A Perspective Review of Passive Techniques Applied to Control the Swirling Flow Instabilities From the Conical Diffuser of Hydraulic Turbines

Hydropower is the most important renewable source, providing 71% of electricity obtained from renewable sources [1]. It is also one of the most important resources in maintaining the global electricity grid. It can supply electricity, or it can be stored to satisfy real-time energy needs. In short, hydropower is a stabilizer of the network - it quickly provides energy after a power outage and addresses peak requirements while maintaining the voltage levels and frequencies in the network [2–4]. Because hydropower is flexible and can be stored, it is complementary to other forms of fluctuating sources such as wind or solar energy. Thus, with hydro - energy it can be ensured that variable power supplies remain constant - even when the sun does not shine, or the wind does not blow.

Because, of fluctuating energy sources, the hydraulic turbines have to operate on a large scale of regimes, far away from their optimum (the best efficiency point, BEP). Thus, Francis-type fixed-blade turbines, which operate at partial flow rates, have a high value of the swirling flow at the inlet of the draft tube because of the mismatch between the swirling flow generated by the guide vane and the angular impulse extracted from the turbine runner [5].

The key feature of swirling flow is self-induced unsteadiness, which is evaluated by pressure fluctuations (periodic or not), accompanied by dissipation of kinetic energy. As a result, the swirling flow loses its stability, and then pressure fluctuations and vibrations are generated.

The physics of the swirling flows has been studied both numerically and experimentally for more than half a century [6]. However, this phenomenon associated with turbomachines running on partial load is an open problem. When the swirling flow in the draft tube decelerates, it becomes unstable, leading to the appearance of the helical vortex (vortex rope) [7–9].

The vortex rope is the major cause of the occurrence of pressure fluctuations in the draft tube of hydraulic turbines operating at partial load [10,11]. Cassidy and Falvey [12,13] have shown that hydrodynamic instabilities generate pressure fluctuations. They also showed that if the intensity of the vortex increases to a critical value; both the Strouhal number (dimensionless frequency) and the pressure amplitude are directly proportional to the intensity of the vortex. Zhang et al. [14] and Wang et al. [15,16] studied the origin of pressure fluctuations in Francis turbines operating at partial load. Susan-Resiga et al. [17] analyzed the downstream flow of Francis turbines, which operate at different operating points, to evaluate the pressure recovery coefficient. Research on the flow field from the conical diffuser of hydraulic turbines, which are operated at part load, was carried out to determine the developing cause of vortex rope. In that way, different instruments were used to measure velocity and pressure fields.

In the world, only a few laboratories have successfully investigated unsteady three-dimensional (3D) swirling flow with precession motion in the conical diffuser, using particle images velocimetry (PIV) and laser doppler velocimetry (LDV), Kirschner et al. [18,19], Avellan [20], Ciocan et al. [21], Iliescu et al. [22], Goyal et al. [4,23].

Decaix et al. [24] developed a comprehensive analysis of the flow stability, as well as the mechanism, which leads to the formation of vortex rope. In optimal conditions, the flow leaving the turbine is axial, without rotational velocity. However, when the turbine (especially turbines with fixed blades, e.g., Francis type), is operating at partial load or far from the maximum efficiency point, vortex rope occurs. When the output power is lower than optimal, the output flow from the runner rotates in the same direction as the runner; the vortex is positive. If the output power is higher than optimal, the output flow from the runner opposes the rotation of the runner, and the vortex is negative.

Thus, the absolute value of the vortex increases and the distribution of the axial velocity in the draft tube becomes distorted. The flow is pushed to the periphery of the draft tube cone, and the helical vortex is appearing, which rotates around the axis of the draft tube; this movement is called the vortex precession. If the pressure in the draft tube is low, up to the vaporization pressure, cavitation appears, making the vortex visible. In addition, if the air is introduced into the draft tube, the vortex can be visualized. The shape of the helical vortex led to the appearance of various names in the literature such as spiral vortex, corkscrew vortex, and vortex rope (Fig. 1).

An outstanding example of the helical vortex is presented by Nishi et al. in the 1980s [25,26]. It shows that a model comprising a “dead” (quasi-stagnation) area of flow, around which swirling flow takes place (Fig. 2), can be satisfactorily represented by the average circumferential velocity profiles.

In the case of operating regimes with higher flow rates than the nominal one, the vortex rope has a cylindrical shape with low-pressure pulsations. At 70% of the nominal flow, the pressure pulsations, because of the swirling flow, have the highest values. At operating regimes below 50% of the nominal flow, it forms two or three vortices [27].

Jacob [28] shows distinct forms of vortex rope on the hill chart, in the draft tube of a Francis turbine. Another example of the vortex rope in the draft tube is presented in the FLINDT project [20]. The aim was to investigate the three-dimensional flow in the draft tube of hydraulic turbines at several operating regimes, for a better understanding of the phenomenon that leads to the appearance of the vortex rope. Other researchers investigate the vortex rope phenomenon [29].

Foroutan et al. [30,31] and Kirschner et al. [18,19,32], show that the vortex rope appearance is connected to the development of the quasi-stagnant region at different operating regimes far from optimal. In addition, a double helix vortex breakdown can occur at a low Reynolds number [33]. Stefan et al. [34] analyzed the flow field of vortex rope using the proper orthogonal decomposition. It is shown that the flow field can be reconstructed with a limited number of modes. A linear global stability analysis of the time-averaged flow field interprets the vortex rope as a globally unstable eigenmode [35,36].

Pressure fluctuations associated with the vortex rope can influence other parts of the hydraulic system, resulting in severe vibrations, and destruction of bearings, runner blades, or turbine shaft [37–40].

Brekke [41–43] presents the accident that occurred at the Shushenskaya hydro-electric power plant in Russia, where because of the partial load operation of the turbine and the large pressure fluctuations, blades break, and it occurred runner cavitation and breaking of the bolts which connected the flanges. Also, cracks in the concrete foundation can occur because of vibrations produced by the vortex rope [44]. This phenomenon can interrupt the turbine operation through power swings [45,46].

To be competitive, the industry is constantly looking for better products with reduced design cycles and low costs. The new requirements on the energy market make it attractive to impose turbines that operate beyond their optimal operating conditions. Also, many of the hydro-electric power plants have old turbines and need refurbishment and modifications. The solutions implemented so far in hydro-electric power plants have led to the development of methodologies, which can mitigate the vortex rope and its related consequences.

Various techniques are being used to control the vortex rope [47]. Blommaert et al. [48] show a classification of swirling flow control techniques in the conical diffuser as active or passive.

Thus, if an external energy source is used to control or mitigate the vortex rope, we have active control. Examples of active control are the injection of air or water into the cone [49,50], and the injection of tangential water jets at the periphery of the cone, Kjeldsen [51].

Passive control means the control of the instabilities of the swirling flow without introducing energy. Moreover, passive techniques involve structural changes in the components of the hydraulic turbine, such as fins mounted on the cone of the diffuser [52] various shapes of the nozzle [53], or the use of channels mounted on the cone Kurokawa et al. [54].

As mentioned in the abstract, the review focuses on the passive techniques of swirling flow control from the conical diffuser of hydraulic turbines. Compared with the active control techniques, the passive ones do not introduce volumetric losses in the system and do not have additional energy consumption that can affect turbine efficiency. In that way, further, as state of the art, will be presented some examples of passive techniques, implemented in hydro-electric power plants.

One passive control technique of mitigating pressure fluctuations that occur at part-load, common in hydro-electric power plants is the air admission into the conical diffuser. This swirling flow control technique improves both the pressure recovery along the cone and the mitigation of the pressure pulsations [55].

The air admission can be made either through the runner nozzle provided with the inner channel (point A), at the periphery of the runner close to the ring (point B), or through the guide vane, upstream of the runner (point C), Fig. 3. The main issue of this technique is finding the optimal amount of air flow, which has to be used, Pappilon et al. [56].

The stabilizer fins (or ribs) mounted longitudinally on the cone (Fig. 4) are used to eliminate the vortex rope and the associated pressure pulsations [57].

Their maximum efficiency is achieved if it mounts them as close as possible to the inlet of the cone, but also through their dimensions, shape, and number. Disadvantages of using fins include decreased turbine efficiency, high-frequency noise, and problems with their installation on the cone.

The J-groove technique (Fig. 5), used by Kurokawa et al. [54] consists in placing cone-shaped channels along the conical diffuser. Thus, the tests performed showed that this technique considerably reduces the swirling flow by about 85%. The disadvantage of this technique is that for each operating regime, other channels of different sizes must be installed so as not to affect the turbine efficiency. Chen et al. [58,59] have optimized the technique to improve the swirl intensity by 1.5%.

Different nozzle extensions of the runner for Francis turbines (Fig. 6), in the conical diffuser, have been tested in situ. The goal of nozzle extensions is to mitigate the quasi-stagnant region that occurs in the center of the flow [49]. Vekve et al. [53] present a study of the swirling flow from the conical diffuser of hydraulic turbines operating at part load, with different configurations of the nozzle shape. The problem with the extended nozzle is that it decreases the transformation of kinetic energy into potential pressure energy, which leads to problems related to the bearing of the runner [49]. Another way to mitigate the pressure pulsations from the conical diffuser is to decrease the recirculation area in the middle of the cone by filling it with a solid body as cylindrical extensions (Fig. 7), from the elbow of the diffuser to the runner (columns) [13]. The major problem of this technique is that the diameter of the column is impossible to be changed, depending on the operating regime of the turbine.

The previous chapter shows that in the literature there are techniques that have been tested and implemented on experimental test rigs and in situ, to mitigate the effects of pressure pulsations and the quasi-stagnation region associated with the vortex rope, which lead to major disadvantages.

Thus, this chapter will be presented new and various passive control techniques of swirling flow instabilities developed and implemented on experimental test rigs over the last decade.

According to Bosioc et al. [60], the source of instability can be practically eliminated by injecting a jet of water along the symmetry axis of the cone (through the runner). The major disadvantage of this technique is the relatively high flowrate of the jet compared to the turbine water flow.

This disadvantage, which introduces significant volumetric losses, or requires additional energy consumption, justified the reluctance of turbine builders to implement this new technique in hydro-electric power plants. Based on these premises, a new passive flow control technique is being developed, which eliminates the above drawbacks, does not introduce volumetric losses, and does not require additional energy consumption [61]. The remark presented above leads to the question of how to supply the jet without volumetric losses and without decreasing the efficiency of the turbine.

Thus, it is observed by examining the swirling flow in the cone of the draft tube of the Francis turbines operating at partial load, that there is a significant excess of static and total pressure at the cone wall. This observation led Susan-Resiga and Muntean [62] to introduce a new technique for controlling the swirling flow in the conical diffuser, called flow-feedback. With the help of this new technique, part of the flow is collected from the cone wall downstream of the runner and transported upstream, to eliminate the rope vortex, by injecting it at the end of the crown. Figure 8 shows a comparison of the streamlines, on a two-dimensional axial-symmetric analysis used by Susan-Resiga and Muntean [62], with and without flow-feedback. Obviously, the flow-feedback generates a jet control, which successfully eliminates the quasi-stagnation area, stabilizing the flow. Figure 9 shows the excess total pressure near the cone wall (top plane) and the decrease in total pressure near the axis when the jet injection through flow-feedback is implemented (bottom plane).

Next, will be presented some elements of design, implementation on the test rig, testing, and experimental/numerical analysis of this technique, which has been detailed in [61,63–68].

The solution proposed for this technique involves taking the flow that supplies the jet, downstream of the draft tube cone, by introducing a spiral case with a double outlet (twin spiral case), downstream of the conical diffuser, through a by-pass system, which takes this flow and inserts at the outlet of the runner crown (Fig. 10(a)).

The entire system has been called flow-feedback (Fig. 11). This solution allows significant decreases of the radial gauge, an imperative condition for the implementation on real turbines, as well as the decrease of hydraulic losses.

Unlike ordinary spiral cases used in the construction of centrifugal pumps, the designed twin spiral case has a meridian flow at the inlet in the axial direction and not radial. That is why the meridian section shown in Fig. 10(a) differs from the classic construction of a spiral case disposed at the outlet of the centrifugal pump impeller.

In Fig. 10(b), the obtained streamlines associated with the tangential flow from the inlet to the outlet can be observed, which offers the same flow configuration as in a pump spiral case.

To evaluate experimentally the flow-feedback technique, it was implemented on the test rig, which has a swirl apparatus offering a similar flow as a Francis turbine that operates at part load—Figs. 12(a) and 12(b) [61]. From the analysis of the unsteady pressure measurements at the wall of the conical diffuser, in four cross sections arranged successively from the minimum section downstream, a mitigation of 30% of the pressure pulsations amplitude is found, according to Fig. 13. Also, the Strouhal number decreases up to 28%, when flow-feedback is implemented. This means that the precession motion of the vortex rope is diminished. An example of the full spectrum of the pressure pulsations with and without FF is shown in Fig. 14, where it can be observed the decrease in amplitude and frequency. Details regarding the frequency spectrum are presented in Refs. [60] and [61].

The results are presented in dimensionless form:

• The frequency is expressed using the Strouhal number, where f is the precessing frequency of the vortex rope, D_t is the diameter of the minimum part of the test section (throat), and V_t is the velocity from the test section throat

  $Sh=fDtVt$

  (1)
• The pressure pulsation is dimensionless using the equivalent amplitude obtained according to Parceval's theory, where $pRMS$ is the random mean square of the fluctuating part of the pressure signal

  $A≡2pRMSρVt2/2$

  (2)

Details of the Parceval theory can be found in Ref. [60]. This first stage of the experimental investigations led to the conclusion that the losses on the hydraulic system, including the spiral case and return pipes, have to be compensated by the pressure difference between the inlet of the spiral case and the nozzle outlet.

Thus, the results obtained with the flow-feedback technique are compared with the results obtained by jet injection with an auxiliary pump, where it is observed that the flow-feedback ensures a jet flow of approximately 10% of the main flowrate below the threshold identified by Bosioc [60] in which there is a sudden and substantial decrease in the amplitude of the pressure pulsations. However, these investigations show that the flow-feedback technique can provide a large part of the flow required for the control jet, and slows down the precession movement of the helical vortex.

Therefore, further will be presented a simple technical solution to supply the jet flow by using a pair of ejector pumps mounted on the return pipes of the spiral case. The solution is simple from a constructive point of view and allows an easy installation in the gauge of the return pipes. Although the ejector pump requires additional energy to supply the main jet, the amount of additional energy is small compared to the energy consumption associated with the swirling flow control jet used by Bosioc et al. [60].

In practice, it is even acceptable to supply the main jet with water under pressure taken from the upstream pipe of the turbine, because the associated volumetric losses are small and comparable to the volumetric losses of the turbine through the labyrinth seals of the runner. The evaluation of flow-feedback technique with additional energy supply (FF+) reveals that the proposed goal—to increase the flow of the control jet over the threshold value necessary to mitigate the instability of swirling flow—has been achieved. It is clear that the jet flow has the desired value and therefore the pressure pulsations are mitigated in all measuring sections of the conical diffuser Fig. 15.

Experimental investigations on the capacity of the flow-feedback system to control the swirling flows were initially focused on evaluating the decrease in the amplitude of pressure pulsations. However, pressure measurements are only performed on the cone wall and provide only indirect information about the swirling flow in the conical diffuser. Therefore, noninvasive measurements of the velocity field using Laser Doppler Velocimetry, also, were performed.

The time-averaged velocity profiles, together with the mean square of the fluctuations, and the 3D Fourier spectrum of the unsteady velocity signal on the measuring axes in the conical diffuser (Fig. 16), highlight the decrease of the velocity field, both for the meridian and circumferential velocity components (Figs. 17–20), together with the use of the flow-feedback system, respectively of the additional energy input with the ejector pump.

The main conclusion of the complex investigations of the velocity field is that the flow-feedback system, with a minimum additional energy input, has fully proved its effectiveness by drastically mitigating the fluctuations of the hydrodynamic field by eliminating the main cause of instability—the helical vortex with precession movement.

Also, a numerical analysis was carried out to validate the experimental data of swirling flow in the conical diffuser. For the analysis of the flow in the test section, a simplified model of turbulent flow, axial-symmetrical, with swirl is used [69]. The numerical results presented confirm that the simplified axial-symmetric model correctly captures the flow-feedback operating mode. However, an important limitation of the model is the way of specifying the hydraulic losses on the return path that ensures the supply of the jet. The relatively complex hydraulic route on the test rig (spiral case, return pipes, elbows, and channels) is modeled in a very simplified version in the axisymmetric version. Therefore, the actual hydraulic losses must be introduced via boundary conditions, to obtain in the numerical simulation jet flow similar to the measured values, without and with additional energy input.

However, the operating regime and the main hydrodynamic characteristics are highlighted by numerical simulation, Fig. 21, of the swirling flow control system that was investigated experimentally.

where V_throat is the velocity from the test section throat and V_{(m*,u)measured} is the measured velocity profile [76].

Also, it investigated the distribution of pressure on the wall, highlighting clearly in Fig. 25 significant improvements in pressure recovery on the conical diffuser with the use of flow-feedback control technique.

The main conclusions on these techniques presented in this chapter show that by identifying the main shortcoming of the swirling flow control in conical diffusers by water jet injections along the symmetry axis, it is proposed to achieve a jet supply system that does not introduce unacceptable volumetric losses for the hydraulic turbine. It is found that the jet can be supplied by recirculating a fraction of the turbine flow taken downstream from the conical diffuser, without influencing the flow and energy transfer from the turbine runner. The proposed technical solution goes through the natural stages of design, verification by numerical simulation, practical realization, testing, and performance evaluation, the approach being completed from a scientific point of view by detailed experimental investigations of the pressure and velocity field, respectively by numerical investigations that provide an image, clear and complete understanding of how the main cause of flow instability is eliminated.

Another technique for eliminating the self-induced instabilities generated by the swirling flow in the conical diffuser of the hydraulic turbines is the passive method with an adjustable diaphragm introduced at the outlet of the conical diffuser [70]. This passive method allows the operation of hydraulic turbines over a much wider range, by eliminating the self-induced instabilities generated by a swirling flow that occurs at partial load. The new technique involves the introduction of an adjustable diaphragm at the end of the conical diffuser, whose goal is to close the quasi-stagnation region associated with the vortex rope—Figs. 26 and 27. The adjustable diaphragm will throttle the cross section area from the outlet of the conical diffuser.

All the positions of the circular cross section are centered on the axis of the turbine. The shutter area of the adjustable diaphragm has to be correlated with the turbine operating regime. As a result, the diaphragm should be retracted to the cone wall, when it is not necessary to be used (i.e., at BEP), to avoid any additional hydraulic losses [71]. By closing the quasi-stagnation region, the self-induced flow instabilities will be eliminated and thus the pressure fluctuations and vibrations so harmful to the hydraulic turbine will disappear. This innovative solution eliminates the disadvantages of other techniques that have a difficult implementation in a hydro-electric power plant and high costs. Moreover, this new technique will open new horizons in research in hydraulic machines.

As in the case of the techniques presented above, this one also benefited from the same approach for its development: unsteady 3D numerical analysis, design, test rig implementation, and testing. It selected four openings corresponding to different shutter areas of the adjustable diaphragm. The inner diameters of d = 0.134 m, 0.113 m, 0.1 m, and 0.088 m and their associated shutter areas of Ad = 0.014 m², 0.01 m², 0.0078 m², and 0.006 m² were considered in this experimental and numerical study. These values of inner diameter correspond to the shutter area ratios (A_a) of 30%, 50%, 60%, and 70% regarding the cone outlet area A₀, see Table 1 [71].

The qualitative results obtained from the 3D numerical simulation in Fig. 28, clearly show that when the flow is obstructed by inserting a diaphragm at the outlet of the cone of the draft tube, the precession movement and the quasi-stagnation area associated with the vortex rope are diminished, by transforming it into a straight vortex.

From the efficiency point of view, the main purpose of the hydraulic turbine draft tube is to convert as much as possible the kinetic energy at the runner outlet into pressure potential energy with minimum hydraulic losses. To analyze the kinetic-to-potential energy transformation process, as well as its efficiency, it was introduced the following integral quantities:

Below is a quantitative analysis of energy loss and recovery coefficients, Figs. 29 and 30. An improvement in energy recovery is observed until the outlet of the test section where there is a decrease because of introducing the diaphragm here and thus recirculation areas appear. The coefficient of hydraulic losses ζ and the rate of conversion of kinetic energy into potential χ, Fig. 30, also have a slight improvement in the first part of the cone for all cases with the diaphragm, but in the last part, it decreases for the same reason presented above. However, it should be borne in mind that the purpose of this technique is to eliminate the pressure pulsations due to the instability of the vortex rope in the conical diffuser, not necessarily to improve it from the energy transfer point of view. Also, it is presented the loss coefficient and kinetic-to-potential conversion ratio versus diaphragm shutter area Fig. 31. It is shown that the losses and the energy conversion ratio reach the maximum values for the highest shutter area of the diaphragm.

Obviously, by throttling the outlet flow from the conical diffuser, the losses increase, but the recovery of pressure increases. However, we recall again the sentences presented above that this control technique addresses the operation of turbines at partial load, the purpose being to eliminate the pressure pulsations associated with the instability of the rope vortex in the conical diffuser, not necessarily to improve it from an energy transfer point of view. According to results obtained from 3D numerical analysis, it was chosen the shutter area and the corresponding diameter of the diaphragm for the experiment. Below, it will be shown that the diaphragm can be operated from 40-60% shutter area ratios, at part load conditions, to be a good balance between hydraulic losses and dynamical behavior.

Tanasa et al. [72,73] show a good correlation between numerical analysis results and experimental ones. Experimentally, the measurements focused on the unsteady pressure and velocity field. Figure 32 shows the pressure recovery coefficient at the wall with and without the diaphragm, where a significant increase in pressure recovery can be observed when the diaphragm is used. For instance, at level L2, in the mid-dle of the cone, the pressure recovery coefficient has increased to a double value. It is clear that by mitigating the vortex rope, the conversion of dynamic pressure into static pressure is more efficient.

For real turbines, this improvement in pressure recovery in the conical diffuser translates into increased turbine efficiency, which operates far from the best efficiency point, especially for low head turbines [74].

At the L1 level, the pressure recovery has a smaller increase, and at the L3 level, there is an increasing overestimation, because of the recirculation zones that appear on the wall near the diaphragm. However, from a hydrodynamic point of view, there is a significant improvement. This overestimation was, also, observed in the results obtained from the 3D numerical analysis. Figure 33 shows, from a global point of view, the decrease in amplitude of the pressure fluctuation on the levels L0…L3, with the increase of the shutter area at the outlet of the test section.

It is observed that with the increase of the shutter area at the outlet of the test section, the equivalent amplitude of the pressure fluctuations decreases significantly. The results of the velocities profile with and without the diaphragm are presented in dimensionless form using the following reference values: the minimum diameter of the test section D_throat = 0.1 m and the mean velocity at the throat corresponding to the discharge Q = 0.03 m³/s [75]. For W1 measuring axis (Fig. 34), shows a quasi-stagnant region associated with the meridian velocity profile for both cases with and without diaphragm d = 0.113m is similar.

For the other cases the quasi-stagnant region decreases below zero, this means recirculation areas occur when the flow is throttled. For the measuring axis W2, in the case without the diaphragm, the quasi-stagnant region is larger than the case from W1. The meridian velocity profile in the case with the diaphragm evolves from a weak profile to an axial jet when the throttling is larger (the inner diameter of the diaphragm is smaller). As a result, the quasi-stagnant region associated with the swirling flow with the vortex rope is mitigated (Fig. 35).

The main remarks of this passive control technique are summarized below:

• The diaphragm method significantly improves the pressure recovery at the cone wall, by reducing hydraulic losses;

• The 3D numerical analysis shows an improvement in the efficiency of the draft tube cone (conversion of kinetic energy into potential energy), especially in the first part of it, as well as hydraulic losses;

• The diaphragm technique mitigates the amplitude of the pressure fluctuations, keeping a constant frequency;

• The rope vortex rope is mitigated, because of the negligible rotating component;

• The velocities profile shows the evolution of the quasi-stagnant region associated with the vortex rope, which is mitigated when the diaphragm is implemented downstream of the conical diffuser.

As recommendations, the diaphragm can be operated from 40-60% shutter area ratios, at part load conditions, to be a good balance between hydraulic losses and dynamical behavior. Moreover, the diaphragm can be retracted to the diffuser wall, when the turbine operates at the best efficiency point.

This paper reviews the passive swirling flow control techniques from the conical diffuser of hydraulic turbines. The problem of swirling flow represents an actual interest for the industry of hydraulic machines, now the hydro-electric power plants are being forced to operate under part load conditions. This type of operation involves the appearance of the so-called vortex rope, in the conical diffuser, which is accompanied by high pressure pulsations. The effects of pressure pulsations caused by the vortex rope, often lead to cracks in the blades or their rupture, pulled out of the ogive from the runner crown, or damage to the cone. Over time, different (passive) techniques have been used to eliminate the vortex rope and its effects on the hydro-electric power plant: air admission, stabilizer fins, J-grooves, runner cone extensions, and columns in the diffuser. All these techniques used so far, eliminate the vortex rope and diminish its effects, but are designed to be operated at a certain regime and are difficult to implement in the hydro-electric power plant.

The new passive techniques developed over the last years (FF, FF+, adjustable diaphragm), have the advantage that besides mitigating the vortex rope from the conical diffuser, they are robust and can be easily implemented in a hydro-electric power plant, which may be new or being refurbished. Anyway, until now, there is no particular technique that is certainly accepted, the choice depending on a case by case according to the challenges in situ.

However, from the point of view of developing passive techniques, in recent years Flow-Feedback would be the most accessible technique for robustness and efficiency, but the adjustable diaphragm would be at the lowest price. Moreover, it is mentioned that this review is more addressed to developments in the laboratory to prove the concept and so far, an economic analysis has not been achieved to implement in situ, if we refer to new passive techniques. Anyway, a panoply of advantages and disadvantages of the passive swirling flow control techniques in the conical diffuser of hydraulic turbines, from those in the specialty literature and those developed in the last decade are shown in Table 2.

The main features of the passive control techniques, listed above (FF, FF+, and adjustable diaphragm), can be summarized as follows:

• can improve pressure recovery and decrease hydraulic losses in the conical diffuser of hydraulic turbines which are operated at part load;

• the amplitude of the pressure pulsations decreases up to 80% and the frequency up to 50% (Fig. 15);

• the evolution of the quasi-stagnation zone is quantified by plotting the meridian and circumferential velocity profiles. It is observed, that the quasi-stagnation region associated with the rope vortex is mitigated with the introduction of passive FF, FF+, or adjustable diaphragm control techniques.

Thus, according to the conclusions summarized above, in our opinion, these techniques for controlling the swirling flow in the conical diffuser of hydraulic turbines, can improve the efficiency and safe operation of turbines at part load regime. Moreover, these new control techniques will open new horizons in the research of hydraulic machines.

Hydropower is still amongst the largest sources of renewable energy. The challenge is to make hydropower in a range available in a time as short as possible. To do this, it will be need optimization of the actual control techniques, increased flexibility, and new technologies to be developed to increase ramping rates and to allow start-stop-cycles, while lifetime of components and respective lifetime prediction methods under heavy-duty operating conditions are considerably improved while avoiding adverse effects on downstream water courses. Nevertheless, sustainability have to maintain the overall value of hydropower by balancing social, economic, and energy market factors correlated to the environment.

This work was supported by a grant of the Ministry of Research, Innovation and Digitization, CCCDI - UEFISCDI, Project No. PN-III-P2-2.1-PED-2021-1014, within PNCDI III. The authors are also very thankful to the researchers/publishers for permission to reproduce some of the figures in this article.

A, B, C =

points where air admission can occur

A_a =

shutter area ratio

A_d =

diaphragm inner area

A₀ =

cone outlet area

A_r =

shutter area

BEP =

best efficiency point

C_PR =

potential energy recovery coefficient

C_KR =

kinetic energy recovery coefficient

d =

diaphragm inner diameter

D_t =

throat diameter

f =

frequency

FF =

flow-feedback

FF+ =

flow-feedback with additional energy

LDV =

laser doppler velocimetry

L0, L1, L2, L3 =

levels of pressure measurements

P_RMS =

random mean square of the fluctuating part of the pressure signal

PIV =

particle image velocimetry

Q =

main discharge

Q_jet =

discharge jet

Sh =

Strouhal number

V_t =

velocity from the throat of the test section

W1, W2 =

survey axis of measuring windows

ρ =

water density

ζ =

energy loss coefficient ζ

χ =

kinetic-to-potential energy conversion ratio