# A Parametric Approach for Determining Fishway Attraction Flow at Hydropower Dams

^{1}

^{2}

^{*}

## Abstract

**:**

^{3}/s). Fundamental to our approach is a design criterion that the attraction flow should maintain its integrity as it propagates downstream from the fishway entrance to beyond the highly turbulent zone characteristic of HPP tailraces to create a discernable migration corridor connecting the fishway entrance to the downstream river. To implement this criterion, we describe a set of equations to calculate the width of the entrance and the corresponding attraction discharge. Input data are usually easy to obtain and include geometrical and hydraulic parameters describing the target HPP and its tailrace. To confirm our approach, we compare model results to four sites at German waterways where the design of attraction flow was obtained by detailed experimental and numerical methods. The comparison shows good agreement supporting our approach as a useful, intermediate alternative for determining attraction flows that bridges the gap between simple guidelines and detailed hydraulic and biological investigations.

## 1. Introduction

^{3}/s, US–American guidelines [15] recommend attraction discharge between 5% and 10% of the design high flow, defined as mean daily streamflow being exceeded 5% of the time during migration period. For fishways in England and Wales a minimum discharge of 5% of the average annual daily flow (MQ) is recommended, and, if possible, considerably more [16]. The same guideline recommends attraction discharge between 5% and 10% of maximum turbine discharge at dams with hydropower usage, the larger value applying at small facilities and those locations where the entrance is not optimally located. Ease of use and rapidity of application are the main advantages of using proportions of a concurrent discharge as the basis of determining attraction flows. However, the effectiveness of the attraction flow not only depends on discharge proportions but also on attraction flow propagation, which in turn depends on flow velocities and is influenced by several other factors, such as the type of turbine, geometric dimensions of the HPP or hydraulic conditions [9], which are neglected by this approach. Notably, using proportions of a concurrent discharge for attraction flow assessment does not address the spatial and temporal complexity of tailrace flow patterns and its impact on fish orientation.

^{3}/s. In the next sections we (1) briefly describe important solid and hydraulic boundary conditions, (2) derive design criteria based on literature on fish and turbulence, (3) establish a design procedure to calculate attraction discharge, (4) apply them at four hydropower dams on German federal waterways, (5) gauge the usefulness of our approach by comparing our results to the results of detailed hydraulic studies available at the four study dams, and (6) discuss the reliability of the proposed methodology and indicate where future research may increase performance.

## 2. Design Approach

#### 2.1. Boundary Conditions in a Turbine Tailrace

^{3}/s which mirrors the approximate design discharges of the respective HPP. A typical design of a dam with navigation lock, weir and HPP and an example of a turbine tailrace are shown in Figure 1.

#### 2.2. Design Criteria

- The attraction discharge should be sufficiently large to prevent the intrusion of turbulent structures associated with turbine operation into the fishway entrance bay. A sufficiently large attraction discharge creates an uninterrupted directional signal that guides fishes towards the entrance and reduces the presence of constantly changing flow vectors which may disorient or hinder the movement of fish towards the fishway entrance, particularly at high discharges [10,23,24].

- 4.
- A migration corridor for fish approaching the HPP should be located laterally to the turbulent zone (see entrance bay in Figure 2).
- 5.
- Minimum time-averaged water velocities of the attraction flow, ${v}_{attraction}$, must (a) significantly exceed the rheotaxis threshold to give a clear signal to migratory fish [8,25] and (b) not exceed design water velocities of the fishway. For our approach, we assume ${v}_{attraction}$ to be 0.8 m/s. The attraction velocity considers design recommendations for entrance velocities of fishways [10,16,26] and investigations on flow perception of fish and their swimming behavior and performance [27,28,29].
- 6.
- Water velocities of the attraction flow must be comprised solely of positive flow vectors to not distract fish [7].
- 7.

#### 2.3. Length of Turbulent Zone

#### 2.4. Propagation Length of Attraction Flow

#### 2.4.1. Turbulent Rectangular Surface Jet

#### 2.4.2. Correction for Ambient Flow

#### 2.4.3. Correction for Slot Geometry and Lateral Wall

#### 2.5. Determination of Width of Entrance Slot and Attraction Discharge

## 3. Results

#### 3.1. Attraction Discharge

#### 3.2. Case Study

- One percent and 1.5% as lower and upper estimates, respectively, of the design discharge of the entire HPP as proposed for French rivers [14].
- Five percent of the design discharge of the turbine adjacent to the fishway as proposed for German Waterways [17].
- Five percent of the maximum HPP discharge proposed for rivers in the UK [16].

^{3}/s or approximately 12%.

## 4. Discussion

#### 4.1. Design Approach

#### 4.2. Validation

#### 4.3. Significance in the Context of Planning

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

^{3}/s of the bankside turbine. Each transect was navigated 120 times and results were averaged to reduce uncertainty due to turbulent fluctuations. During calibration, the draft tube exit plane velocity distribution was adjusted to minimize the root mean square error (RSME) between simulated velocities and measurements in both transects (RSME = 0.13 m/s).

^{3}/s. The principal velocity distribution at the draft tube exit section was kept for all scenarios, but the discharge was scaled linearly. Tailrace water levels were constant in all scenarios and attraction flow of the fishway was 1.73 m

^{3}/s. Examples of the resulting mean flow field for 0 and 70 m

^{3}/s turbine discharge are given in Figure A1.

**Figure A1.**Top view of tailrace and entrance bay of the hydrodynamic-numerical model of the dam in Eddersheim (Main River); streamlines of the attraction flow ($v0.8\mathrm{m}/\mathrm{s}$) and the mean flow field of the turbine are plotted for (

**a**) turbine discharge = 0 m

^{3}/s, (

**b**) turbine discharge = 70 m

^{3}/s.

## Appendix B

**Figure A2.**Aerial photos of dams on the Neckar River at (

**a**) Lauffen and (

**b**) Kochendorf, the Moselle River at (

**c**) Lehmen, and the Main River at (

**d**) Wallstadt.

^{3}/s for low water levels ($U{W}_{30}$), 1.4 m

^{3}/s for design conditions of the HPP, and for 2.1 m

^{3}/s for high water levels ($U{W}_{330}$) were determined.

^{3}/s for high tailwater levels corresponding to $U{W}_{330}$ is sufficient to ensure a contiguous migration corridor. This discharge is split into a discharge of 1.35 m

^{3}/s for the near-surface entrance and to 0.35 m

^{3}/s for the bottom entrance. At low tailwater levels, the discharge for the upper entrance opening reduces to 0.8 m

^{3}/s.

^{3}/s [53]. In contrast to the other case study locations, three fishway entrances are currently planned for this dam, including two near the draft tube and one farther downstream of the turbines. A constant discharge of about 5 m

^{3}/s is provided for all three entrances and hydraulic conditions. A sluice gate at each entrance regulates the flow height to ensure a constant velocity for all tailrace water levels. The maximum slot width of the main entrance located near the draft tube is 1.7 m and releases an attraction discharge ranging from 2.5–3.1 m

^{3}/s.

^{3}/s for high tailwater levels (corresponding to $U{W}_{330}$) with an entrance slot width of 0.6 m produces an acceptable migration corridor. An attraction discharge of 1.1 m

^{3}/s produced an acceptable migration corridor for low water levels (corresponding to $U{W}_{30}$).

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**Figure 1.**(

**a**) Typical scheme of a hydropower dam at federal waterways in Germany. (

**b**) Photograph of turbine tailrace of Lauffen (Neckar River, Germany).

**Figure 2.**Scheme of fishway entrance at hydropower plant tailwater. Entrance bay and attraction flow are used to create a migration corridor where flow conditions meet hydraulic requirements such as directional flow and comparatively low turbulence; ${L}_{AF}=$ length of a coherent attraction flow jet; ${L}_{TZ}=$ length of the turbulent zone.

**Figure 3.**Schematic longitudinal section of the turbulent zone in a tailrace downstream of a vertically mounted Kaplan turbine with elbow draft tube; ${L}_{TZ}=$ length of the turbulent zone; ${v}_{vertical}$= vertical velocity; ${v}_{m}=$ bulk mean velocity at draft tube exit section; tailwater levels $U{W}_{30}$, $U{W}_{330}$ with 30 and 330 days of nonexceedance and $U{W}_{design}$ at design discharge of HPP; ${h}_{DT}=$ water depth at draft tube exit section.

**Figure 4.**Normalized length of turbulent zone ${L}_{TZ}/{h}_{DT}$, as recorded from site inspections, for various bulk velocities ${v}_{m}$ at the draft tube exit section for horizontally mounted turbines (HMT) and vertically mounted turbines (VMT). Linear fit from Equation (2) with ${v}_{vertical}=0.56\mathrm{m}/\mathrm{s}$ for VMT and point estimate at ${v}_{m}=1.58\mathrm{m}/\mathrm{s}$ with ${v}_{vertical}=0.7\mathrm{m}/\mathrm{s}$ for HMT.

**Figure 6.**Schematic sketch to visualize the recirculation zone and reverse flow present in a fishway entrance bay; ${x}_{r}=$ length of recirculation zone; ${v}_{r}=$ reverse flow velocity; ${v}_{a}=$ mean ambient velocity; ${y}_{r}=$ lateral offset of fishway entrance bay.

**Figure 7.**Reduction of the normalized propagation length ${L}_{x,a}/{L}_{x}$ of turbulent jets in reverse flows for velocity ratios ${v}_{r}/{v}_{0}$ as obtained from [32]. Normalization with propagation length ${L}_{x}$ without reverse flow. Approximation with an exponential fit (Equation (9)). Comparison with results from 3D-hydrodynamical simulations in the tailrace of Eddersheim Dam.

**Figure 8.**Attraction discharge ${Q}_{AF}$ normalized by design discharge of the adjacent turbine ${Q}_{design,T}$ at hydropower plant for a velocity at entrance slot ${v}_{ES}=1.5\mathrm{m}/\mathrm{s}$ and a form factor $k=1$ determined using Equations (10)–(14) for hydraulic conditions at ${Q}_{design}$ (

**a**) for vertically mounted Kaplan turbines and (

**b**) for horizontally mounted Kaplan turbines;${v}_{attraction}=$ minimum attraction velocity; ${h}_{design}$ = downstream water depth at the entrance slot; ${h}_{DT}=$ water depth at draft tube exit section; ${A}_{DT}$ = area of the draft tube exit section.

**Figure 9.**Comparison of the results of the present methods and case study results for (

**a**) slot width $b$ and (

**b**) attraction discharge ${Q}_{AF}$. Where available discharges are compared for three different hydraulic conditions as given in Table 3.

**Table 1.**Parameters of the inspected dams where the length of turbulent zones were assessed by visual observation; VMT or HMT = vertically or horizontally mounted turbines.

Water Body | Dam | No. of Turbines | Design Discharge (m^{3}/s) | Draft Tube Area (m ^{2}) | Water Depth (m) | Turbine Type | Estimated Length of Turbulent Zone (m) |
---|---|---|---|---|---|---|---|

Moselle | Lehmen | 4 | 400 | 63.0 | 8.46 | HMT | 20 |

Müden | 4 | 400 | 63.0 | 8.38 | HMT | 20 | |

Fankel | 4 | 400 | 63.2 | 8.51 | HMT | 18 | |

St. Aldegund | 4 | 400 | 64.6 | 8.55 | HMT | 18 | |

Main | Eddersheim | 3 | 180 | 71.2 | 7.22 | VMT | 13 |

Kleinostheim | 2 | 204 | 55.6 | 7.20 | VMT | 20 | |

Obernau | 2 | 175 | 66.0 | 6.10 | VMT | 14 | |

Wallstadt | 2 | 150 | 61.4 | 6.07 | VMT | 14 | |

Freudenberg | 2 | 145 | 66.2 | 6.48 | VMT | 17 | |

Neckar | Gundelsheim | 1 | 80 | 73.3 | 6.35 | VMT | 12 |

Kochendorf | 3 | 94 | 24.3 | 5.35 | VMT | 14 | |

Horkheim | 2 | 75 | 27.4 | 4.56 | VMT | 12 | |

Lauffen | 2 | 80 | 24.6 | 4.43 | VMT | 12 |

Parameters | Units | Lauffen (Neckar) | Kochendorf (Neckar) | Lehmen (Moselle) | Wallstadt (Main) |
---|---|---|---|---|---|

Tailwater level $U{W}_{30}$ | m NHN ^{1} | 161.62 | 142.97 | 65.12 | 112.66 |

Tailwater level $U{W}_{design}$ | m NHN | 161.99 | 143.3 | 66.36 | 112.90 |

Tailwater level $U{W}_{330}$ | m NHN | 162.64 | 143.64 | 67.62 | 113.58 |

Bottom draft tube | m NHN | 157.68 | 138.00 | 57.9 | 106.80 |

Bottom entrance slot | m NHN | 160.42 | 141.87 | 63.92 | 111.46 |

HPP discharge ${Q}_{design}$ | m^{3}/s | 80 | 100 | 400 | 135 |

Number of turbines ${N}_{T}$ | - | 2 | 3 | 4 | 2 |

Draft tube area ${A}_{DT}$ | m^{2} | 29.75 | 32 | 63 | 61.38 |

Turbine type | - | vertical | vertical | horizontal | vertical |

Velocity at entrance slot ${V}_{ES}$ | m/s | 1.53 | 1.53 | 1.53 | 1.61 |

^{1}m NHN is meters above standard elevation zero, a vertical datum used in Germany.

**Table 3.**Length of turbulent zone ${L}_{TZ}$, slot width $b$ and attraction discharge ${Q}_{AF}$ during different hydraulic conditions for the fishway entrance near the turbine draft tube exit calculated with the parametric design approach, detailed methods and simple approaches for the case study locations; values for [14] are for 1% and 1.5% (in parentheses).

Dam | Parameter | Units | Parametric Approach | Detailed Approach | Simple [14] | Simple [17] | Simple [16] |
---|---|---|---|---|---|---|---|

$\mathrm{Lauffen}$ | ${L}_{TZ}$ | m | 10 | ||||

[51] | Slot width $b$ | m | 0.68 | 0.70 | |||

${Q}_{AF}\left(U{W}_{30}\right)$ | m^{3}/s | 1.2 | 1.1 | ||||

${Q}_{AF}\left(U{W}_{design}\right)$ | m^{3}/s | 1.5 | 1.5 | ||||

${Q}_{AF}\left(U{W}_{330}\right)$ | m^{3}/s | 2.1 | 2.1 | 0.8 (1.2) | 2.0 | 4.0 | |

Kochendorf | ${L}_{TZ}$ | m | 10 | ||||

[9] | Slot width $b$ | m | 0.58 | 0.50 | |||

${Q}_{AF}\left(U{W}_{30}\right)$ | m^{3}/s | 0.9 | 0.8 | ||||

${Q}_{AF}\left(U{W}_{design}\right)$ | m^{3}/s | 1.2 | |||||

${Q}_{AF}\left(U{W}_{330}\right)$ | m^{3}/s | 1.4 | 1.35 | 1.0 (1.5) | 1.7 | 5.0 | |

Lehmen | ${L}_{TZ}$ | m | 19 | ||||

[53] | Slot width $b$ | m | 1.42 | 1.7 | |||

${Q}_{AF}\left(U{W}_{30}\right)$ | m^{3}/s | 2.4 | 3.05 | ||||

${Q}_{AF}\left(U{W}_{design}\right)$ | m^{3}/s | 4.9 | |||||

m^{3}/s | 7.4 | 4.0 (6.0) | 5.0 | 20.0 | |||

Wallstadt | ${L}_{TZ}$ | m | 12 | ||||

[52] | Slot width $b$ | m | 0.63 | 0.60 | |||

${Q}_{AF}\left(U{W}_{30}\right)$ | m^{3}/s | 1.1 | 1.1 | ||||

${Q}_{AF}\left(U{W}_{design}\right)$ | m^{3}/s | 1.4 | |||||

${Q}_{AF}\left(U{W}_{330}\right)$ | m^{3}/s | 2.0 | 1.9 | 1.4 (2.1) | 3.4 | 7.0 |

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## Share and Cite

**MDPI and ACS Style**

Heneka, P.; Zinkhahn, M.; Schütz, C.; Weichert, R.B.
A Parametric Approach for Determining Fishway Attraction Flow at Hydropower Dams. *Water* **2021**, *13*, 743.
https://doi.org/10.3390/w13050743

**AMA Style**

Heneka P, Zinkhahn M, Schütz C, Weichert RB.
A Parametric Approach for Determining Fishway Attraction Flow at Hydropower Dams. *Water*. 2021; 13(5):743.
https://doi.org/10.3390/w13050743

**Chicago/Turabian Style**

Heneka, Patrick, Markus Zinkhahn, Cornelia Schütz, and Roman B. Weichert.
2021. "A Parametric Approach for Determining Fishway Attraction Flow at Hydropower Dams" *Water* 13, no. 5: 743.
https://doi.org/10.3390/w13050743