Keywords

1 Introduction

Paraguay is one of the most remarkable countries in the South American continent when it comes to clean and renewable energy generation. Paraguayan hydropower plants satisfy the entirety of the local energy demand, as well as a significant percentage of the energy demand in two of its neighboring countries: Argentina and Brazil. It is for this reason that hydropower plants play an essential role in the socio economical development of Paraguay.

The Yacyretá Hydropower Plant, also known as Entidad Binacional Yacyreta (EBY) in Spanish, is located on the Paraná River, this is, the border between Paraguay and Argentina. This plant counts with 20 generating units equipped with vertical axis Kaplan turbines, and it has an average gross electricity yearly generation of 20.000 GWh.

Kaplan turbines are highly efficient axial flow turbines, and its ideal application is in projects with a large flow volume and a small net head.

The main advantage of Kaplan turbines, when compared to other types of turbines, is the possibility to automatically adjusting blade attack angles, during machine operation, to adjust to the optimal efficiency angle, in function to the energy demand.

Cavitation has been a subject of study for decades, its effect brings erosion and chemical corrosion on the blade surfaces and other components. This in turn decreases efficiency and generates noise with intense vibrations [3]. These are few of the other consequences cavitation effects may arise. Therefore, in order to obtain optimal efficiency and reduce maintenance cost;, in practice, turbines are allowed to operate under controlled cavitation conditions, in which the damage caused to the blades can be easily repaired during scheduled maintenance operations, keeping generating units operating as continuous as possible.

Since the turbines of this case study are not exempt from the cavitation phenomenon, different manufacturer guaranteed “safe operation” points. In this work, these points were analyzed through the use of Computational Fluid Dynamics.

2 Materials and Methods

2.1 Model and Mesh Configuration

The CAD software used to design the Kaplan turbine was Solid Edge. This model was provided by the technical department team at the Yacyretá Hydropower Plant to the Mechanical Engineering Department of the Faculty of Engineering at Universidad Nacional de Asunción.

The analysis was performed by first establishing an internal flow of water in the computational domain, which includes the turbine pre-distributor and the top region of the draft tube, as shown in Fig. 1.

Fig. 1.
figure 1

Control volume adopted for the internal flow analysis. Its position in the CAD model is outlined in red.

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An academic version of the flow simulation software SolidWorks was employed to conduct this part of the analysis. The main reason this software was chosen for the analysis was the simplicity it offers when it comes to setting up boundary conditions. This is useful given that technicians and engineers from the plant have expressed their interest in testing different operating points themselves in the future once the model is validated.

The mesh configuration was set up as a combination of two different mesh types: a level 5 global mesh for the entire computational domain, along with a level 3 local mesh located on the top and bottom blade surfaces.

This configuration was applied in order to obtain sufficient finite volume elements in critical regions, like the turbine blades and rotor. This is critical to obtain a reliable and accurate results.

2.2 Simulation Parameters and Considerations

In order to perform as much realistic simulation as possible, real turbine operating conditions were adopted. The applied conditions were the following:

  1. a)

    The working fluid employed for the simulation was water at a temperature of 30 ℃.

  2. b)

    The operating points chosen for the analysis are located within the region delimited by the enclosed polygon shown in the Prototype Collinear Hill Diagram provided by the turbine manufacturer. This region is also known as the continuous or warranted operation region. The diagram parameters are detailed in Fig. 2 but are presented in dimensionless form for copyright reasons.

Fig. 2.
figure 2

Prototype Collinear Hill Diagram provided by the turbine manufacturer with dimensionless parameters

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  1. c)

    The inlet condition is the absolute pressure of a point located on the midplane between the pre-distributor and the turbine (Level 52 msnm), and the outlet condition is the operating volume flow of the turbine.

  1. d)

    The selected turbine operating points are detailed in Table 1. The pressure and head values were obtained during on-site measurements by plant personnel, and the volume flow values were obtained from the Prototype Collinear Hill Diagram from Fig. 2.

Table 1. Selected turbine operating points
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2.3 Equations Used

In this section we will detail the analytical process used to obtain the boundary conditions for each operating point, i.e., pressures and volume flows.

Moreso, a cavitation analysis using Thoma's cavitation coefficient is included.

2.3.1 Determination of the Turbine Operating Point and the Pre-distributor Pressure

For the calculation of pressure p2 at the computational domain inlet, Bernoulli’s Eq. (1) [3] was employed between points 1 and 2. Point 1 is located on the reservoir level of the dam and point 2 is located on the pre-distributor midplane inside the semi-spiral chamber.

$$\frac{{p}_{1}}{\rho g}+{z}_{1}+\frac{{{V}_{1}}^{2}}{2g}-{H}_{r1-2}=\frac{{p}_{2}}{\rho g}+{z}_{2}+\frac{{{V}_{2}}^{2}}{2g}$$
(1)

The density and water saturation pressure employed are, respectively, 995,65 [kg/m3] and 4.246,7 [Pa]. The acceleration of gravity at this location is of 9,7912 [m/s2].

2.3.2 Thoma’s Cavitation Coefficient

As a way to verify the accuracy of the results obtained from the CFD simulations at the analyzed operating points, cavitation coefficients or Thoma coefficient σ were calculated. The formula is detailed in Eq. (2) [4].

$$\sigma =\frac{\frac{\left({p}_{atm}-{p}_{s}\right)}{\rho g}-{H}_{s}}{H}$$
(2)

For the studied turbines, the suction height is the height difference between the centerline of the impeller, located at level 48,00 msnm, and the restitution head.

The results obtained from Eq. (2) are then compared to the sigma value of the plant σplant of the original project, equal to 0,68.

The criteria adopted for the analysis is the following: if the resulting Thoma coefficient for a specific operating point is lower than the project value σplant, this would hint the presence of cavitation in the turbine.

The cavitation coefficients for each operating point are detailed in Table 2.

Table 2. Cavitation coefficient at operating points
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3 Results

In Fig. 3, CFD simulation results for Table 1 operating points can be observed. All images show pressure distribution on the blades on the low-pressure side of the turbine.

Fig. 3.
figure 3

Pressure distribution in blades on the low-pressure side of the turbine (a) 75 MW – Point 1, (b) 120 MW – Point 2, (c) 128 MW – Point 3, (d) 135 MW – Point 4, (e) 145 MW – Point 5 and (f) 155 MW – Point 6.

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All results obtained from the simulations suggest the absence of cavitation for the points inside the safe operating zone warranted by the turbine manufacturer.

These results coincide with the estimated cavitation coefficients calculated previously.

4 Conclusions

Through this research work the CFD results, using CAD model provided by EBY, was validated. This model, along with the computational software Solidworks Flow Simulation, showed reliable results on the study of cavitation phenomena in these turbines. This proved to be a very useful tool for the future analysis of a wider range of turbine operating points, especially by the power plant operators.

Furthermore, the analytical results and the results obtained through the use of CFD simulations demonstrated that, effectively, the analyzed operating points correspond to the safe operating points warranted by the manufacturer.