n increased obviously with the runaway head, which indicates that the influence of the rotation speed is enhanced with the large runaway head. Additionally, the C p value among MP1-4 is similar to each other, owing to the ring column arrangement. In addition, the C p value of MP5 is slightly lower than that of MP4 with the same runaway head. However, the C p value of MP6 is close to zero for the location away from the rotation axial. According to Ref. [33], the low-frequency component of the pressure pulsation a counts from the wake vortex, and the empirical formula is as follows: Considering the C p value of f BPF in Figure 6b, the low change of the C p value is contrary to that of f n . The C p value of f BPF decreased slightly with the runaway head, which means the effect of the rotor-stator interaction (RSI) [31,32] was weakened. Besides, the C p value of MP5 and MP6 was close to zero, which indicates that the RSI was weakened with distance between MP and the impeller. Under normal pump and turbine conditions, the severe RSI always contributes to the high-frequency harmonics of f BPF , namely 2f BPF and 3f BPF . However, the values of 2f BPF and 3f BPF were close to zero among MP1-6 under the runaway condition. This means the RSI is obviously weakened during the runaway process, and thus such amplitude of the high-frequency harmonics of f BPF can be ignored.
According to Ref. [33], the low-frequency component of the pressure pulsation accounts from the wake vortex, and the empirical formula is as follows: where f 1 is the wake vortex frequency [Hz], K is the empirical parameter, and the value generally ranges from three to four, but K is about 2.9 under the runaway condition of our model.
When the frequency f being less than f n is considered in Figure 5, the wake vortex rope is the main factor leading to the low frequency. In Figure 5d, the wake vortex frequency f 1 among MP1-6 is the same value, i.e., 7.03 Hz, and the value K under this condition is equal to 2.88. As for the other runaway head (Figure 5a-c), the value K was equal to 2.84, 2.85, and 2.86. Although the value K seemingly increased slightly with the runaway head, the judgement is also under the restriction of the measurement accuracy.
The C p value of f 1 among MP1-6 with different runaway heads are displayed in Figure 7. The C p value of f 1 increased obviously when the runaway head transformed from H = 0.65 m to H = 1.28 m, but increased slightly when the runaway head was above H = 2.05 m. The different C p value of f 1 accounts from the different location of MP1-6 ( Figure 2). Since the MP2 and MP3 are symmetrically distributed at the two sides of the model pump, the C p value of f 1 between MP2 and MP3 were similar. The same reason leads to the similar C p value of f 1 between MP1 and MP4. However, the C p value of f 1 of MP2 was rather higher than that of MP1, which means the wake vortex core is away from the center of the rotation axis in elbow-type conduit. To be more specific, the rotation core of wake vortex in the elbow-type conduit was close to MP2 away from MP1. As for MP5, the C p value of f 1 with H above 2.05 m was similar to that of MP2, meaning the influence degree of the wake vortex is similar. Besides, the C p value of f 1 of MP6 was lower than those of MP1-5 due to the remote location. In order to compare the Cp value at the interface of the impeller and the inlet conduit (i.e., MP1~4) at different blade angles, the average pressure coefficient In order to compare the C p value at the interface of the impeller and the inlet conduit (i.e., MP1~4) at different blade angles, the average pressure coefficient C * p is introduced as follows: where m is the number of MP to be around the impeller, here m = 4, and C pi is the pressure coefficient of MPi. The C * p values under different runaway conditions are displayed in Figure 8. It is observed from Figure 8a that the C * p value of f n increased obviously with the runaway head. However, the C * p of f n changed inconspicuously at different blade angles with the same runaway head, which may account from the randomness of the model test and the small difference of rotation speed at different blades. As for the C * p value of f BPF in Figure 8b, the C * p value of f BPF decreased slightly with the runaway head, which means the RSI was weakened under runaway condition. In addition, the C * p value of f BPF decreased slightly with the blade angle, owing to the higher rotation speed at smaller blade angles. In Figure 8c, it is shown that the change ruler of the C * p value of f 1 was the same as that of f n , which indicates the wake vortex is related to the rotation impeller. Moreover, the C * p value of f 1 was higher than that of f n with the same runaway head, which shows that the pressure pulsation degree caused by the wake vortex is higher.

Conclusions and Expectation
In this paper, the characteristics of pressure pulsation with different blade angles and different runaway head were tested and researched. To deeply analyze the pressure pulsation coefficient Cp at different locations, MP1-4 were uniformly arranged at the impeller inlet section and, additionally, MP5 and MP6 were placed above and below the inlet conduit respectively. The time domain and frequency domain analysis were the main methods to obtain the change regulations. The main conclusions are summarized as follows:

Conclusions and Expectation
In this paper, the characteristics of pressure pulsation with different blade angles and different runaway head were tested and researched. To deeply analyze the pressure pulsation coefficient C p at different locations, MP1-4 were uniformly arranged at the impeller inlet section and, additionally, MP5 and MP6 were placed above and below the inlet conduit respectively. The time domain and frequency domain analysis were the main methods to obtain the change regulations. The main conclusions are summarized as follows: (1) The C p value of the rotation frequency f n among MP1-4 increased obviously with the runaway head, but changed slightly at different blade angles with the same runaway head. Besides, the C p values of f n of MP5 and MP6 were lower than those among MP1-4, which means the influence range of the pressure pulsation caused by the rotation impeller is limited.
(2) Since the rotor-stator interaction is weakened during the runaway process, the C p value of the blade passing frequency f BPF changed little with the runaway head, and the high-frequency harmonics of f BPF are close to zero.
(3) Under the runaway condition, the wake vortex was easily induced in the inlet conduit. Moreover, the wake vortex frequency f 1 is related to f n (i.e., f n /f 1 is about 2.9 at α = +2 • ). However, the C * p value of f 1 was higher than that of f n with the same runaway head, which shows that the pressure pulsation degree caused by the wake vortex is higher.
(4) The C p value of f 1 among MP1-4 differed a lot, which means the wake vortex core is not in the center of the rotation axis.
(5) More deep research about the pressure pulsation under runaway conditions with different pump models can be carried out as the next step, and the characteristics of different multiples of rotation frequency should be different.