# CFD as a Decision Tool for Pumped Storage Hydropower Plant Flow Measurement Method

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## Abstract

**:**

## 1. Introduction

## 2. Current State

#### 2.1. Peak Load Hydropower Plant Orlík

#### 2.2. Planned Transformation to PSP

#### 2.3. CFD Model—Setup and Validation

#### 2.3.1. Three-Dimensional (3D) Model

#### 2.3.2. Computational Mesh

- Inlet with part of the reservoir;
- Screens (represented by porous domains);
- Intake object (with grooves and transition piece);
- Penstock DN6250;
- Spiral.

^{3}.s

^{−1}), the value of y

^{+}was 100 to 200. The planned turbulence model is SST, and for the automatic wall function, all the first cells should be located in the log-law region near the wall [20] with y+ value between 30 and 200. The relationship between y+, the turbulence model and the wall function is discussed in detail Carloni et al. [21] or Nicolle et al. [22] A simplified mesh dependency test was performed on the computational grid size for 2 million and approximately 7.3 million elements (see details of mesh parts in Figure 3). The mesh size effect on the value of the hydraulics losses and the behaviour of the velocity field in the penstock was monitored. The resulting influence was minimal compared to model settings such as turbulence model and porous domain settings, and therefore, a detailed grid convergence index (GCI) analysis [23] was not performed. A grid with a higher number of elements was used for further calculation.

#### 2.3.3. Numerical Setup

#### 2.3.4. Comparison of Historical Measurements

^{3}.s

^{−1}. The resulting measured velocity fields in the plane of the eight-arm test section (Figure 4) were compared with the CFD results. According to the information available for the 1994 measurements, the uncertainty of the flow measurement was determined to be 1.2%. It should be noted here that this is an uncertainty in the calculation of the entire flow rate in the profile and does not describe an error in the description of the shape of the velocity field. Because the flow rates (respectively, mean velocity) in the numerical model and the actual measurement were not completely identical, the values had to be normalised to mean velocity of the profile (normalised normal velocities). The differences in point velocities between the actual measurement and the numerical model were then calculated (Figure 5).

#### 2.3.5. Hydraulic Losses

^{3}.s

^{−1}, a comparison was made with the measured values of the hydraulic losses of the entire penstock up to profile G2 (Figure 6). The measured flow values (red in the graph) represent the curve of the measured average values from the TG3 efficiency measurement from 1994. During the measurement, pressures were measured in the G2 profile, and the flow rate was determined using a measuring section plane in the profile marked in Figure 4.

## 3. CFD Simulations for Planned PSP

#### 3.1. Turbine Regime

^{3}.s

^{−1}.

^{+}on all walls of the model were displayed (Figure 7). The figure below shows the y

^{+}values in the penstock. In the part of the main interest (inlet to the neck of the spiral), the average value is 93. In the detail of the figure, the parts in the grooves with higher y

^{+}values are marked.

#### 3.2. Pump Regime

^{3}.s

^{−1}. The boundary conditions have to be altered. The lower boundary condition is set, as the direction of the velocity vectors at the outlet of the distributor is very angled (the flow has a significant rotational component)—the rotational (tangential) component forms an angle of 61° with the normal (radial) component. This angle was determined according to the assumed nominal position of the guide vanes. A very similar shape is also found in the existing Dalešice PSP. A significant value is also the turbulence intensity at the inlet, which is set at a value of 5% by the example given by Feng et al. [29]. The upper boundary condition remains the same as in the turbine regime—set as Opening.

#### 3.3. Comparison of Turbine and Pump Regime

#### 3.3.1. Coefficient for Non-Uniform Axial Velocity Profile [31]

^{−1}) is the point velocity, $\overline{\mathrm{U}}$ (m.s

^{−1}) is the mean normal velocity, and S (m

^{2}) is the cross-sectional area.

#### 3.3.2. Index of Asymmetry

_{i}(m.s

^{−1}) is mean velocity calculated from the individual point velocity measurements in the i-th radius, U (m.s

^{−1}) is the mean axial fluid velocity calculated by ISO 3354, and n (-) is the number of radii.

^{3}.s

^{−1}. The value of the Y index is higher in the part closer to the spiral (P12 to G2) for the pump regime. However, in the straight upper section (P4 to P10), it is higher for the turbine regime. So, it says that at the upper section of the penstock, the non-uniformity of normal velocities for a given stationary array of current meters is higher in the turbine regime than in the pump regime and conversely.

#### 3.3.3. Pressure Field in the Penstock

## 4. Assessment of Flow Measurement Methods

#### 4.1. Current Meter Method

- If the swirl angle is <5°, Y < 0.05 and low turbulence when applying 6 probe radii, the total uncertainty of the flow measurement can be below 1.5%
- If the value of Y < 0.25 and when applying at least 6 measuring radii, the uncertainty of the flow measurement can be up to 2.2%.

- The positions of the measuring profiles from the 1994 measurement in the TG3 penstock have been adopted.
- For these positions, the values of normal velocities were subtracted from the CFD model simulation results.
- The mean cross-sectional velocity was calculated from these values according to ISO 3354.

_{ISO3354}(m/s) is mean cross-sectional velocity calculated current meters by ISO 3354 and v

_{CFD}(m/s) is mean cross-sectional velocity from CFD-Post.

#### 4.2. Pressure–Time Method (Gibson Method)

^{−1}) is added. The variable p

_{dyn}(dynamic pressure) is the velocity head (the α value is considered equal to 1). In the standard, p

_{dyn}is also called specific kinetic energy.

- “Individual average pressure measurements around the measuring section should not differ from one another by more than 0.5% (0.5% E) of the specific hydraulic energy of the machine or 20% (20% p
_{dyn}) of the specific kinetic energy calculated from the average velocity in the measuring sections.” [34] (Chapter 11.4.2) - “… the difference between the pressure measured at any one tap and the average of the pressures measured at all taps shall not exceed 20% of the dynamic pressure (20% p
_{dyn}). The average of the readings from any pair of opposite taps shall not differ from the average from any other pair of taps in the same cross-section by more than 10% of the dynamic pressure (10% p_{dyn}).” [34] (Chapter 10.4.2.4)

#### Equivalent Geometrical Factor F

_{ei}and adjustment of the distances between the profiles to the distances between the centres of gravity of the individual profiles. In the circular profile penstock, the change in distances is negligible, and the change in flow areas is dominant.

#### 4.3. Ultrasonic Method

- Definition of chordal path positions in the base plane.
- Path rotation according to the position and inclination of the plane (A and B).
- Extraction of velocity components at the intersection of the created paths and plane sections (A and B) (Figure 18).
- Created averaged velocity components u, v, w.
- Transformation of velocities into two components—in the path direction and transverse component.
- The following flow calculation is exact according to ASME PTC 18-2020 for the given plane rotation and position in the conduit. The Gauss–Jacobi Method with OWICS weights was used in our case for four and nine paths.

**Figure 18.**Interpolation of velocity components for 9 paths of plane A in pseudoplane ZY. The circle symbols represent the points with interpolated velocities of each ultrasonic path.

_{ultrasonic}(m

^{3}.s

^{−1}) is a flowrate calculated from paths by integration with using the Gaus–Jacobi method with OWICS weights and Q

_{CFD}(m

^{3}.s

^{−1}) is a flowrate from CFD-Post.

## 5. Tables of Suitability of Measurement Profiles and Uncertainty Quantification

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Part of 3D penstock model. Profiles P1 to P15 are artificially made for the purpose of the hydraulic characteristics evaluation. Profiles G1 and G2 represent actual profiles with the pressure taps for the pressure-time method.Each inlet is made up of a rounded intake object of a confusor shape with a rectangular cross-section (Figure 2—profiles P3 and upstream). The inlet is divided into two parts by a vertical inlet pillar. Two coarse screen sections with 140 mm spacing are supported by side walls and the inlet pillar. Then, there are the grooves of the stop logs, which are followed by the grooves of the emergency shut-down gate. This is followed by a transition piece from a rectangular cross-section to an inclined circular cross-section. In this transition piece, the DN 1200 pipe is included as an aeration for the eventual triggering of the shutdown gate. The transition piece is followed by a 6250 mm diameter penstock with a centreline length of approximately 59.1 m. This circular section consists of a 35.2 m long section with a slope of approx. 32° (Figure 2—profile P3 to P8). Next is the bend section and a short straight section to which the spiral is connected (Figure 2, profile P8 to G2). This is followed by a stay ring, guide vanes and an eight-bladed Kaplan turbine runner with a diameter of 4.6 m. The runner chamber is connected to an elbow draft tube.

**Figure 3.**Example of computational grid: (

**a**) part of water reservoir representing inlet, (

**b**) intake section, (

**c**) part of penstock.

**Figure 5.**Normal velocities (position of current meters are marked with red dots): (

**a**) Current meter measurement 1994, (

**b**) Velocity contour for CFD, (

**c**) Differences of normalised velocities (in %).

**Figure 8.**Absolute velocity contours: (

**a**) in the profile P4, (

**b**) in the profile G2. The arrows represent normalized velocity vectors projection, i.e., the behaviour of the non- normal velocity components (swirl velocity).

**Figure 16.**Values of relative pressures (in metres of water column) on the wall for profiles P4 and G2: (

**a**) turbine regime, (

**b**) pump regime.

Table of Basic Technical Information | Current State | Planned State | ||
---|---|---|---|---|

Turbine Type | Kaplan | Francis | Reversible Francis | |

Turbine | Pump | |||

Heads range (m) | 45–71.5 | 45–71.5 | 50–71.5 | 50–71.5 |

Discharge range (m^{3}.s^{−1}) | 47.5–160 | 80–150 | 80–150 | 110 |

Unit installed power (MW) | 91 | 93 | 91 | 76 |

Variable | Value | Units | Description |
---|---|---|---|

ρ | 999.9 | kg.m^{−3} | specific mass |

ν | 1.43 × 10^{−6} | m^{2}.s^{−1} | kinematic viscosity |

D | 6250 | mm | penstock diameter |

L | 69.92 | m | centreline length G1 to G2 |

Δ_{1} | 0.5 | mm | equivalent sand grain roughness of steel |

Δ_{1}/D | 8 × 10^{−5} | - | relative roughness of steel |

Δ_{2} | 4 | mm | equivalent sand grain roughness of concrete |

Δ_{2}/D | 6.4 × 10^{−4} | - | relative roughness of concrete |

**Table 3.**Deviations between values determined from the entire cross-section and from point values in post-processing of the numerical model according to ISO 3354.

Deviation | P4 | P8 | G2 |
---|---|---|---|

Turbine 150 m^{3}.s^{−1} | −0.2% | −1.4% | −0.5% |

Pump 110 m^{3}.s^{−1} | −0.1% | −0.3% | +2.4% |

Regime | Q | D | U | p_{dyn} | 20%p_{dyn} | 10%p_{dyn} | 0.5%E |
---|---|---|---|---|---|---|---|

(m^{3}.s^{−1}) | (m) | (m.s^{−1}) | (m w.c.) | (m w.c.) | (m w.c.) | (m w.c.) | |

Turbine | 150 | 6.25 | 4.9 | 1.2 | 0.24 | 0.12 | 0.31 |

Pump | 110 | 6.25 | 3.6 | 0.7 | 0.13 | 0.07 | 0.31 |

**Table 5.**Recommending the applicability of profiles and quantifying the uncertainty of flow measurement for turbine regime. The arrows represent water flow in turbine regime.

^{1}Voser, A. Analyse und Fehleroptimierung der Mehrpfadigen Akustischen Durchflussmessung in Wasserkraftanlagen. Ph.D. Thesis, Zürich, Switzerland, 1999, [42].

**Table 6.**Recommending the applicability of profiles and quantifying the uncertainty of flow measurement for pump regime.

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**MDPI and ACS Style**

Souček, J.; Nowak, P.; Kantor, M.; Veselý, R.
CFD as a Decision Tool for Pumped Storage Hydropower Plant Flow Measurement Method. *Water* **2023**, *15*, 779.
https://doi.org/10.3390/w15040779

**AMA Style**

Souček J, Nowak P, Kantor M, Veselý R.
CFD as a Decision Tool for Pumped Storage Hydropower Plant Flow Measurement Method. *Water*. 2023; 15(4):779.
https://doi.org/10.3390/w15040779

**Chicago/Turabian Style**

Souček, Jiří, Petr Nowak, Martin Kantor, and Radek Veselý.
2023. "CFD as a Decision Tool for Pumped Storage Hydropower Plant Flow Measurement Method" *Water* 15, no. 4: 779.
https://doi.org/10.3390/w15040779