# 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 $U{W}_{30}$).

## References

- European Union. Directive 2000/60/EG of the European Parliament and of the Council-Framework for Community Action in the Field of Water Policy: Directive 2000/60/EG-Water Framework Directive; European Union: Brussels, Belgium, 2000. [Google Scholar]
- Larinier, M. Fishways-General considerations. Bull. Fr. Pêche Piscic.
**2002**, 364, 21–27. [Google Scholar] [CrossRef][Green Version] - Venus, T.E.; Smialek, N.; Pander, J.; Harby, A.; Geist, J. Evaluating Cost Trade-Offs between Hydropower and Fish Passage Mitigation. Sustainability
**2020**, 12, 8520. [Google Scholar] [CrossRef] - Williams, J.G.; Armstrong, G.S.; Katopodis, C.; Larinier, M.; Travade, F. Thinking like a fish: A key ingredient for development of effective fish passage facilities at river obstructions. River Res. Appl.
**2012**, 28, 407–417. [Google Scholar] [CrossRef][Green Version] - Enders, E.C.; Boisclair, D.; Roy, A.G. The effect of turbulence on the cost of swimming for juvenile Atlantic salmon (Salmo salar). Can. J. Fish. Aquat. Sci.
**2003**, 60, 1149–1160. [Google Scholar] [CrossRef] - Čada, G.; Carlson, T.; Ferguson, J.; Richmond, M.; Sale, M. Exploring the Role of Shear Stress and Severe Turbulence in Downstream Fish Passage. In Hydro’s Future: Technology Markets and Policy, Proceedings of the Waterpower Conference 1999, Las Vegas, NV, USA, 6–9 July 1999; Brookshier, P.A., Ed.; American Society of Civil Engineers: Reston, VA, USA, 1999; pp. 1–9. ISBN 978-0-7844-0440-9. [Google Scholar]
- Liao, J.C. A review of fish swimming mechanics and behaviour in altered flows. Philos. Trans. R. Soc. B Biol. Sci.
**2007**, 362, 1973–1993. [Google Scholar] [CrossRef] [PubMed][Green Version] - Pavlov, D.; Lupandin, A.; Skorobogatov, M. The Effects of Flow Turbulence on the Behavior and Distribution of Fish. J. Ichthyol.
**2000**, 40, 232–261. [Google Scholar] - Gisen, D.C.; Weichert, R.B.; Nestler, J.M. Optimizing attraction flow for upstream fish passage at a hydropower dam employing 3D Detached-Eddy Simulation. Ecol. Eng.
**2017**, 100, 344–353. [Google Scholar] [CrossRef][Green Version] - DWA-Regelwerk. Merkblatt DWA-M 509: Fischaufstiegsanlagen und fischpassierbare Bauwerke—Gestaltung, Bemessung, Qualitätssicherung; DWA-Regelwerk: Hennef, Germany, 2014. [Google Scholar]
- Kopecki, I.; Tuhtan, J.A.; Schneider, M.; Ortlepp, J.; Thonhauser, S.; Schletterer, M. Assessing Fishway Attraction Flows Using an Ethohydraulic Approach. In Proceedings of the 3rd IAHR Europe Congress, Porto, Portugal, 14–15 April 2014; ISBN 978-989-96479-2-3. [Google Scholar]
- Visser, K.P.; Ruys, B.; Viaene, P.; Creëlle, S.; Mulder, T.D. Assessment of the attraction flow in a fish passage. In Proceedings of the 5th IAHR International Junior Researcher and Engineer Workshop on Hydraulic Structures, Spa, Belgium, 28–30 August 2015. [Google Scholar]
- Musall, M.; Oberle, P.; Nestmann, F.; Fust, A. 3-D-Strömungssimulation zur Bewertung der Leitströmung eines Umgehungsgerinnes am Hochrheinkraftwerk Ryburg-Schwörstadt. WasserWirtschaft
**2008**, 98, 37–42. [Google Scholar] [CrossRef] - Larinier, M. Location of fishways. Bull. Fr. Pêche Piscic.
**2002**, 364, 39–53. [Google Scholar] [CrossRef][Green Version] - National Marine Fisheries Service (NMFS). Anadromous Salmonid Passage Facility Design; NMFS, Northwest Region: Portland, OR, USA, 2011.
- Armstrong, G.S.; Aprahamian, M.W.; Fewings, G.A.; Gough, P.J.; Reader, N.A.; Varallo, P.V. Environment Agency Fish Pass Manual: Guidance Notes on the Legislation, Selection and Approval of Fish Passes in England and Wales; Document-GEHO 0910 BTBP-E-E; Environment Agency: Bristol, UK, 2010.
- Weichert, R.; Kampke, W.; Deutsch, L.; Scholten, M. Zur Frage der Dotationswassermenge von Fischaufstiegsanlagen an großen Fließgewässern. WasserWirtschaft
**2013**, 33–38. [Google Scholar] [CrossRef] - Grünzner, M.; Haimerl, G. Numerical Simulation of Downstream Attraction Flow at Danube Weir Donauwörth. In Proceedings of the 9th International Symposium on Ecohydraulics, Vienna, Austria, 17–22 September 2012. [Google Scholar]
- Sakamoto, M.; Müller, A.; Andolfatto, L.; Hashii, T.; Yamaishi, K.; Avellan, F. Experimental investigation and numerical simulation of flow in the draft tube elbow of a Francis turbine over its entire operating range. IOP Conf. Ser. Earth Environ. Sci.
**2019**, 240, 72009. [Google Scholar] [CrossRef] - Cook, C.B.; Richmond, M.C.; Serkowski, J.A. Observations of velocity conditions near a hydroelectric turbine draft tube exit using ADCP measurements. Flow Meas. Instrum.
**2007**, 18, 148–155. [Google Scholar] [CrossRef] - Avellan, F. Flow Investigation in a Francis Draft Tube: The Flindt Project. In Proceedings of the 20th IAHR Symposium on Hydraulic Machinery and Systems, Charlotte, NC, USA, 6–9 August 2000; pp. 1–18. [Google Scholar]
- Deniz, S.; Bosshard, M.; Speerli, J.; Volkart, P. Saugrohre bei Flusskraftwerken; VAW-Mitteilung No. 106; Vischer, D., Ed.; Laboratory of Hydraulics, Hydrology and Glaciology, ETH Zürich: Zürich, Switzerland, 1990. [Google Scholar]
- Odeh, M.; Noreika, J.F.; Haro, A.; Maynard, A.; Castro-Santos, T.; Čada, G.F. Evaluation of the Effects of Turbulence on the Behavior of Migratory Fish; Final Report 2002; BPA Report DOE/BP-00000022-1; Bonneville Power Administration: Portland, OR, USA, 2002.
- Silva, A.T.; Katopodis, C.; Santos, J.M.; Ferreira, M.T.; Pinheiro, A.N. Cyprinid swimming behaviour in response to turbulent flow. Ecol. Eng.
**2012**, 44, 314–328. [Google Scholar] [CrossRef][Green Version] - Adam, B.; Schwevers, U. Das Verhalten von Fischen in Fischaufstiegsanlagen. Osterr. Fisch.
**1997**, 50, 82–97. [Google Scholar] - U.S. Fish and Wildlife Service (USFWS). Fish Passage Engineering Design Criteria; USFWS, Northeast Region R5, USFWS: Hadley, MA, USA, 2019.
- Bak-Coleman, J.; Court, A.; Paley, D.A.; Coombs, S. The spatiotemporal dynamics of rheotactic behavior depends on flow speed and available sensory information. J. Exp. Biol.
**2013**, 216, 4011–4024. [Google Scholar] [CrossRef] [PubMed][Green Version] - Castro-Santos, T.; Sanz-Ronda, F.J.; Ruiz-Legazpi, J.; Jonsson, B. Breaking the speed limit—Comparative sprinting performance of brook trout (Salvelinus fontinalis) and brown trout (Salmo trutta). Can. J. Fish. Aquat. Sci.
**2013**, 70, 280–293. [Google Scholar] [CrossRef] - Ebel, G. Modellierung der Schwimmfähigkeit europäischer Fischarten—Zielgrößen für die hydraulische Bemessung von Fischschutzsystemen. Wasserwirtschaft
**2014**, 104, 40–47. [Google Scholar] [CrossRef] - Enders, E.C.; Boisclair, D.; Roy, A.G. A model of total swimming costs in turbulent flow for juvenile Atlantic salmon (Salmo salar). Can. J. Fish. Aquat. Sci.
**2005**, 62, 1079–1089. [Google Scholar] [CrossRef][Green Version] - Tritico, H.M.; Cotel, A.J. The effects of turbulent eddies on the stability and critical swimming speed of creek chub (Semotilus atromaculatus). J. Exp. Biol.
**2010**, 213, 2284–2293. [Google Scholar] [CrossRef][Green Version] - Kraatz, W. Ausbreitungs-und Mischvorgänge in Strömungen. Ph.D. Thesis, Technische Universität Dresden, Dresden, Germany, 1975. [Google Scholar]
- Seo, I.W.; Kwon, S.J. Experimental Investigation of Three-Dimensional Nonbuoyant Rectangular Jets. J. Eng. Mech.
**2005**, 131, 733–746. [Google Scholar] [CrossRef] - Sforza, P.M.; Steiger, M.H.; Trentacoste, N. Studies on three-dimensional viscous jets. AIAA J.
**1966**, 4, 800–806. [Google Scholar] [CrossRef] - Krothapalli, A.; Baganoff, D.; Karamcheti, K. On the mixing of a rectangular jet. J. Fluid Mech.
**1981**, 107, 201–220. [Google Scholar] [CrossRef] - Rajaratnam, N. Turbulent Jets; Elsevier Scientific Pub. Co: Amsterdam, The Netherlands, 1976; ISBN 0-444-41372-3. [Google Scholar]
- Walker, D.T. On the origin of the ‘surface current’ in turbulent free-surface flows. J. Fluid Mech.
**1997**, 339, 275–285. [Google Scholar] [CrossRef] - Bergmann, L. Numerische Modellierung der Strömung aus dem Einstieg einer Fischaufstiegsanlage mittels OpenFOAM. Master’s Thesis, Karlsruhe Institute of Technology, Karlsruhe, Germany, 2017. [Google Scholar]
- Rajaratnam, N.; Humphries, J.A. Turbulent non-buoyant surface jets. J. Hydraul. Res.
**1984**, 22, 103–115. [Google Scholar] [CrossRef] - Giger, M.; Dracos, T.; Jirka, G.H. Entrainment and mixing in plane turbulent jets in shallow water. J. Hydraul. Res.
**1991**, 29, 615–642. [Google Scholar] [CrossRef] - Madnia, C.K.; Bernal, L.P. Interaction of a turbulent round jet with the free surface. J. Fluid Mech.
**1994**, 261, 305–332. [Google Scholar] [CrossRef] - Gholamreza-Kashi, S.; Martinuzzi, R.J.; Baddour, R.E. Mean Flow Field of a Nonbuoyant Rectangular Surface Jet. J. Hydraul. Eng.
**2007**, 133, 234–239. [Google Scholar] [CrossRef] - Demissie, M. Diffusion of Three-Dimensional Slot Jets with Deep and Shallow Submergence. Ph.D. Thesis, University of Illinois at Urbana-Champaign, Champaign, IL, USA, 1980. [Google Scholar]
- Adams, E.W.; Johnston, J.P. Effects of the separating shear layer on the reattachment flow structure part 2: Reattachment length and wall shear stress. Exp. Fluids
**1988**, 6, 493–499. [Google Scholar] [CrossRef] - Tihon, J.; Legrand, J.; Legentilhomme, P. Near-wall investigation of backward-facing step flows. Exp. Fluids
**2001**, 31, 484–493. [Google Scholar] [CrossRef] - Chen, Y.T.; Nie, J.H.; Armaly, B.F.; Hsieh, H.T. Turbulent separated convection flow adjacent to backward-facing step—Effects of step height. Int. J. Heat Mass Transf.
**2006**, 49, 3670–3680. [Google Scholar] [CrossRef] - Prych, E.A. An analysis of a jet into a turbulent ambient fluid. Water Res.
**1973**, 7, 647–657. [Google Scholar] [CrossRef] - Khorsandi, B.; Gaskin, S.; Mydlarski, L. Effect of background turbulence on an axisymmetric turbulent jet. J. Fluid Mech.
**2013**, 736, 250–286. [Google Scholar] [CrossRef][Green Version] - Perez Alvarado, A. Effect of Background Turbulence on the Scalar Field of a Turbulent Jet. Ph.D. Thesis, McGill University, Montreal, QC, Canada, 2016. [Google Scholar]
- Mahl, L.; Heneka, P.; Henning, M.; Weichert, R.B. Numerical Study of Three-Dimensional Surface Jets Emerging from a Fishway Slot. Water
**2021**, submitted. [Google Scholar] - Heinzelmann, C.; Weichert, R.; Wassermann, S. Hydraulische Untersuchungen zum Bau einer Fischaufstiegsanlage in Lauffen am Neckar. WasserWirtschaft
**2013**, 103, 26–32. [Google Scholar] [CrossRef] - Federal Waterways Engineering and Research Institute (BAW). Gutachten über die Bestimmung der FuE-Szenarien für den Leitdurchfluss an der Fischaufstiegsanlage Wallstadt/Main; Report B3953.01.31.10109; BAW: Karlsruhe, Germany, 2020.
- Institute for Water and River Basin Management (IWG). 3D-numerische Modellstudie zur Analyse/Optimierung der Strömungscharakteristik im Mündungsbecken der geplanten Fischwechselanlage Lehmen (Mosel); IWG, Karlsruhe Institute of Technology: Karlsruhe, Germany, 2018. [Google Scholar]
- Lacey, R.J.; Neary, V.S.; Liao, J.C.; Enders, E.C.; Tritico, H.M. The IPOS framework: Linking fish swimming performance in altered flows from laboratory experiments to rivers. Special Issue Paper. River Res. Appl.
**2012**, 28, 429–443. [Google Scholar] [CrossRef] - Cotel, A.J.; Webb, P.W. Living in a Turbulent World—A New Conceptual Framework for the Interactions of Fish and Eddies. Integr. Comp. Biol.
**2015**, 55, 662–672. [Google Scholar] [CrossRef] [PubMed][Green Version] - Sagnes, P.; Statzner, B. Hydrodynamic abilities of riverine fish: A functional link between morphology and velocity use. Aquat. Living Resour.
**2009**, 22, 79–91. [Google Scholar] [CrossRef][Green Version] - Fiedler, G.; Mahl, L.; Weichert, R.B. Design of Auxiliary Water Systems for Fishways. In Proceedings of the International Symposium on Hydraulic Structures, Aachen, Germany, 15–18 May 2018. [Google Scholar] [CrossRef]
- Henning, M.; Schütz, C. Design and special constructions of fishway pilot sites on German Federal Waterways. In Proceedings of the 5th International Conference on Engineering & Ecohydrology for Fish Passage, Groningen, The Netherlands, 22–24 June 2015. [Google Scholar]
- Weller, H.G.; Tabor, G.; Jasak, H.; Fureby, C. A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput. Phys.
**1998**, 12, 620–631. [Google Scholar] [CrossRef] - Deshpande, S.S.; Anumolu, L.; Trujillo, M.F. Evaluating the performance of the two-phase flow solver interFoam. Comput. Sci. Discov.
**2012**, 5, 14016. [Google Scholar] [CrossRef] - Menter, F.R. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J.
**1994**, 32, 1598–1605. [Google Scholar] [CrossRef][Green Version] - Sokoray-Varga, B.; Weichert, R.; Lehmann, B. Flow investigations for fish pass Lauffen/Neckar in field and laboratory. In Wasserkraft-mehr Wirkungsgrad + mehr Ökologie = mehr Zukunft. 34, Proceedings of the Dresdner Wasserbaukolloquium 2011: Wasserkraft: Mehr Wirkungsgrad + mehr Ökologie = mehr Zukunft, Dresden, Germany, 10–11 March 2011; Stamm, J., Graw, K.U., Eds.; Selbstverlag der Technischen Universität Dresden: Dresden, Germany, 2011; pp. 87–94. ISBN 3867801983. [Google Scholar]
- Federal Waterways Engineering and Research Institute (BAW). Gutachten über den Leitabfluss der geplanten Fischaufstiegsanlage am Kraftwerk Kochendorf/Neckar; Report A395 301 10096; BAW: Karlsruhe, Germany, 2013. (In German)

**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