Vibration and Flow Characteristics of a 200 MW Kaplan Turbine Unit under Off-Cam Conditions

Abstract

Kaplan turbine units can adjust their blades to achieve wider outputs without a significant loss of efficiency. The combination of guide vane angle (GVA) and blade angle (BA) is selected based on efficiency curves obtained from cam tests. However, the vibration characteristics are not considered in the test. The vibration and flow characteristics are complex with different combinations of guide vane and blade angles. Different cam relation selection principles lead to varying machine vibration and flow characteristics. In this research, the flow and vibration characteristics were obtained by means of field test and numerical simulation. Vibration, pressure pulsation, and other stability indicators have been extracted and investigated under off-cam conditions. The flow and variation rules of different indicators have been thoroughly researched. The findings suggest that the magnitude of vibration in the X direction surpassed that in the Y direction for the head cover, upper frame, and lower frame under 22 experimental conditions. The disparity between the head cover and upper frame in both directions was not significant, whereas a substantial contrast existed between the lower frame in the X and Y directions. The calculation results indicate that when the guide vane angle was small, vortices appeared near the high-pressure edge of the runner in the vaneless region and caused disorganized flow lines in the runner, and this complex vortex behavior led to multiple frequency components in the pressure pulsation frequency domain. The conclusions provide references for the designers of Kaplan turbine units and improves the operating safety of Kaplan turbine power stations.

1. Introduction

Kaplan turbines are primarily utilized in hydropower stations with low head and large flow [1]. They are distinguished by the capability to adjust the turbine blades in response to varying water flow conditions, thereby ensuring optimal operational efficiency. However, Kaplan turbines can cause vibration and pressure pulsation during operation, stemming from hydraulic, mechanical, or electromagnetic factors. Excessive vibration can result in mechanical fatigue, structural damage, and equipment failure. Similarly, pressure pulsation may lead to resonance within the turbine’s internal structure. Both phenomena are directly linked to the operational safety of the power station. This will not only impact its operational efficiency but also has the potential to result in equipment damage and even pose a risk of safety accidents. During turbine operation, periodic pressure fluctuations occur due to water flow, de-flow, secondary water impact, and the interaction between runner blade and water flow. These pressure pulsations exert forces on the turbine’s structural components, causing periodic changes that may induce mechanical vibration. Particularly when the frequency of these pressure pulsations aligns closely with or matches the natural frequency of the turbine structure, resonance can occur and exacerbate vibration issues.

The root causes of turbine vibration include hydrodynamic effects, asymmetry or damage to blades or components, instability in water flow, and structural resonance. The main measures for controlling vibration are adjusting blade angles, optimizing structural design, and using damping materials. In terms of the analysis of vibration causes and methods for controlling vibration, a Kaplan turbine unit exhibits significant vibration and generates high levels of noise during no-load operation at high speeds. Moraga et al. [2] conducted modal analysis testing on the runner to address this issue, as well as high-speed no-load testing on the unit under accelerated conditions. The results indicated that the source of the high amplitude vibration and excessive noise was located near the head cover. By modifying the diameter and distribution of the air inlet, both vibration and noise levels were significantly reduced. Roig et al. [3] conducted a no-load speed test of the guide vane and runner blade combination at various angles on a reduced-size Kaplan turbine model, under both non-cavitating and cavitating conditions. The study revealed that the presence of multiple simultaneous vortex structures in the vaneless region led to torsional vibration of the rotor. Furthermore, it was observed that the induced structural response on the low-pressure side of the turbine increased when operating under cavitation conditions. Dunca et al. [4] conducted a field test to determine the optimal three-dimensional combination of runner blade opening and guide blade opening for different water head values. The optimal cam for vibration levels when operating in different states was determined.

In the realm of numerical simulation, advanced technologies such as computational fluid dynamics (CFD) are commonly utilized to forecast and analyze the flow field characteristics of hydraulic turbines [5]. These technologies are also combined with vibration characteristics to comprehend the mechanism behind vibration generation. The study of fluid-structure coupling vibration characteristics of Kaplan turbine runner is relatively limited compared to other types. This is attributed to the fact that the blades rotate with changes in load, and the interaction within the blades may impact the additional mass and damping of the runner. Zhang et al. [6] conducted a comparison between natural frequencies predicted by acoustic FSI and those from one-way FSI analysis in order to analyze how internal blade interaction influences additional mass and damping mechanisms. Puolakka et al. [7] proposed a simplified method for calculating the unsteady vibration of turbine shafting based on unsteady airfoil theory. The method assumes that the runner, as a rigid body, oscillates in rotation and axial heave, and decomposes the reaction force into additional mass and damping. It was observed that over the frequency range of interest, there were moderate changes in increased mass and little changes in increased damping.

In terms of experimental research, vibration data are collected through model tests or prototype tests to verify the accuracy of numerical simulations and the effectiveness of vibration control strategies. For experimental monitoring methods, due to the limited number of studies on the feasibility of applying vibration measurement-based diagnostic techniques to turbine units and the absence of appropriate sensors installed on the units, Pennacchi et al. [8] utilized this diagnostic tool to address the issue of hydraulic instability and proposed a highly automated condition monitoring system. Feng et al. [9] conducted a study to measure the vibration signals of the rotor and draft pipe of a Kaplan turbine under various cavitation states. They utilized the multifractal detrended fluctuation analysis (MF-DFA) method to analyze the vibration signals and found that both the runner and draft pipe exhibited multifractal characteristics.

Pressure pulsation can lead to turbine vibration and the vibration of its attached structure. Prolonged and intense vibration poses a significant threat to the safe operation of the unit, with the potential to cause fatigue damage to the structure. Due to its unique structure and working principle, Kaplan turbines are particularly sensitive to pressure pulsation. Hence, the examination of pressure pulsation in these turbines is imperative to ensure the stability of unit operations.

Several scholars have conducted in-depth investigations into pressure pulsation by integrating experimental measurements with numerical simulations. Experimental studies have yielded valuable data under actual operating conditions, while numerical simulations have offered a more comprehensive understanding of flow dynamics and the ability to forecast pressure pulsations across various operational scenarios [10]. Minakov et al. [11] employed the Reynolds Mean Navier–Stokes (RANS) model, separate eddy simulation model (DES), and large eddy simulation model (LES) in their numerical simulations and laboratory experiments on a Kaplan turbine runner model. In contrast to the Limited Eddy Viscosity Model (LEVM), the RSM, DES, and LES could accurately replicate the intensity of pressure pulsations. Liu et al. [12] utilized a three-dimensional full-channel unsteady turbulence method incorporating dynamic and static interaction to predict the pressure pulsation of a Kaplan turbine runner. They conducted tests on a test platform to compare the calculation results and found that the largest low-frequency pressure pulsation was generated by the draft tube. Rivetti et al. [13] employed a combination of computational simulation and empirical measurements to investigate the pressure pulsation in a large Kaplan runner, encompassing the entire prototype. Pressure sensors were positioned at both the guide vane outlet and the draft pipe inlet. The findings revealed that the mean pressure exhibited fluctuations corresponding to variations in the guide vane channel within the rotating reference frame.

In the realm of numerical simulation, the characteristics of pressure pulsation have been analyzed, and the mechanism of pressure pulsation has been discussed. Wu et al. [14] conducted a simulation of the unsteady flow in a prototype Kaplan turbine full channel by integrating the Reynolds-averaged Navier–Stokes equation with the RNG k-epsilon turbulence model. The simulation results revealed a sudden increase in pressure pulsation frequency in the draft tube, which may have been attributed to the resonance characteristics of the prototype. Yan et al. [15] conducted an analysis of the internal flow characteristics of Kaplan turbine runner blades and draft tubes. The results revealed that when the guide vane opening was small, low-frequency and high-amplitude pressure pulsations occurred on the high- and low-pressure edges of blades. Additionally, the discrimination number was proposed as a quantitative measure for evaluating the flow uniformity of draft tubes. Altimemy et al. [16] conducted a simulation of the internal flow structure of a Kaplan turbine operating at the peak of the designed flow rate in OpenFOAM. The simulation results indicated that the strong swirling flow away from the runner had a detrimental effect on the pressure pulsation. Luo et al. [17] carried out a three-dimensional unsteady numerical analysis of a prototype Kaplan turbine operating under high head conditions. The findings revealed that the presence of eddy currents in the vaneless zone led to significant pressure pulsations when the guide vane opening was small under high head conditions. Iovanel et al. [18] conducted a study on the limitations of unsteady Reynold-averaged Navier–Stokes (RANS) simulation in modeling internal flow within axial turbines. The study evaluated the classical turbulence model, the curvature correction model, and scaled the adaptive simulation-Shear Stress transport (SAS-SST) turbulence model. The findings revealed that while the pressure fluctuation frequency on the flow channel blade could be accurately captured, there was a significant underestimation of its amplitude.

For experimental measurement, Amiri et al. [19] measured the unsteady pressure of blades and fixed components in the Kaplan turbine model during load change. It was discovered that the change of partial load caused the draft tube surge, forming a rotating vortex rope with two forms of fluctuation components, including rotation and plunging. This phenomenon caused flow oscillation throughout the entire flow passage, leading to local pressure fluctuations caused by the rotating vortex rope. Amiri et al. [20] also conducted measurements on the unsteady pressure of the runner blades of the Kaplan turbine model. The findings revealed that the formation of a rotating vortex rope by the turbine during partial load operation was identified as one of the primary sources contributing to the oscillating force exert on the runner blades. This phenomenon subsequently led to pressure pulsations at two sub-synchronous frequencies within the runner. Dehkharqani et al. [21] conducted experiments on the prototype Kaplan turbine during start-up, focusing on measuring the unsteady pressure and strain of the runner blade and shaft, as well as the bending and torsional strain of the shaft. The results indicated that low-frequency pressure fluctuations of the runner blade occurred after the guide vane was opened from its completely closed position.

In an effort to enhance the mitigation of pressure pulsation and propose methods for controlling fluctuations, Starecek et al. [22] developed an approach to enhance operational stability in Kaplan turbines. The design incorporated six non-uniform blade flow channels, each featuring varying axial distances between blades and guide vanes. This configuration effectively mitigated pressure pulsation resulting from the interaction between the rib and the runner. Angulo et al. [23] conducted air injection experiments on both a prototype and a model type of Kaplan turbine in order to investigate the impact of varying jet flow velocities on mitigating pressure pulsation in the draft tube and exhaust ring. The findings revealed that air injection effectively reduced pressure pulsation in the prototype experiment, while the extent of efficiency decrease in the model experiment was found to be overestimated. Rivetti et al. [24] conducted air injection experiments on a Kaplan turbine runner at various loads and net heads, and they observed that within a specific range, the level of pulsation decreased in direct correlation with the rate of air flow.

Based on previous studies, the vibration and internal flow characteristics of Kaplan turbines during operation have a significant impact on the stable operation and safety of the turbines. However, there is a lack of comprehensive research combining experimental measurement and numerical simulation in this area. This paper deeply investigates the vibration and internal flow characteristics of Kaplan turbines using a combination of field tests, sensor monitoring, data analysis, and the computational fluid dynamics (CFD) method. The goal is to reveal the law and influencing factors of vibration and pressure fluctuation, providing theoretical basis and technical support for optimizing turbine design and improving operation stability.

2. Materials and Methods

2.1. Experimental Method

This experiment aims to test the vibration signal of a prototype Kaplan turbine under non-associative working conditions. The automatic association was disabled, and the adjustment of the blade angle (BA) and guide vane was carried out manually. The test was conducted with a fixed blade angle and variable guide vane configuration. Two different blade angles (BA = 35° and BA = 55°) were chosen for testing, 9 guide vane angles (GVAs) were tested under the BA = 35° condition, while 13 guide vane angles were tested under the BA = 55° condition, as illustrated in Figure 1. The unit was tested after achieving stable operation, with each working point being tested for 5 min while maintaining a constant power factor. Since the head cover, upper frame, and lower frame of the turbine are its primary load-bearing structures responsible for bearing the weight of the entire unit and the hydraulic load generated during operation, these three components are key areas for monitoring vibration signals in this project. Consequently, the measurement points for vibration signals in this experiment were located in the X and Y directions of the head cover, upper frame, and lower frame, as depicted in Figure 2.

2.2. Calculation Method

The subject of investigation in this paper pertains to a large-flow low-head Kaplan turbine. A three-dimensional solid modeling approach has been employed to depict the intricate details of the turbine. Its primary flow components encompassed the draft tube, runner, guide vane, stay vane, and spiral casing, as illustrated in Figure 3. The specifications and principal parameters of the prototype Kaplan turbine are shown in the

Table 1. Values of Kaplan turbine parameters.

Parameter	Value
Design head H	25.0 m
Runner diameter D	10.4 m
Rated output	200 MW
Rated speed	68.2 rpm
Highest efficiency	95.67%
Number of stay vanes Zs	24
Number of guide vanes Zg	28
Number of blades Zb	6

.

The tetrahedral mesh offers the flexibility to adapt to complex and irregular geometric shapes, allowing it to maintain high mesh quality when dealing with complex boundaries. On the other hand, hexahedral meshes are more efficient for regular geometric shapes and generally provide higher computational accuracy at the same size. Therefore, in this numerical simulation, a combination of both types of meshes was used to match geometric features better. Specifically, a hexahedral structured mesh was employed for the draft tube, runner, guide vane, and stay vane, while a tetrahedral unstructured mesh was utilized for the spiral casing region. The mesh of each subdomain can be seen in Figure 4.

Based on the professional fluid simulation solver ANSYS CFX, the Reynolds Average Navier–Stokes method (RANS) was used to simulate the internal flow of the Kaplan turbine. In order to simulate the flow situation in the near-wall region more accurately and stably, the Shear Stress Transport (SST) k-ω turbulence model was utilized to simulate the transient state. Total pressure boundary conditions were applied at the inlet, static pressure boundary conditions at the outlet, and no-slip boundary conditions were implemented at the wall. The discrete format of the convection term was set to the high resolution, and the convergence residual was set to 10⁻⁶ for convergence criteria.

The appropriate time step was selected in this numerical simulation. In field tests, displacement sensors were used for the vibration measurement. The peak-peak values were extracted from the 95% confidence interval of the vibration wave. Spectra were calculated from the vibration signal of different measurement points. Figure 5 and Figure 6 show the spectra of 2 measurement points (proximity probe and vibration sensor on turbine bearing and) with different blade angles under the low guide vane angle level. As shown in the figures, the main frequencies were the frequency of the vortex rope (around 0.2f_f), rotating frequency (f_f = 1.14 Hz), and RSI (2 × f_b = 13.64 Hz). So in the numerical simulation, the time-step was selected as 252 times of rotating frequency (42 times of blade passing frequency), which covered most of the frequency components in the stability test.

Three sets of grids with different numbers were used for grid independence verification. The calculated efficiency under different grid schemes was compared, as shown in the Figure 7. As the number of grids increased, the efficiency curve gradually stabilized and became less sensitive to the grid size. Considering the computational resources and accuracy, a grid division scheme with approximately 5 million grids was ultimately adopted, as indicated by the red circle in Figure 7.

To validate the accuracy of the numerical model, the efficiency calculated under 4 different guide vane angle conditions at BA = 35° was compared with the efficiency measured through experimentation. The error between the experimental and calculated values is depicted in Figure 8, showing that all errors were below 0.7%.

According to the experimental conditions, 5 guide vane opening conditions covering the experimental range with the appropriate blade angle were selected at BA = 35° and BA = 55°, respectively. A total of 10 working conditions were numerically calculated as shown in the

Table 2. The 10 numerical calculation working points.

BA (°)	GVA (°)
55	42.9
55	46.9
55	53.6
55	64.7
55	74.4
35	37.6
35	44.3
35	49.8
35	64.3
35	69

.

3. Results

3.1. Experimental Results

3.1.1. Vibration Characteristics of the Head Cover

In Kaplan turbine vibration monitoring, the head cover plays a crucial role in monitoring as its vibrations can result in noise, material fatigue, and ultimately lead to cracks and fractures. During actual operation, the head cover is subjected to multi-directional forces. In this experiment, the vibration measurement points were mainly arranged in the X and Y directions of the head cover with the aim of identifying vibration issues caused by unbalance, misalignment, bearing failure, or hydrodynamic instability. Figure 9a and Figure 9b depict the measured vibration displacement of the head cover in the X and Y directions at blade angles of 35° and 55°, respectively.

As depicted in Figure 9a, when the blade angle was 35°, the range of guide blade angle values was extensive. The vibration of the head cover in the X and Y directions showed a trend of initially decreasing and then increasing. Specifically, when the guide vane angle increased from 27.6° to 44.3°, the vibration of the head cover in the X direction decreased as it gradually approached the optimal operating zone, as shown in Figure 10; however, as it further increased from 44.3° to 59.1°, the vibration continued to rise. Notably, when the guide vane angle was between 44.3° and 49.8°, its vibration displacement did not exceed 1.9 μm. Upon reaching an angle of 59.1°, there was a decrease in vibration which persisted as the angle continued to increase up to 64.3°; thereafter, vibrations increased with further angles. Similarly, for vibrations in the Y direction, an increase in guide vane angle from 27.6° to 45.9° resulted in decreased vibrations; however, this trend reversed as angles continued beyond that pointed up to an angle of 69°. It should be noted that during an interval where guide vane angle ranged from 44.3 ° to 49.8°, the vibration displacement of the guide vane was not more than 2.2 μm.

As depicted in Figure 9b, the vibration of the head cover was measured with the guide vane angle ranging from 42.9° to 74.4° while the blade angle was set at 55°. It was observed that as the guide vane angle increased, the vibration of the head cover in both X and Y directions also increased. Specifically, when the guide vane angle range was between 42.9° and 61.5°, the vibration of the top cover exhibited a more rapid increase compared to when it ranged between 61.5° and 74.4°. This trend indicates a correlation between guide vane angle and head cover vibration, suggesting potential implications for further investigation into turbine vibration and flow characteristics.

During the process of adjusting the blade angle and guide blade angle, the water flow into the runner and its direction were altered, leading to changes in pressure distribution inside the turbine. This subsequently affected the pressure load on the head cover. Improper combinations of blade angle or guide blade angle may result in an imbalance in runner load, leading to increased mechanical vibration and potential uneven water flow. These issues can cause water percussion or eddy currents, resulting in significant fluctuations in turbine pressure and intensified vibration of the head cover.

3.1.2. Vibration Characteristics of the Upper and Lower Bracket

The upper bracket of the turbine is typically utilized for the fixation and support of bearings or guide bearings, ensuring proper alignment and stability of the rotating shaft. The lower bracket is primarily responsible for providing support to the shaft and rotor of the turbine, serving as the foundation of the entire machine and needing to withstand both the force exerted by water flow on the runner and the mechanical weight of the rotor. When the blade angle was between 35° and 55°, Figure 11 shows the vibration displacement of the upper bracket and lower bracket in the X and Y directions. It was observed that the vibration of the upper bracket was greater than that of the lower bracket. Additionally, the vibration of the upper bracket and the lower bracket was greater in the X direction than in the Y direction. Furthermore, the difference in vibration between the X and Y directions of the upper bracket was not significant, whereas there was a substantial difference in vibration between the X and Y directions of the lower bracket.

As shown in Figure 11a, when the blade angle was 35°, the vibration displacement of the upper bracket initially decreased and then increased with the increase of the guide blade angle. Meanwhile, the vibration displacement of the lower bracket first increased and then stabilized with the increase of the guide blade angle. When the GVA was relatively small, vortex rope and resonance occurred, resulting in resonance with a large displacement at both ends and a small displacement in the middle of the vibration shape. This phenomenon implies that the node was located in the middle of the shafting under this mode. Consequently, compared with Figure 9a, under the small guide vane angle, the vibration amplitude of the head cover and upper bracket was larger. When the angle of the guide vane increased from 37.6° to 44.3°, there was a decrease in vibration of the upper bracket and an increase in vibration of the lower bracket. Continuing to increase from 44.3° to 59.4°, both brackets experienced an ongoing increase in vibration. Beyond 59.4°, there was a continuous increase in X-direction vibration for the upper bracket while Y-direction vibration for both brackets tend towards stability. As shown in Figure 11b, at a blade angle of 55°, both upper and lower bracket vibrations continued to increase with increasing guide blade angle, while the rate of increase decreased.

3.2. Calculation Results

3.2.1. Flow Characteristics of Vaneless Area and Runner

Five representative operating conditions covering the experimental guide vane angle range at BA = 35° and BA = 55° were selected, respectively, and a total of 10 operating conditions were numerically calculated. Figure 12 illustrates the velocity flow lines of the Kaplan turbine’s vaneless area and runner in the Z section under different working conditions. It was observed that due to the action of the guide vane, the flow into the vaneless area tended to be more uniform. Additionally, it was noted that the guide vane played a crucial role in adjusting the direction of water flow, causing water to bend as it passed through the vaneless area.

As the blade angle increased, both the speed of the vaneless and the runner zone also increased. Specifically, when BA = 35°, GVA = 37.6°; and when BA = 55°, GVA = 42.9° and 46.9°, it was observed that with a less open guide blade, the flow line became more curved and irregular while the speed distribution of the flow line became non-uniform. Consequently, water flow would generate secondary flow due to centrifugal force and pressure gradient effects, leading to the formation of a vortex area with lower speed near the suction surface of the runner blade. This phenomenon has an impact on both water flow stability and runner efficiency. It was noted that as the guide vane angle increased, velocity distribution tended to become more uniform.

Generally, there was a specific velocity gradient in the flow line of the vaneless region, with the velocity gradually changing from the inner wall to the outer wall. This was attributed to the varying resistance and acceleration of water flow through the guide vane. When the guide vane angle was small, vortices appeared near the runner suction surface (marked with a red circle in the Figure 12), and the flow line in this area became disordered. Therefore, a monitoring point was established for further calculation and analysis.

3.2.2. Pressure Pulsation Characteristics of Vaneless Area

A monitoring point was set in the vortex area near the high-pressure edge of the runner in the vaneless region. The pressure signal in the time domain was then converted to the frequency domain to obtain the spectrum diagram of pressure pulsation, as depicted in Figure 13. The complex behavior of vorticity in these two working conditions may lead to multiple frequency components in the pressure pulsation frequency domain, resulting in relatively chaotic overall frequency.

The main frequency of pressure pulsation in the bladeless region is the blade passing frequency f_r, and f_r is the product of runner frequency f_n and runner blade number Z_r, as shown in Formula (1).

$$f_r=f_n\times Z_r$$

(1)

As depicted in the Figure 13, the vaneless area was located near the runner blade, and the passing frequency of the blade represents the primary frequency of pressure pulsation in this area. Consequently, pressure pulsation in the vaneless area primarily originated from the inlet of the runner blade and turbulent flow from the blade to the stationary region. These pulsations propagated to the vaneless region in the form of pressure waves.

In the case of BA = 35°, when GVA = 37.6°, GVA = 44.3°, and GVA = 69.0°, the main frequency of the vaneless area was 1 blade frequency (1f_r), and the harmonic was the integral multiple frequency component of the fundamental frequency, which was 2 blade frequency (2f_r). When GVA = 49.8° and GVA = 64.3°, the main frequency of the vaneless area was 1 time the runner frequency (1f_n).

In the case of BA = 55° and GVA = 42.9°, GVA = 46.9°, the main frequency was 1 blade frequency (1f_r), while the overall frequency appeared to be relatively chaotic. This may be attributed to the strong disturbance caused by the runner blade on the water flow, leading to alternating high and low pressure in the vaneless area, resulting in blade frequency pressure pulsations. Additionally, this phenomenon also generated various low-frequency pressure pulsations.

When the GVA angles were 53.6°, 64.7°, and 74.7°, the main frequency of the leafless region was at 1 blade passing frequency (1f_r), with harmonics occurring at 2 blade passing frequency (2f_r).

Periodic pressure changes in the vaneless region are also caused by interaction between the runner blade and guide vane. Therefore, it is important to analyze the pressure pulsation characteristics of the runner as well. The vortex near the runner in the vaneless area may have been caused by the wake of the guide vane, mutual interference between the blades and boundary layer separation. The vortex and turbulence generated by the guide vane will interact with the blade surface as it passes, causing pressure fluctuations. Therefore, further analysis of the pressure pulsation characteristics in the guide vane region was necessary.

3.2.3. Pressure Pulsation Characteristics of Runner Blade

Monitoring points were arranged on both the suction surface (SS) and pressure surface (PS) of the runner blade, as depicted in the Figure 14 and Figure 15. To illustrate the dynamic pressure characteristics of the blade at various frequencies, an analysis of the pressure pulsation frequency domain for both surfaces was conducted.

As shown in the Figure 14, when BA = 35° and GVA = 37.6°, the frequency components of the blade SS and PS of the runner exhibited complexity, with the pressure pulsation amplitude reaching its peak. This indicates that the pressure pulsation intensity was most intense under this working condition, and the flow line of the vaneless region and runner were also most chaotic. When GVA = 44.3°, GVA = 49.8° and GVA = 64.3°, it was observed that the main frequency of the SS aligned with a single rotation frequency without any discernible harmonics present. Similarly, for the PS, its main frequency was also 1 time the rotation frequency with an occurrence frequency twice that of rotation. However, when GVA reached 69.0°, it resulted in a weakening of pressure pulsation intensity. The primary frequency of both SS and PS was 1.0 times the rotational frequency.

As shown in the Figure 15, when BA = 55°, GVA = 42.9°, and GVA = 46.9°, the pressure pulsation was intense, and the main frequency of the SS and PS was 1 time the main frequency. The angle of the guide vane was small in these working conditions, causing an irregular flow line and uneven speed distribution. Consequently, a low-speed vortex area was generated, which produced low-frequency components. Under GVA = 53.6°, GVA = 64.7°, and GVA = 74.4°, the main frequency of the SS and the PS was 1 time the main frequency, with a small pulsation intensity.

3.2.4. Flow Characteristics of Guide Vane

The guide vane guides and accelerates the fluid into the runner blade. As shown in the Figure 16, there was an obvious velocity gradient from the inlet to the outlet of the guide vane, and the speed gradually increased with the increase of the blade angle. When BA = 35° and GVA = 37.6°, the outlet velocity of the guide vane was large. When BA = 55° and GVA = 42.9 ° and 46.9°, the flow velocity at the outlet of the guide vane was higher. The reason for this phenomenon is that when the angle of guide vane is reduced, pressure energy at its inlet will be partially converted into kinetic energy, resulting in a higher flow speed at its outlet. However, this reduction in angle also increases resistance to fluid flow, leading to increased head loss. To overcome this loss and maintain fluid flow, it passes through at a higher speed as a result.

Increasing angle size within a selected range leads to decreased difference between inlet and outlet speeds until reaching maximum angle where no significant difference exists. Compared with the Francis turbine, the guide vane of the Kaplan turbine usually has more flat and concentrated velocity flow line because fluid mainly flows along axial direction while runner blade can be adjusted according to different flow rates and loads.

3.2.5. Pressure Pulsation Characteristics of Guide Vane

The occurrence of pressure pulsation in the guide vane region was typically attributed to static and dynamic interference, or variations in the angle of the guide vane. As shown in Figure 17a, when BA = 35° and GVA = 37.6°, the pressure pulsation pattern in the guide vane area was primarily low frequency pulsation pattern. The primary frequency of the pressure pulsation of the pressure pulsation generated by the guide vane was 1.0 times the rotation frequency. The spectrum components of the pressure pulsation were intricate, with multiple low-frequency components exhibiting varying amplitudes. Under this operating condition, a significant velocity gradient existed from the inlet to the outlet of the guide vane. An increase in turbulence intensity would lead to an elevation in pressure pulsation amplitude and a more complex spectrum component. And the amplitude of pressure pulsation in this working condition was remarkably substantial, which could be attributed to the small angle of the guide vane. It significantly impacted the uniformity and stability of fluid flow, consequently leading to an exacerbation of pressure pulsation. For GVA values of 44.3°, 49.8°, 64.3°, and 69.0°, it was observed that the main frequency of the pressure pulsation aligned with blade frequency, while the secondary frequency corresponded to 4 times the rotation frequency.

As shown in Figure 17b, when BA = 55° and GVA = 42.9°, the main frequency was 1.0 time the rotation frequency, accompanied by low frequency and blade passing frequency. The pressure pulsation in the guide vane was a combination of low-frequency pressure pulsation pattern and rotor and stator interaction pressure pulsation pattern. When GVA = 46.9°, the primary frequency became equivalent to the rotational frequency. It was observed that under these two working conditions, the pressure pulsation amplitude was higher compared to other working conditions when BA = 55°. Under low angle conditions, where there was a narrowing of flow channel and an increase in flow rate, it led to more turbulent fluid flow resulting in higher-frequency pressure pulsation. This led to additional energy loss and reduced efficiency of the system, as well as structural fatigue and vibration noise, which was not conducive to system stability. Additionally, at GVA values of 53.6°, 64.7°, and 74.4°, it was found that the main frequency of pressure pulsation corresponded to 1 time blade frequency, which caused by the rotor and stator interaction; and the secondary frequency corresponded to 4 times rotation frequency.

4. Conclusions

(1) In the vibration test of the head cover and the upper and lower frame, it was observed that at a blade angle of 35°, the vibration displacement of the head cover in both the X and Y directions initially showed a slight decrease, followed by an increase as the guide vane angle increased. However, there was only a small increase in vibration when the guide vane angle was between 44.3° and 49.8°. On the other hand, at a blade angle of 35°, there was an overall increase in vibration of the head cover in both X and Y directions with an increase in the guide vane angle. Additionally, it was found that regardless of whether the blade angle was 35° or 55°, the vibration displacement of the head cover in X direction exceeded that in Y direction.

(2) When the blade angle was 35° and 55°, the vibration displacement of the upper frame in the X and Y directions surpassed that of the lower frame. Furthermore, it was observed that the vibration displacement of the upper frame in the X direction exceeded that of the lower frame in the Y direction. Interestingly, there was little disparity between the vibration displacement of the upper and lower frames in the Y direction. When the blade angle was set at 35°, the vibration displacement of the upper frame initially decreased and then increased as the guide blade angle widened. In contrast, the vibration displacement of the lower frame first increased and then stabilized as the guide blade angle expanded. However, when the blade angle was adjusted to 55°, both the upper and lower frame experienced an increase in vibration displacement as the guide blade angle widened, albeit at a decreasing rate.

(3) When the blade angle was 35° and 55°, five representative working conditions covering the experimental guide blade angle range were selected for numerical simulation. A total of 10 working conditions were carried out to cover this range. Due to the regulating effect of the guide vane on the direction of water flow, the water flow into the vaneless zone became more uniform and curved. As the blade angle increased, both the velocity in the vaneless zone and runner also increased. The velocity distribution tended to become more uniform with an increase in the guide vane angle. However, under conditions of a small guide vane angle, vortices appeared near the high-pressure edge of the runner in the vaneless zone, leading to relatively disorganized flow lines in that area. In terms of frequency components in pressure pulsation frequency domain at these vortices within the vaneless zone, multiple frequencies appeared due to their complex behavior. For a blade angle of 35°, dominant frequencies in the vaneless zone were either 1 time the blade passing frequency or runner rotating frequency. When BA = 55°, regardless of different guide vane angles, the main frequency remained at 1 time the blade passing frequency.

(4) When the guide vane angle was small (BA = 35°, GVA = 37.6°; BA = 55°, GVA = 42.9°, 46.9°), the frequency components of the suction surface and pressure surface of the runner blade became more complex, with the most intense pressure pulsation intensity. In other working conditions, the main frequency of the suction surface and pressure surface was either 1 or close to 1 time the runner rotating frequency, and the pressure pulsation intensity was relatively weak when there was a large guide vane angle in the working condition.

(5) The velocity flow line of the guide vane exhibited a relatively linear and concentrated trajectory, with a noticeable velocity gradient from the inlet to the outlet. As the blade angle increased, there was a gradual rise in speed. When the guide vane angle was small (BA = 35°, GVA = 37.6°; BA = 55°, GVA = 42.9°, 46.9°), a portion of the fluid’s pressure energy at the inlet was transformed into kinetic energy, resulting in an accelerated flow out of the guide vane and consequently leading to higher outlet velocities for the guide vane. These phenomena were accompanied by multiple low-frequency components characterized by varying amplitudes. In other operational conditions, the main frequency of the guide vane was 1 blade frequency, and the secondary frequency was mostly 4 times the transfer frequency.

(6) One of the most critical limitations of the current study is the lack of direct comparisons between experiments and numerical simulations. The CFD calculations only provide pressure results. Future studies could aim to better correlate vibration measurements with CFD pressure through the fluid–structure coupling (FSI) method and investigate the consequences of different combinations of blade angle and guide blade angle (e.g., structural deviation, stress, fatigue, etc.).