Innovative Device to Control Self-Induced Instabilities Associated with the Swirling Flow from the Discharge Cone of Hydraulic Turbines

Abstract

In our previous research work, we investigated different methods to mitigate the vortex rope that appears in the draft tube of a Francis turbine when it operates at off-design operating points. The most promising results were obtained for a method involving an axial jet of water. The minor disadvantage of this method was the high value of the flow rate of the water jet. Our present work focuses on another method that decreases the value of the flow rate of the jet. In this sense, a new device has been developed that produces a pulsating water jet, which mitigates the pressure fluctuations associated with the swirling flows. The objective of this paper is to use our experimental test rig to validate the efficiency of a pulsating water jet in mitigating the vortex rope. To perform that, pressure measurements were carried out at four test levels to evaluate the pressure amplitude evolution when the pulsating jet was deployed. From preliminary investigations, the results indicate that this method leads to a decrease of the pressure amplitude of the vortex rope, with a lower value of the flow rate of the jet.

1. Introduction

The acute problems faced by hydraulic turbines (especially those with fixed blades, such as the Francis turbine) that operate at partial load have been known since the beginning of the last century. Problems that arise when the hydraulic turbines operate at partial load are felt more strongly today because of the compensation of fluctuating energies (wind, photovoltaic) in the energy market [1,2,3,4]. Thus, even if the hydraulic turbines are designed to operate at an optimal point, they end up working at other points far from the optimal one. For example, the Francis turbine, which operates at 60–70% from the optimal design point, develops a swirling flow with precession motion in its discharge cone, which is known in the specialized literature as a rope vortex, shown in Figure 1a [5]. An example of spiral vortex formation was presented by Nishi et al. in the 1980s [6,7]. They concluded that a quasi-stagnation area of the flow around the swirling flow can be represented by the average circumferential velocity profiles. To conclude, the generated vortex sheet occurs between the quasi-stagnant area and the main area, shown by Figure 1b.

Another component of the hydraulic turbine is the draft tube, whose goal is to convert the kinetic energy from the runner outlet into potential energy. At partial load, pressure recovery is small with high hydraulic losses due to the appearance of the rope vortex that presents severe pressure fluctuations, resulting in change associated with turbine output (power swing), shown by Figure 1c [8].

The drawbacks of hydraulic turbines operated with partial load are: (1) breakage of the connecting bolts of the draft tube, (2) tearing and weakening of the ogives, (3) breakage of the blades, (4) destruction of the sealing gaskets, and (5) uneven bearing wear [9].

Over time, different techniques have been developed to control the swirling flow of the discharge cone of hydraulic turbines. Most control techniques are designed to mitigate/eliminate the severe pressure fluctuations associated with swirling flow. More precisely, the techniques for mitigating the vortex rope phenomenon aim either to remove the cause of flow instability or to mitigate the effects. The swirling flow techniques can be passive or active.

The following passive technical solutions are known: (1) air admission, (2) stabilizing fins inserted into the conical diffuser of the turbine, (3) the introduction of concentric cylinders into the conical diffuser, (4) the J-Groove method, (5) stator downstream of the runner, (6) the introduction of separating vanes in the elbow of the diffuser, (7) the introduction of guide vanes in the elbow of the discharge cone, (8) the introduction of elongated central bodies with the attachment in the vicinity of the runner hub, (9) adjustable diaphragm, and (10) the flow-feedback technique [10,11,12,13,14,15]. Although these techniques have led to significant improvements in the operation of turbines, in terms of operating regimes, they are far from optimal. Additionally, these solutions cannot be removed when they are not necessary, thus introducing additional losses when operating at the best efficiency point.

Active techniques generally employ water jet injection or air injection using a secondary power supply as one of the following: (1) injection at the trailing edge of the stay vanes, (2) air injection through an annular chamber that surrounds the conical diffuser, (3) the introduction of an air manifold to the wall inside the conical diffuser, (4) the mixed injection of air and water through the turbine cover, (5) water injection at the trailing edge of the vanes of the directing apparatus, (6) injection with water jet tangent to the wall of the conical diffuser, (7) injection with axial water jet with high speed and low discharge, (8) injection with axial water jet with low speed and high discharge [16,17,18]. The injection of water through the runner crown axis is effective at a jet flow rate from 10% to 14% of the nominal flow rate. From a practical point of view, this technique raises a new problem in terms of supplying the necessary flow rate of the axial jet. According to Resiga et al. [17], the jet can be supplied with water upstream of the runner, but there is an unacceptable increase in the so-called volumetric losses because the flow of the control jet will not be used for energy transformation. The alternative is to take the water downstream from the conical diffuser by installing a double spiral case, which leads the water through return pipes through the turbine shaft and ogive runner (flow-feedback technique) [11]. The last technique is expensive to implement in hydroelectric power plants from the installation point of view.

Besides the advantages/disadvantages of the panoply of techniques for controlling unsteadiness associated with the vortex rope, there are still open issues. Nowadays, the challenge is to find a control technique (and this is the purpose of this paper) that neither introduces nor produces disadvantages such as those listed above. In that way, the main goal of the paper is to present an innovative device named VO, which uses a new type of valve (Figure 2) to control the self-induced instabilities with the corresponding pressure pulsations associated with the vortex rope. The novelty of this device is that it produces a pulsating water jet and addresses the main cause of the formation of the vortex rope: namely, the vortex sheet [6]. Pulsating jets are known in the literature and used in various engineering problems such as (1) twin jets to enhance mixing and heat transfer, focusing on controllable characteristics and the impact of nozzle spacing and phase changes between jet frequencies [19]; (2) axisymmetric jets subjected to large amplitude pulsations and plane jets forced to flap about a mean direction, providing experimental insights into their behavior [20]; (3) J-Stage explored how variations in amplitude and frequency affect the characteristics of pulsating jets, including large-amplitude cases, offering valuable data for industrial applications [21]. Abdolahipour et al. [22,23,24] used a pulsed jet actuator for flow separation control. The investigation aided in designing and optimizing flow control actuators in aerodynamics and combustion chambers. Such a solution can also be implemented to enhance the aerodynamic efficiency of an aircraft’s vertical tail [25]. Pulsating jet applications are also found in environmental, industrial, and aerospace fields, as well as in underwater propulsion systems [26,27,28,29].

To summarize the above sentences, if the vortex sheet is stopped from the beginning, then the vortex rope cannot occur. The innovative solution presented in this paper dynamically fragments the vortex sheet to prevent vortex rope formation. The investigations carried out from this research are to mitigate/eliminate the effects of hydraulic instabilities and offer an optimal flow configuration in the discharge cone, which will consist of experimental investigations of pressure fields with and without VO on the test rig.

2. Materials and Methods

The innovative device for controlling unsteadiness associated with the vortex rope from the discharge cone of hydraulic turbines operated at partial load consists of two cylindrical parts with axial slots, one fixed and one rotating, as is shown in Figure 2. The rotating part is driven with the help of a variable speed motor so that the transited water flow is fragmented due to the relative movement of the slots on the two cylindrical parts, generating a closing/opening effect of the flow path depending on the speed of rotation induced to the rotating part. The rotating speed of the motor is controlled by the voltage from an amplifier. In this way, the frequency of the water jet can be adjusted to a value that gives maximum efficiency for the annihilation of the vortex sheet that occurs when the turbine operates at the partial-flow regime. In our case, the number of slots is 16, which means that the frequency of the pulsation of the water jet will be 16 Hz for a complete rotation during a time interval of 1 s [30].

VO was designed in such a way as to provide a jet frequency similar to that of the vortex obtained on the experimental test rig. Compared to conventional hydraulic control valves, the main advantage of VO is the fact that it can provide high frequencies of the pulsating jet [31].

The testing of the device utilized unsteady pressure field measurements on the test rig for swirling flow control within the Hydraulic Machines Laboratory from Politehnica University Timisoara. The test rig detailed in [18] according to Figure 3a has as its main component a swirl generator located inside a test section, which produces a similar flow to the one generated by a Francis turbine operated at 60–70% partial load [32]. At this operating point, pressure pulsations are the largest [33]. The components of the swirl generator are the struts, guide vanes, the runner, and the nozzle.

To determine the unsteady pressure field, a set of 8 capacitive transducers was used. The displacement of the transducers was on 4 levels along the cone: L0, L1, L2, and L3.

L0 was located in the throat of the test section. The locations of the other transducers were 50 mm, 100 mm, and 150 mm along the cone. The accuracy of the transducers measured ±0.13% with a range of ±100 kPa. The transducers were flush mounted along the draft tube cone wall. The time interval for one measurement was 32 s with a sampling rate of 256/s. At least 10 sets of measurements were performed in order to check the repeatability of the results. For all investigations, the standard deviation σ has a value of ~±1%. The standard deviation is defined as:

$$\mathsf{\sigma }=\sqrt{{\displaystyle \frac{{\displaystyle \sum {\left({\mathrm{p}}_{\mathrm{i}}-\overline{\mathrm{p}}\right)}^2}}{\mathrm{N}-1}}},$$

(1)

The nominal discharge of Q_nom = 30 l/s with the corresponding Reynolds number of 3.8 × 10⁵ and a flow rate coefficient of q = 0.23 [-] was used for each measurement [18,34],

$$q={\displaystyle \frac{Q}{\omega \cdot \pi \cdot R_{ref}^3}},Q={\displaystyle \underset{A}{\int }\overrightarrow{V}}\cdot \overrightarrow{n}dA ,$$

(2)

where $\omega$ is radial speed of the runner, R_ref is the runner radius, $\overrightarrow{V}$ represents the velocity vector, and $\overrightarrow{n}$ the normal unit vector.

The nominal discharge was measured using an electromagnetic flow meter (Figure 3a) with an accuracy of ±0.15%. The test rig was filled with water with no air inside, resulting in a non-cavitating vortex with a constant value of the water density.

The technique developed by Bosioc et al. [18] was applied to assess the performance of the VO. In doing so, the results for the cases with and without VO were compared. As shown in Figure 4, the new VO was implemented in a secondary circuit of the test rig.

A control valve regulated the flow of water taken from the secondary circuit that passed through a buffer tank, and with the help of the new device, the VO generated the pulsating jet, which was inserted through the shaft into the test section (conical diffuser). The goal of the new VO was to provide the necessary frequency of the pulsating jet to eliminate/mitigate the instabilities related to the swirling flow that occurs in the discharge cone when the turbine operates far away from the best efficiency point.

3. Results and Discussion

The pressure fluctuations and the corresponding fast Fourier transform (FFT) for all levels in the cases with and without a pulsating jet for Q_nom = 30 l/s are shown in Figure 5. The FFT shows a decrease in frequency across all levels, from 16.4 Hz in the case without a pulsating water jet (vortex rope) to 10.5 Hz in the case with a pulsating water jet of Q-jet = 3.6 l/s (the decrease is 36%). In the same case (Q-jet = 3.6 l/s), the amplitudes have a small decrease because the vortex is well-developed. In the case of a pulsating jet with a Q-jet = 3.8 l/s, the amplitudes are mitigated or even eliminated. The outcomes presented above are plotted from the preliminary measurements.

For a better understanding of the phenomenon, we chose to analyse the equivalent amplitude and the corresponding frequency (as a Strouhal number) along the cone. In order to conduct that analysis, the Parseval theory described in [18] was utilized. Parseval’s theory is supposed to analyse one harmonic of the signal amplitude, which corresponds to the sum of the amplitudes of all harmonics. On the other hand, using Parseval’s theory, we can determine the value of the amplitude for a sinusoidal signal with the same average as the initial and the same frequency (Strouhal number) [35].

Figure 6 presents the equivalent amplitudes and S_h numbers in dimensionless form for all levels (L0–L3) that were obtained after using Parceval’s theory, both without a pulsating jet (Q-jet = 0 l/s) and with a pulsating jet (Q-jet = 3.6 l/s). According to Figure 5, Parceval’s theory is unapplicable to the case with a pulsating jet at Q-jet = 3.8 l/s due to the significant decrease in the amplitudes (up to zero). Therefore, we will focus on the case of the pulsating jet at Q-jet = 3.6 l/s. This remark is important to have a minimum pulsating jet discharge to avoid the high value of volumetric losses, considering that the water supply comes from the runner upstream.

The dimensionless amplitude is calculated by applying the equation:

$${\overline{A}}_{eq}={\displaystyle \frac{\sqrt{2}{p}_{RMS}}{\rho \cdot \frac{v_{throat}^2}{2}}}\hspace{0.17em},$$

(3)

The Strouhal number is defined as:

$$Sh={\displaystyle \frac{f\cdot D_{throat}}{v_{throat}}},$$

(4)

where v_throat is the velocity from the throat of the test section Equation (5), p_RMS is the random mean square Equation (6), D_throat = 0.1 m is the diameter corresponding to the throat test section, f is the main frequency, and Q = 30 l/s is the nominal discharge.

$$v_{throat}={\displaystyle \frac{4\cdot Q}{\pi \cdot D_{throat}^2}},$$

(5)

$$p_{RMS}=\sqrt{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N{\left(p_i-\overline{p}\right)}^2}},$$

(6)

First, we saw that the Strouhal number decreased when a pulsating water jet was introduced. For the nominal case, the frequency was 16.4 [Hz] corresponding to S_h = 0.43; for the case with a pulsating jet, the frequency was 10.5 [Hz] with S_h = 0.26. The decrease was ~37%. If the decrease of amplitude at the L0 level was approximately 16.5% when the pulsating jet was introduced, then at levels L1 and L2, the mitigation of amplitude was lower. The decrease in amplitude was ~26% for L1 and ~22% for L2. At L3, the pressure amplitude has increased by approximately 58% when the pulsating jet was injected.

This phenomenon occurs because of the large dissipation area with noise and eccentricity of the vortex. The test section was designed to be twice as long compared to the original outlet section of the draft tube, in order to see how the pulsating jet influenced the flow. The evolution of the pressure pulsations in the first three measurement levels (L0, L1 and L2) are of the most interest.

To have an image of how the pulsating jet created with this device could have negative effects on the other components, the device was evaluated according to three configurations (Figure 7). The tests concentrated on the L0 level (at the inlet of the test section), where three cases were studied: with a pulsating jet generated by the device VO and no operating flow rate, with a pulsating jet generated by the device VO and an operating flow rate, and without a pulsating jet generated by the device VO and an operating flow rate (with vortex rope). It was observed that when the pulsating jet was injected in the test section, the equivalent amplitude had a value of 0.03 at Q_nom = 0 l/s, which represents was 12% from the equivalent pressure amplitude generated by the swirling flow with the vortex rope (Q_nom = 30 l/s). Therefore, the pulsating jet amplitude has a small order of magnitude for damaging the hydraulic components of the turbine. Moreover, when the pulsating jet was in operation (Q-jet = 3.6 l/s, Q_nom = 30 l/s), no additional frequencies and pressure amplitudes were detected in Fourier spectra compared to the control values.

4. Conclusions

The paper introduces an innovative device for mitigating the self-induced instabilities associated with swirling flows with precession motion. The goal of this device is to introduce a pulsating water jet along the discharge cone axis through the runner of a hydraulic machine (e.g., Francis turbine). The pulsating water injection technique uses an additional energy input. We performed experimental investigations on the cases with and without a pulsating jet. The device that produces the pulsating jet was introduced on a test rig that offered the same configuration of the flow as a Francis turbine that operates at part load conditions. The main conclusions are presented below.

(1) The pulsating jet injection technique provided by the new device mitigated the amplitude and dominant frequency of pressure fluctuations. The dominant frequency is reduced to 37% from the initial value without the pulsating jet and the pressure amplitude, regarding the values without the pulsating jet, is reduced to 16.5% at L0, to 26% at L1, and to 22% at L2. However, a larger pulsating jet discharge is needed in order to practically remove all amplitudes and consequently eliminate the helical vortex.

(2) The discharge of the pulsating jet necessary to mitigate pressure fluctuations, compared to the axial water jet injection technique, is 10−12% from the nominal discharge. We mention that the initial results presented in the manuscript are to prove the concept of pulsating water jet control technique using a new device. According to Bosioc et al. [6], 14% of the nominal discharge is needed in order to eliminate pressure pulsations for continuous and constant water jet injection.

There exists a difference of 2% between pulsating jet and constant axial jet injection. Once again, we mention that the tests were performed on a surrogate model. Most likely, when utilized on a real size Francis turbine model, the difference will be significant. In future work, the target will be to decrease the discharge of the pulsating jet using this new device compared to the injection of constant axial jet flow. The last remark can be achieved by modifying the frequency of the pulsating water jet and finding the right configuration between the frequency of the swirling flow with vortex rope from the conical diffuser and the frequency generated by the VO.

(3) From the experimental investigations, it was observed that the pulsating water jet with VO did not introduce supplementary frequencies and pressure amplitudes that could damage other mechanical components, as resulted from the Fourier spectra.