# Experimental Hydraulic Investigation of Angled Fish Protection Systems—Comparison of Circular Bars and Cables

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. General

^{3}/s), these solutions are not yet feasible [11].

#### 1.2. Basic Equations

_{v}through a physical barrier similar or equal the flexible fish fence (FFF). In particular, it was evaluated how the specific geometry including the bar spacing, rack angle, bar shape and hydraulic conditions affect head loss through the FFF. The evaluation of the local head loss h

_{v}is based on Bernoulli’s equation and the comparison of two cross sections, which are numbered in flow direction. By assuming that the kinetic energy correction factor is equal to 1 (-), the head loss h

_{v,total}between two sections can be calculated as following [15]:

_{1,2}, pressure p

_{1,2}and velocity v

_{1,2}were needed for each cross section as well as two constants, namely density of water ρ and gravity acceleration g. Furthermore, the loss h

_{v,cont}based on surface roughness between the two measurement positions had to be eliminated to identify the local head loss h

_{v}due to the structure. For the current case, the flume was used in its horizontal position (z

_{1}= z

_{2}) and the water depth h

_{1,2}could replace the formulation of the pressure to

_{v}and the velocity height ${v}_{ref}^{2}/(2\xb7g)$:

_{ref}was needed [16,17]. For the quantification of head loss at trash racks, the undisturbed cross upstream the structure was used (mean approach velocity) [18]. It was assumed that the velocity distribution over the complete cross section is homogeneous. For some applications and under specific circumstances, the velocity of the complete cross section of the trash rack can change significantly, which could be part of future investigations [19]. For the presented results, the velocity v

_{1}was used as v

_{ref}, hence this is a section that is in most cases easily accessible and does not include the influence of the trash rack (Section 3.2).

_{1}was used as well as the continuity equation. Consequently, the local head loss coefficient ξ of the trash rack can be calculated as followed:

_{1}and the discharge Q. The coefficient ξ

_{v,cont}, which includes roughness and the influence of the support structure for the trash rack in the experimental set-up, had to be evaluated separately (Section 3.3).

#### 1.3. Literature Values

_{ref}in Equation (3)). Extensive experiments on trash racks with vertical bars were also carried out by Meusburger [18], who expanded the basic equation introduced by Kirschmer [20]. The blockage ratio through the rack structure (including spacers and supporting elements) and through debris or trash clogging is added. Furthermore, the flow angle θ is taken in account based on adjusted calculation approaches [21,22,23]. Based on his results, the head loss coefficient ${\xi}_{M}$ is given by:

## 2. Materials and Methods

#### 2.1. Experimental Setup

^{−1}, which corresponds to approach velocities from 0.16 to 0.72 m s

^{−1}, and bar Reynolds numbers $R{e}_{b}$ from 750 to 3500. The Bar–Reynolds number is thereby defined by

_{1}in front of the installation was used and consequently the water depth h

_{1}multiplied by the width B of the flume allowed connecting the discharge Q. With the kinematic viscosity ν, the properties of water were taken into account and, for the characteristic linear dimension, the diameter s of the bars/cables was used (Table 1).

#### 2.2. Measurement

#### 2.3. Investigated Parameters

_{v,cont}, which includes the surface friction as well as the supporting structures (trash rack without bars or FFF without cables, respectively). Those were conducted for the whole discharge range and all observed angles α. Consequently, the main study was based on 216 basic experiments and 36 reference tests.

## 3. Results

#### 3.1. Overview

#### 3.2. Measurement Accuracy and Data Verification

_{v}with the velocity height in front of the installation, as presented in Equation (3). For the verification of the calculation, the total head loss h

_{v,total}based on Equation (1) was applied for the two main sections US2 and US7 (Figure 2).

_{1}was chosen as a reference velocity v

_{ref}in Equation (3) for the calculation of the total local head loss coefficient ξ*, respectively, ξ for the main investigations.

_{DPT}can be put in opposition with the ultrasonic sensors difference Δh

_{US}= US2–US7, as shown in Figure 4. Ideally, all points of each individual measurement would lay on the blue line of equality for this analysis. Obviously, the pressure head values differ considerably and partially strong outliers are produced by the ultrasonic measurement, which can also be seen in Figure 3. If the individual measured values are averaged for each measurement (Figure 4, right), it can be seen that the single outliers do not have such a significant influence on the mean value. Nevertheless, the previous comparison highlights the importance of the DPT to measure the differential pressure Δp

_{DPT}with a very high accuracy, as known from previous studies [15,19]. The DPT was further chosen as input values for the ξ-calculation based on Equation (4).

_{1}, Δp

_{DPT}and Q on the local head loss coefficient was investigated based on Equation (4). For this, the variable ξ* was used, which is based on the total loss including also those separately investigated (Section 3.3), h

_{v,cont}or ξ

_{v,cont}. The coefficient ${\xi}_{ij}^{*}$ was calculated based on each of the 2700 single measured values (j) for each parameter combination and rack option (i). Those results were standardised by the corresponding mean value of the measurement and presented in three classes depending on the Bar–Reynolds Number $R{e}_{b}$ in Figure 5. The fluctuations are in the range of 0.1 (-) and decrease with a higher discharge. In a previous step, the influence of the averaging was investigated. The difference between the mean value of ${\xi}_{i}^{*}$ and a single calculation of the coefficient ${\xi}_{ij}^{*}$ based on the previously averaged measurement values is negligible.

#### 3.3. Head Loss Through Supporting Structures and Surface Friction

_{v,cont}was measured without bars/cables and only remaining supporting structures. Thus, h

_{v,cont}includes the influence of the supporting structure as well as the friction of the flume boundary. The bar plots in Figure 7 demonstrate that head loss coefficients ξ

_{v,cont}for both rack types and the studied rack angles are all in a similar range of ξ

_{v,cont}≈ 0.2, which is a substantial part of the measured loss in comparison to those due to the investigated structure. For the perpendicular CBTR (α = 90°), ξ

_{v,cont}tends to be slightly lower, which is probably due to the fact that flow separation is concentrated at one location. Obviously, the proportion of ξ

_{v,cont}on ξ* is relatively high depending on the rack configurations up to 2/3 of ξ*.

#### 3.4. Head Loss Coefficients of the Rack Configurations

_{v,cont}(Section 3.3) from the total head loss coefficient ξ*. As expected, ξ increases disproportionally with increasing blockage ratios for both investigated rack options. Thereby, the increase of ξ with p positively depends on the angle (Figure 8). Furthermore, the comparison of the results with α equal 30° in Figure 8 reveal that the influence of p on ξ is more pronounced for the FFF.

_{v,cont}(Figure 7). In this respect, it is worth noting that ξ

_{v,cont}of the FFF is probably lower for full-scale conditions, since the supporting structures are there usually not exposed to the flow.

#### 3.5. Empirical Relations to Predict Head Loss of Angled Racks

_{m}values at the FFF and 70% at the CBTR deviate from the predicted ξ

_{p}coefficients with Equation (10) (less than ±25%), while the proportion is slightly lower for ξ

_{p}with Equation (9). The comparison of predicted and measured head loss coefficients also revealed a positive overestimation of ξ

_{m}for both formulae. Again, this is slightly more pronounced for the formula of Kirschmer (Equation (9)). Additionally, the deviation of predicted and measured ξ is correlated with the angle. There is an overestimation with the smallest angles and particularly for the highest blockage ratio p = 0.5 and a slight underestimation with the highest angles (α= 90° for CBTR and α= 40° for FFF). To compensate this overestimation, ξ

_{fitted}was introduced based on a modified Equation (10), in which the measured head loss coefficients ξ

_{m}are used to obtain the coefficients k

_{0}to k

_{2}:

_{0}to k

_{2}, R

^{2}and RMSE (root-mean-square error) for the measured head loss coefficients at the CBTR and the FFF. The exponent of $\frac{p}{1-p}$ is defined by k

_{1}and is 1.30 for the CBTR and 1.44 for the FFF, respectively, and in a similar range of both equations. In contrast, the exponent k

_{2}of sin(α) with 1.70 for the CBTR and 1.96 for the FFF option varies widely from the proposed value of Kirschmer [20]. At least, the coefficient k

_{0}with exp(0.59) = 1.8 for the CBTR matches well with the bar shape coefficient of 1.79 for circular bar shapes given by Equation (9). For the FFF configurations, k

_{0}is comparably higher with exp(1.16) = 3.19 (Table 4). Further tests are needed to confirm and refine this analysis.

## 4. Discussion

#### 4.1. Accuracy and Scale Effects

_{ref}= v

_{1}). Consequently, the accuracy of the measurements and the analysis are crucial. The verification analysis, presented in Section 3.2, clearly indicated the use of the water height in front of the trash rack as well as the differential pressure transducer instead of a second ultrasonic measurement downstream of the investigated structures. The deployment of a discharge measurement with a better accuracy would be desirable but would have been required to bypass the existing fix installation of the flume. All used measurements were independently checked by a redundant system continuously or randomly manually. The long observation period for each run of 10 min allowed finding a very stable mean value of the local head loss.

#### 4.2. Effect of Blockage and Angle

#### 4.3. Prediction of Head Loss Coefficients of Angled Racks with Empirical Equations

_{2}in Table 4), it is obvious that rack angle α has a stronger effect on head loss for the observed rack options. Furthermore, the fitted functions correspond more to the approach of Raynal et al. [25] for vertical inclined trash racks with low values of β [25]. Moreover, the exponents of the blockage term $\frac{p}{1-p}$ with 1.3 and 1.44 for CBTR and FFF, respectively (${k}_{1}$ in Table 4 ), are slightly below the value of 1.5 in Equation (6). Particularly, for the CBTR configurations, it fits better to Kirschmer’s description with ${\frac{s}{b}}^{(4/3)}$, where transversal elements of trash racks are unattended [20]. However, the higher exponent of the blockage term for FFF compared to CBTR seem to be a result of the cable vibrations, which are intensified particularly at higher blockage ratios. The last regression coefficient ${k}_{0}$ corresponds to the bar shape coefficient ${k}_{F}$ proposed by Kirschmer [20]. For the CBTR configuration, it is 1.8 (${k}_{0}$ in Table 4), which matches very well with the bar shape coefficient ${k}_{F}$ of 1.79 for circular bar shapes given by Kirschmer [20]. For the FFF configurations, ${k}_{0}$ is comparably higher (3.19, Table 4), which may be again due to flow-induced vibrations and a stronger interaction between the cables.

#### 4.4. Transferability of the Results to Technical Applications and Outlook

## 5. Conclusions

- Head loss coefficient ξ is independent from the Bar–Reynolds number in the studied range of $R{e}_{b}$ of 750–3500 and scale effects can be neglected.
- The coefficient ξ is significantly affected by the blockage ratio and the rack angle (Section 3.4, Table 3). The strong increase of head loss with decreasing bar spacings, which are necessary for fish protection, can be countered by designing lower rack angles (α≤ 45°).
- With increasing blockage ratios, the head loss coefficient at the FFF is up to 53% higher compared to the CBTR. This phenomenon is likely resulting from the effect of flow-induced cable vibrations and hence a further increase of blockage. Since amplitudes and frequencies of the vibrations are depending on parameters such as preload forces, cable length or flow velocity, the transferability to full-scale applications is limited.
- Head loss at the CBTR and FFF can be roughly estimated with a modified version of Equation (10) originally published by Meusburger [18], where the horizontal angle is used instead of the vertical rack inclination. However, the comparison of measured and estimated head loss revealed a systematic bias, which is more pronounced for rack options with low angles and high blockage.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Notation

A | = area (m^{2}) | α | = rack angle in relation to the vertical wall (°) |

b | = spacing between the bars (m) | β | = rack angle in relation to the ground plane (°) |

B | = width of the flume (m) | λ | = scale factor (-) |

F | = Froude number (-) | ρ | = mass density of water ≈ 997 (kg m^{−3}) |

g | = gravity acceleration (m s^{−2}) | $\nu $ | = kinematic viscosity (m^{2} s^{−1}) |

h | = water depth (m) | $\xi $ | = head loss coefficient (-) |

h_{v} | = head loss (m) | ξ* | = total head loss coefficient (-) |

${k}_{F}$ | = bar shape coefficient (-) | ${\xi}_{p}$ | = predicted head loss coefficient |

k | = constant | ${\xi}_{m}$ | = measured head loss coefficient |

l | = bar length (in cross section) (m) | ${\xi}_{v,cont}$ | = ξ due to supports and surface friction (-) |

${p}_{1,2}$ | = pressure (Pa) | $\Delta p$ | = differential pressure $={p}_{1}-{p}_{2}$ (Pa) |

p | = blockage ratio (-) | CBTR | circular bar trash rack |

Q | = discharge (m^{3} s^{−1}) | DPT | differential pressure transducer |

$Re$ | = Reynolds Number (-) | FFF | Flexible Fish Fence |

$R{e}_{b}$ | = Bar–Reynolds Number (-) | PG | point gauge |

s | = diameter of the bar/cable (m) | US | ultrasonic sensor |

v_{1,2} | = velocity (m s^{−1}) | ||

z | = elevation (m) |

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**Figure 1.**Angled trash rack with circular bars (CBTR) with: α = 30° and b = 5 m (upstream view) (

**a**); detailed side view of bar option from the side of the flume (

**b**); Flexible Fish Fence (FFF) with α = 30° and b = 5 mm (

**c**); and detailed side view of the flow pattern at the tail water of the FFF (

**d**).

**Figure 2.**Schematic side view of the experimental flume including the local coordinate system—the locations of the points are given in Table 2.

**Figure 3.**Analysis of the individual measured value standardised by the mean value of each geometry set-up: water depth at measurement points US1–US8 with ultrasonic sensors (

**left**); and differential pressure transmitter (DPT) and difference between US7 and US2 (

**right**).

**Figure 4.**Comparison of pressure head loss $\Delta {h}_{US}$ and $\Delta {h}_{DPT}$ including all measuring points (

**left**); and as a mean value for each geometrical set-up (

**right**).

**Figure 5.**Head loss coefficients ${\xi}_{ij}^{*}$ calculated for each data point (j = 1–2700) subtracted by the mean value of ${\xi}_{i}^{*}$ of each measurement for three ranges of Bar–Reynolds number $R{e}_{b}$.

**Figure 6.**Head loss coefficient ${\xi}^{*}$ versus Bar–Reynolds number $R{e}_{b}$ for selected CBTR (

**left**) and FFF configurations (

**right**).

**Figure 7.**Proportion of head loss coefficient ${\xi}_{v,cont}$ through the supporting structure and friction and $\xi $ for rack option CBTR (

**above**) and FFF (

**below**) on the total head loss coefficient ${\xi}^{*}$.

**Figure 8.**Head loss coefficient ξ versus blockage ratio p for the CBTR (

**left**) and FFF option (

**right**).

**Figure 10.**Percentage deviation of the predicted head loss coefficients ${\xi}_{p}$ by Equation (10) (

**left**) and Equation (9) (

**right**) from the measured head loss coefficients ${\xi}_{m}$. The two rack options are highlighted in grey (CBTR) and black (FFF) and differentiated by the related blockage ratios of the rack configurations. The dashed and dotted lines represent the ±75% and ±25% deviation of ${\xi}_{p}$ from ${\xi}_{m}$.

Parameter | Rods | Cables |
---|---|---|

Bar diameter s (mm) | 5 | 5 |

* Spacing b (mm) | 5, 10, 15 | 5, 10, 15 |

* Angle α (°) | 90, 45, 30 | 40, 30, 20 |

* Discharge Q (l s^{−1}) | 50–200 | 80–230 |

Bar shape coefficient ${k}_{F}$ (-) | 1.79 | 1.79 |

$s/b$ (-) | 0.33, 0.5, 1,0 | 0.33, 0.5, 1.0 |

Blockage ratio p (-) | 0.25, 0.33, 0.5 | 0.25, 0.33, 0.5 |

Bar length l (m) | 0.80, 1.24, 1.60 | 1.25, 1.60, 2.34 |

Approach velocity v (m s^{−1}) | 0.16–0.63 | 0.25–0.72 |

Bar–Reynolds-No. $R{e}_{b}$ (-) | 750–3000 | 1250–3500 |

Reynolds-No. $Re$ (-) | 31,000–125,000 | 50,000–144,000 |

Froude F (-) | 0.08–0.3 | 0.13–0.36 |

**Table 2.**Location of the measurement points of the ultrasonic sensors (US) and the point gauge (PG) shown in Figure 2.

US1 | US2 | US3 | US4 | US5 | US6 | US7 | PG | US8 | |
---|---|---|---|---|---|---|---|---|---|

x (m) | 5.3 | 6.5 | 7.5 | 8.3 | 11.3 | 13.7 | 16.1 | 17 | 17.3 |

**Table 3.**Local head loss ξ measured for the trash rack with circular bars (CBTR) and the flexible fish fence (FFF) depending on the blockage ratio p and rack angle α—differences between the two rack options for α = 30°.

CBTR | FFF | Difference | |||||
---|---|---|---|---|---|---|---|

p (-) | α (°) | ${\mathit{\xi}}_{\mathit{CBTR}}$ (-) | p (-) | α (°) | ${\mathit{\xi}}_{\mathit{FFF}}$ (-) | $\mathbf{\Delta}\mathit{\xi}={\mathit{\xi}}_{\mathit{FFF}}-{\mathit{\xi}}_{\mathit{CBTR}}$ (-) | $\mathbf{\Delta}\mathit{\xi}/{\mathit{\xi}}_{\mathit{CBTR}}$ (%) |

0.25 | 45 | 0.198 | 0.25 | 20 | 0.075 | - | - |

0.33 | 45 | 0.37 | 0.33 | 20 | 0.162 | - | - |

0.50 | 45 | 0.957 | 0.50 | 20 | 0.385 | - | - |

0.25 | 30 | 0.146 | 0.25 | 30 | 0.148 | 0.002 | 1.4% |

0.33 | 30 | 0.242 | 0.33 | 30 | 0.322 | 0.08 | 33.1% |

0.50 | 30 | 0.533 | 0.50 | 30 | 0.818 | 0.285 | 53.5% |

0.25 | 90 | 0.449 | 0.25 | 40 | 0.305 | - | - |

0.33 | 90 | 0.775 | 0.33 | 40 | 0.488 | - | - |

0.50 | 90 | 1.884 | 0.50 | 40 | 1.295 | - | - |

**Table 4.**Results of the multiple linear regression analysis for Equation (11).

${\mathit{k}}_{0}$ | ${\mathit{k}}_{1}$ | ${\mathit{k}}_{2}$ | ${\mathit{R}}^{2}$ | $\mathit{RMSE}$ | |
---|---|---|---|---|---|

CBTR | 1.80 | 1.3 | 1.7 | 0.9904 | 0.0414 |

FFF | 3.19 | 1.44 | 1.96 | 0.9861 | 0.0006 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Böttcher, H.; Gabl, R.; Aufleger, M.
Experimental Hydraulic Investigation of Angled Fish Protection Systems—Comparison of Circular Bars and Cables. *Water* **2019**, *11*, 1056.
https://doi.org/10.3390/w11051056

**AMA Style**

Böttcher H, Gabl R, Aufleger M.
Experimental Hydraulic Investigation of Angled Fish Protection Systems—Comparison of Circular Bars and Cables. *Water*. 2019; 11(5):1056.
https://doi.org/10.3390/w11051056

**Chicago/Turabian Style**

Böttcher, Heidi, Roman Gabl, and Markus Aufleger.
2019. "Experimental Hydraulic Investigation of Angled Fish Protection Systems—Comparison of Circular Bars and Cables" *Water* 11, no. 5: 1056.
https://doi.org/10.3390/w11051056