# Head Losses of Horizontal Bar Racks as Fish Guidance Structures

^{*}

## Abstract

**:**

## 1. Introduction

_{d}≤ 120 m³ s

^{−1}were equipped with horizontal bar rack bypass systems in the past decade [1,2]. Nevertheless, there is still a lack of systematic studies on the hydrodynamic optimization and verification of these state-of-the-art downstream fish guidance structures.

_{n}) should not exceed 0.5 m s

^{−1}to avoid fish impingement and thus fish injuries [1,14,15]. Because approach flow velocities at HPPs are typically larger than 0.5 m s

^{−1}and a guidance effect towards a bypass is missing, physical barriers oriented perpendicular to the approach flow (Figure 1a) are often unsuitable [16].

_{d}≤ 120 m³ s

^{−1}) in multiple countries. On the basis of experiences at several pilot HPPs, Ebel [1] specified a number of design guidelines: The horizontal approach flow angle α is selected to match the swimming capabilities and life stage of the relevant target fish species. Approach flow velocities, typically varying between U

_{o}= 0.40 and 0.80 m s

^{−1}, lead to α = 20°–40°. The rack angle is therefore a compromise between limiting V

_{n}on the one hand and the rack length on the other hand. The clear bar spacing s

_{b}of such physical barriers depends on the target fish species, typically resulting in a recommendation of s

_{b}≤ 15 mm [1].

_{b}= 10, 20, and 30 mm (prototype dimensions); two different bar depths; and various overlay configurations. Their studies were limited to rectangular bars and rectangular bars with a rounded tip (“one-side rounded bars”). The latter were investigated for α = 30° only. Böttcher et al. [22] studied angled racks with horizontally aligned, cylindrical bars without overlays in a 1:2 Froude-scaled model. Racks with α = 30°, 45°, and 90° and s

_{b}= 10, 20, and 30 mm (prototype dimensions) were investigated. All laboratory studies presented so far focused on sectional models, where only a section of the rack was investigated. Other associated structures such as a bypass for fish downstream migration or an adjacent weir were not included in these models. Some studies such as Berger [23] and Szabo-Meszaros et al. [24] focused on physical models of HBRs including a bypass, which makes it difficult to compare the head loss coefficients obtained in these studies with the losses of sectional models.

## 2. Experimentation

#### 2.1. Test Setup

_{ch}= 0.50 m wide, and 0.70 m deep laboratory channel (Figure 2 and Figure 3a) as a sectional model with 1:1 Froude-scaled model racks. Therefore, the individual bars were on a prototype scale, but only a section of the rack was modelled. The channel bottom and back wall were made of PVC (polyvinyl chloride), whereas the front wall was made of glass to allow for visual observations. The discharge of the closed water circulation system was controlled with a gate valve and measured with a magnetic-inductive flow meter. To achieve symmetrical approach flow conditions, a honeycomb flow straightener was placed at the channel inlet. Two 1 m long hard foam floaters were used to reduce surface waves. The water level was controlled with a downstream flap gate, creating a free overfall into the outlet basin. The measurement traverse carried an ultrasonic distance sensor, and the downstream rack end was positioned 4.2 m downstream of the honeycomb flow straightener. The coordinate system was defined as x, y, and z for the streamwise, transversal, and vertical coordinates, respectively. The origin was set at the bottom of the right channel wall at the downstream rack end (Figure 3a). The bypass flow was neglected in the physical model as it is typically in the range of 2–5% of the total HPP discharge [1], and has therefore only a small effect on the hydraulic losses. To investigate the effect of the HPP layout, additional experiments were carried out with larger approach flow widths w

_{o}and a sharp contraction to the width of the turbine intake w

_{ds}downstream of the HBR, thereby representing block-type HPPs (Figure 3b). The entire discharge was diverted through the rack, so that the layout corresponded to an abrupt contraction.

_{bp}= 10 mm thick bottom plate (subscript bp) and up to 22 bars (subscript b), depending on the selected bar spacing. The bars were assembled on two threaded bars (“vertical tie-bars”) located at Y = y w

_{ds}

^{−1}= 0.25 and 0.75. They are indicated as filled circles (•) in Figure 3a,b. The bar spacing was adjusted with cylindrical spacers (subscript s) with an outer diameter of 15 mm. To mount the bottom plate and all bar ends flush with the channel walls, they were cut with the respective horizontal approach flow angle α. On the basis of measurements on 13 different days, the average friction loss within the l

_{ch}= 4.2 m long channel section without a rack was determined as Δh

_{f}= 1.7 mm, which corresponds to a friction slope of 0.40‰, with a standard deviation of σ = 0.2 mm.

#### 2.2. Parameter Range and Test Program

_{b}= 8 mm and bar depth d

_{b}= 60 mm in flow direction (Figure 4). The bar thickness and the clear bar spacing s

_{b}are defined as the streamwise projection of both values, that is, the maximum bar thickness and the smallest spacing between two bars, respectively (Figure 5). The relative bar depth D

_{b}= d

_{b}t

_{b}

^{−1}is defined as the ratio between bar depth and bar thickness. The bar thickness at mid cross section (the mounting location) was t

_{b}

_{,m}= 5 mm, except for the rectangular bars (S1), where t

_{b,m}= 8 mm (Figure 4). The relative bottom (subscript Bo) and top (subscript To) overlay heights (H

_{Bo}= h

_{Bo}h

_{o}

^{−1}and H

_{To}= h

_{To}h

_{o}

^{−1}) were calculated using the respective bottom and top overlay heights (h

_{Bo}, h

_{To}) and the approach flow depth h

_{o}for normalization. The total overlay height was defined as H

_{Ov}= H

_{Bo}+ H

_{To}. The top overlay height h

_{To}was measured as the distance between the approach flow water level z = h

_{o}and the lower overlay tip, and therefore neglected the flow stagnation height at the overlay (Figure 5). The horizontal approach flow angle α was defined as the horizontal angle between the rack and the main flow (Figure 5). The approach flow angles α = 30° and 45° were investigated for all bar shapes and bar spacings.

_{b}= 10, 20, and 30 mm. Each rack configuration was tested without overlays, and with six different overlay setups: (1) H

_{Bo}= 0.1, H

_{To}= 0; (2) H

_{Bo}= 0, H

_{To}= 0.1; (3) H

_{Bo}= 0.2, H

_{To}= 0; (4) H

_{Bo}= 0, H

_{To}= 0.2; (5) H

_{Bo}= H

_{To}= 0.1 (H

_{Ov}= 0.2); and (6) H

_{Bo}= H

_{To}= 0.2 (H

_{Ov}= 0.4). In an additional set of experiments, an approach flow angle of α = 90° and the effect of the relative bar depth D

_{b}were investigated. Measurements were conducted for (a) S1-bars with s

_{b}= 10, 20, and 30 mm and (b) S2-bars with s

_{b}= 20 mm. The effect of the relative bar depth D

_{b}= 3.5, 5.5, 7.5, 9.5, 12, 15 was investigated with S2-bars for (a) α = 90° and s

_{b}= 20 mm and (b) α = 30° and s

_{b}= 10, 20, and 30 mm. Contraction ratios of w

_{o}w

_{ds}

^{−}

^{1}= 1.25, 1.5, and 2.0 were studied for the bar shape S4, s

_{b}= 20 mm, and α = 30° and 45° with all overlay configurations listed above. A multiple linear regression was performed to develop head loss prediction equations. These equations were then validated with the data of Maager [20] and Albayrak et al. [21], and Böttcher et al. [22].

_{b}), the spacers (BR

_{s}), and the bottom plate (BR

_{bp}) with Equation (1) as

_{b}is the number of horizontal bars (−), n

_{s}is the number of spacers per vertical tie-bar (−), n

_{v}is the number of vertical tie-bars (−), and t

_{s}is the spacer thickness (outer diameter). Depending on the rack configuration, the uppermost horizontal bar or spacer was only partially submerged, such that n

_{b}or n

_{s}was not a whole number. The exact values of BR are listed in Table 1. Because the bar thickness reduced from tip to tail for the hydrodynamic bars (S2–S4), a larger proportion of the vertical tie-bars (spacers) was exposed to the flow, thus leading to slightly larger BR for S2–S4 in comparison to S1 (Table 1). For a preliminary design, the blocking ratio of the bottom plate BR

_{bp}can be neglected, and a constant bar thickness can be assumed, leading to the approximate blocking ratio $B{R}^{\ast}\cong {\left({s}_{b}+{t}_{b}\right)}^{-1}\left({t}_{b}+{s}_{b}\text{}{n}_{v}\text{}{t}_{s}\text{}{w}_{ch}{}^{-1}\right)$. The deviation to the exact blocking ratio $\left|BR-B{R}^{\ast}\right|B{R}^{-1}$ was then 0.8% to 6.5%, depending on the configuration.

#### 2.3. Experimental Procedure

_{o}

^{−1}= −5.6; Y = y w

_{ds}

^{−1}= 0.1, 0.5, 0.9) and three transversal locations downstream (subscript ds; X = 4.9; Y = 0.1, 0.5, 0.9) of the rack (circle outlines ( ) in Figure 3a) with a measurement duration of 30 s. To account for measurement inaccuracies due to air temperature variations, the reference distance between the measurement cart and the channel bottom was measured prior to each test series. For each rack configuration, the downstream flap gate was adjusted to obtain h

_{o}= 0.40 m. The corresponding flow velocities U

_{o}and U

_{ds}were determined from continuity (Equation (2)) and the hydraulic head loss Δh

_{R}caused by the rack was calculated with the Bernoulli equation (Equation (3)):

_{t}is the turbine discharge (m

^{3}s

^{−1}). Independent of the HPP layout, U

_{th}≈ U

_{ds}for small head losses. At diversion HPP setups in a straight channel with constant w

_{ch}and without a bypass, U

_{th}= U

_{o}(Figure 3a). By using U

_{th}instead of U

_{o}or U

_{ds}, the assessment was independent of potential weir and bypass discharge in case of a block-type HPPs (Figure 3b), but still accounted for Δh

_{R}. The resulting rack head loss coefficient ξ

_{R}was then determined with Equation (5):

#### 2.4. Measurement Uncertainties

_{R}was assessed with a Monte Carlo simulation with 10

^{7}model runs. This uncertainty estimation included the magnetic-inductive flow meter measurements, the ultrasonic distance sensor reference measurements to the bottom, and the water level measurements up- and downstream of the rack. The required input probability density functions were experimentally determined from 480 min of measurement duration. The measured time series was divided into 960 values, each corresponding to a 30 s time average. Finally, a normal distribution was fitted to these data. The probability density function of the ultrasonic distance sensor reference measurements to the channel bottom resulted from 60 min of measurement duration, which was split up into 360 values corresponding to a 10 s time average. The resulting standard deviations of the ultrasonic distance sensor (UDS) and the magnetic-inductive flow meter (MID) were σ

_{UDS,bottom}= 1.0 mm, σ

_{UDS,water}= 2.7 mm, σ

_{MID}= 2.5 L s

^{−1}. These measurement uncertainties led to a 95% quantile of ξ

_{R}= ±0.035, independent of the rack configuration.

#### 2.5. Model Effects

_{o}and U

_{th}was investigated for racks with S1- and S4-bars, α = 45°, and s

_{b}= 20 mm (BR ≈ 0.35) at the diversion HPP setup (U

_{o}= U

_{th}).

_{R}as a function of h

_{o}for the bar shapes S1 and S4, respectively, with U

_{th}= 0.50 m s

^{−1}. For both bar shapes, ξ

_{R}was independent of the approach flow depth if h

_{o}≥ 0.20 m (h

_{o}≥ 25 t

_{b}). Because the channel walls slightly deformed for h

_{o}≥ 0.40 m due to the hydrostatic load, h

_{o}= 0.40 m (corresponding to a flow depth to bar thickness ratio of h

_{o}t

_{b}

^{−1}= 50) was selected as an optimum flow depth in terms of experimental handling. Figure 6c,d shows ξ

_{R}as a function of U

_{th}for bar shapes S1 and S4, respectively, for constant h

_{o}= 0.40 m. The coefficient ξ

_{R}was independent of U

_{th}for U

_{th}≥ 0.2 m s

^{−1}, corresponding to a bar Reynolds number

`R`

_{b}= t

_{b}U

_{th}ν

^{−1}≥ 1600, with ν = 1.01 × 10

^{−6}m

^{2}s

^{−1}as the kinematic viscosity of water at 20 °C. For U

_{th}> 0.6 m s

^{−1}, surface waves reduced the measurement accuracy. Therefore, all further main experiments were conducted at a constant theoretical flow velocity of U

_{th}= 0.5 m s

^{−1}(Q

_{t}= 0.1 m

^{3}s

^{−1}, Equation (4)) with

`R`

_{b}= 4000, Froude number

`F`= U

_{th}g

^{−}

^{0.5}h

_{o}

^{−}

^{0.5}= 0.25, and Reynolds number

`R`= 4 R

_{h}U

_{th}ν

^{−1}= 3·10

^{5}, involving the hydraulic radius R

_{h}= h w

_{ch}(2h+w

_{ch})

^{−1}. This flow velocity was an optimum value, thereby representing prototype conditions. Furthermore, the selected parameters were in excess of the threshold values h

_{o}t

_{b}

^{−1}≥ 40 and

`R`

_{b}≥ 1500 to avoid model effects for different rack types specified in the literature [11,12,18,19].

## 3. Results

#### 3.1. General Observations

_{R}as a function of (a) the bar shape S, (b) the blocking ratio (BR), and (c) the approach flow angle α for all tested rack configurations without overlays and D

_{b}= 7.5. Depending on the individual rack configuration, the determined values ranged from ξ

_{R}= 0.17–2.53 without overlays (Figure 7) and up to ξ

_{R}= 8.57 with overlays (not shown in Figure 7). Three governing effects were observed:

- (I)
- ξ
_{R}reduced from rectangular to hydrodynamic bars for all s_{b}(Figure 7a). The difference between S1 and S2 was large, whereas S3 and S4 led to similar ξ_{R}as for S2. - (II)
- ξ
_{R}increased with increasing BR, corresponding to smaller s_{b}, for all bar shapes and approach flow angles (Figure 7b). This effect was larger for S1 as compared to S2, S3, and S4. - (III)
- ξ
_{R}increased with increasing α (Figure 7c). The angle effect was most pronounced for S1 with s_{b}= 10 mm (BR ≈ 0.49) and almost negligible for S4 with s_{b}= 30 mm (BR ≈ 0.28).

_{R}as a function of the relative bar depth D

_{b}with S2-bars for (a) α = 90° and (b) α = 30°. For α = 90°, D

_{b}had no significant effect on ξ

_{R}(Figure 8a). In contrast, for α = 30°, shorter bars led to smaller ξ

_{R}(Figure 8b). This effect was more pronounced for s

_{b}= 10 mm than for s

_{b}= 20 and 30 mm. Although the ξ

_{R}values were almost identical for short bars with D

_{b}= 3.5 and D

_{b}= 5.5, they increased linearly between D

_{b}= 5.5 and D

_{b}= 15 (Figure 8b). Figure 8 also shows that the effect of D

_{b}on ξ

_{R}was similar for all overlay configurations. Overall, within the typical application range of HBRs (α = 30°, D

_{b}= 5–10, H

_{Ov}< 0.4), the effect of D

_{b}on ξ

_{R}was small, that is, ≤±10%.

#### 3.2. General Equation for Head Loss Prediction

_{R}was defined as the product of five individual coefficients: blocking ratio coefficient C

_{BR}, approach flow angle coefficient C

_{α}, bar shape coefficient C

_{S}, bar depth coefficient C

_{Db}, and overlay coefficient C

_{Ov}. On the basis of a curve fitting analysis for the hydrodynamic bars, Equation (6) was proposed to predict the head losses of HBRs with hydrodynamic bars. The computation of the individual coefficients is described in the following sections. The experimentally determined rack head loss coefficients ξ

_{R,m}(subscript m = measured) were in good agreement with the predicted (subscript p) values ξ

_{R,p}on the basis of Equation (6) for S2–S4 without overlays (Figure 9a). The mean prediction error ($\overline{PE}$, Equation (7)) was less than 22% for all measurement data with S2–S4 (Figure 9b). The error bars show the 95% quantile of the measurement uncertainty as described in Section 2.4. For ξ

_{R,m}> 0.5, the measurement uncertainties were small (<±7%), whereas they were relatively large for ξ

_{R,m}< 0.2 (>±17.5%; Figure 9b). However, with HPP approach flow velocities in the range of U

_{o}= 0.3–1.0 m s

^{−1}, the resulting total losses are small (∆h

_{R}= ξ

_{R}U

_{o}

^{2}(2g)

^{−}

^{1}≈ 1.0 cm; with U

_{o}= 1 m/s and ξ

_{R}= 0.2) and this uncertainty becomes negligible for energy production. Equation (6) can also be applied for rectangular bars (S1) but then leads to a significant deviation for higher ξ

_{R}

_{,p}(Figure 9). Therefore, an alternative equation for rectangular bars is presented below, which is proposed to predict ξ

_{R}more accurately for S1-bars, accounting for the different hydraulic behavior of rectangular and hydrodynamic bars.

#### 3.2.1. Blocking Ratio Coefficient C_{BR}

_{b}= 10 mm, the corresponding high BR ≈ 0.5 results in C

_{BR}= 1.0. This value reduces to C

_{BR}= 0.33 for low BR = 0.25.

#### 3.2.2. Approach Flow Angle Coefficient C_{α}

_{α}was determined on the basis of experiments with α = 30° and 45° and validated with α = 90° for S2 and s

_{b}= 20 mm (BR ≈ 0.35). The validation for α > 45°, shown in Section 3.3, indicates an application range of Equation (9) of α = 30°–90°. For α = 90°, C

_{α}= 1.0, whereas for α = 30°, it reduces to C

_{α}= 0.63.

#### 3.2.3. Bar Shape Coefficient C_{S}

_{R}reduces on average by ≈27% from S1 to S2 and by ≈42% from S1 to S3/S4.

#### 3.2.4. Bar Depth Coefficient C_{Db}

_{R}, as long as the bars are deep enough for the separated flow to reattach to the side face of the bars. The bar depth effect is accounted for with Equation (10). For the standard relative bar depth D

_{b}= 7.5, C

_{Db}= 1. Bars with D

_{b}< 7.5 lead to C

_{Db}< 1, whereas D

_{b}> 7.5 leads to C

_{Db}> 1. For an HBR with α = 30°, C

_{Db}= 0.90 for D

_{b}= 5, and C

_{Db}= 1.10 for D

_{b}= 10. For α = 90°, no significant effect of D

_{b}on ξ

_{R}was observed in the range of D

_{b}= 3.5–15 (Figure 8a). Therefore, C

_{Db}= 1 for α = 90° (Equation 10). The coefficient C

_{Db}linearly increases from α = 90° to α = 30°. The recommended application limit of Equation (10) is 5 ≤ D

_{b}≤ 15, which covers the typical range of HBRs at prototype HPPs.

#### 3.2.5. Application of General Head Loss Equation to Rectangular Bars

**,**allowing for the application of the above equations for rectangular bars. However, the hydraulic processes at racks with rectangular bars significantly differ from those at racks with hydrodynamic bars. Because flow separations at the tip of rectangular bars additionally decrease the hydraulically active area between two bars, the BR effect is more pronounced for S1-bars. Therefore, ξ

_{R}increases disproportionately for rectangular bars for larger α and smaller s

_{b}(Figure 7b,c). The loss coefficient ξ

_{R,p}is underestimated by Equation (6) for S1, large α, and small s

_{b}(Figure 9). Hence, Equation (11) is proposed to estimate ξ

_{R}for rectangular bars, where the larger effects of α and s

_{b}are taken into account with larger exponents.

_{R,m}is compared to the predictions on the basis of Equation (6) (star-shaped symbols) and Equation (11) (square symbols). For small head loss coefficients (ξ

_{R}≤ 0.5), Equations (6) and (11) lead to similar ξ

_{R,p}, whereas for ξ

_{R}> 0.5, Equation (6) underestimates ξ

_{R}for the S1-bars. Therefore, Equation (6) is recommended for racks with rectangular bars, only if s

_{b}≥ 20 mm.

_{R,m}and ξ

_{R,p}results if Equation (6) is applied to hydrodynamic bars and in parallel Equation (11) for rectangular bars (Figure 11). Including all measurement data with α = 30° and 45°, $\overline{PE}$ was only 5.8% with individual maximum deviations of 22%.

#### 3.2.6. Overlay Coefficient C_{Ov}

_{Ov}= f(C

_{OL}, BR, α, C

_{S}, H

_{Ov}), where C

_{OL}is the overlay layout coefficient with C

_{OL}= 1 if either bottom or top overlays are applied and C

_{OL}= 0.9 for combined bottom and top overlays (Equation (12)). Equation (12) can be applied to calculate C

_{Ov}in both Equations (6) and (11).

_{Ov}= 1.0. On the basis of the investigated rack configurations with overlays and α = 30° and 45°, C

_{Ov}is minimal for S1, α = 30°, s

_{b}= 10 mm (BR ≈ 0.49), and H

_{Ov}= 0.1 (C

_{Ov}= 1.2). It is maximal for S3/S4, α = 45°, s

_{b}= 30 mm (BR ≈ 0.28), and H

_{Bo}= H

_{To}= 0.2 (H

_{Ov}= 0.4; C

_{Ov}= 7.2). In other words, overlays increase the head losses by 20%–620%, depending on the bar shape and rack configuration.

_{R,p}values are in good agreement with the experimentally determined loss coefficients ξ

_{R,m}using Equation (6) for S2–S4 and Equation (11) for S1 (Figure 12a). For the vast majority of data, PE is within ±20% for the configurations with combined bottom and top overlays (Figure 12b), bottom overlays only (Figure 12c), and top overlays only (Figure 12d). The outlier in Figure 12b with the largest error of PE ≈ 40% resulted for a worst case combination of rectangular bars (S1) with α = 30°, small bar spacing s

_{b}= 10 mm, and a very large overlay blocking H

_{Bo}= H

_{To}= 0.2. However, this deviation has little practical relevance, as HBRs with s

_{b}= 10 mm (BR ≈ 0.49) and H

_{Ov}= 0.4 are typically equipped with hydrodynamic bars.

#### 3.3. Application of Equations to Larger Approach Flow Angles

_{b}= 20 mm (BR = 0.35), and S1, s

_{b}= 10, 20, 30 mm (BR = 0.483, 0.342, 0.272) for all overlay combinations listed in Section 2.2 (Figure 13). Without overlays, the mean prediction errors are small $({\overline{PE}}_{\mathrm{S}1}\text{}=\text{}8\%,\text{}{\overline{PE}}_{\mathrm{S}2}\text{}=\text{}3\%)$. With overlays, the predicted ξ

_{R,p}values also agree well with ξ

_{R,m}. The individual PE was below 35% for all configurations, except for S1, α = 90°, H

_{Bo}= H

_{To}= 0.2 with s

_{b}= 20 mm and s

_{b}= 30 mm (PE = 44%, PE = 64%). This overprediction of ξ

_{R}for rack configurations with rectangular bars (S1), α = 90°, and large overlay blockage is of low importance, because of the low practical relevance of that configuration. The mean prediction error of all rack configurations with α = 90° is ${\overline{PE}}_{\mathrm{S}1}\text{}=\text{}20.2\%$ and ${\overline{PE}}_{\mathrm{S}2}\text{}=\text{}14.3\%$, indicating an application range of α = 30°–90° for the proposed equations.

#### 3.4. HPP Layouts

_{ds}is determines with Equation (13) as

_{o}is the approach flow cross-sectional area and A

_{ds}is the cross-sectional area downstream of the contraction. The predicted losses of a sharp contraction without an HBR installed are in good agreement (PE ≤ 25%) with the measurements (ξ

_{c}

_{,p}= 0.15, 0.22, 0.30 vs. ξ

_{c}

_{,m}= 0.12, 0.20, 0.29 for w

_{o}w

_{ds}

^{−}

^{1}= 1.25, 1.5, and 2, respectively). The head loss coefficients derived from the measurements at the block-type HPP setup with an HBR (ξ

_{(R + c),m}) were consistently larger than the sum of the predicted rack head losses (ξ

_{R}

_{,p}, Equation 6) and the predicted contraction losses (ξ

_{c,p}, Equation (13)). The measurements indicate that HBRs at block-type HPPs do not only induce rack head losses, but they also increase the contraction losses by a factor of 1.7. Therefore, with the contraction head loss $\mathsf{\Delta}{h}_{c}={\xi}_{c}\text{}{U}_{ds}^{2}\text{}{\left(2g\right)}^{-1}$, Equation (3) is expanded to determine the rack head losses in general form to

_{R}is the rack length.

## 4. Discussion

#### 4.1. Bar Depth Effect

_{b}= 5–20 mm and d

_{b}= 40–100 mm, typically leading to relative bar depths of D

_{b}= d

_{b}t

_{b}

^{−}

^{1}= 5–10. On the one hand, bars with large D

_{b}implicate a large surface area and thus higher friction losses. On the other hand, longer bars may improve the flow straightening effect and therefore reduce losses caused by vortex shedding. The coefficient 0.04 in Equation (10) was determined by a multiple linear regression for bar depths D

_{b}= 5.5, 7.5, 9.5, 12, and 15, as a linear trend was observed within this range (Figure 8b). In the present study, the bar depth was investigated for α = 30° and α = 90°. In addition to α = 30°, a rack angle of α = 45° was investigated by Maager [20] and Albayrak et al. [21] for D

_{b}= 5 and 10, and BR = 0.55, 0.39, and 0.33 (s

_{b}= 10, 20, and 30 mm; prototype dimensions) for rectangular bars with various overlay configurations. On the basis of 38 measurements with S1-bars, H

_{Ov}≤ 0.4 and α = 30°, the rack head loss coefficient ξ

_{R}reduced on average by 15% if the bar depth was halved from D

_{b}= 10 to D

_{b}= 5. For α = 45°, this reduction was only 10%. The bar depth effect observed for α = 45° therefore reduces to C

_{Db}

_{,red}≈ 10%/15% ≈ 67% of the bar depth effect observed for α = 30° (Figure 15, asterisk symbols). This effect of the rack angle α on the bar depth effect, where C

_{Db}is calculated with Equation (10), results in Equation (16).

_{Db,}

_{red}for α = 45° and Equation (16) supports the linear relation between α and C

_{Db}.

_{b}= 2.5, 5, 10) on the rack head loss coefficient for traditional trash racks with rectangular vertically oriented bars (γ = 90°, BR = 0.37). He found no significant effect of D

_{b}on ξ

_{R}. This can be explained by the small blocking ratios and the perpendicular orientation of the bars to the main flow. In the present work, D

_{b}had an effect on ξ

_{R}for α = 30° but not for α = 90°. Similarly, it is possible that the effect of D

_{b}on ξ

_{R}was not negligible for γ ≠ 90 (Figure 1). However, it is still feasible to apply the equation of Kirschmer [17] for the head loss prediction of traditional trash racks, as γ is typically close to γ = 90°, that is, in the range of γ = 70°–80° [19]. However, if the equation of Kirschmer [17] is applied for racks with small α or γ, ξ

_{R}would be expected to be overpredicted for short bars (D

_{b}<< 5) and underpredicted for deep bars (D

_{b}>> 5). Although the effect of D

_{b}on ξ

_{R}was investigated for S2-bars only, due to the similar head loss behavior of S2–S4 bars, it is assumed that the trend can be transferred to all hydrodynamic bar shapes. The measurements of [20] and [21] further indicate that Equation (10) can also be used for rectangular bars. Therefore, C

_{Db}is also included in Equation (11). The measurements in Figure 8b show that the effect of D

_{b}on ξ

_{R}is most pronounced for s

_{b}= 10 mm (BR ≈ 0.49). However, the bar depth effect was similar for s

_{b}= 20 mm (BR ≈ 0.35) and s

_{b}= 30 mm (BR ≈ 0.28), which is supported by other studies [20,21]. Therefore, the effect of s

_{b}on C

_{Db}is neglected in Equation (10). For practical application at a typical HBR with α = 30° and D

_{b}= 5–10, the effect of D

_{b}on ξ

_{R}is small (±10%). However, if the bars are very short (D

_{b}= 3.5) or very deep (D

_{b}= 15), ξ

_{R}can reduce by 16% or increase by 30%, respectively, in comparison to D

_{b}= 7.5.

#### 4.2. Effect of Vertical Tie-Bars

_{R}(S1, α = 45°, s

_{b}= 10 mm) these mounting parts accounted for only 3% of the overall losses. However, for a hydrodynamically optimized rack configuration (S4, α = 30°, s

_{b}= 30 mm) with small overall losses, they accounted for up to 25% of ξ

_{R}. The effect of the mounting parts is included in Equations (6) and (11) by calculating the BR of racks with cylindrical tie-bars.

#### 4.3. Comparison of Head Loss Prediction Equations with Literature Data

_{Ov}up to 0.5, creating a large flow diversion and corresponding loss coefficients up to ξ

_{R,m}= 28. Herein, only the head loss measurements of rack configurations with H

_{Bo}≤ 0.2 and H

_{To}≤ 0.2 were used to validate (subscript val) the proposed equations of the present investigation. Figure 16a compares the head loss coefficients of racks with rectangular bars measured by Maager [20] ξ

_{R}

_{,m,val}with the corresponding ξ

_{R}

_{,p}values predicted using Equation (11). The majority of data points were predicted with an accuracy of ±30% with $\overline{PE}\text{}=\text{}13.3\%$ (Figure 16a). If the proposed equation for hydrodynamic bars (Equation (6)) was used for the one-side rounded bars of Maager (2016) [20], significant deviations result, indicating that the hydraulic processes at the latter were more similar to rectangular bars. A good agreement ($\overline{PE}\text{}=\text{}11.7\%$) was found for the one-side rounded bars if the proposed equation for rectangular bars (Equation (11)) was used with a prefactor reduction from 2.33 to 1.60 (Figure 16b). This means that the predicted hydraulic losses of one-side rounded bars were 31% smaller than the hydraulic losses of rectangular bars. The loss reduction implicated by the shape factors of Kirschmer [17] is 24%.

#### 4.4. Engineering Application

_{b}= 20 mm (BR ≈ 0.35), t

_{b}= 8 mm, D

_{b}= 7.5, and S4-bars without overlays is as low as ξ

_{R}= 0.22 (Equation (6)), assuming no blockage by floating debris. For U

_{o}= 0.8 m s

^{−}

^{1}, this results in head losses of Δh

_{R}= 7 mm. The predicted head loss increases by a factor of 4.5 if bottom and top overlays of H

_{Bo}= H

_{To}= 0.2 are installed (ξ

_{R}= 0.98, Δh

_{R}= 32 mm). For rectangular bars (S1), the head losses increase by ≈ 70% (ξ

_{R}= 0.37 and Δh

_{R}= 12 mm) without overlays, and by ≈ 50% (ξ

_{R}= 1.47 and Δh

_{R}= 48 mm) with overlays, relative to the S4 configuration (Equation (11)). For the S1-bars, the overlays thus result in an increase of ξ

_{R}by a factor of 4. If constructional considerations are not limiting (e.g., mounting of tie-bars), bars with a relative depth of D

_{b}= 5.5 are recommended to reduce costs and hydraulic losses. For practical applications, the effect of D

_{b}on ξ

_{R}can be larger than described in Section 4.1 if algae growth increases the surface roughness.

_{d}≥ 25 m

^{3}s

^{−}

^{1}. The head loss coefficients with respect to U

_{th}of traditional trash racks were ξ

_{R}= 0.10–5.04 with an average of 1.67 and a standard deviation of σ = 1.20. The head losses of clean, unclogged HBRs are therefore of comparable order. No pronounced increase of head losses is expected if these traditional trash racks were replaced by HBRs, provided that substantial clogging can be prevented by an automated rack cleaning machine. Meusburger [19] also showed that the head losses of traditional trash racks at existing HPPs are significantly higher than predicted by the equation proposed by Kirschmer [17], who conducted his measurements in a straight laboratory flume representing diversion HPPs. However, his empirical equation is often applied to block-type HPPs without considering the oblique approach flow and the effect of increased contraction losses due to the rack, as described in Section 3.4. It is important to consider not only the rack itself, but also the HPP layout when head losses are estimated for engineering applications. The higher losses might also be caused by partial clogging of racks at prototype HPPs, which was not considered by Kirschmer [17]. During high flows or even flood events in autumn, some HPP operators report head losses at HBRs caused by foliage clogging of up to Δh

_{R}= 30 cm, requiring HPP shutdowns as a safety measure. In addition, Kirschmer’s [17] equation does not include the effects of further support bars or intermediate piers, which are typically needed for large flow depths to distribute the substantial additional load in case of rack clogging. When the equations of the present work are used for practical applications, further support bars can be considered with an increased BR. Potential foliage clogging can be accounted for by substituting the clogged areas with overlays (Equation (12)). If no site-specific information is available, Turnpenny and O’Keeffe [4] suggest assuming that at least 20% of the rack area gets clogged.

#### 4.5. Fish Protection

_{n}is often larger than the sustained fish swimming speed, increasing the risk of fish impingements [1,4]. Top and bottom overlays are part of an HBR design, which can significantly increase head losses. Despite this, laboratory studies indicate higher guidance for bottom- and surface-oriented fish [9,27]. Additionally, overlays improve the routing of driftwood and sediments towards the bypass [1]. Overall, the selection of geometric parameters for an optimum HBR design with regard to high fish guidance and protection depends not only on head loss but also on the resulting velocity field, which influences the fish behavior. Therefore, velocity fields of a range of HBR configurations for different HPP layouts are published in the accompanying paper [25]. They can be used to estimate the fish behavior at fish guidance structures during the planning phase. Feigenwinter et al. [28] present a conceptual approach for the evaluation of potential locations of fish guidance structures combining traditional design principles with computational fluid dynamics and novel findings from ethohydraulic research. The approach is based on the three key aspects fish fauna, structural conditions, and hydraulic conditions such as velocity fields and head losses. Nevertheless, to reliably assess the fish behavior at HBRs, live fish tests or extensive field monitoring campaigns at HPPs equipped with HBRs are indispensable.

## 5. Conclusions

_{b}= 10, 20, and 30 mm; approach flow angles α = 30°, 45°, and 90°; relative bar depths D

_{b}= d

_{b}t

_{b}

^{−}

^{1}= 3.5–15; and a wide range of overlay configurations. Additional experiments were conducted for a wider upstream channel to account for different hydropower plant layouts (diversion vs. block-type). The head losses of horizontal bar racks can be predicted using Equations (6) and (11) for hydrodynamic and rectangular bars, respectively, thereby incorporating the following key findings:

- (I)
- The hydraulic processes at racks with rectangular bars differed significantly from hydrodynamic bars. Therefore, separate head loss prediction equations were proposed.
- (II)
- Head losses were significantly reduced by foil-shaped bars. On average, foil-shaped bars led to more than 40% smaller losses compared with rectangular bars. This loss reduction was more pronounced for racks with large blocking ratios BR, large approach flow angles α, and small relative overlay blocking ratios H
_{Ov}. - (III)
- For practical applications at an HBR with an approach flow angle α = 30° and a relative bar depth of D
_{b}= 5–10, the effect of D_{b}on ξ_{R}is small (≤±10%). However, if very short (D_{b}= 3.5) or very deep bars (D_{b}= 15) are used in combination with small clear bar spacing (s_{b}= 10 mm, blocking ratio BR ≈ 0.49), ξ_{R}can reduce by 16% or increase by 30%, respectively, in comparison to D_{b}= 7.5. - (IV)
- Overlays strongly increased head losses. For typical hydropower plants (approach flow angle α = 30°, clear bar spacing s
_{b}= 20 mm, blocking ratio BR ≈ 0.35), the application of bottom and top overlays with a height of 20% of the flow depth (H_{Bo}= H_{To}= 0.2) increased the loss coefficient ξ_{R}by a factor of 4.0–4.5. - (V)
- The validation showed that the measured head losses of horizontal bar racks with rectangular and cylindrical bars found in the literature can be predicted by Equation (11) with an accuracy of ±30%. A comparable accuracy was reached for one-side rounded and cylindrical bars with Equation (11) if the shape factor was reduced from 2.33 to 1.60 and 1.72, respectively.
- (VI)
- In addition to diversion hydropower plants, the proposed equations can also be applied for block-type hydropower plants. Horizontal bar racks installed at block-type hydropower plants with a sharp contraction increased the contraction losses by a factor of 1.7.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

HBR | Horizontal bar rack |

HPP | Hydropower plant |

Notation | |

A_{ds} = cross-sectional area downstream of the rack (m^{2}), A_{ds} = h_{ds} w_{ds} | |

A_{o} = approach flow cross-sectional area (m^{2}), A_{o} = h_{o} w_{o} | |

BR = total blocking ratio (−) | |

BR^{*} = approximate blocking ratio (−) | |

BR_{b} = blocking ratio of the horizontal bars (−) | |

BR_{bp} = blocking ratio of the bottom plate (−) | |

BR_{s} = blocking ratio of the spacers (−) | |

C_{BR} = blocking ratio coefficient (−) | |

C_{Db} = bar depth coefficient (−) | |

C_{Db}_{,red} = reduction of C_{Db} (%) | |

C_{OL} = overlay layout coefficient (−) | |

C_{Ov} = overlay coefficient (−) | |

C_{S} = bar shape coefficient (−) | |

C_{α} = approach flow angle coefficient (−) | |

d_{b} = bar depth (m) | |

D_{b} = relative bar depth (−), D_{b} = d_{b} t_{b}^{−1} | |

F = Froude number (−), F = U_{o} g^{−0.5} h_{o}^{−0.5} | |

g = gravity acceleration constant (m s^{−2}), g = 9.81 m s^{−2} | |

h_{Bo} = bottom overlay height (m) | |

H_{Bo} = relative bottom overlay height (−), H_{Bo} = h_{Bo} h_{o}^{−1} | |

h_{ds} = downstream flow depth (m) | |

h_{To} = top overlay height (m) | |

H_{To} = relative top overlay height (−), H_{To} = h_{To} h_{o}^{−1} | |

h_{o} = approach flow depth (m) | |

H_{Ov} = total relative overlay height (−), H_{Ov} = H_{Bo} + H_{To} | |

l_{ch} = channel length (m) | |

l_{R} = rack length (m), l_{R} = w_{ds} sin(α)^{−1} | |

n = number of data points (−) | |

n_{b} = number of horizontal bars (−) | |

n_{s} = number of spacers per vertical tie-bar (−) | |

n_{v} = number of vertical tie-bars (−) | |

PE = prediction error (%) | |

$\overline{PE}$ = mean prediction error (%) | |

Q_{d} = design discharge (m^{3} s^{−1}) | |

Q_{t} = turbine discharge (m^{3} s^{−1}) | |

R = Reynolds number based on hydraulic radius (-), R = 4 R_{h} U_{o} ν^{−1} | |

R_{b} = bar Reynolds number (−), R_{b} = t_{b} U_{o} ν^{−1} | |

R_{h} = hydraulic radius (m), R_{h} = h w_{ch} (2h+w_{ch}) ^{−1} | |

s_{b} = clear bar spacing (m) | |

t_{b} = bar thickness at thickest point (m) | |

t_{b,m} = bar thickness at mid cross section (m) | |

t_{bp} = thickness of the bottom plate (m) | |

U_{ds} = mean downstream flow velocity (m s^{−1}) | |

U_{th} = theoretical average flow velocity (m s^{−1}) | |

U_{o} = mean upstream approach flow velocity from continuity (m s^{−1}) | |

V_{n} = flow velocity component normal to the rack (m s^{−1}) | |

w_{ch} = constant channel width (diversion HPP) (m) | |

w_{ds} = downstream channel width (m) | |

w_{o} = upstream channel width (m) | |

x, y, z = coordinates in streamwise, transversal, and vertical direction (m) | |

X = normalized streamwise coordinate (−), X = x h_{o}^{−1} | |

Y = normalized transversal coordinate (−), Y = y w_{ds}^{−1} | |

α = horizontal approach flow angle (°) | |

γ = rack inclination angle (°) | |

Δh_{c} = contraction head loss (m) | |

Δh_{f} = friction head loss (m) | |

∆h_{R} = rack head loss (m) | |

ν = kinematic viscosity (m^{2} s^{−1}) | |

ξ_{c} = contraction head loss coefficient (−) | |

ξ_{R} = rack head loss coefficient (−) | |

σ = standard deviation |

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**Figure 1.**Rack layouts: (

**a**) perpendicular, (

**b**) inclined, and (

**c**) angled to the approach flow; adapted from [6]. α: horizontal approach flow angle, γ: rack inclination angle.

**Figure 2.**Sketch of the experimental channel for a diversion hydropower plant setup including: ① magnetic-inductive flow meter, ② gate valve, ③ inlet tank, ④ perforated inlet pipe, ⑤ floater, ⑥ honeycomb flow straightener, ⑦ traverse system and measurement cart carrying an ultrasonic distance sensor, ⑧ horizontal bar rack, ⑨ flap gate, and ⑩ outlet basin.

**Figure 3.**Channel top view with (

**a**) coordinate system and measurement locations of a diversion hydropower plant and (

**b**) configuration of a block-type hydropower plant (here w

_{o}w

_{ds}

^{−1}= 2.0); the location of the vertical tie-bars is indicated with filled circles (•) and the ultrasonic distance sensor measurement locations with circle outlines ( ); w

_{ch}: constant channel width, w

_{o}: upstream channel width, w

_{ds}: downstream channel width, U

_{o}: mean upstream approach flow velocity from continuity, U

_{ds}: mean downstream flow velocity, x: streamwise coordinate, X: normalized streamwise coordinate, y: transversal coordinate, Y: normalized transversal coordinate, h

_{o}: approach flow depth.

**Figure 4.**Dimensions of investigated bar shapes (

**a**) rectangular (S1), (

**b**) circular tip (S2), (

**c**) ellipsoidal tip and tail (S3), and (

**d**) foil-shaped (S4); all measures in millimeters. t

_{b}: bar thickness at thickest point, t

_{b,m}: bar thickness at mid cross section, d

_{b}: bar depth.

**Figure 5.**Definition sketch of the governing rack parameters. h

_{o}: approach flow depth, h

_{ds}: downstream flow depth, U

_{o}: mean upstream approach flow velocity from continuity, U

_{ds}: mean downstream flow velocity, h

_{Bo}: bottom overlay height, h

_{To}: top overlay height, s

_{b}: clear bar spacing, t

_{b}: bar thickness at thickest point, d

_{b}: bar depth.

**Figure 6.**Rack head loss coefficients ξ

_{R}as a function of approach flow depth h

_{o}with constant theoretical average flow velocity U

_{th}= 0.50 m s

^{−1}for bar shapes (

**a**) S1 and (

**b**) S4, and as a function of the theoretical average flow velocity U

_{th}with constant approach flow depth h

_{o}= 0.40 m for bar shapes (

**c**) S1 and (

**d**) S4. t

_{b}: bar thickness at thickest point,

`R`

_{b}: bar Reynolds number.

**Figure 7.**Rack head loss coefficients ξ

_{R}as a function of (

**a**) bar shape S1–S4, (

**b**) blocking ratio BR, and (

**c**) horizontal approach flow angle α for all tested rack configurations without overlays and a relative bar depth of D

_{b}= 7.5. s

_{b}: clear bar spacing.

**Figure 8.**Rack head loss coefficients ξ

_{R}as a function of relative bar depth D

_{b}for S2-bars with approach flow angle of (

**a**) α = 90° and (

**b**) α = 30° and different overlay configurations. s

_{b}: clear bar spacing, H

_{Bo}: relative bottom overlay height, H

_{To}: relative top overlay height.

**Figure 9.**Rack head loss coefficients for configurations with S1–S4-bars without overlays with (

**a**) comparison of predicted (Equation (6)) and measured values (ξ

_{R,p}, ξ

_{R,m}) and (

**b**) prediction errors PE as a function of the measured rack head loss coefficients ξ

_{R}

_{,m}. α: horizontal approach flow angle, s

_{b}: clear bar spacing.

**Figure 10.**Comparison of measured rack head loss coefficients ξ

_{R,m}and predicted rack head loss coefficients ξ

_{R,p}with Equations (6) and (11) for racks with rectangular bars (S1). α: horizontal approach flow angle, s

_{b}: clear bar spacing.

**Figure 11.**Rack head loss coefficients ξ

_{R}for configurations without overlays with (

**a**) comparison of measured (ξ

_{R,m}) and predicted values (ξ

_{R,p}; Equation (6) for hydrodynamic bars and Equation (11) for rectangular bars) and (

**b**) prediction error PE as a function of measured rack head loss coefficients ξ

_{R,m}. α: horizontal approach flow angle, s

_{b}: clear bar spacing.

**Figure 12.**Rack head loss coefficients ξ

_{R}for configurations with and without overlays with (

**a**) comparison of measured (ξ

_{R}

_{,m}) and predicted values (ξ

_{R}

_{,p}; Equation (6) for hydrodynamic bars and Equation (11) for rectangular bars) for all tested configurations, and prediction errors PE as a function of measured rack head loss coefficients ξ

_{R}

_{,m}for (

**b**) combined bottom and top overlays (Bo + To), (

**c**) bottom overlays only (Bo), and (

**d**) top overlays only (To). w/o Ov: racks without overlays.

**Figure 13.**Comparison of measured and predicted rack head loss coefficients ξ

_{R,m}and ξ

_{R,p}(Equation (6) for hydrodynamic bars and Equation (11) for rectangular bars) for rack configurations with S1- and S2-bars and approach flow angle α = 90°. w/o Ov: racks without overlays, Bo: racks with bottom overlays only, To: racks with top overlays only, Bo+To: racks with combined bottom and top overlay.

**Figure 14.**(

**a**) Comparison of predicted and measured head loss coefficients at block-type hydropower plants with horizontal bar racks and (

**b**) corresponding prediction errors PE. ξ

_{(R + c),m}: measured rack head loss coefficient at block-type hydropower plants; ξ

_{R,p}: predicted head loss coefficient of the horizontal bar rack; ξ

_{c}

_{,p}: predicted contraction head loss coefficient (Equation (13)); w

_{o}: upstream channel width; w

_{ds}: downstream channel width.

**Figure 15.**Effect of approach flow angle α on bar depth coefficient C

_{Db}for a reduction of relative bar depth D

_{b}by 50%.

**Figure 16.**Validation of predicted rack head loss coefficients ξ

_{R}

_{,p}, on the basis of Equation (11), with rack head loss coefficients measured by Maager [20] ξ

_{R}

_{,m,val}for (

**a**) rectangular bars and (

**b**) one-side rounded bars (with prefactor of 1.60 instead of 2.33 in Equation (11)). w/o Ov: racks without overlays, Bo: racks with bottom overlays only, To: racks with top overlays only, Bo + To: racks with combined bottom and top overlay.

**Figure 17.**Comparison of rack head loss coefficients ξ

_{R,m}measured by Böttcher et al. [22] with predicted rack head loss coefficients ξ

_{R}

_{,p}for cylindrical bars (Equation (11), adapted). BR: blocking ratio, α: horizontal approach flow angle.

**Table 1.**Exact blocking ratios BR of the model racks and approximate blocking ratios BR

^{*}for a preliminary design of racks with different clear bar spacing s

_{b}and bar shapes S1–S4 (cf. Figure 4)

s_{b} (mm) | BR of S1 | BR of S2–S4 | BR^{*} of S1–S4 |
---|---|---|---|

10 | 0.482 | 0.492 | 0.478 |

20 | 0.342 | 0.348 | 0.329 |

30 | 0.272 | 0.276 | 0.258 |

**Table 2.**Investigated bar shapes S1–S4 and the corresponding bar shape coefficients C

_{S}(cf. Figure 4).

Denotation | S1 | S2 | S3 | S4 |
---|---|---|---|---|

Shape | ||||

C_{S} | 1.13 | 0.83 | 0.67 | 0.64 |

© 2020 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/).

## Share and Cite

**MDPI and ACS Style**

Meister, J.; Fuchs, H.; Beck, C.; Albayrak, I.; Boes, R.M.
Head Losses of Horizontal Bar Racks as Fish Guidance Structures. *Water* **2020**, *12*, 475.
https://doi.org/10.3390/w12020475

**AMA Style**

Meister J, Fuchs H, Beck C, Albayrak I, Boes RM.
Head Losses of Horizontal Bar Racks as Fish Guidance Structures. *Water*. 2020; 12(2):475.
https://doi.org/10.3390/w12020475

**Chicago/Turabian Style**

Meister, Julian, Helge Fuchs, Claudia Beck, Ismail Albayrak, and Robert M. Boes.
2020. "Head Losses of Horizontal Bar Racks as Fish Guidance Structures" *Water* 12, no. 2: 475.
https://doi.org/10.3390/w12020475