Pressure Fluctuation Characteristics Analysis of Centrifugal Pump as Turbine in Its Start-Up Process

: In order to study pressure ﬂuctuation characteristics of a centrifugal pump as turbine (PAT) in its start-up process, Fluent was used to do numerical simulation of the PAT start-up process. Time and frequency domain analyses were performed on the data acquired at different positions and different heads. The results show that a large number of low-pressure areas and strong vortexes are formed within the impeller at the initial time of start-up. With the increase in rotating speed, the vortexes rapidly decrease and are concentrated on the blade non-working face. The pressure ﬂuctuation amplitude is the maximum at the start-up initial instant; with increase in rotating speed, it reduces rapidly at the volute spiral part. The pressure ﬂuctuation number within one impeller rotation cycle is consistent with blade number, and the dominant frequency of pressure ﬂuctuation is 6 times the impeller rotational frequency. The dominant frequency amplitude of radial pressure ﬂuctuation increases with decrease in radial size in the volute. The pressure ﬂuctuation in the impeller is much more intensive than that in the volute, and its maximum dominant frequency amplitude occurs in the middle of the impeller towards the inner edge. With the increase in head, the number of pressure ﬂuctuation and the amplitude of dominant frequency increase at the same time during the start-up process.


Introduction
A centrifugal pump as turbine (PAT) is more and more widely used in hydrocracking, wastewater treatment, seawater desalination and so on. The development of PAT energy recovery technology is of great significance to energy saving and emission reduction and achieving sustainable green development [1][2][3]. Performance parameters such as rotating speed, flow rate and pressure during the PAT start-up process change dramatically in a short time, and the internal fluid is in an unstable transient flow state, which can easily cause huge pressure fluctuation and shock [4]. Generating vibration and noise in the start-up process can result in damage to the PAT itself or failure of the operation normally, so it is particularly important to predict and prevent the pressure fluctuation during PAT start-up.
Some scholars have proposed PAT performance prediction methods under stable working conditions through theoretical analysis, numerical simulation and experimental tests. The different conversion formulas of flow rate and head between pump and PAT were derived and provided reference for performance prediction and selection design of PAT [5][6][7][8]. There were some papers introducing pressure fluctuation characteristics of a centrifugal pump, mixed-flow pump, axial flow pump and PAT under stable working conditions. Yao et al. proposed that the fluctuation behavior at the blade-passing frequency was the most prominent near the volute tongue zone and the pressure waves propagated in both the radial and circumferential directions [9]. Huang et al. indicated that the root cause of low-frequency pressure fluctuation was the eddies generated due to streamline distortion where ΣM i is the resultant torque on the rotor, J is the rotational inertia of the rotor, ω is the angular speed of the rotor, M t is the fluid flow torque on the rotor, M l is the load torque on the rotor, M f is the frictional resistance torque on the rotor, ρ is the fluid density, g is the acceleration of gravity, H is the head, Q is the flow rate, η is the efficiency. Formulas (2) and (3) are substituted in Formula (1), and Formula (4) is derived as follows.
Actuators 2022, 11, 132 3 of 16 where N l is the load consumption power, N f is the frictional resistance loss power. When the inlet pressure and outlet pressure are both stable, the H is constant. For fixed valve opening, the η is approximately constant during transient process. The formula of relationship between angular speed and time during PAT start-up is obtained by integrating Equation (4):

Calculation Method
The interface between PAT impeller and volute or outlet pipe is definite, that is, there are two overlapping surfaces at the interface. The Fluent sliding mesh model allows us to create a problem where different regions move relative to each other, so the sliding mesh can be used instead of dynamic mesh model for transient calculation. On the basis of ensuring better mesh quality, sliding mesh can avoid negative mesh and save calculation time [26]. The UDF program of PAT passive rotating is written from the rotation equation of rotor and compiled in Fluent, and the torque on the blade is calculated by the Compute_Force_And_Moment function, and the angular speed of rotator is obtained by the rotation equation [25]. The angular speed is transferred into the sliding mesh flow field solver by macro DEFINE_ZONE_MOTION, and the impeller domain mesh is being adjusted dynamically. Starting from ω 0 = 0, the angular speed ω n+1 is iterated for each time step. As the time step advances, the resultant torque of the impeller gradually decreases, and the rotating speed gradually approaches the rated speed, so as to complete the start-up process. The simulation process of solving the PAT start-up process is shown in Figure 1.
tionship between angular speed and time during PAT start-up is obtained b Equation (4):

Calculation Method
The interface between PAT impeller and volute or outlet pipe is def there are two overlapping surfaces at the interface. The Fluent sliding me lows us to create a problem where different regions move relative to each sliding mesh can be used instead of dynamic mesh model for transient cal the basis of ensuring better mesh quality, sliding mesh can avoid negative m calculation time [26]. The UDF program of PAT passive rotating is written fr tion equation of rotor and compiled in Fluent, and the torque on the blade by the Compute_Force_And_Moment function, and the angular speed of r tained by the rotation equation [25]. The angular speed is transferred int mesh flow field solver by macro DEFINE_ZONE_MOTION, and the imp mesh is being adjusted dynamically. Starting from ω0 = 0, the angular spee ated for each time step. As the time step advances, the resultant torque of gradually decreases, and the rotating speed gradually approaches the rated to complete the start-up process. The simulation process of solving the P process is shown in Figure 1.

Computational Model
The IS80-50-315 centrifugal pump as turbine (PAT) is taken as the research object. Its main design parameters are: design rate of flow Q = 50 m 3 /h, design head H = 50 m, rated speed n = 1450 r/min and impeller rotation frequency f n = 24.17 Hz. Its main structural parameters are shown in Table 1. The IS100-65-250 centrifugal pump is selected as the energy dissipation pump, and its rated power is 2.05 kW. The output power of PAT matches the energy dissipation pump well, and rotational inertia of the whole rotor system is 0.35 kg·m 2 .  Figure 2 shows the main strcture and pressure monitoring points of PAT. In order to monitor the pressure fluctuation at each position in the PAT, a series of monitoring points are set up and represent fluid particles at different locations in the PAT. The points 1, 2, 3, 4, 5, 6, 7 and 8 in the volute area are monitored, and the points 9, 10 and 11 in the impeller area are monitored. parameters are shown in Table 1. The IS100-65-250 centrifugal pump is selected energy dissipation pump, and its rated power is 2.05 kW. The output power o matches the energy dissipation pump well, and rotational inertia of the whole rot tem is 0.35 kg·m 2 .  Figure 2 shows the main strcture and pressure monitoring points of PAT. In to monitor the pressure fluctuation at each position in the PAT, a series of mon points are set up and represent fluid particles at different locations in the PA points 1, 2, 3, 4, 5, 6, 7 and 8 in the volute area are monitored, and the points 9, 10 in the impeller area are monitored.  Figure 3 shows the computational domain and meshing of PAT flow field. The flo calculation domain of the PAT includes three parts: the volute, the impeller and th tube. When the pump is used as PAT, the outlet of pump is the inlet of PAT, and let of pump is the outlet of PAT. The fluid enters into the volute at the inlet of PA impacts the impeller to rotate. The entire flow domains are generated using PT software. The hexahedron structured grids are generated with ICEM CFD [26]. M finement of near-wall and blade head regions is performed, and most of y+ on the less than 50. Different grid scales are used to perform the grid independence a corresponding to 7.16 × 10 5 , 1.14 × 10 6 , 1.90 × 10 6 , 2.82 × 10 6 and 3.66 × 10 6 nodes. As  Figure 3 shows the computational domain and meshing of PAT flow field. The flow field calculation domain of the PAT includes three parts: the volute, the impeller and the draft tube. When the pump is used as PAT, the outlet of pump is the inlet of PAT, and the inlet of pump is the outlet of PAT. The fluid enters into the volute at the inlet of PAT and impacts the impeller to rotate. The entire flow domains are generated using PTC Creo software. The hexahedron structured grids are generated with ICEM CFD [26]. Mesh refinement of near-wall and blade head regions is performed, and most of y+ on the wall is less than 50. Different grid scales are used to perform the grid independence analysis corresponding to 7.16 × 10 5 , 1.14 × 10 6 , 1.90 × 10 6 , 2.82 × 10 6 and 3.66 × 10 6 nodes. As shown in Figure 4, when the number of grids reaches 1.90 × 10 6 , the relative change in efficiency and head is less than 1.5%. Therefore, 1.90 × 10 6 is selected as the number of grids for all simulations in this study. in Figure 4, when the number of grids reaches 1.90 × 10 6 , the relative change in efficiency and head is less than 1.5%. Therefore, 1.90 × 10 6 is selected as the number of grids for all simulations in this study.

Boundary Condition
Fluent is used to simulate the start-up process of PAT. RNG k-ε turbulence model is selected. The coupling mode of pressure and velocity is SIMPLEC. The solid wall is non-slip boundary condition, and the standard wall function is used near the wall. The incoming flow pressure is approximately considered as constant during start-up process, and the inlet and outlet boundary conditions are set by pressure. The inlet pressure is consistent with that under steady condition. To prevent the hydraulic turbine from getting cavitated, the 0.4-0.6 MPa pressure is normally reserved at the outlet of PAT; therefore, the outlet pressure is set at 0.5 MPa [27]. The independence of time step is verified by comparing the rotating speed at the same time in the start-up process. When the time step is 0.0005 s, it basically meets the independence requirement. Therefore, 0.0005 s is selected as the time step of transient calculation in this study. In the calculation process, the residual convergence target is set at 10 −4 , and the maximum iteration number of each time step is 20. The steady calculation results under design conditions are used as the initial flow field. Starting from the stationary state, when the resultant torque of rotor is less in Figure 4, when the number of grids reaches 1.90 × 10 6 , the relative change in efficiency and head is less than 1.5%. Therefore, 1.90 × 10 6 is selected as the number of grids for all simulations in this study.

Boundary Condition
Fluent is used to simulate the start-up process of PAT. RNG k-ε turbulence model is selected. The coupling mode of pressure and velocity is SIMPLEC. The solid wall is non-slip boundary condition, and the standard wall function is used near the wall. The incoming flow pressure is approximately considered as constant during start-up process, and the inlet and outlet boundary conditions are set by pressure. The inlet pressure is consistent with that under steady condition. To prevent the hydraulic turbine from getting cavitated, the 0.4-0.6 MPa pressure is normally reserved at the outlet of PAT; therefore, the outlet pressure is set at 0.5 MPa [27]. The independence of time step is verified by comparing the rotating speed at the same time in the start-up process. When the time step is 0.0005 s, it basically meets the independence requirement. Therefore, 0.0005 s is selected as the time step of transient calculation in this study. In the calculation process, the residual convergence target is set at 10 −4 , and the maximum iteration number of each time step is 20. The steady calculation results under design conditions are used as the initial flow field. Starting from the stationary state, when the resultant torque of rotor is less

Boundary Condition
Fluent is used to simulate the start-up process of PAT. RNG k-ε turbulence model is selected. The coupling mode of pressure and velocity is SIMPLEC. The solid wall is non-slip boundary condition, and the standard wall function is used near the wall. The incoming flow pressure is approximately considered as constant during start-up process, and the inlet and outlet boundary conditions are set by pressure. The inlet pressure is consistent with that under steady condition. To prevent the hydraulic turbine from getting cavitated, the 0.4-0.6 MPa pressure is normally reserved at the outlet of PAT; therefore, the outlet pressure is set at 0.5 MPa [27]. The independence of time step is verified by comparing the rotating speed at the same time in the start-up process. When the time step is 0.0005 s, it basically meets the independence requirement. Therefore, 0.0005 s is selected as the time step of transient calculation in this study. In the calculation process, the residual convergence target is set at 10 −4 , and the maximum iteration number of each time step is 20. The steady calculation results under design conditions are used as the initial flow field. Starting from the stationary state, when the resultant torque of rotor is less than the calculation residual, the rotating speed meanwhile reaches the rated speed, which indicates the transient calculation of the start-up process is completed.

Experimental Verification
The PAT performance test experimental device is mainly composed of feed pump, PAT, consume pump, water tank, circulation pipeline system and test system. The NC-3 torque meter with measurement accuracy of 0.2 grade is set between PAT and consume pump to measure speed and torque. The LWGY-100 turbine flowmeter with measurement accuracy of 0.5 grade and rated pressure of 1.6 MPa is set in the inlet pipeline of PAT to measure the inlet flow of PAT [28]. The WT-151 pressure transmitter with measurement accuracy of 0.2 grade is set in the inlet and outlet pipeline of PAT to measure the inlet and outlet pressure. The PAT test principle and test rig are shown in Figures 5 and 6. than the calculation residual, the rotating speed meanwhile reaches the rated which indicates the transient calculation of the start-up process is completed.

Experimental Verification
The PAT performance test experimental device is mainly composed of feed PAT, consume pump, water tank, circulation pipeline system and test system. Th torque meter with measurement accuracy of 0.2 grade is set between PAT and co pump to measure speed and torque. The LWGY-100 turbine flowmeter with me ment accuracy of 0.5 grade and rated pressure of 1.6 MPa is set in the inlet pipe PAT to measure the inlet flow of PAT [28]. The WT-151 pressure transmitter with urement accuracy of 0.2 grade is set in the inlet and outlet pipeline of PAT to meas inlet and outlet pressure. The PAT test principle and test rig are shown in Figures 5  The head and efficiency of PAT at stable operation under different flow ra tested and compared with the simulation results as shown in Figure 7. The torq rotating speed signals are collected and processed once every 0.1 s in the start-up p and the rotating speeds acquired by testing are compared with those by simula shown in Figure 8. It can be seen from the diagrams that the simulation results ar cally consistent with those of experiments. The hydraulic pulsation characteristics turbine are indirectly verified by monitoring the vibration characteristics of the PA FLUKE F802 vibrometer with the accuracy of ±5% is used to measure the hori vertical and axial vibration velocities by setting test points at the base of the PAT body, the middle suspension and the bearing box position, respectively. The roo than the calculation residual, the rotating speed meanwhile reaches the rated speed, which indicates the transient calculation of the start-up process is completed.

Experimental Verification
The PAT performance test experimental device is mainly composed of feed pump, PAT, consume pump, water tank, circulation pipeline system and test system. The NC-3 torque meter with measurement accuracy of 0.2 grade is set between PAT and consume pump to measure speed and torque. The LWGY-100 turbine flowmeter with measurement accuracy of 0.5 grade and rated pressure of 1.6 MPa is set in the inlet pipeline of PAT to measure the inlet flow of PAT [28]. The WT-151 pressure transmitter with measurement accuracy of 0.2 grade is set in the inlet and outlet pipeline of PAT to measure the inlet and outlet pressure. The PAT test principle and test rig are shown in Figures 5 and 6.  The head and efficiency of PAT at stable operation under different flow rates are tested and compared with the simulation results as shown in Figure 7. The torque and rotating speed signals are collected and processed once every 0.1 s in the start-up process, and the rotating speeds acquired by testing are compared with those by simulation as shown in Figure 8. It can be seen from the diagrams that the simulation results are basically consistent with those of experiments. The hydraulic pulsation characteristics of the turbine are indirectly verified by monitoring the vibration characteristics of the PAT. The FLUKE F802 vibrometer with the accuracy of ±5% is used to measure the horizontal, vertical and axial vibration velocities by setting test points at the base of the PAT pump body, the middle suspension and the bearing box position, respectively. The root mean The head and efficiency of PAT at stable operation under different flow rates are tested and compared with the simulation results as shown in Figure 7. The torque and rotating speed signals are collected and processed once every 0.1 s in the start-up process, and the rotating speeds acquired by testing are compared with those by simulation as shown in Figure 8. It can be seen from the diagrams that the simulation results are basically consistent with those of experiments. The hydraulic pulsation characteristics of the turbine are indirectly verified by monitoring the vibration characteristics of the PAT. The FLUKE F802 vibrometer with the accuracy of ±5% is used to measure the horizontal, vertical and axial vibration velocities by setting test points at the base of the PAT pump body, the middle suspension and the bearing box position, respectively. The root mean square of vibration velocity (v u ) directly reflects the strength of vibration, which is defined as follows: where v(t) is the vibration velocity related to time, T is the sampling time, and v u is the root mean square of vibration velocity. The root mean square of vibration velocity for high speed pump is required to v u ≤ 3.0 mm/s according to API610 [28]. The test results meet the allowable range of API610, which shows that the analysis of pressure fluctuation for PAT is reliable in this study.
Actuators 2022, 11, x FOR PEER REVIEW square of vibration velocity (vu) directly reflects the strength of vibration, whic fined as follows: where v(t) is the vibration velocity related to time, T is the sampling time, and root mean square of vibration velocity. The root mean square of vibration velo high speed pump is required to vu ≤ 3.0 mm/s according to API610 [28]. The tes meet the allowable range of API610, which shows that the analysis of pressure tion for PAT is reliable in this study.

Evolution Analysis of Internal Flow Field
The pressure distributions of the vertical axis plane changing over time wer tigated in order to explore the evolution law of the internal flow field during start-up. Figure 9 shows the pressure distributions of the axial vertical plane du start-up process. It can be observed from Figure 9 that there are a large nu Actuators 2022, 11, x FOR PEER REVIEW square of vibration velocity (vu) directly reflects the strength of vibration, whic fined as follows: where v(t) is the vibration velocity related to time, T is the sampling time, and root mean square of vibration velocity. The root mean square of vibration velo high speed pump is required to vu ≤ 3.0 mm/s according to API610 [28]. The tes meet the allowable range of API610, which shows that the analysis of pressure tion for PAT is reliable in this study.

Evolution Analysis of Internal Flow Field
The pressure distributions of the vertical axis plane changing over time wer tigated in order to explore the evolution law of the internal flow field during start-up. Figure 9 shows the pressure distributions of the axial vertical plane du start-up process. It can be observed from Figure 9 that there are a large nu

Evolution Analysis of Internal Flow Field
The pressure distributions of the vertical axis plane changing over time were investigated in order to explore the evolution law of the internal flow field during the PAT start-up. Figure 9 shows the pressure distributions of the axial vertical plane during the start-up process. It can be observed from Figure 9 that there are a large number of low-pressure areas in the impeller channel at t = 0.5 s. With the increase in rotating speed, the low-pressure areas in the impeller gradually decrease. After t = 1.5 s, the rotating speed tends to be stable and reaches the rated speed, the pressure in the volute decreases gradually along the volute channel, and it has gradient distribution in the impeller. The low-pressure areas are mainly concentrated in the inner edge of the impeller.  Figure 11 shows the time domain diagrams of pressure fluctuation at volute radial location monitoring points 2, 3 and 4 during the start-up process (t = 0~2.5 s), the first circle of impeller rotation (t = 0~0.255 s) and a circle of impeller rotation after stable speed (t = 2.458~2.5 s), respectively. Figure 12 shows the frequency domain diagram of pressure fluctuation at radial location of the volute obtained by fast Fourier transform (FFT). The abscissa in the frequency domain diagram is the multiple of the fluctuation frequency f  Figure 11 shows the time domain diagrams of pressure fluctuation at volute radial location monitoring points 2, 3 and 4 during the start-up process (t = 0~2.5 s), the first circle of impeller rotation (t = 0~0.255 s) and a circle of impeller rotation after stable speed (t = 2.458~2.5 s), respectively. Figure 12 shows the frequency domain diagram of pressure fluctuation at radial location of the volute obtained by fast Fourier transform (FFT). The abscissa in the frequency domain diagram is the multiple of the fluctuation frequency f and the impeller rotational frequency fn. It can be observed from the diagrams that the pressure fluctuation law of each radial monitoring point is similar. Under the impact of    Figure 13 shows the time domain diagrams of pressure fluctuation at vol cumferential location monitoring points 1, 2, 5, 6, 7 and 8 during the start-up pro 0~2.5 s), the first circle of impeller rotation after start-up (t = 0~0.255 s) and a c impeller rotation after stable speed (t = 2.458~2.5 s), respectively. Figure 14 sho frequency domain diagram of pressure fluctuation of the volute circumferential l obtained by FFT. It can be observed from the diagrams that the pressure of volu position at point 1 is relatively stable during start-up, and its pressure fluctuati plitude is small. The pressure fluctuation amplitude of the volute spiral part at e cumferential position is the largest at the initial time of start-up. With the increas tating speed, the pressure fluctuation amplitude decreases rapidly, and the time between adjacent peaks of the time domain curve decreases gradually. A variation of circumferential pressure fluctuation is also consistent with rotation period of peller. The number of pressure fluctuation in each variation period is consiste blade number, but the pressure fluctuation waveform at each circumferential p monitoring point is not the same in one rotation period. The dominant frequenc pressure fluctuation in each circumferential position of the volute is 6 times the i rotational frequency. The dominant frequency amplitude of the pressure fluctu point 7 is the largest, followed by point 2 and point 5, and it is smaller at poin point 8. There are obvious secondary fluctuations in one fluctuation period at poin point 8. The main reason is that point 7 is located at the front end of the volute and point 8 is located at the volute tongue. When the fluid flows along the flow c to the volute tongue, the cross section of the volute is the smallest and the pressu is the largest. In addition, point 7 and point 8 are closest to the coupling surface b the impeller and the volute, and they are affected by the dynamic and static inter between the impeller and the volute. It can be indicated that the pressure fluctu the front end of the volute tongue is the largest.  Figure 13 shows the time domain diagrams of pressure fluctuation at volute circumferential location monitoring points 1, 2, 5, 6, 7 and 8 during the start-up process (t = 0~2.5 s), the first circle of impeller rotation after start-up (t = 0~0.255 s) and a circle of impeller rotation after stable speed (t = 2.458~2.5 s), respectively. Figure 14 shows the frequency domain diagram of pressure fluctuation of the volute circumferential location obtained by FFT. It can be observed from the diagrams that the pressure of volute inlet position at point 1 is relatively stable during start-up, and its pressure fluctuation amplitude is small. The pressure fluctuation amplitude of the volute spiral part at each circumferential position is the largest at the initial time of start-up. With the increase in rotating speed, the pressure fluctuation amplitude decreases rapidly, and the time interval between adjacent peaks of the time domain curve decreases gradually. A variation period of circumferential pressure fluctuation is also consistent with rotation period of the impeller. The number of pressure fluctuation in each variation period is consistent with blade number, but the pressure fluctuation waveform at each circumferential position monitoring point is not the same in one rotation period. The dominant frequency of the pressure fluctuation in each circumferential position of the volute is 6 times the impeller rotational frequency. The dominant frequency amplitude of the pressure fluctuation at point 7 is the largest, followed by point 2 and point 5, and it is smaller at point 6 and point 8. There are obvious secondary fluctuations in one fluctuation period at point 7 and point 8. The main reason is that point 7 is located at the front end of the volute tongue, and point 8 is located at the volute tongue. When the fluid flows along the flow channel to the volute tongue, the cross section of the volute is the smallest and the pressure drop is the largest. In addition, point 7 and point 8 are closest to the coupling surface between the impeller and the volute, and they are affected by the dynamic and static interference between the impeller and the volute. It can be indicated that the pressure fluctuation at the front end of the volute tongue is the largest.   Figure 15 shows the time domain diagrams of pressure fluctuation at impeller monitoring points 9, 10 and 11 during the start-up process (t = 0~2.5 s), the first circle of impeller rotation after start-up (t = 0~0.255 s) and a circle of impeller rotation after stable speed (t = 2.458~2.5 s), respectively. Figure 16 shows the frequency domain diagram of   Figure 15 shows the time domain diagrams of pressure fluctuation at i monitoring points 9, 10 and 11 during the start-up process (t = 0~2.5 s), the first impeller rotation after start-up (t = 0~0.255 s) and a circle of impeller rotation afte speed (t = 2.458~2.5 s), respectively. Figure 16 shows the frequency domain dia  Figure 15 shows the time domain diagrams of pressure fluctuation at impeller monitoring points 9, 10 and 11 during the start-up process (t = 0~2.5 s), the first circle of impeller rotation after start-up (t = 0~0.255 s) and a circle of impeller rotation after stable speed (t = 2.458~2.5 s), respectively. Figure 16 shows the frequency domain diagram of pressure fluctuation in the impeller obtained by FFT. It can be observed from the figure that the pressure fluctuation in the impeller is a step waveform. With the increase in the rotating speed, the time interval between the adjacent peaks of the time domain curve decreases gradually. The amplitude of the pressure fluctuation attenuates slowly with the increase in the rotating speed, and the amplitude of the secondary dominant frequency and the impeller rotational frequency doubling are still large. One variation period of pressure fluctuation in the impeller is also consistent with the impeller rotation period, and the number of pressure fluctuation in each variation period is consistent with blade number. The dominant frequency of pressure fluctuation in each position of the impeller is 6 times the impeller rotational frequency, and the dominant frequency amplitude and secondary dominant frequency amplitude at point 11 are the largest. It indicates that the pressure fluctuation in the middle part near the inner edge of the impeller is the strongest. Combined with Figure 14, it can be observed that the dominant frequency amplitude of the maximum pressure fluctuation at point 11 in the impeller is 10 times that at point 7 in the volute, which indicates that the pressure fluctuation in the impeller is much larger than that in the volute.

Analysis of Pressure Fluctuation at Various Head
Since the pressure fluctuation of each monitoring point has the same variati the head, the monitoring point 7 is taken as an example for analysis. By monitoring tating speed of the start-up process, it can be observed that the rotating speed is 49 after the first circle of impeller rotation under the design head, and the rotating 1455 r/min after completing start-up. Under the low-pressure head of 0.8H, the speed is 322 r/min after the first circle of impeller rotation, and the rotating speed r/min after completing start-up. Under the high pressure head of 1.2H, the rotating 657 r/min after the first circle of impeller rotation, and the rotating speed is 1631 r/m completing start-up. Figure 17 shows the time domain diagrams of pressure fluctu point 7 during the start-up process (t = 0~2.5 s, t = 0~0.255 s, and t = 2.458~2.5 s) un ferent heads. Figure 18 shows the frequency domain diagram of pressure fluctua tained by FFT. It can be observed from the diagrams that the number of pressure tion under the low head is less than that under the high head at the same time, tha impeller needs a longer time to rotate one circle and the rotating speed increas slowly under the low head during the start-up process. The dominant frequency am at point 7 under the high head 1.2H is 1.34 times that under the design head H, an the low head 0.8H it is 0.65 times that under the design head H. It can be indicated pressure fluctuation degree under the low head is weaker, and the dominant fr amplitude is smaller. With the increase in the head, the time required to comp start-up reduces and the rotating speed increases after completing start-up. Meanw number of pressure fluctuation at the same time, the fluctuation amplitude, the do frequency amplitude and the secondary dominant frequency amplitude of pressu tuation increase during the start-up process.

Analysis of Pressure Fluctuation at Various Head
Since the pressure fluctuation of each monitoring point has the same variation with the head, the monitoring point 7 is taken as an example for analysis. By monitoring the rotating speed of the start-up process, it can be observed that the rotating speed is 495 r/min after the first circle of impeller rotation under the design head, and the rotating speed is 1455 r/min after completing start-up. Under the low-pressure head of 0.8H, the rotating speed is 322 r/min after the first circle of impeller rotation, and the rotating speed is 1168 r/min after completing start-up. Under the high pressure head of 1.2H, the rotating speed is 657 r/min after the first circle of impeller rotation, and the rotating speed is 1631 r/min after completing start-up. Figure 17 shows the time domain diagrams of pressure fluctuation at point 7 during the start-up process (t = 0~2.5 s, t = 0~0.255 s, and t = 2.458~2.5 s) under different heads. Figure 18 shows the frequency domain diagram of pressure fluctuation obtained by FFT. It can be observed from the diagrams that the number of pressure fluctuation under the low head is less than that under the high head at the same time, that is, the impeller needs a longer time to rotate one circle and the rotating speed increases more slowly under the low head during the start-up process. The dominant frequency amplitude at point 7 under the high head 1.2H is 1.34 times that under the design head H, and under the low head 0.8H it is 0.65 times that under the design head H. It can be indicated that the pressure fluctuation degree under the low head is weaker, and the dominant frequency amplitude is smaller. With the increase in the head, the time required to complete the start-up reduces and the rotating speed increases after completing start-up. Meanwhile, the number of pressure fluctuation at the same time, the fluctuation amplitude, the dominant frequency amplitude and the secondary dominant frequency amplitude of pressure fluctuation increase during the start-up process.

Conclusions
In the current paper, the flow field behaviors and pressure fluctuation characteristics of the PAT start-up process were studied using numerical simulation and experiments. The primary conclusions can be summarized as follows:

Conclusions
In the current paper, the flow field behaviors and pressure fluctuation charac of the PAT start-up process were studied using numerical simulation and exper The primary conclusions can be summarized as follows:

Conclusions
In the current paper, the flow field behaviors and pressure fluctuation characteristics of the PAT start-up process were studied using numerical simulation and experiments. The primary conclusions can be summarized as follows: (1) At the beginning of start-up, there are a large number of low-pressure areas and strong vortexes in the impeller. With the increase in rotating speed, the pressure has a gradient distribution along the flow channel, and the vortexes rapidly decrease and are concentrated on the blade non-working face. (2) The pressure fluctuation amplitude is the largest at the initial start time. With the increase in rotating speed, the pressure fluctuation amplitude of the spiral part in the volute attenuates rapidly, but it attenuates slowly in the impeller. The number of pressure fluctuation at each position in one impeller rotation cycle is consistent with the blade number, and the dominant frequency of pressure fluctuation is 6 times that of the impeller rotation frequency.