Pressure pulsation test of Wanjiazhai Francis turbine at different loads

In this paper, the pressure pulsation of Wanjiazhai Francis turbine at six monitoring points under different loads is monitored. Fast Fourier Transform(FFT) was used to perform time-frequency conversion, and the data was analyzed from both time-domain and frequency-domain perspectives. From a time perspective, the pressure pulsation at the upstream bladeless area is the most sensitive to changes in power. From a frequency perspective, the frequency components of pressure pulsation are more complex when P=40kW, while the frequency domain diagrams of pressure pulsation at each monitoring point are similar when P=80kW and P=120kW.


Introduction
Hydropower is one of the most commonly used renewable energy sources [1], and its development is relatively mature [2].China has abundant water resources and has built many hydropower stations to fully utilize these resources [3].Turbines are the core equipment of hydropower stations.Francis turbine is widely used because of its compact structure and wide application range [4].During the operation of hydraulic turbines, pressure pulsation is one of the key concerns [5].Under certain loads, pressure pulsation caused by water flow may cause resonance of the unit equipment [6], affecting the safe operation of the water turbine.Many scholars have conducted corresponding research on the pressure pulsation of hydraulic turbines.Some scholars have found that the pressure pulsation in the vaneless zone of hydraulic turbines has the greatest impact on their operation [7].The low-frequency pressure pulsation caused by draft tube vortex belt cannot be ignored [8].The pressure pulsation in the sealing ring is also of concern [9].In addition to the time-domain characteristics of pressure pulsation, frequency characteristics are also the focus of scholars' research.Fast Fourier transform(FFT) [10] can conveniently obtain the frequency components of signals and is a commonly used data processing method.
In this paper, the pressure pulsation of Wanjiazhai Francis turbine unit at different positions under different working conditions is tested, monitored and analyzed, and time-frequency conversion is carried out using fast Fourier transform.The time and frequency characteristics of pressure pulsation at different monitoring points were analyzed to understand the operating characteristics of the unit.
The aim was to improve the operational stability of the unit and provide guidance for its safe and efficient operation.

Hydro-turbine Parameters
Wanjiazhai Francis turbine is composed of volute, fixed guide vane, moving guide vane, runner and draft tube.The number of blades for fixed guide vanes, moving guide vanes, and runner is 24, 24, and 13 respectively.The rated speed of the runner n is 100 rpm.The model of the turbine is shown in Figure 1.

Monitoring Points
In this test, six monitoring points are selected to collect pressure pulsation data, which are named as monitoring point 1, 2, 3, 4, 5 and 6 respectively.The locations of each monitoring point are shown in Table 1.The pressure pulsation of power P=40kW, P=80kW, P=120kW and P=180kW are monitored respectively.
Table 1.The locations of pressure pulsation monitoring points.tailwater cone pipe The model and monitoring points shown in Figure 2 illustrate the specific locations of monitoring points 1, 4, and 6.The components at the locations of the remaining three monitoring points were not modeled.The corresponding locations of the three points can be obtained from Table 1.For each monitoring point, pressure pulsations are collected at 1000Hz for 20s.Data from the last 10s are selected for analysis, totaling 10,000 data points.

Testing Instrument
The 112A22 dynamic pressure sensor is used to measure pressure pulsation, with a resonance frequency greater than 250kHz, a response time less than 2.0 microseconds, and a resolution less than 0.1kPa.Flush with the inner surface of the flow channel during installation.
The calibration of the sensor is based on the on-site calibration instrument provided by PCB company, using the impact method.Firstly, adjust the calibrator to the specified pressure, then activate the quick opening valve to quickly complete the impact of the pressure on the sensor.The computer records the output waveform of the sensor and calculates the maximum response value.Then, release the pressure and adjust the calibrator to the next pressure.Perform the impact response under each pressure one by one to obtain the relationship between sensor output and pressure.

Time-Domain Analysis
The pressure pulsation data are dimensionless processed and pressure coefficient Cp is used to characterize the pressure pulsation.The calculation method is shown in Eq.1.
where, p is the pressure pulsation data, kPa; p∞ is the pressure at the stable flow position upstream of the turbine, kPa; ρ is the liquid density, kg/m 3 , Hd is the design head, m。 Figure 3 shows the pressure pulsation at each monitoring point under different operating conditions.It can be seen that the periodicity of pressure pulsation at each monitoring point is most obvious under P=80kW and P=120kW.As shown in Figure 3(a), the pressure pulsation has an obvious overall trend over a long period of time, but oscillates in a short observation time.
From Figure 3, it can be found that the average pressure pulsation of each monitoring point has obvious variation regularity under different operating conditions.At monitoring point 1, the operating condition with the highest average pressure pulsation is P=40kW.With the increase of power, the average pressure pulsation decreases.However, the opposite rule appears at monitoring points 2, 3 and 4. The regularity at monitoring points 5 and 6 is similar to that at monitoring point 1, but the average pressure pulsation under P=40kW and P=80kW are similar.
In addition, the change of power P has different effects on the change of the average pressure pulsation at each monitoring point.The pressure pulsation at monitoring point 1 is least sensitive to changes in power.Average pressure pulsation at monitoring point 4 is most affected by power change, which indicates that different operating conditions have greater influence on pressure pulsation in upstream vaneless area.On the other hand, under the same operating condition, the pressure pulsation of each monitoring point also has obvious regularity.Figure 4 shows the pressure pulsation different monitoring points under each operating condition.Obviously, under each operating condition, the maximum of the pressure pulsation mean appears at the monitoring point 1.The second was monitoring point 4. The mean pressure pulsation at monitoring point 6 is relatively stable.Mean pressure pulsation at monitoring points 2 and 3 increase with increasing power, which is opposition to that at monitoring point 5.

Frequency-Domain Analysis
Fast Fourier transform (FFT) is used to realize time-frequency conversion of pressure pulsation data collected.Figure 5 left shows the pressure pulsation frequency distribution at monitoring point 1 under each operating condition, while the figure on the right shows the pressure ripple frequency distribution at each monitoring point under P=80kW.It can be seen that the pressure pulsation in all cases is mainly composed of low frequency components less than 20Hz, and in the high frequency region only the more prominent components appear near 280Hz, 360Hz and 438Hz.Therefore, the subsequent analysis focuses on the low frequency range of 0~20Hz.Figure 6 shows the frequency domain diagram of pressure pulsation low frequency region under different operating conditions at each monitoring point.It can be seen from the diagram that when P=180kW, the corresponding amplitude of each frequency of pressure pulsation spectrum at each monitoring point is significantly smaller than that under other operating conditions.The maximum amplitude of the main frequency appears at P=80kW, which is slightly larger than P=120kW, and the trend of spectral changes in these two working conditions is relatively similar.This indicates that when the power of the hydraulic turbine is too large or too small, the frequency composition of pressure pulsation is more complex, while when the power is moderate, the frequency composition is more similar.7 shows the low-frequency frequency domain diagrams of pressure pulsation at different monitoring points under different working conditions.When P=40kW, the spectrum of pressure pulsation at each monitoring point is the most complex.Except for the frequency components of monitoring points 1 and 2, which are mainly concentrated below 2Hz, the composition of other monitoring points is relatively complex.The frequency components of other monitoring points are relatively similar.
For the two operating conditions of P=80kW and P=120kW, the frequency components of pressure pulsation at each monitoring point are basically the same, with the main frequency mainly concentrated in the frequencies of 0.8Hz and 0.9Hz, which is also similar to 0.83Hz, which equals to half of the hydraulic turbine's rotating frequency fn=n/60=100/60=1.67Hz.The remaining frequency components are mainly harmonic frequencies of fn/2.
When P=180kW, there is no very prominent amplitude of the frequency of the pressure pulsation at monitoring points 1, 2, 3, and 6.The frequency-domain diagrams of pressure pulsation at monitoring points 4 and 5 with high amplitude frequencies exhibit similar trends, with their main frequencies occurring at 3.3Hz, which is around 2fn.The other main frequency components are harmonic frequencies of 1.1Hz.

Conclusions
In this paper, pressure pulsation of six monitoring points of Wanjiazhai Francis Turbine under different conditions is monitored by test, time-frequency conversion of pressure pulsation data is carried out by FFT method, and pressure pulsation in time and frequency domain is analyzed.For the time-domain, different operating conditions have the least influence on the pressure pulsation at the inlet of the volute and the largest impact on the upstream vaneless area.Under the same operating condition, the pressure pulsation at the inlet of the volute is the largest, followed by the vaneless area on the upstream side.From the frequency-domain, the pressure pulsation at each monitoring point is mainly composed of low frequency components, and only three prominent components in high frequency region.The frequency component at P=40kW is the most complex, while at P=80kW and P=120kW, the components of pressure pulsation at each monitoring point are similar, and their main frequency is both near fn/2.When P=180kW, the main components of pressure pulsation at each monitoring point are 1.1Hz and its harmonic frequency.

Figure 2 .
Figure 2. Location of some monitoring points.For each monitoring point, pressure pulsations are collected at 1000Hz for 20s.Data from the last 10s are selected for analysis, totaling 10,000 data points.

Figure 3 .
Figure 3. Time-domain diagram of pressure pulsation under different conditions at each monitoring point.On the other hand, under the same operating condition, the pressure pulsation of each monitoring point also has obvious regularity.Figure4shows the pressure pulsation different monitoring points under each operating condition.Obviously, under each operating condition, the maximum of the pressure pulsation mean appears at the monitoring point 1.The second was monitoring point 4. The mean pressure pulsation at monitoring point 6 is relatively stable.Mean pressure pulsation at

Figure 4 .
Figure 4. Time-domain diagram of pressure pulsation at different monitoring points under each operating condition.

Figure 5 .
Figure 5. Two frequency-domain diagrams of pressure pulsation.Left: Pressure pulsation at monitoring point 1 under different operating conditions; Right: Pressure pulsation at different monitoring points under P=80kW.

Figure 6 .
Figure 6.Frequency-domain diagrams of pressure pulsation in the low-frequency range at eachmonitoring point under different operating conditions Figure7shows the low-frequency frequency domain diagrams of pressure pulsation at different monitoring points under different working conditions.When P=40kW, the spectrum of pressure pulsation at each monitoring point is the most complex.Except for the frequency components of monitoring points 1 and 2, which are mainly concentrated below 2Hz, the composition of other monitoring points is relatively complex.The frequency components of other monitoring points are relatively similar.For the two operating conditions of P=80kW and P=120kW, the frequency components of pressure pulsation at each monitoring point are basically the same, with the main frequency mainly concentrated in the frequencies of 0.8Hz and 0.9Hz, which is also similar to 0.83Hz, which equals to half of the hydraulic turbine's rotating frequency fn=n/60=100/60=1.67Hz.The remaining frequency components are mainly harmonic frequencies of fn/2.When P=180kW, there is no very prominent amplitude of the frequency of the pressure pulsation at monitoring points 1, 2, 3, and 6.The frequency-domain diagrams of pressure pulsation at monitoring points 4 and 5 with high amplitude frequencies exhibit similar trends, with their main frequencies occurring at 3.3Hz, which is around 2fn.The other main frequency components are harmonic frequencies of 1.1Hz.

Figure 7 .
Figure 7. Frequency-domain diagram of pressure pulsation in low frequency range at different monitoring points under each operation conditions.