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On-site power and mass flow rate measurements were conducted in a hydroelectric power plant (Mexico). Mass flow rate was obtained using Gibson's water hammer-based method. A numerical counterpart was carried out by using the commercial CFD software, and flow simulations were performed to principal components of a hydraulic turbine: runner and draft tube. Inlet boundary conditions for the runner were obtained from a previous simulation conducted in the spiral case. The computed results at the runner's outlet were used to conduct the subsequent draft tube simulation. The numerical results from the runner's flow simulation provided data to compute the torque and the turbine's power. Power-versus-efficiency curves were built, and very good agreement was found between experimental and numerical data.

Nowadays, there is a clear need for low-degrading and low-polluting energy transformation processes. In this respect, wind and hydraulic turbines have taken an important role due to the intrinsic absence of combustion in the electricity production. Along this line of thinking, this work illustrates an effort taking place in Mexico which addresses the performance of hydropower stations and, in particular, the enhancement of the efficiency of the turbine components.

In Mexico, the energy generation through hydroelectric power plants corresponds to 22.14% of the total (11,094.90 MW) [

Although Gibson’s method has been recently improved [

In this work, both aspects have been considered. First, on-site measurements of flow rate and power were conducted at the hydropower plant in the state of Oaxaca in Mexico, then, simulations were performed using the commercial software ANSYS CFX to reproduce aspects of the real-life situation.

This method, devised to measure the rate flow in a hydraulic turbine, is based on the water hammer phenomenon taking place in a closed pipe. It was introduced by Gibson [

Penstock and measuring sections in Gibson’s method.

In order to derive a relationship for computing the flow rate

a closed pipe with a flow section area

initial constant velocity and pressure fields between two given sections along of the penstock,

that the water flow be completely stopped when the water hammer occurs,

constants density and constant flow section during the water hammer.

Based in these assumptions, the relation between the parameters of the one-dimension unsteady flow between two selected sections of the pipe can be described using the energy balance equation

For a penstock with constant diameter

The leakage flow

To carry out the measurements, two separate systems of signal acquisition were used [

Scheme of sensing points.

A waterproof manifold with details of the absolute pressure transducer location.

The signal acquisition system, in addition to capturing the behavior of the pressure, also recorded the opening of the wicked gates, the active power, and the level of tailwater. The level in the tailwater was measured manually and compared with indications from the pressure measured in Section 2-2; these measurements were necessary to calculate the efficiency of the turbine.

The data recording was made with the sampling frequency of 500 Hz, and the files are prepared in ASCII format with 100 Hz frequency. The flow rate was calculated with the program GIB-ADAM developed in the Szewalski Institute of Fluid-Flow Machinery in Poland [

The flow rate was determined from the recorded pressure time histories using a GIB-ADAM [

Guide vane closure percentage and change in pressure between section 2-2 depending on time

Once made, the 8 rejects of charge and recorded all the data. Flow measurements were conducted in five loading conditions: 25%, 50%, 75%, 85%, and 100% of load. A summary of measurements is show on Table

Summary of measurements.

Test number | Opening of the wicked gate | Mechanical power | Flow rate ^{3}/s] | Leakage flow ^{3}/s] | Total flow ^{3}/s] | Net head | Efficiency |
---|---|---|---|---|---|---|---|

1 | 98.8 | 31.65 | 88.97 | 0.7 | 89.67 | 42.40 | 85.10 |

2 | 86.7 | 30.71 | 81.30 | 0.7 | 82.00 | 42.64 | 89.80 |

3 | 78.4 | 29.03 | 75.44 | 0.7 | 76.14 | 42.75 | 91.16 |

4 | 69.5 | 26.05 | 68.03 | 0.7 | 68.73 | 43.09 | 89.91 |

5 | 61.4 | 22.63 | 60.29 | 0.7 | 60.99 | 43.18 | 87.84 |

6 | 52.9 | 19.02 | 52.20 | 0.7 | 52.90 | 43.27 | 84.92 |

7 | 45.5 | 15.72 | 45.41 | 0.7 | 46.11 | 43.52 | 80.08 |

8 | 36.7 | 10.14 | 34.98 | 0.7 | 35.68 | 44.10 | 65.89 |

For simulations a three-dimensional incompressible flow was considered, with constant properties and isothermal at 25°C·

The commercial software used employs the finite volume numerical method for solving the RANS equations and

To perform the numerical simulations, measurement results in Tests 1, 3, 5, 6, and 8 showed in Table

The selected convergence criteria of the numerical simulations was RMS (root mean square) normalized values of the equation residuals with a value of E-006.

In the runner, the boundary conditions were stipulated as follows:

inlet: defined as Mass flow inlet,

turbulence intensity:

outlet: defined as Static Pressure (measured at the inlet of draft tube),

turbulence intensity: zero gradient,

blade, shroud and hub: were defined as wall with no movement and as a smooth surface.

Before obtaining the final results of the numerical simulation, we carried out a mesh independence analysis called grid convergence index (GCI for its acronym) to estimate the percentage of error in the solution. According to the work done by Roache [

Analysis GCI.

Mesh number | No. of elements | Average size of element [mm] | Torque [J] | GCI | GCI [%] | ||
---|---|---|---|---|---|---|---|

1 | 795,618 | 200 | 1,583,510 | ||||

2 | 965,632 | 150 | 1,613,960 | −0.0189 | 1.33 | 0.0728 | 7.2771 |

3 | 1,759,261 | 75 | 1,634,405 | −0.0125 | 2.00 | 0.0125 | 1.2509 |

4 | 3,284,658 | 50 | 1,638,950 | −0.0028 | 1.50 | 0.0067 | 0.6655 |

Considering the processing time and storage volume of the files generated by numerical simulation results, to obtain the final results mesh no. 3 was selected, which has a convergence index that is reasonable (according to references, it is ideal when it is less than 1.5)

From the simulations on the runner, torque was obtained, with which it proceeds to the calculation of mechanical power and compare it with the measurements. The results are presented in Table

Comparison between numerical and experimental data.

^{3}/s] | Power measured [MW] | Power simulated [MW] | Efficiency measured [%] | Efficiency simulated [%] |
---|---|---|---|---|

89.67 | 31.65 | 31.95 | 85.10 | 85.25 |

76.14 | 29.03 | 30.02 | 91.16 | 91.82 |

60.99 | 22.63 | 22.88 | 87.84 | 88.39 |

52.90 | 19.02 | 19.93 | 84.92 | 86.00 |

35.68 | 10.14 | 10.23 | 65.89 | 66.09 |

Efficiency curves.

At the point of 91.16% efficiency, special attention was taken on the results of simulations, which should be analyzed carefully, as these results represent the maximum efficiency. One of the most important issues is the cavitation; in Figure

(a) Pressure contours at 76.14 m^{3}/s, (b) Pressure contours at one blade.

Figure

Blade loading in midspan, at 76.14 m^{3}/s.

In Figure

Velocity vectors at midspan.

From the results of simulations on the runner, the boundary condition at the draft tube inlet for different measured flow rates was obtained; thereby, the behavior in this component was discovered, which is significant because it is very difficult to make direct measurements.

Figures

Streamlines at different flow rates (a) 76.14 m^{3}/s and (b) 89 m^{3}/s.

Pressure contours in cross-section at different flow rates (a) 76.14 m^{3}/s and (b) 89 m^{3}/s.

In Figure

With these results, we will propose amendments to this component geometry to increase efficiency.

The mechanical power and efficiency obtained from the simulations have good agreement with those obtained on-site measurements.

From the results at the maximum efficiency, adverse conditions in the flow will not appear, so the turbine can work properly at this head, and thereby improve the performance of flow in the unit of study.

Therefore, these results can be considered reliable enough for the speeds at the exit of the runner and could be used in the boundary condition at the entrance of the draft tube.

The results show that the flow in draft tube is sufficiently approximate to the actual flow, according to revised bibliography.

Density

Hydrometric levels

Pressure drop caused by friction losses

Flow before the closing of the wicked gates

Leakage flow

Geometrical modulus of the penstock segment

Length of the segment of the penstock

Transversal area of the penstock

Ratio of slack flow (0.65–0.7)

Clear area of the wicked gate

pressure difference between inlet and outlet of the distributor

Recovery ratio

Acceleration of gravity

Reynolds Number

Diameter

Kinematic viscosity

Mass flow

Dynamic viscosity

Empirical constant

Kinetic turbulent energy

Turbulence dissipation rate

Axial velocity

Radial velocity

Tangential velocity

Static pressure

Effective viscosity

Turbulent viscosity

Turbulence constant

Turbulence constant

Turbulence constant

Turbulence constant

Turbulence production by viscosity forces

Shear stress

Von Karman constant

Grid Convergence Index

Relative error

Element size ratio

Pressure coefficient

Average static pressure

Volume

Turbulence frequency

Efficiency

Flow

Mechanical power.

The authors are grateful to the Federal Electricity Commission (CFE) for the facilities provided for the present study and to the National Council of Science and Technology (CONACYT) for the scholarship granted to the Ph.D. student.