# Holistic Design Approach of a Throttled Surge Tank: The Case of Refurbishment of Gondo High-Head Power Plant in Switzerland

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

_{d}value of an orifice is not constant throughout the flow ratio (flow in the branch pipe divided by the flow upstream of the T-section under dividing flow conditions; flow in the branch pipe divided by the flow downstream of the T-section for combining flow conditions). This issue has been also highlighted in a recent study through CFD modeling [15]. However, in the authors’ opinion, and based on literature search, the effect of a varying throttle’s head loss coefficient with the flow share on the conclusions of a 1D transient analysis has not been investigated so far.

**Table 1.**Summary of existing studies on throttled surge tanks (extended from [2]).

Goal | Physical Scale | 1D Numerical Simulation | 3D Numerical Simulation (CFD) | Prototype Validation | Source |
---|---|---|---|---|---|

Geometry optimization and flow visualization | Done | Not done | Done | Not done | [16] |

Throttle optimization | Not done | Done | Not done | Not done | [17] |

Throttle optimization | Not done | Not done | Done | Not done | [18] |

Throttle optimization | Not done | Done | Not done | Not done | [19] |

Flow visualization | Done | Not presented | Done | Not done | [12] |

Geometry optimization and flow visualization | Done | Not done | Done | Not done | [13] |

Geometry optimization | Done | Done | Not done | Not done | [9] |

Geometry optimization | Done | Done | Not done | Not done | [3] |

Geometry optimization and flow visualization | Done | Done | Done | Not done | [6] |

Geometry optimization and flow visualization | Done | Not done | Done | Not done | [20] |

Geometry optimization and flow visualization | Done | Not done | Done | Not done | [21] |

Geometry optimization | Not done | Done | Not done | Not done | [22] |

Geometry optimization and flow visualization | Done | Done | Done | Not done | [15] |

Geometry optimization and flow visualization | Done | Done | Done | Done | Current study |

## 2. Materials and Methods

#### 2.1. Case Study Summary

^{3}/s up until the 1980s when a third Pelton turbine (8 MW) was installed. The discharge was then increased to 12.1 m

^{3}/s. The project, Renewal of Group 3, aimed to replace the third turbine by a more efficient and powerful one, which allows increasing the discharge flowing through the plant up to 14.7 m

^{3}/s.

^{3}/s could be safely done if the following two conditions are met:

- Increase of the existing injectors closure time to fulfill admissible maximum pressure in the penstock (load case: peak of Michaud)
- A solution is found to prevent surge tank dewatering (load case: unloading followed by a unit reloading)

#### 2.2. CFD Model

#### 2.2.1. Geometry and Meshing

#### 2.2.2. Pre-Processing: Physical Parameters, Boundary Conditions, and Turbulence Model

^{2}).

#### 2.2.3. Post-Processing: Visualization of Results and Head Loss Coefficient Estimation

^{3}/s flow going from A to B (turbine opening). The lower chamber of the surge tank experiences high flow disturbances accompanied by recirculation zones. Very high velocities are noticed as the water passes through the narrow throttle spacings.

^{3}/s flowing from A to B. Clearly, the linear head losses are negligible as we observe a quasi-horizontal energy grade line which experiences a slight drop by the end of the connecting gallery (due to a sudden contraction of the flow followed by a gradual expansion in the lower chamber of the surge tank). A sharp drop in the total head is later noticed at the location of the throttle (bottom of the lower chamber of the surge tank). Note that at this location, the flow experiences high disturbances, and some streamlines are discontinuous.

^{3}/s surge tank inflow and outflow during mass oscillations. These results highlight the importance of the orientation of the rack throttle’s trapezoidal bars. The streamlines for a flow entering the surge tank are forced in one direction, hence they are more guided than the case of a flow exiting the surge tank. This should result in lower head loss coefficients in the upsurge direction than the downsurge direction as previously determined from the physical model and as proven subsequently with the CFD model.

- S
_{1}–S_{5}for direction A–C (flow out of the surge tank during mass oscillation) - S
_{5}–S_{1}for direction C–A (flow into the surge tank during mass oscillation) - S
_{1}–S_{4}for direction A–B (flow out of the surge tank following a turbine opening) - S
_{5}–S_{4}for direction C–B (steady flow during turbine operation)

_{i}and S

_{j}under steady-state simulations (similarly to the physical model), for several discharges. The computation is based on the Bernoulli equation, which is valid along a streamline:

_{ref}being the velocity in the reference cross-section, based on which the head loss coefficient k is evaluated. It consists of a horseshoe section located at the intersection between the bottom chamber of the surge tank and the junction between the pressure tunnel and the pressure shaft (Figure 6).

## 3. Results

#### 3.1. Validation with the Physical Model Results

_{CB}< k

_{CA}< k

_{AB}< k

_{AC}is valid numerically and experimentally.

#### 3.2. Impact of the Connecting Gallery

_{1}–S

_{5}) for surge tank outflow A–C and k (S

_{5}–S

_{1}) for surge tank inflow C–A. The same sections were chosen in the 3D model analysis aiming to validate the physical model results (kindly refer to Section 2.2.3). However, in order to investigate the impact of the connecting gallery on the head loss coefficients presented above, a reevaluation of these coefficients between section S

_{5}(located in the pressure tunnel) and three different sections in the surge tank was conducted for flow directions A–C and C–A:

- Section S
_{0}(in the middle of the upper surge tank chamber, above the connecting galley) - Section S
_{1}(in the middle of the connecting gallery) - Section S
_{2}(in the middle of the lower surge tank chamber, below the connecting gallery)

_{1}which is why it was primarily used in the physical model as a pressure measurement section in the surge tank.

_{Lower Chamber}which is measured between the pressure tunnel section S

_{5}and the lower chamber of the surge tank S

_{0}.

_{Lower Chamber}is 1 meaning the surge tank inflow or outflow loss coefficient corresponds to the throttle’s loss coefficient. If the water level reaches the connecting gallery, the value of k increases, as it includes the effect of the conical section variation in addition to the throttle’s head loss coefficient. The value of k reaches its maximum when the water level in the surge tank reaches the upper chamber of the surge tank. At this point, the calculated value of k includes the throttle’s head loss coefficient in addition to the local losses caused by the gradual and sudden surge tank section variations. Note that linear head losses are negligible in the surge tank which is why a constant behavior of k is observed within each section of the tank, rather than a linear one.

_{Lower Chamber}. This means that the variations in the section of the surge tank result in very negligible local head losses when compared to the ones induced by the throttle.

#### 3.3. Impact of the Flow Share

_{B}= 0. This is nothing but the flow in C–A and A–C directions as presented in the previous sections of this study.

_{AB}) and inflow (k

_{CA}) head loss coefficients of the throttle under combining (1) and dividing (2) flow conditions are presented in Figure 10. Similar to the previous analyses, the value of k is computed with respect to the reference section at the bottom of the surge tank.

_{B}= 10 m

^{3}/s, reservoir level at 1277 m a.s.l). Results showed that a variable inflow and outflow head loss coefficient with the flow share of the surge tank does not alter the transient analysis. Neither the water level extremes of the surge tank, nor the periods of mass oscillation seem to be affected. Pressure plots at the bottom of the surge tank were evaluated for the same scenarios, and they do not seem to be affected either.

_{A}refers to a flow going out of the surge tank into the main waterway galleries (pressure tunnel–pressure shaft) and a negative value of Q

_{A}refers to a flow entering the surge tank from the main waterway galleries. A negative Q

_{C}refers to a reverse flow in the pressure tunnel.

- 0 ≤ t < 40 s: the flow in the pressure tunnel Q
_{C}is null, which is expected since the surge tank takes the role of the upstream reservoir to supply the penstock with the demanded flow. It is therefore the flow configuration (1) with Q_{A}= Q_{B}(Q_{C}= 0, no flow sharing). - 40 ≤ t < 120 s: the flow supplied by the tank decreases gradually and the upstream reservoir starts to supply the system with an increasing Q
_{C}. It is therefore flow configuration (1) with 0 < Q_{A}/Q_{B}< 1. - 120 ≤ t < 500 s: mass oscillation between the upstream reservoir and the surge tank takes place. A flow entering the surge tank (negative flow) creates a demand for the flow in the system in addition to the one required by the penstock. This results in an increased pressure tunnel flow Q
_{C}to accommodate both demands. This phase consists of successive alternations between modes (2) and (1) in which and 0 < Q_{A}/Q_{C}< 1 and 0 < Q_{A}/Q_{B}< 1. After 500 s, the steady generation mode is reached, and the mass oscillation phenomenon ends.

- 0 < t < 65 s: the flow in the pressure tunnel Q
_{C}is shared by both the surge tank and the penstock. It is therefore the flow configuration (2) with 0 < Q_{A}/Q_{C}< 1. Note that the zone in which the flow ratio is below 20% constitutes about 18 s. - t > 65 s: the flow in the penstock Q
_{B}becomes null by around 65 s. Then, mass oscillation takes place. In this case, alternations between flow configurations (3) and (2) occur with Q_{B}≈ 0. No flow sharing takes place, Q_{A}≈ Q_{C}.

## 4. Discussion

- 1D numerical modeling:
- Advantages: It is a fast method that can provide sufficient data for analyzing transient events and designing appropriate transient control devices in the system (surge tank dimensions for instance) based on critical load cases.
- Limitations: It can only provide the required head loss coefficients of the throttle and cannot serve as a tool to design its geometry. The throttle is modeled as a local restriction that has specific head loss characteristics without reflecting the real flow conditions (formation of the jet upstream or downstream, development of regions of swirling or flow separation). Current commercial 1D software are unable to model complex geometries of surge shafts, failing to reflect the real flow conditions across the expansion chambers.

- Physical Modeling:
- Advantages: It is adequate to represent the flow conditions of the real system on a reduced scale.
- Limitations: The design, construction, and systematic investigations are time-consuming. A sufficient number of measurements should be done for higher precision. Measurements of very small pressures or velocities that are in the same order of magnitude of the tolerance of the sensors may bias the results. Additionally, physical modeling does not allow obtaining flow parameters or visualizing flow patterns in all locations, despite the common usage of Plexiglas walls and the tests with dye injection. The latter does not lead to perceptible flow field features in a scaled model due to very rapid plume dispersion. Non-intrusive measurements e.g., using ultrasonic Doppler profiler (UVP) or particle image velocimetry (PIV) can reduce this limitation but require advanced instrumentation.

- 3D Numerical Modeling:
- Advantages: It allows the extraction of hydrodynamic values (numerical measurements) anywhere in the flow domain as well as the visualization of the flow fields on a prototype scale, the flow field being the major indicator of the effectiveness of the throttle arrangement and design. Iterations on the numerical model in the geometry optimization process are generally not as costly as the ones constructed and tested on a physical scale model.
- Limitations: It is accompanied by errors and uncertainties in the modelling approaches that should preferably be validated by a physical model. It takes a long computational time if a high mesh precision is required; a symmetry boundary condition may not always be used since a symmetrical geometry does not always imply symmetrical flow conditions.

- Hybrid Modeling As a Necessity

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Sketch of the waterway and the hydroelectric power plant [2].

**Figure 2.**3D model of the system consisting of the pressure tunnel, pressure shaft, surge tank and a throttle installed at its entrance (black-dotted arrows indicate the flow direction from C to B in turbining mode i.e., normal operation).

**Figure 4.**Variation of the total head and piezometric head as plotted along a measurement axis passing through the middle of the pipeline (Q = 14 m

^{3}/s, in the A-B direction during turbine opening).

**Figure 5.**Velocity streamlines during mass oscillation: (

**a**) flow into the surge tank (direction C–A); (

**b**) flow exiting the surge tank (direction A–C) (Q = 5 m

^{3}/s).

**Figure 7.**Head loss coefficient for the four flow directions (the best linear fit of combined numerical and experimental data series is shown).

**Figure 8.**Variation of relative value of the head loss coefficient k

_{AC}(surge tank outflow) and k

_{CA}(surge tank inflow) with the water level in the surge tank.

**Figure 10.**(

**a**) Variation of k

_{AB}with the flow share; (

**b**) Variation of k

_{CA}with the flow share.

**Figure 13.**Holistic approach to design throttled surge tanks (during a refurbishment of a high-head power plant).

Investigated Flow Direction | k (Combined Data Series Best Fit) | k (Experimental Data Series) | k (Numerical Data Series) | Relative Difference (%) |
---|---|---|---|---|

A–C (S_{1}–S_{5}) | 45.7 ± 0.48 | 45.9 ± 0.70 | 45.2 ± 0.12 | 1.42 |

A–B (S_{1}–S_{4}) | 40.6 ± 0.35 | 39.8 ± 0.35 | 42.1 ± 0.33 | 6.05 |

C–A (S_{5}–S_{1}) | 28.4 ± 0.25 | 29.6 ± 0.54 | 28.2 ± 0.013 | 4.93 |

C–B (S_{5}–S_{4}) | 0.95 ± 0.02 | 0.98 ± 0.02 | 0.86 ± 0.004 | 12.24 |

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**MDPI and ACS Style**

Seyfeddine, M.; Vorlet, S.; Adam, N.; De Cesare, G.
Holistic Design Approach of a Throttled Surge Tank: The Case of Refurbishment of Gondo High-Head Power Plant in Switzerland. *Water* **2020**, *12*, 3440.
https://doi.org/10.3390/w12123440

**AMA Style**

Seyfeddine M, Vorlet S, Adam N, De Cesare G.
Holistic Design Approach of a Throttled Surge Tank: The Case of Refurbishment of Gondo High-Head Power Plant in Switzerland. *Water*. 2020; 12(12):3440.
https://doi.org/10.3390/w12123440

**Chicago/Turabian Style**

Seyfeddine, Mona, Samuel Vorlet, Nicolas Adam, and Giovanni De Cesare.
2020. "Holistic Design Approach of a Throttled Surge Tank: The Case of Refurbishment of Gondo High-Head Power Plant in Switzerland" *Water* 12, no. 12: 3440.
https://doi.org/10.3390/w12123440