**1. Introduction**

The "International Electrotechnical Commission—60041" (IEC—60041) Standard establishes various test development methods to determine the hydraulic performance of different hydraulic turbomachinery, such as the Reel method, Pitot tubes, and Pressure-Time (also called Gibson), among which is the Thermodynamic Method ™. According to the standard, this method allows, in a hydroelectric power station, for the measurement of flow properties extracted in the high- and low-pressure section (inlet and outlet of the turbine or pump, respectively), to calculate the hydraulic efficiency of the turbomachinery. This method is less invasive compared to others, for example, the Pressure-Time method (also called the Gibson method). The Pressure-Time method is accurate and can inexpensively perform indirect flow measurements for low head turbines. However, it could be risky due to the phenomenon used for measurement. The application of TM instead of the Gibson method aims to avoid damage in any component of the hydraulic turbine, such as the penstock, valves, or distributor. In addition, it allows for the calculation of continuous efficiency by simultaneously measuring the interest variables without stopping power energy generation.

The IEC—60041 Standard establishes that the application of TM is limited to specific hydraulic energy values greater than 1000 J/kg (heads higher than 100 m). However, under

**Citation:** Castañeda Magadán, E.O.; Urquiza Beltrán, G.; Castro Gómez, L.L.; García Castrejón, J.C. Application of CFD to the Design of Manifolds Employed in the Thermodynamic Method to Obtain Efficiency in a Hydraulic Turbine. *Energies* **2021**, *14*, 8359. https:// doi.org/10.3390/en14248359

Academic Editors: Adam Adamkowski and Anton Bergant

Received: 7 October 2021 Accepted: 7 December 2021 Published: 11 December 2021

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favorable conditions, the measurement interval could be extended to lower values of the specific hydraulic energy or heads lower than 100 m [1,2].

Given the inherent difficulties in directly measuring the flow that define the hydraulic efficiency (*ηh*), it is possible to carry out their extractions in manifolds that are especially designed for the determination of temperature, pressure, and velocity in the fluid, installing them in the inlet and outlet sections of the turbine, respectively (Figure 1).

**Figure 1.** Conceptual diagram showing the location of manifolds to measure flow properties to compute power and efficiency according to IEC—60041.

The manifolds must be designed to ensure that the velocity inside is at a specific interval, so that the flow is uniform when it comes into contact with the installed temperature transducers. This guarantees that the temperature will remain constant inside the manifold and around the sensor. Moreover, the precision and sensitivity of the temperature measurement instruments should be sufficient to provide an indication of a temperature difference of at least 0.001 K between the measurement points. In addition, the temperature of the extracted water should be continuously monitored by thermometers of at least ±0.05 K precision and 0.01 K sensitivity [2]. According to different authors, Pt-100 Resistive Temperature Detectors (RTD's) are commonly used for measurement due to their high stability and precision [3–5].

According to TM, the direct operating procedure or direct method is used to measure the efficiency of the turbine under study. This method measures temperature, velocity, and pressure, extracting water from the penstock at the high-pressure side of the turbine to a manifold with a minimum expansion. Hydraulic losses and friction cause an increase in the temperature of the water passing through the turbine. This phenomenon can be calculated using the specific heat of the water. Although the authors of [6] defined that the decrease in the head in a turbine reduces the temperature difference between the inlet and outlet, they are directly proportional.

On the other hand, although this is a numerical case, in experimental cases, authors such as [4] propose a procedure for the normalization of experimental tests from the opening of the closing control device. After 10 min stabilization in the generator's frequency, the temperature data recording is started by means of Pt-100 type sensors during the first 2 min. At the end, the average value of the temperature difference is calculated (high and low pressure). During this period, the measurements of the other parameters, such as inlet and outlet pressure and power, are simultaneous. This procedure is repeated for different openings of the closing control device, that is, for different load values in the unit, as in the present case.

Hydraulic turbines and the geodesic points where these are installed can present aspects of great complexity, such as installing manifolds on the low-pressure side embedded in concrete tubes. However, with a correct design of collecting tubes that are long enough for sample extraction, the measured temperature values could be considered adequate [7]. In the high-pressure section, the optimal length for penetration of the detraction into the pipe can be calculated. However, the length established by IEC-60041 could be enough [8–11].

IEC-60041 establishes that the design of detraction probes for the high-pressure zone must present the appropriate structural study to avoid total or partial detachment, and that it reaches essential areas such as the runner, causing significant damage. To select the correct materials for the probes that support the loads, the typical properties of the materials used in engineering can be consulted [10,11].

According to [3], the design of a horizontal sampling system at the outlet of the turbine is better than vertical. However, the research is based on a Pelton-type turbine. According to the turbine types, the power distribution and partial flow passage can demonstrate significant differences for the present study.

On the other hand, the system can be designed by two or more means of sampling; for example, a system composed of an arrangement of horizontal tubes with a central mixing chamber, in which the relevant sensors are coupled. Furthermore, perforated tubes are located at the turbine's outlet, and temperature sensor is placed at different heights to measure temperature changes throughout the section.

A hybrid vertical detraction system and a mixing chamber for each tube would reduce the number of sensors required and improve measurement. In addition, the use of perforated tubes for the water samples at the outlet of the turbine omits the presence of elbows to avoid friction losses [12].

The development of accurate instruments allows for the application of TM in low head turbines; for example, most hydroelectric power plants in Mexico have heads lower than 100 m, such as 22 and 76 m. Consequently, the present study focuses on a 52-m head Francis-type hydraulic turbine installed in a hydroelectric plant in México. This has a rotational velocity of 180 RPM (18.84 rad/s) under normal operating conditions, i.e., constant volumetric input flow (between values of 89.67 m3/s and 35.68 m3/s), and a 3.5 m maximum tip diameter for the runner.

With these values, the specific speed in the turbine is calculated according to [13–16], see Equation (1). *N* is expressed in RPM, *Q* is the volumetric flow in (m3/s) and *H* is the head in meters.

$$\text{Ns} = \mathcal{N}\left(\frac{\mathcal{Q}^{0.5}}{H^{0.75}}\right) = \frac{638}{H^{0.512}}\tag{1}$$

The turbines can be classified according to the specific speed, at the head (*H*), a range from 50 to 240 m can be found the Francis turbine, and their specific speed is between 51 and 255 dimensionless (Power in kW) [16]. Therefore, the specific speed value for the studied turbine is 87.93, i.e., a Francis slow turbine.

On the other hand, an example comparison of the efficiency calculations in a turbine was performed using the Gibson Method (GM) and the TM at the Gråsjø power plant in Norway, which show differences between the efficiency curves below 0.5%, for the entire range measured below 0.15% and for relative powers between 0.5 and 1.15%. The Gråsjø power plant is equipped with a vertical Francis turbine and has a net height of 50 m [17], which serves as a reference for current research development.
