# Preliminary design of adjustable Guide Vanes for PaTs in Pumped storage applications

Domenico Filannino, Michele Stefanizzi, Tommaso Capurso, Rosada Quattromini, Rosario Monteriso, Francesco Annese, Marco Torresi

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Domenico Filannino, Michele Stefanizzi, Tommaso Capurso, Rosada Quattromini, Rosario Monteriso, et al.. Preliminary design of adjustable Guide Vanes for PaTs in Pumped storage applications. IOP Conference Series: Earth and Environmental Science, 2024, 1411 (1), pp.012038. 10.1088/1755-1315/1411/1/012038. [hal-05361253](https://hal.science/hal-05361253v1)

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# Preliminary design of adjustable Guide Vanes for PaTs in Pumped storage applications

Domenico Filannino¹, Michele Stefanizzi¹, Tommaso Capurso², Rosada Quattromini³, Rosario Monteriso³, Francesco Annese³, Marco Torresi¹

¹Department of Mechanics, Mathematics and Management (DMMM), Polytechnic University of Bari, Bari, 70126, Italy.

²Arts et Metiers Institute of Technology, CNAM, LIFSE, Paris, 75013, France.

³Nuovo Pignone Tecnologie Srl, Strada Provinciale Modugno Bari 10, 70123 Bari, Italy.

E-mail: domenico.filannino@poliba.it

**Abstract.** Pumped-Storage Hydropower Plants (PSHPs) are a well-established technology for storing large amounts of energy and enhancing the power systems flexibility. In the framework of Micro and Mini Hydropower, Pumps as Turbines (PaTs) could represent a valid cost-effective solution also for PSHPs. Nonetheless, the lack of a control device could represent a problem, mainly with non-fixed operating conditions. Additionally, PaTs show generally a steep efficiency decrease at part load. Thus, since conventional PaTs do not present adjustable geometries, a preliminary sizing of an adjustable Inlet Guide Vane (IGV), referring to turbine mode, is proposed in this work. The aim of this work is to propose a methodology suitable to modify a baseline PaT introducing an adjustable IGV to perform a high efficient control in terms of flow rate and pressure drop. The machine selected for the proposed study is a centrifugal pump with a specific speed, $n_q$, equal to 16. The adjustable IGV are inserted between the volute cutwater and the impeller by reducing impeller diameter. To obtain an initial solution for the stationary blades row profile, a review of Francis turbines guide vanes design methods is conducted. Finally, a numerical study on the influence of guide vanes number is performed.

## 1. Introduction

Pumps as Turbines (PaTs), also referred to as Hydraulic Power Recovery Turbines (HPRTs), are becoming a more and more consolidated technology, especially for Micro and Mini Hydropower (respectively with power in range 5÷100 kW and 100 kW ÷ 1 MW). Morevoer, PaTs could represent a valid solution also for Pumped-Storage Hydropower Plants (PSHPs) [1]. In fact, in recent times, there has been growing interest in micro and small scale facilities, thanks to their potential integration with Renewable Energy Systems (RES) in off-grid island networks [2]. In the last years, several works have focused on how to increase efficiency of PaTs. Doshi et al. [3] investigated numerically and experimentally the effect of impeller trailing edge and shroud rounding. This study was carried out on four centrifugal pumps with different specific speed number, finding out a 1 ÷ 2.5% rise in efficiency. Since the number of impeller blades of a PaT is lower then the one of a Francis turbine, [4] Yang et al. [5, 6] analyzed the effect of increasing the number of impeller blades and the addition of splitter blades. While modifying the number of impeller blades can increase efficiency of 1.5%, the introduction of splitter blades can shift

<figure><img src="image_2.png" /></figure>

Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
the entire efficiency curve up of a significant 3.4%. Other works have focused on the effects of cutwater radial distance [7] and shape optimization [8]. While radial distance affects marginally the best efficiency, showing anyway an optimal value for 14% of the impeller diameter, optimizing its shape could lead to an increase of efficiency of 3.9%. Polak [9] modified a centrifugal pump according to Francis turbine design [10], showing very different characteristic curves from the original prototype but improving the best efficiency value of 7.9%.

However, the implementation of PaTs with variable operating conditions is highly problematic for their poor part load performance due to the absence of inlet flow control. This is crucial especially when it is not possible to perform control by adjusting the rotational speed. In order to increase the PaT Best efficiency and to flatten the efficiency curve, some works proposed fixed guide vanes for PaT. For example, Shi et al. [11] performed a numerical study of a mixed type centrifugal pump with fixed guide vanes, showing significant improvements in terms of efficiency. Hongyu et al. [12] analyzed numerically and experimentally the influence of the clocking effect, i.e., the relative position of guide vanes with respect to the volute tongue, showing the existence of an optimum relative position. In another work, Shi et al. [13] proposed a numerical and experimental work on a mixed type centrifugal pump, different from the one analyzed before, with fixed guide vanes. The introduction of guide vanes changed completely the flow rate range, highlighting the necessity of the guide vanes to be adjustable.

Thus, a preliminary sizing of an adjustable Inlet Guide Vanes (IGV), referring to turbine mode, is proposed in this work, with a specific focus on the effect of the number of IGV. The kinematics of IGV is designed to be fully inside the machine and to have only one shaft passing through the pump body. This was to simplify the hydraulic seals and to obtain a compact solution. The aim of this work is to propose a methodology suitable to modify a baseline PaT by introducing an adjustable IGV to perform control in terms of flow rate and pressure drop. Moreover, a review of Francis turbines guide vanes design methods is carried out to support the proposed methodology.

## 2. Case study

The machine selected for the proposed study is a centrifugal pump with a specific speed number, $n_q$, equal to 16 [rpm, m³/s, m]. It is a single suction and double volute radial centrifugal pump. This machine was selected as the best one among all the pumps available at Nuovo Pignone Tecnologie Srl (Bari, Italy) compatible with the Polytechnic of Bari hydraulic test rig limits [14, 15, 16]. With the purpose to introduce the minimum number of modifications to the original machine, the adjustable IGV is supposed to be introduced between the volute cutwater and the impeller by reducing impeller diameter. Besides, having a low specific speed number machine allows to save enough radial space to install the IGV while avoiding large differences in the impeller outer blade angle, $\beta_{2,blade}$. Figure 1 shows the evolution from the original machine to the PaT equipped with IGV.

<figure><img src="image_3.png" /><figcaption>Figure 1: IGV allocation process.</figcaption></figure>

The choice of trimming the impeller instead of enlarging the volute, as done by Giosio et
al. [17] and Shi et al. [13], is due to the limits of the hydraulic test rig in terms of dimension and power limits. To be sure to have enough space for the IGV, the impeller was trimmed to the minimum allowable diameter, according to manufacturer correlations. After the impeller trimming, the blade height and the blade angle changed as reported in Table 1.

<table><caption>Table 1: Comparison between baseline and trimmed impeller data.</caption><thead><tr><td>Description</td><td>Parameter</td><td>Baseline</td><td>Modified</td></tr></thead><tbody><tr><td>Impeller outer diameter</td><td>D<sub>2</sub></td><td>D<sub>2,ref</sub></td><td>0.77 D<sub>2,ref</sub></td></tr><tr><td>Impeller outer blade height</td><td>b<sub>2</sub></td><td>b<sub>2,ref</sub></td><td>1.09 b<sub>2,ref</sub></td></tr><tr><td>Impeller outer blade angle</td><td>β<sub>2,blade</sub></td><td>β<sub>2,blade,ref</sub></td><td>0.9 β<sub>2,blade,ref</sub></td></tr></tbody></table>

## 3. Methods

### 3.1. Francis turbines guide vanes design methods

By introducing an adjustable Inlet Guide Vanes (IGV) to a Pump as Turbine (PaT), it is possible to provide a cost effective solution in comparison to small scale Francis turbines. In this way, it is possible to obtain a larger operational range than traditional PaT while increasing off-design efficiency. Due to manufacturers' confidentiality, there is no a vast literature about guide vanes design approaches used for hydraulic turbomachineries. In this work, a new procedure to design IGV for PaT is presented. Nonetheless, Francis IGV correlations have been used as good engineering standards for position and size.

A resume of the design approach is described below. To define the radial cascade of statoric blades it is necessary to define its inlet and outlet diameters, $D_{3d}$ and $D_{2d}$, as well as the radius of the pivots circumference, $D_{ax}$, the cascade height, $b_{IGV}$, the number of blades, $Z_{IGV}$, angle and thickness distributions along the blade camber line. All the involved parameters are summarized and graphically described in Table 2 and Figure 2.

<table><caption>Table 2: Radial cascade parameters.</caption><thead><tr><td>Param.</td><td>Description</td></tr></thead><tbody><tr><td>D<sub>3</sub></td><td>Cutwater diameter</td></tr><tr><td>D<sub>3d</sub></td><td>IGV inlet diameter</td></tr><tr><td>D<sub>ax</sub></td><td>IGV pivots diameter</td></tr><tr><td>D<sub>2d</sub></td><td>IGV outlet diameter</td></tr><tr><td>D<sub>2</sub></td><td>Impeller inlet diameter</td></tr><tr><td>Z</td><td>Num. of impeller blades</td></tr><tr><td>b<sub>2</sub></td><td>Impeller inlet height</td></tr><tr><td>Z<sub>IGV</sub></td><td>Num. of guide vanes</td></tr><tr><td>b<sub>IGV</sub></td><td>IGV height</td></tr><tr><td>L<sub>IGV</sub></td><td>IGV length</td></tr><tr><td>a<sub>2d,q</sub></td><td>IGV throat distance</td></tr><tr><td>φ<sub>IGV</sub></td><td>IGV pitch angle</td></tr><tr><td>θ<sub>IGV</sub></td><td>IGV wrapping angle</td></tr><tr><td>α<sub>3d</sub></td><td>IGV inlet angle</td></tr><tr><td>α<sub>2d</sub></td><td>IGV outlet angle</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>Figure 2: Radial cascade representation.</figcaption></figure>

Nechleba [10] proposed empirical correlations to determine IGV height and IGV outlet diameter according to the maximum flow rate operating condition. Then, it is possible to
estimate the number of IGV blades as:

$$Z_{IGV} = \frac{\sqrt{D_{2d}}}{4} + (4 \div 6) \qquad (1)$$

where $D_{2d}$ is the outlet diameter of the guide vanes expressed in mm. It is suggested to sharpen symmetrically the trailing edge with an angle from 12° to 20°. Moreover, the implementation of a standard airfoil profile is recommended.

Raabe et al. [18] proposed typical values for some of the main parameter of Francis turbines according to the specific speed of the turbine. In particular, for the lowest value reported, i.e., 17 [rpm, m³/s, m], $b_{IGV}/D_2 = 0.055$ and $D_{2d}/D_2 = 1.04$. Lazarevikj et al. [19] proposed the following relations between impeller inlet diameter, $D_2$, and IGV outlet diameter, $D_{2d}$, and between IGV outlet diameter and IGV inlet diameter, $D_{3d}$:

$$D_{2d} = 1.075D_2 \qquad (2)$$

$$D_{3d} = 1.125D_{2d} \qquad (3)$$

while the guide vanes pivot axis location, $D_{ax}$, is computed according to the specific speed number:

$$D_{ax} = D_2(0.29\Omega + 1.07) \qquad (4)$$

where $\Omega$ is:

$$\Omega = \frac{\omega\sqrt{Q}}{(2gH)^{0.75}} \qquad (5)$$

The outflow absolute angle of the guide vanes, $\alpha_{2d}$ is computed by applying the free vortex from the impeller inlet in the nominal working condition considering impeller shock-free inlet. The inflow angle of the guide vanes, $\alpha_{3d}$ is equal to $\alpha_{2d}$ in Lazarevikj's work. Then, the camber line is defined as a third order polynomial while the thickness distribution is described by Bézier polynomial curve with eight control points.

Dahal et al. [20] suggested to estimate the guide vane outlet diameter, $D_{2d}$ as 5% higher than the runner inlet diameter. The guide vanes pivot axis location, $D_{ax}$, is computed through equations 4 and 5. Then, a 10-20% overlap factor is suggested. The guide vane inlet diameter, $D_{3d}$ is evaluated such that pivot axis are located at 2/3 of guide vanes length. For the guide vanes profiles it is suggested to use a NACA airfoil.

Stojkovski et al. [21] proposed guide vanes pivot axis location, $D_{ax}$, as average of $D_{3d}$ and $D_{2d}$. Ghimire et al. [22] proposed to design the guide vanes and stay vanes of a Francis turbine for micro hydro applications (for power plants with power lower than 100 kW). In the aforementioned work, the guide vanes outlet diameter, $D_{2d}$, is suggested to be 5% higher than $D_2$, using a coverage factor in the range from 1.10 to 1.15. Stojkovski et al. [23] proposed a coverage factor higher than 1.05 and the following values for IGV radii: $D_{2d}/D_2 = 1.05 \div 1.25$; $D_{ax}/D_2 = 1.16 \div 1.20$; $D_{3d}/D_{2d} = 1.10 \div 1.25$.

## 3.2. Design approach

For the design of kinematics it was chosen to have only one shaft passing through the pump body. This was to simplify the hydraulic seals. Referring to Figure 3, the action shaft is linked to the red pin, allowing the inner green ring and the connected pins to rotate. Then, the rotation of the small pins makes all the IGV shafts to rotate along their axis, in order to perform their angle control. The design condition of the first IGV configuration is chosen at the maximum Guide Vanes opening, i.e., at full load, considering a discharge 25% higher than the Best Efficiency flow rate of the PaT with the trimmed impeller. In fact, the nominal discharge
<figure><img src="image_5.png" /><figcaption>Figure 3: IGV kinematics front view.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Figure 4: Impeller inlet velocity triangle.</figcaption></figure>

of Francis turbines, i.e., the one at BEP, is always lower than the full load discharge. In the design operating condition the shock-free tangential velocity $c_{u2}$ is computed as follows:

$$c_{m2} = \frac{Q\eta_v}{\pi D_2 b_2 \xi_2} \qquad (6)$$

$$w_{u2} = \frac{c_{m2}}{\tan(\beta_2)} \qquad (7)$$

$$c_{u2} = w_{u2} + u_2 \qquad (8)$$

where $\beta_2$ is the impeller inlet angle with respect to the tangential direction, $D_2$ is the impeller inlet diameter, and $\xi_2$ is the blade blockage factor. Then, it is possible to compute the required tangential velocity at IGV outlet, $c_{u2d}$. By considering free vortex in the vaneless space it follows:

$$c_{u2d} = c_{u2} \frac{D_2}{D_{2d}} \qquad (9)$$

Moreover, the height of the distributor is almost double the impeller one. This with the variation of the absolute tangential component affects the absolute angle at the impeller inlet, $\alpha_2$.

It is important to point out that without a control device, i.e., the IGV, it is not possible to control the flow direction at the impeller inlet. In fact, from the numerical analysis of the PaT with trimmed impeller, the incidence angle at impeller inlet change from -15° to 15° in the range from $Q_{BEP,t,trim}$ to $1.35Q_{BEP,t,trim}$.

The distributor inlet angle was computed to obtain the shock-free condition. Knowing the volute outlet velocity components, $c_{u3a}$ and $c_{m3a}$, and the design discharge, it is possible to compute the distributor inlet angle as follows:

$$c_{u3d} = c_{u3} \frac{D_3}{D_{3d}} \qquad (10)$$

$$c_{m3d} = \frac{Q}{\pi D_{3d} b_{IGV} \xi_{3d}} \qquad (11)$$
$$ \alpha_{3d} = \arctan \left( \frac{c_{m3d}}{c_{u3d}} \right) \qquad (12) $$

Having estimated the inlet and the outlet angle of the first IGV configuration, a coverage factor $k_f = \theta_{IGV}/\phi_{IGV} = 1.2$ was chosen. The camber line then, was determined having a linear relation between the radius and the blade angle as follows:

$$ \alpha(R) = \alpha_{3d} + (\alpha_{2d} - \alpha_{3d}) \frac{(R - R_{2d})}{(R_{3d} - R_{2d})} \qquad (13) $$

The thickness distribution was assigned according to Figure 5 proposed in [24]. This thickness distribution is assigned after having applied the conformal transformation as shown in Figure 6.

<figure><img src="image_7.png" /><figcaption>Figure 5: Thickness distribution.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Figure 6: Conformal transformation.</figcaption></figure>

On this geometry a numerical analysis was carried out. Three IGV opening degrees were simulated with 3D URANS, and for each opening degree 4 flow rates were analyzed. The outcome of this first analysis was that the IGV allows flow control correctly as expected while increasing efficiency at part loads. Nonetheless, the best efficiency was almost the same of the machine with the trimmed impeller. This leads to negligible benefits in terms of power recovery at higher flow rates. For this reason, it was chosen to analyze the effect of number of guide vanes on the characteristic curves to explore different design solutions. For this study the radial and axial dimension of the IGV were kept constant, as well as the maximum blade profile thickness used for the previous IGV. The camber and the thickness distribution were redefined in order to have a better parametrization of the IGV for further analyses. The camber was described by Bézier polynomial curve with three control points. These three control points are selected to guarantee the inlet and outlet desired tangent and to have a coverage factor $k_f$ of 1.15.

The thickness distribution was assigned with a Bézier polynomial curve with eight control points, as done by Lazarevikj et al. [19]. In this case the parametrization was made in the conformal plane since it is a radial blade raw. Having defined all the parameters of the blade rows, it is possible to compute the IGV throat distance, $a_{2d,q}$ and then the expected $Q_{BEP}$ by matching $c_{u2}(Q)$ and the actual tangential velocity, $c_{u2,act}(Q)$, from equations 8 and 16.

$$ c_{2d,q} = \frac{Q}{Z_{IGV} a_{2d,q} b_{IGV}} \qquad (14) $$

$$ c_{u2d} = c_{2d,q} \cos(\arcsin\left(\frac{a_{2d,q}}{\pi D_{2d}/Z_{IGV}}\right)) \qquad (15) $$
$$c_{u2} = c_{u2d} \frac{D_{2d}}{D_2} \qquad (16)$$

For the present study four different number of blades were chosen: 8, 9, 11 and 13, as shown in Figure 7.

<figure><img src="image_9.png" /><figcaption>Figure 7: IGV configurations</figcaption></figure>

<table><caption>Table 3: Main parameters.</caption><thead><tr><th>Z<sub>IGV</sub></th><th>L<sub>IGV</sub><br>[mm]</th><th>a<sub>2d,q</sub><br>[mm]</th><th>ξ<sub>2d</sub><br>[-]</th></tr></thead><tbody><tr><td>8</td><td>138.2</td><td>11.6</td><td>0.915</td></tr><tr><td>9</td><td>122.9</td><td>11.5</td><td>0.904</td></tr><tr><td>11</td><td>100.8</td><td>11.2</td><td>0.882</td></tr><tr><td>13</td><td>85.6</td><td>10.6</td><td>0.856</td></tr></tbody></table>

Then, numerical simulations were carried out. For each configuration were simulated 3 IGV opening degrees, and for each opening degree 3 flow rates were simulated, for a total of 36 simulations. 3D URANS were carried out with the commercial software ANSYS Fluent. $k-ω$ SST was chosen as turbulence model. The time step, $dt$, was set such as there are 16 time steps in each blade passing period (see equation 17).

$$dt = \frac{1}{16} \frac{60}{NZ_{IGV}Z} \qquad (17)$$

For each case, five full revolutions were simulated. All the results shown in the next paragraph have been calculated as averaged values on one complete revolution of the impeller.

## 4. Results and Discussion

For brevity's sake, only results with the lowest (8) and highest (13) number of statoric blades are shown in Figure 8. These curves are adimensionalized with the BEP flow rate and head of the PaT with trimmed impeller, i.e., $Q_{BEP,t,trim}$ and $H_{BEP,t,trim}$. Therefore, $q = Q/Q_{BEP,t,trim}$ and $h = H/H_{BEP,t,trim}$.

In Figure 8, $h-q$ and $\eta-q$ curves are represented for different opening degree of the IGV (50%, 75% and 100%). In all the simulation performed it is possible to notice the feasibility to control the flow at the inlet on the impeller both at part and over loads through change in IGV opening degree. In fact, every IGV opening degree corresponds to a different head-discharge curve. Having as a reference point the BEP of the PaT with the trimmed impeller, Tables 4 and 5 summarize the available ranges in discharge with $h=1$, and in head with $q=1$.
<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /><figcaption>Figure 8: Head and efficiency dimensionless curves for $Z_{IGV} = 8$ and 13: $h$ vs $q$ and $\eta$ vs $q$.</figcaption></figure>

<table><caption>Table 4: Discharge difference at $H_{BEP,t,trim}$.</caption><thead><tr><th>Z<sub>IGV</sub></th><th>min %</th><th>max %</th><th>total %</th></tr></thead><tbody><tr><td>8</td><td>-25.8</td><td>13.4</td><td>39.2</td></tr><tr><td>13</td><td>-9.1</td><td>24.0</td><td>33.1</td></tr></tbody></table>

<table><caption>Table 5: Head difference at $Q_{BEP,t,trim}$.</caption><thead><tr><th>Z<sub>IGV</sub></th><th>min %</th><th>max %</th><th>total %</th></tr></thead><tbody><tr><td>8</td><td>-15.3</td><td>52.5</td><td>67.8</td></tr><tr><td>13</td><td>-26.3</td><td>14.2</td><td>40.5</td></tr></tbody></table>

By increasing the number of IGV, all the $h-q$ curves with the same opening degree are shifted to the right, as well as their BEPs. This is due to the increase in total throat area, $a_{2d,q,tot} = a_{2d,q}Z_{IGV}$ and justified by equations from eq. 14 to eq. 16. The effect of the shift to the right of the $h-q$ curves is quantified in Tables 4 and 5. Regarding the $\eta-q$ curves it is not noticed a relevant increase in the best efficiency value, since it varies of 2% between the extreme cases. The general trend is that with lower number of guide vanes all the efficiency curves are flatter, resulting in better performance at both part load and overload. To further analyse the results of the new design, the distribution of flow rates in the guide vanes and flow angle distribution have been investigated.

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /><figcaption>Figure 9: Flow rates distribution in statoric channels.</figcaption></figure>

Figure 9 shows the distribution of flow rates in the guide vanes. In both figures the first IGV is the first after the volute tongue and the the numeration follows the direction of the flow. The results are taken at $Q_{BEP,t,trim}$ with 100% IGV opening. Figure 9 shows a remarkable unevenness in the mass flow split when passing from $Z_{IGV} = 8$ to $Z_{IGV} = 13$. In fact, for the configuration with 13 guide vanes the channels 1, 2 and 8 have almost the double of the
<figure><img src="image_16.png" /><figcaption>Figure 10: Absolute angle distribution at IGV inlet.</figcaption></figure>

<caption>Figure 11: velocity vector</caption>

discharge of the other channels. Even though the flow rate is split fairly uniformly in the short and long volute channels (respectively 52.5 % and 47.5 %) for both $Z_{IGV} = 8$ and $Z_{IGV} = 13$, the distribution of flow angle at IGV inlet is different. Looking at Figure 10, in particular, the range of $\alpha_{3d}$ is wider for $Z_{IGV} = 13$, thus implying a worse match between volute and IGV. Therefore, in order to correctly design the IGV, a simplified numerical analysis of only the statoric components, i.e., volute and IGV, could lead to improvements in terms of flow and stress distribution. As a consequence of this pronounced flow rates and inlet angles uneven distribution among the guide vanes, most of the statoric channels present flow detachment as shown in Figure 11. Finally, the effect of these inhomogeneities is clearly visible on the relative flow angle, $\beta$. The relative flow angle is measured at impeller inlet along a circumference at blade mid height for different flow rates and it is shown in Figure 12.

<figure><img src="image_17.png" /><figcaption>Figure 12: $\beta_2$ distribution at impeller inlet.</figcaption></figure>

Since this study was mainly focused on the influence of the number of statoric blades, the theoretical matching of relative flow angle, $\beta_2$ was not prioritized in the design phase. The differences between the expected values and the actual ones can be explained through the inhomogeneities among the statoric channels and through the vaneless space losses, which are not taken into account in the 1D model.

In conclusion, to correctly enhance the performance of the PaT with the IGV, an additional study on the matching between volute and IGV and between IGV and impeller is required.

**5. Conclusions**

In this work, the authors present the implementation of a PaT with a new inlet flow control. To address this, a methodology for preliminary sizing of adjustable Inlet Guide Vanes (IGV) in turbine mode is proposed. Then, the impact of varying the number of IGVs has been investigated, considering 8, 9, 11, 13 statoric channels. The proposed method is based on
Francis IGV design literature with the introduction of Bezier curves to control the shape of the IGV profiles. For each number of guide vanes, 3D URANS simulations were carried out to evaluate the performance of different IGV configurations. For each configuration, 3 opening degrees with 3 flow rates each were simulated. The results show the feasibility to perform flow control on the analyzed PaT, obtaining significant improvements in efficiency at part load, i.e., 13% at $0.6Q_{BEP,t,trim}$. However, challenges come up regarding flow distribution, particularly with a higher number of IGVs, leading to flow detachment and uneven distribution. Therefore, further studies are needed to optimize the interaction between the volute, IGVs, and impeller to achieve optimal performance across a wide range of operating conditions. The pump modified with the IGV will be tested at the hydraulic test rig for turbomachines of Polytechnic University of Bari in order to experimentally investigate how the IGV could enhance power recovery.

## References

[1] Morabito A and Hendrick P 2019 *Applied energy* **241** 567-579

[2] Licheri F, Petrollese M, Cocco D and Cambuli F 2023 Pumps as turbines for pumped hydro energy storage systems-a small-size case study *Journal of Physics: Conference Series* vol 2648 (IOP Publishing) p 012046

[3] Doshi A, Channiwala S and Singh P 2017 *Experimental Thermal and Fluid Science* **82** 333-348

[4] Capurso T, Stefanizzi M, Pascazio G, Camporeale S M and Torresi M 2019 Dependency of the slip phenomenon on the inertial forces inside radial runners *AIP conference proceedings* vol 2191 (AIP Publishing)

[5] Yang S S, Kong F Y, Qu X Y and Jiang W M 2012 Influence of blade number on the performance and pressure pulsations in a pump used as a turbine

[6] Sun-Sheng Y, Fan-Yu K, Jian-Hui F and Ling X 2012 *International Journal of Rotating Machinery* **2012**

[7] Yang S S, Liu H L, Kong F Y, Xia B and Tan L W 2014 *Journal of Fluids Engineering* **136** 054501

[8] Morabito A, Vagnoni E, Di Matteo M and Hendrick P 2021 *Renewable Energy* **175** 807-824

[9] Polák M 2021 *Energies* **14** 2698

[10] Nechleba M 1962 *Hydraulic Turbines - Their Design and Equipment*

[11] Shi F, Yang J, Wang X and Li C 2013 Numerical prediction for effects of guide vane blade numbers on hydraulic turbine performance *IOP Conference Series: Materials Science and Engineering* vol 52 (IOP Publishing) p 052029

[12] Hongyu G, Wei J, Yuchuan W, Hui T, Ting L and Diyi C 2021 *Renewable Energy* **168** 21-30

[13] Shi F, Yang J and Wang X 2018 *Advances in Mechanical Engineering* **10** 1687814018780796

[14] Stefanizzi M, Filannino D, Capurso T, Camporeale S and Torresi M 2023 *Applied Energy* **344** 121246

[15] Filannino D, Stefanizzi M, Capurso T, Balacco G, Camporeale S M and Torresi M 2022 Bypass control strategy of a pump as turbine in a water distribution network for energy recovery *Journal of physics: conference series* vol 2385 (IOP Publishing) p 012123

[16] Balacco G, Fiorese G D, Alfio M R, Totaro V, Binetti M, Torresi M and Stefanizzi M 2023 *Energy* **282** 128366. https://doi.org/10.1016/j.energy.2023.128366

[17] Giosio D, Henderson A, Walker J, Brandner P, Sargison J and Gautam P 2015 *Renewable Energy* **78** 1-6

[18] Raabe J 1985 *Hydro power. The design, use, and function of hydromechanical, hydraulic and electrical equipment*

[19] Lazarevikj M, Stojkovski F, Markov Z, Iliev I and Dahlhaug O G 2022 *Journal of Sustainable Development of Energy, Water and Environment Systems* **10** 1-16

[20] Dahal D R, Neopane H P, Thapa B S, Paudel N, Chitrakar S and Thapa B 2021 A simplified francis turbine for micro hydro application: Design and numerical analysis *IOP Conference Series: Earth and Environmental Science* vol 627 (IOP Publishing) p 012018

[21] Stojkovski F, Lazarevikj M, Markov Z, Iliev I and Dahlhaug O G 2021 *Energies* **14** 2667

[22] Ghimire A, Dahal D, Kayastha A, Chitrakar S, Thapa B S and Neopane H P 2020 Design of francis turbine for micro hydropower applications *Journal of Physics: Conference Series* vol 1608 (IOP Publishing) p 012019

[23] Stojkovski F, Markov Z and Kostikj Z 2020 Design of radial blade cascades using parametrization and correlation of geometry and flow parameters *Proceedings of the International Conference COMETa, Jahorina, Bosnia and Herzegovina* pp 26-28

[24] Vivier L 1966 *Turbines hydrauliques et leur régulation: théorie, construction, utilisation* Progrès des sciences et techniques (A. Michel)