# Evaluation of Hydraulics and Downstream Fish Migration at Run-of-River Hydropower Plants with Horizontal Bar Rack Bypass Systems by Using CFD

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## Abstract

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## 1. Introduction

_{d}< 120 m

^{3}/s in Europe [37]. During operation, HBR-BSs can be beneficial due to small head losses [37,38] and the potential to pass floating debris automatically downstream through the bypass [28,37]. State-of-the-art reviews of HBRs and HBR-BSs can be found in Meister [37] and Maddahi et al. [39].

_{p}should be larger than the rack normal velocity component v

_{n}(v

_{p}/v

_{n}> 1) [11,28,42]. Therefore, HBRs are usually designed angled to the side. For example, Ebel [28] recommends rack angles between α = 20° and 40° to the unaffected flow direction for high fish guidance efficiencies. To avoid fish being impinged against the rack, v

_{n}should be lower or equal than the sustainable swimming speed v

_{sus}(v

_{n}≤ v

_{sus}), where v

_{sus}is the aerobic swimming activity that fish can sustain for more than 200 min without fatigue, depending on fish length and water temperature [26,28]. Moreover, the flow velocities at the bypass entrance also play an important role, since an efficient bypass is considered to be a key point for the successful design of downstream migration facilities [30,39,43,44,45]. The flow conditions at the bypass entrance are often described in design guidelines with the relative bypass discharge Q

_{by,rel}as the ratio of the bypass discharge Q

_{by}to the design discharge Q

_{d}(Q

_{by,rel}= Q

_{by}/Q

_{d}). In order to obtain moderate flow velocities at the bypass entrance and thus favorable flow accelerations for fish downstream passage, a minimum Q

_{by,rel}between 2% and 5% is recommended for HBR-BSs [28]. By following this recommendation, the ratio between the velocity at the bypass entrance v

_{by}and the mean approach flow velocity v

_{0}should be between v

_{by}/v

_{0}= 1.0 and 1.5, in trout waters even up to 2.0, which is considered to be an attractive value to guide fish into the bypass [34]. Similar values in this range are recommended by other authors, e.g., Meister [37], who obtained higher fish guidance efficiencies at v

_{by}/v

_{0}= 1.2 in ethohydraulic experiments with HBR-BSs.

_{p}/v

_{n}> 1 and v

_{n}≤ v

_{sus}, while other flow parameters such as abrupt velocity changes and turbulent flow structures were not taken into account. In addition, since the bypass was excluded in the approach, the flow conditions at the bypass entrance could not be investigated.

## 2. Materials and Methods

#### 2.1. Studied HPPs

#### 2.1.1. Initial Designs

_{0}= 50 m

^{3}/s, typically in the grayling region (Hyporhithral), and the second at an alpine river with Q

_{0}= 10 m

^{3}/s, typically in the lower trout region (Metarhithral). In this regard, a greater diversity of fish species generally occurs at the site of the pre-alpine river than at that of the alpine river [66]. Subsequently, block-type HPPs were projected for both sites, with the powerhouse located next to the weir. Herein, only the weir and the powerhouse were considered among the components shown in Figure 1a, since it can be assumed that both the navigation lock and fishway have no or only a negligible effect on the hydraulic conditions in the area of interest for this study. The powerhouse and weir are separated by a dividing pier, which was designed according to the design recommendations of Häusler [67] to optimize the flow conditions towards the turbines for the HPP Landau on the Isar River in Germany. In front of the turbine inlets, the concrete bottom is inclined downward. In addition, more simplifications were made in the design process of the associated 3D models, used for the numerical simulations, to reduce the complexity of the HPPs, and thus also the computational costs. For instance, the section downstream of the weir and turbines was not modeled. Moreover, the banks at all sites are designed simplified vertical, and the soil has no slope. The main characteristics and parameters of these HPPs are listed in Table 1.

#### 2.1.2. Variations

#### 2.1.3. Examined Operating Case

_{0}is divided into a small part for Q

_{by}and a large part for Q

_{d}(Q

_{0}= Q

_{d}+ Q

_{by}). The corresponding values are listed in Table 1. Note that the share of Q

_{0}flowing through the fishway is neglected here, since the fishway was not included in the numerical models.

#### 2.2. Numerical Models

#### 2.2.1. General

_{w}. Further details regarding the fundamental governing equations can be found in the ANSYS Fluent Theory Guide [70].

#### 2.2.2. Boundary Conditions

_{0}, Table 1) was defined as the boundary condition. Water flows out of the domains through the turbines and the bypass. Constant values for the outflow discharges (Q

_{by}and Q

_{d}, Table 1) were used at both locations. In order to achieve more homogeneous outflow conditions in the cross-section of the turbines, the turbines were simplified using circular cylinders, each extended by one meter in the downstream direction and having the identical constant outflow discharge at the end. The downstream domain end at the bypass was located a few meters downstream of the sloping weir (Figure 2) to include effects due to water flowing over the weir. A symmetry boundary condition was applied at the top of the air-domain. All other boundaries were set to no-slip walls.

#### 2.2.3. Spatial and Temporal Discretization

#### 2.2.4. Implementation of the Fish Guidance Structure in the Numerical Model

#### 2.3. Criteria Used for the Evaluation

_{p}/v

_{n}> 1 is fulfilled [11,28,42]. In this case, the horizontal angle between the approach flow and the FGS θ is smaller than 45° (Figure 2). Consequently, the main flow direction occurs along the FGS, and fish are guided towards its downstream end and further into the bypass. Moreover, impingement to the FGS or entering the headrace channel can be avoided as long as acceptable values of v

_{n}occur, which should be less than or equal to v

_{sus}(v

_{n}≤ v

_{sus}) [26,28]. Turnpenny and O’Keeffe [26] recommended that 90% of downstream migrating fish should be able to swim against v

_{n}for at least 200 min without being impinged against the FGS. Therefore, the critical swimming speed in many guidelines is often defined with 200 min. Besides v

_{sus}, the swimming speed of fish can also be described by the prolonged swimming speed v

_{pro}, which can be maintained for 1 to 200 min without exhaustion [74]. Hereafter, the swimming duration t of v

_{pro}is defined as 1 min. To determine fish swimming speed v

_{f}, Ebel [28] proposed multivariate models for European fish species based on literature data, distinguishing between a general model and specific models for rheophilic and non-rheophilic species. For the study area in the Austrian catchment area of the Danube river, the model for rheophilic species is of particular relevance, defined as

_{pro}and v

_{sus}, calculated using Equation (1), as a function of TL. For the definition of T, typical values for mean summer water temperatures (July to September) in Austrian rivers in the grayling region (Hyporhithral) and lower trout region (Metarhithral) with 8 to 14 °C and 5 to 10 °C, respectively, were used [75]. Based on this, T at the HPP on the pre-alpine river was defined as 11 °C, and at the HPP on the alpine river as 8 °C.

_{f}is the spatial velocity gradient experienced by fish (and expressed in cm/s/cm or 1/s), v

_{H}is the velocity at the head of the fish, and v

_{T}is the velocity at its tail. Note that different notations were used for SVG to distinguish between Equation (3) (used in general) and Equation (4) (applied to fish). Since fish are known to orient themselves in the flow in a streamwise direction to conserve energy [10], it was assumed that a fish would align itself in the direction of a flow vector, but not perpendicular to it. Based on this, the normalized velocity vectors from the results of the numerical simulations were used to estimate SVG

_{f}. Herein, the velocities at the tip of the considered vector and at its tail were used for v

_{H}and v

_{T}, respectively, and its length for TL. As Equation (4) uses the absolute value of the difference between v

_{H}and v

_{T}, the velocity gradient can be determined regardless of the orientation of the fish in either positive (tail first) or negative (head first) rheotaxis.

_{f}in this study. Rather, only enhanced values were pointed out, and relative considerations between initial designs and variations were made. However, the values obtained will be compared with literature data in Section 4.1.

_{0}= 0.5), and (iii) near the water surface (0.5 m below the water surface). Thus, the swimming depths of different fish species could be considered individually. Further, to evaluate the flow conditions upstream of the FGS, a vertical plane 0.1 m in front of the FGS was used, considering only areas where α

_{w}was equal or higher than 0.5.

## 3. Results

#### 3.1. Overview

#### 3.2. HPP on the Pre-Alpine River

#### 3.2.1. Overall Flow Field

_{0}= 0.5). Note that the green line indicates the position of the FGS in the model. In general, similar flow patterns occur near the riverbed at z = 0.1 m (z/h

_{0}= 0.025), in mid-flow depth at z = 2.0 m (z/h

_{0}= 0.5), and near the water surface at z = 3.5 m (z/h

_{0}= 0.875). However, the most relevant single deviation for this study appears at the bypass entrance, described in Section 3.2.3. As expected for a block-type HPP, the flow in the area upstream of the HPP is deflected towards the headrace channel, and the velocities increase due to the reduced width of the channel compared to the overall width of the river upstream of the HPP (Figure 5a). Thus, the velocities towards the FGS also increase continuously. The flow gets slightly deflected by the FGS, in front of the FGS slightly parallel to the FGS, which can be observed particularly at the downstream end of the FGS, and behind the FGS slightly in the direction perpendicular to the FGS. The free water surface at α

_{w}= 0.5 increases in front of the FGS and decreases after the FGS depending on the local velocity distribution. Therefore, the largest difference between the water level upstream and downstream of the FGS (Δh = 0.05 m) occurs in the area of highest local velocities close to the downstream end of the FGS. At lower velocities, the effect of the FGS on the water level is negligible. Downstream of the FGS, the flow velocities increase continuously on the orographic right side of the headrace channel. On the orographic left side, the highest velocity in the numerical model (v

_{m,max}= 1.38 m/s), excluding the increased flow velocities in the bypass as an effect of the sloping weir, occurs next to the upstream end of the turbine-side part of the dividing pier at z = 3.5 m (z/h

_{0}= 0.875). Further downstream, the flow becomes more homogenous over the width of the headrace channel. However, the headrace channel was designed too short to allow uniform flow conditions to establish themselves towards the turbines. Compared to the flow deflection caused by the block-type layout, the FGS has a minor effect on the turbine approach flow. Moreover, in the vicinity of the weir, flow-calmed areas with relatively low flow velocities occur.

#### 3.2.2. Hydraulic Parameters in Front of the FGS

_{FGS}is defined as the distance from the downstream end (x

_{FGS}= 0 m) along the FGS to the upstream end (x

_{FGS}= 25.94 m), and z is the distance from the riverbed to the water surface (at α

_{w}= 0.5). The velocities v

_{a}(Figure 6a) and v

_{n}(Figure 6b) increase gradually along the FGS in the direction of the bypass, with local maxima close to the downstream end, where v

_{a,max}= 1.03 m/s at z = 0.06 m (z/h

_{0}= 0.03) and v

_{n,max}= 0.87 m/s at z = 2.0 m (z/h

_{0}= 0.5), respectively. Both values are above the calculated v

_{pro}= 0.83 m/s for fish with TL = 0.11 m (Figure 4). Since the velocities converge to zero at the walls, minima of the flow velocities can only be estimated (v

_{a,min}≈ 0.3 m/s and v

_{n,min}≈ 0.2 m/s, respectively, close to the right bank). In comparison, the mean v

_{n}, calculated as the ratio of Q

_{d}= 48 m

^{3}/s and the hydraulically active area of the FGS A

_{FGS,hyd}= 103.76 m

^{2}, is $\overline{{v}_{n}}$ = 0.46 m/s. Figure 6c shows v

_{p}along the FGS. Note that v

_{p}is defined positive in the direction of the bypass, while negative values imply a rack parallel velocity component along the FGS towards its upstream end. This makes it possible to distinguish between favorable flow conditions towards the bypass (v

_{p}> 0) and unfavorable ones in the opposite direction (v

_{p}< 0). At x

_{FGS}≈ 18 to 20 m, v

_{p,max}= 0.44 m/s occurs. From there towards the downstream end of the FGS, v

_{p}decreases, with negative values occurring at the downstream end, especially near the bottom. This leads to the absence of a guiding effect in the direction of the bypass over the entire water depth in this area, which can also be observed by means of the velocity vectors in Figure 5b. Consequently, fish must actively swim against the rack parallel flow to reach the bypass as they migrate along the FGS. The ratio v

_{p}/v

_{n}has favorable values above 1 only near the upstream end of the FGS (Figure 6d). Thus, this indicates that without further optimization, favorable conditions for downstream migration of fish along the FGS will not occur. Nevertheless, the FGS leads to relatively small increases in TKE and SVG 0.1 m in front of the FGS, as shown exemplarily in Figure 6e for TKE. Although the smaller hydraulically active area of the FGS A

_{FGS,hyd}results in locally increased velocities and thus also increased SVG, the latter effects are only very local, as can be seen in Figure 7b, where SVG was calculated with Equation (3). Therefore, the hydraulic parameter SVG 0.1 m in front of the FGS is not included in Figure 6.

#### 3.2.3. Hydraulic Parameters at the Bypass Entrance

_{0}= 0.5). The flow around the weir-side part of the dividing pier becomes relatively fast at the upstream end, similar to the turbine-side part described in Section 3.2.1, with a local velocity maximum of v

_{m,max}= 1.14 m/s at z = 3.5 m (z/h

_{0}= 0.875, Figure 8b). From there in the direction of the bypass, a favorable flow direction occurs, as can be seen using the velocity vectors in Figure 5b. However, the velocities first decelerate before they slowly accelerate again in front of the inlet gate. The flow around the weir-side part of the dividing pier leads to a local velocity minimum at the upstream end of the turbine-side part and at the downstream end of the FGS, respectively, where the water flows directly onto the dividing pier. Moreover, this results in more turbulent flow conditions (TKE

_{max}= 0.07 m

^{2}/s

^{2}at z = 2.0 m, z/h

_{0}= 0.5, Figure 7a), and in increased SVG above 2.0 cm/s/cm (Figure 7b). However, fish swimming from the weir around the weir-side part of the dividing pier towards the bypass also experience more complex flows with TKE

_{max}= 0.05 m

^{2}/s

^{2}and SVG

_{max}= 1.8 cm/s/cm at z = 2.0 m (z/h

_{0}= 0.5). Overall, a continuous increase of velocities into the bypass as well as low TKE and SVG, as recommended in common guidelines, are not present for fish migrating along the FGS nor for those approaching from the weir.

_{0}= 0.025) due to a local velocity minimum over the whole width of the bypass entrance (v

_{m,max}= 0.37 m/s, Figure 8a). In contrast, at mid-flow depth (z = 2.0 m, z/h

_{0}= 0.5, Figure 5b) and near the water surface (z = 3.5 m, z/h

_{0}= 0.875, Figure 8b), higher velocities occur in this area (v

_{m,max}= 0.68 m/s at both water levels). This effect can be attributed to some extent to the sloping weir, which decelerates the inflow into the bypass near the riverbed (z = 0.1 m, z/h

_{0}= 0.025). Consequently, flow velocities increase to a local maximum close to the downstream end of the FGS at the same water level, as shown in Figure 6a.

_{f}, which were calculated based on the normalized velocity vectors with a length of 0.2 m in the rectangular grid of 0.2 m distance and Equation (4). Note that SVG

_{f}could not be calculated automatically by the software during the analysis process. Therefore, only the maximum values near the two parts of the dividing pier and the inlet gate as well as in front of the FGS are shown in Figure 5b and Figure 8. In the area upstream of the FGS and at the bypass entrance, SVG

_{f}exceeds the value of 1.0 cm/s/cm only at a flow depth of z = 3.5 m (z/h

_{0}= 0.875) at two vectors near the local velocity minimum at the turbine-side part of the dividing part and close to the inlet gate, with SVG

_{f}= 1.05 cm/s/cm and SVG

_{f}= 1.06 cm/s/cm, respectively (Figure 8b). Compared to Figure 7b, the values for SVG are significantly higher than those of SVG

_{f}.

#### 3.3. Variations

#### 3.3.1. Variation 1 (V1): Shifting the Weir-Side Part of the Dividing Pier 1.0 m in the Upstream Direction

_{0}= 0.5, Figure 9), resulting in consistently positive values for v

_{p}(Figure 10d). However, negative values for v

_{p}still occur near the riverbed and near the water surface in this region, with v

_{p,min}= −0.42 m/s at z = 0.04 m (z/h

_{0}= 0.01, Figure 10d). Furthermore, V1 only slightly affects v

_{a}and v

_{n}(Figure 10b) in front of the FGS, resulting in no significant improvement related to the ratio v

_{p}/v

_{n}. At the bypass entrance, the velocities increase due to the geometric variation, especially at the weir-side part of the dividing pier (from v

_{m,max}= 1.14 m/s to v

_{m,max}= 1.36 m/s, increase of 19.3%, at z = 3.5 m, z/h

_{0}= 0.875) and close to the inlet gate (from v

_{m,max}= 1.17 m/s to v

_{m,max}= 1.20 m/s, increase of 2.6%, at z = 3.5 m, z/h

_{0}= 0.875). Moreover, the velocities increase in the area of low velocities at the turbine-side part of the dividing pier, described in Section 3.2.3, with this area being shifted slightly towards the downstream end of the FGS compared to the initial design (Figure 5b). The increased velocities also increase TKE (from TKE

_{max}= 0.07 m

^{2}/s

^{2}to TKE

_{max}= 0.09 m

^{2}/s

^{2}, increase of 24.3%, at z = 2.0 m, z/h

_{0}= 0.5) at the bypass entrance as well as SVG, which does not decrease below SVG = 1 cm/s/cm over the whole entrance width near the inlet gate. Similarly, SVG

_{f}increases, involving two vectors directly adjacent to SVG

_{f}> 1 cm/s/cm upstream of the FGS (Figure 9 and Figure 10a). Overall, V1 increases v

_{p}towards the bypass and thus the FGE into the bypass, which could lead to fish finding the bypass more easily and migrating downstream of the HPP more quickly. However, the increased velocities and more complex flow conditions may also increase the probability of avoidance reactions.

#### 3.3.2. Variation 2 (V2): Changing the Shape and Width of the Weir-Side Part of the Dividing Pier

_{0}= 0.875) in comparison with the initial design. As expected, the flow around the weir-side part of the dividing pier is slower and more uniform in V2, with v

_{m,max}= 1.14 m/s and SVG

_{f,max}= 0.96 cm/s/cm at z = 3.5 m (z/h

_{0}= 0.875) in the initial design and v

_{m,max}= 0.96 m/s (decrease of 15.8%) and SVG

_{f,max}= 0.67 cm/s/cm (decrease of 30.2%) at the same water level in V2. However, except for this area, V2 hardly affects the general flow field. Close to the inlet gate and in the area of low velocities at the turbine-side part of the dividing pier, velocities decrease marginally (Figure 11), as does TKE. Furthermore, the effect of this variation on the flow conditions at the FGS is negligible. Overall, V2 slightly improves the FGE due to lower velocities and more uniform flow, especially for fish approaching the bypass from the area of the weir.

#### 3.3.3. Variation 3 (V3): Installing the Inlet Gate at the Turbine-Side Part of the Dividing Pier

_{m,max}= 1.14 m/s to v

_{m,max}= 1.16 m/s, increase of 1.8%, at z = 3.5 m, z/h

_{0}= 0.875) and close to the inlet gate (from v

_{m,max}= 1.17 m/s to v

_{m,max}= 1.37 m/s, increase of 17.1%, at z = 3.5 m, z/h

_{0}= 0.875), a large-scale increase of TKE from the bypass entrance until shortly after the constriction at the inlet gate occurs. However, the maximum value of TKE remains at TKE

_{max}= 0.07 m

^{2}/s

^{2}(z = 2.0 m, z/h

_{0}= 0.5). Moreover, SVG also increases slightly in this area. Overall, V3 leads to larger flow deflections and more complex flow conditions, which may increase the probability that fish swimming towards the bypass show an avoidance reaction.

#### 3.3.4. Variation 4 (V4): Doubling Q_{by} by Lowering the Sloping Weir

_{by}was increased by reducing the height of the sloping weir. For both variations, the HPP on the alpine river was used as the initial design due to lower velocities at the bypass entrance (Figure 13a) compared to the HPP on the pre-alpine river (Figure 5b). Additionally, the initial design shows unfavorable backflow effects and partly high SVG

_{f}(SVG

_{f,max}= 1.85 cm/s/cm at z = 1.0, z/h

_{0}= 0.5) due to vortex formation at the bypass entrance near the weir-side part of the dividing pier (Figure 13a). It should be noted that for the calculation of SVG

_{f}at the HPP on the alpine river, TL = 0.1 m was assumed, while TL = 0.2 m was used for the HPP on the pre-alpine river. In V4, Q

_{by}was doubled compared to the initial design (from Q

_{by}= 0.5 m

^{3}/s, 5% of Q

_{0}, to Q

_{by}= 1.0 m

^{3}/s, 10% of Q

_{0}). Since Q

_{0}remains constant, Q

_{d}decreases and thus also v

_{n}towards the FGS (from v

_{n,max}= 0.78 m/s to v

_{n,max}= 0.75 m/s, decrease of 3.2%, 0.1 m in front of the FGS). Moreover, the FGE along the FGS is slightly improved, with higher v

_{p}, although negative values for v

_{p}continue to occur at the downstream end of the FGS (from v

_{p,min}= −0.59 m/s to v

_{p,min}= −0.34 m/s, increase of 42.4%, 0.1 m in front of the FGS). Figure 13b shows the velocity field of V4 at the bypass entrance in mid-flow depth (z = 1.0, z/h

_{0}= 0.5). While in the area where the FGS is fixed to the turbine-side part of the dividing pier, the velocities are still relatively low, and a flow deceleration occurs, a consistent increase in velocity can be observed from the bypass entrance to the inlet gate. However, the flow velocities around the weir-side part of the dividing pier increase (from v

_{m,max}= 0.97 m/s to v

_{m,max}= 1.23 m/s, increase of 26.8%, at z = 1.0, z/h

_{0}= 0.5), and further also SVG

_{f,max}(from 1.35 cm/s/cm to 1.71 cm/s/cm, increase of 26.7%, at z = 1.0, z/h

_{0}= 0.5). Accordingly, more complex flow conditions with increasing values for TKE and SVG occur in this area. Overall, it can nevertheless be assumed that V4 has a positive effect on the FGE both along the FGS and at the bypass entrance.

#### 3.3.5. Variation 5 (V5): Quadrupling Q_{by} by Lowering the Sloping Weir

_{by}was doubled in V5 compared to V4 and quadrupled compared to the initial design, respectively (Q

_{by}= 2.0 m

^{3}/s, 20% of Q

_{0}). At the FGS, basically the same tendencies are evident in V5 as in V4, with decreasing v

_{a}and v

_{n}, as well as increasing v

_{p}at the downstream end. Except for a small area near the water surface at the downstream end, the values for v

_{p}along the FGS are continuously positive in V5. Nevertheless, the ratio v

_{p}/v

_{n}does not increase above the value of 1 in the downstream half of the FGS. At the bypass entrance, the flow velocities increase significantly (Figure 13c) compared to the initial design, such as at the weir-side part of the dividing pier (from v

_{m,max}= 0.97 m/s to v

_{m,max}= 1.70 m/s, increase of 75.3%, at z = 1.0 m, z/h

_{0}= 0.5) and close to the constriction of the inlet gate (from v

_{m,max}= 0.74 m/s to v

_{m,max}= 2.60 m/s, increase of 251.4%, at z = 1.0 m, z/h

_{0}= 0.5). In addition, the flow conditions become more complex, e.g., with SVG

_{f,max}= 3.20 cm/s/cm at z = 1.0 m (z/h

_{0}= 0.5) near the turbine-side part of the dividing pier at the bypass entrance (Figure 13c). Overall, despite the improved FGE along the FGS, V5 indicates very high flow velocities and more complex flow conditions at the bypass entrance, and therefore it can be assumed that fish show avoidance reactions when swimming into this area.

#### 3.3.6. Variation 6 (V6): Changing α to 20°

_{FGS}increased from 10.58 m to 20.19 m. Similar to the initial design, the FGS was attached tangentially to the upstream end of the turbine-side part of the dividing pier, which altered the location of the FGS in the model. Figure 14 shows the velocities v

_{n}and v

_{p}0.1 m in front of the FGS for V6 compared to the initial design, and Figure 15 shows the velocity field at the downstream end of the FGS and the bypass entrance in mid-flow depth (z = 1.0 m, z/h

_{0}= 0.5). Due to the larger A

_{FGS,hyd}in V6, $\overline{{v}_{n}}$ decreases from 0.45 m/s to 0.24 m/s (decrease of 46.7%). Moreover, v

_{n,max}decreases from 0.78 m/s to 0.70 m/s (decrease of 10.3%, 0.1 m in front of the FGS, Figure 14a,c). However, since the FGS has only a minor effect on the flow conditions at its downstream end as described in Section 3.2.2, the decrease of v

_{n,max}can be attributed primarily to the new location of the FGS in the model (Figure 15). Furthermore, with decreasing α, θ also decreases, resulting in almost consistently positive values for v

_{p}along the FGS (Figure 14d). Nevertheless, negative values for v

_{p}still occur at the downstream end (from v

_{p,min}= −0.60 m/s to v

_{p,min}= −0.29 m/s, increase of 51.7%, 0.1 m in front of the FGS), implying that no guiding effect in the bypass direction appears in this region. The ratio v

_{p}/v

_{n}has a value above 1 over more than half of l

_{FGS}, which is favorable for the FGE. As expected, due to the minor effect of the FGS on the flow, the flow field hardly changes at the bypass entrance (Figure 15). Overall, V6 has a positive effect on the FGE from a hydraulic perspective and based on the evaluation criteria defined in Section 2.3.

#### 3.3.7. Variation 7 (V7): Implementing a Bottom Overlay with a Height of 0.2 m

_{bo}= 0.2 m (h

_{bo}/h

_{0}= 0.1) was applied to the FGS of the HPP on the alpine river in V7. The bottom overlay is represented in the numerical model as an impermeable body with the same thickness as the FGS, and thus reduces A

_{FGS,hyd}by 10%. In V7, further flow deflections occur in front of the FGS towards its upstream end, particularly near the riverbed at z = 0.1 m (z/h

_{0}= 0.05, Figure 16). At this flow depth, v

_{n}decreases significantly (Figure 17a,c), while v

_{p}hardly changes compared to the initial design (Figure 17b,d). For the ratio v

_{p}/v

_{n}, values above 1 occur in the upstream half of the FGS, but remain below 1 in the downstream half, even though v

_{n}is close to 0. This is due to the fact that the flow vectors are aligned against the bypass direction (Figure 16). Moreover, V7 also leads to more complex flow conditions with increased TKE and SVG near the riverbed (z = 0.1 m, z/h

_{0}= 0.05). The latter can be related to accelerations and decelerations caused by the bottom overlay. In mid-flow depth (z = 1.0 m, z/h

_{0}= 0.5) and near the water surface (z = 1.5 m, z/h

_{0}= 0.75), the bottom overlay has a small effect on the flow field. While v

_{n,max}hardly changes due to the variation (v

_{n,max}≈ 0.78 m/s, 0.1 m in front of the FGS), marginally higher v

_{n}and lower v

_{p}occur in the x

_{FGS}-direction (Figure 17). At the bypass entrance, the effect of the bottom overlay is low, with the largest differences near the riverbed at z = 0.1 m (z/h

_{0}= 0.05, Figure 16). It should be noted that the bottom overlay also affects the flow field downstream of the FGS, particularly with significant flow deflections parallel to the FGS near the riverbed at z = 0.1 m (z/h

_{0}= 0.05, Figure 16). However, this area is not part of the present study. Overall, the flow vectors close to the bottom overlay at z = 0.1 m (z/h

_{0}= 0.05) are strongly deflected in the upstream direction, which can lead to a deterioration of the findability of the bypass and to delays for fish migrating downstream. Nevertheless, fish are effectively protected from impingement on the FGS due to low v

_{n}towards the bottom overlay, which are lower than v

_{sus}even for small fish.

#### 3.3.8. Variation 8 (V8): Integrating the FGS into the Headrace Channel with the Bypass on the Orographic Right Side

_{FGS}= 23.34 m) to be integrated into the headrace channel in front of the inclined concrete bottom. Figure 18 shows the velocity field of V8 in mid-flow depth (z = 2.0 m, z/h

_{0}= 0.5). In V8, the flow around the dividing pier is relatively fast (v

_{m,max}= 1.78 m/s, z = 3.5 m, z/h

_{0}= 0.875), and more complex flow conditions with TKE

_{max}= 0.07 m

^{2}/s

^{2}at z = 2.0 m (z/h

_{0}= 0.5) appear. In the headrace channel, high velocities (v

_{m}≥ 0.9 m/s) occur upstream of the FGS. However, the approach flow to the FGS is favorable with θ ≤ 40° along the FGS. As a result, the values of v

_{n}are relatively evenly distributed over A

_{FGS,hyd}0.1 m in front of the FGS (v

_{n,max}= 0.74 m/s), and consistently positive values occur for v

_{p}(v

_{p,max}= 1.07 m/s). Consequently, the ratio v

_{p}/v

_{n}is also consistently above the value 1. At the bypass entrance, the velocities are slightly reduced, partly due to the inlet gate, which was not considered in V8 due to high velocities along the FGS. Moreover, this also leads to increased SVG and SVG

_{f}in this area compared to the main headrace channel, with SVG

_{f,max}= 0.72 cm/s/cm upstream of the FGS at z = 2.0 m (z/h

_{0}= 0.5, Figure 18b). In addition, backflow effects occur at the bypass entrance near the riverbed (z = 0.1 m, z/h

_{0}= 0.025), which can be attributed to the sloping weir located relatively close to the bypass entrance. Overall, although V8 shows favorable flow conditions regarding v

_{p}, v

_{n}and v

_{p}/v

_{n}in front of the FGS, high flow velocities (v

_{m}≥ 0.9 m/s) occur upstream of the FGS in the headrace channel, which are above v

_{pro}for fish with TL ≤ 0.12 m (Figure 4). A constant velocity increase into the bypass, as recommended by guidelines, would increase these velocities even further.

## 4. Discussion

#### 4.1. Interpretation of the Results and Comparison with the Literature

_{n,max}= 0.87 m/s significantly exceeds $\overline{{v}_{n}}$ = 0.46 m/s by 89.1% at the upstream end (Section 3.2.2). Therefore, using simplified averaged values, as frequently adopted in common guidelines, can result in adverse conditions for downstream migrating fish by ignoring the spatial deviation of the flow field, as well as the temporal deviation [82], which, however, was not examined in the present study. Similar unfavorable velocity distributions upstream of an FGS were also observed by Berger [80] at an HPP with an HBR. Comparing Figure 4, Figure 5 and Figure 6, the criterion v

_{n,max}≤ v

_{sus}is met for fish with TL ≥ 0.22 m, and v

_{n,max}≤ v

_{pro}for fish with TL ≥ 0.12 m. Maddahi et al. [39] compared calculated values for v

_{sus}and v

_{pro}with video and ARIS Sonar monitoring results of fish upstream of an HBR-BS at a diversion HPP, and observed that fish can swim against the flow in front of the HBR even at v

_{n}between v

_{sus}and v

_{pro}. Thus, the use of v

_{n}≤ v

_{sus}represents the conservative approach. A high proportion of downstream migrating fish consists of small species or small individuals [83]. Geist [84] assumed that the majority of fish (typically > 90%) in European streams and rivers are smaller than TL = 0.15 m. This indicates that in worst case scenarios (worst case operating conditions, fish swimming in or close to areas with v

_{n,max}), risks can occur for most fish at the HPP on the pre-alpine river. Furthermore, the results of the numerical simulations of the initial designs showed that the approach flow to the downstream end of the FGS is perpendicular or even slightly deflected against the bypass direction, which is comparable to the results of Meister et al. [41] for block-type layouts. A suitable FGE with v

_{p}/v

_{n}> 1 occurs only in the upstream half of the FGS. In this regard, it should be noted that the approach conditions to HBRs are not only important for fish protection; there are also operational aspects since, for instance, suitable values for v

_{p}are needed for automated rack cleaning at HBRs, or local head losses are increased with velocity quadratically and with sin(θ) linearly (for 0° ≤ θ ≤ 90°) [37]. Besides the FGS, the flow conditions at the bypass entrance at the HPP on the pre-alpine river are not favorable either (Section 3.2.3).

^{2}/s

^{2}in the intake area of the HPP, and TKE ≤ 0.03 m

^{2}/s

^{2}in the main river course. They concluded that, for TKE between 0.03 and 0.24 m

^{2}/s

^{2}, the swimming performance of fish was affected, while for TKE < 0.03 m

^{2}/s

^{2}it was positively influenced. Liao [48] confirmed that low turbulent flows, which do not pose a threat, can be attractive for fish. He concluded that there is a relation between fish size and turbulence strength in which fish like to remain [48]. Other values at which different fish species respond to increased TKE can be found in the literature; e.g., Silva et al. [85] showed that barbel are adequately adapted for TKE < 0.05 m

^{2}/s

^{2}, while Li et al. [86] indicated that juvenile cyprinids with TL ≈ 0.11 m may react to TKE < 0.005 m

^{2}/s

^{2}. Even native fishes can respond differently to turbulent flows, as shown by Link et al. [87] for two Chilean native fish species. Furthermore, Szabo-Meszaros et al. [81] determined values for TKE between 0.01 and 0.04 m

^{2}/s

^{2}in laboratory experiments at the bypass entrance, and TKE smaller than ≈ 0.005 m

^{2}/s

^{2}upstream of the HBR. Even lower values for TKE upstream of the HBR were found by Meister et al. [40]. The results of the HPP on the pre-alpine river in this study show that TKE is between 0.04 and 0.07 m

^{2}/s

^{2}over the entire width of the bypass entrance (Figure 7a), and in front of the FGS mostly < 0.01 m

^{2}/s

^{2}, except for the area close to the downstream end. Therefore, the computed values for TKE seem plausible compared to previous studies. However, a prediction of the possible fish behavior is hardly possible due to the lack of data [31,34,48], especially for the relevant fish species in the grayling and lower trout regions. Nevertheless, it cannot be excluded that values for TKE between 0.04 and 0.07 m

^{2}/s

^{2}could result in impairments of swimming performance, or fish could show avoidance responses. Further studies with the relevant fish species are needed to validate this assessment.

_{f}are generally lower than those for SVG. In addition, the values for SVG

_{f}are lower at the HPP on the pre-alpine river compared to those at the HPP on the alpine river, which may be explained by the fact that TL = 0.1 m was assumed for the evaluation of the former, and TL = 0.2 m for the latter. It can be expected that the smaller the length of the vectors are, and the finer the rectangular mesh is resolved, the higher the values for SVG

_{f}increase until they reach the values of SVG at very fine resolutions. Further, the proposed approach to determine SVG

_{f}is highly position dependent; e.g., in the case of vortices, significantly different SVG

_{f}can occur depending on the position of the vectors considered (cf. Figure 13). However, it should be noted that some previous studies (e.g., [88]) also investigated the influence of acceleration on fish behavior, but not using SVG. Overall, more data is needed to make further conclusions about how fish react to abrupt acceleration and deceleration.

_{by,rel}, as shown by comparing the flow conditions at the bypass entrance of both initial designs (Figure 5b and Figure 13a). This agrees with the recommendation of Boes et al. [43] to define Q

_{by}based on the hydraulic characteristics at the bypass entrance for an efficient bypass design. For the FGE along the FGS, the increase of Q

_{by}has a negligible effect. Additionally, V5 shows that the bypass discharge cannot be increased arbitrarily without creating adverse conditions for downstream migrating fish. Injuries or mortalities cannot be excluded if fish are unable to react quickly enough due to rapidly changing flow conditions. In the case of V5, it may be more beneficial to open a weir at least partially, thus providing another downstream migration opportunity, which is consistent with adding a spillway that can be beneficial for downstream migration at low head HPPs [89,90]. However, it should be noted that an additional downstream corridor may alter the flow conditions at the FGS and the bypass entrance [41]. In V6, α = 20° was defined for the HPP on the alpine river, which improves the hydraulic conditions in the area of interest as well as the FGE. For the HPP on the pre-alpine river, on the other hand, α = 20° would lead to l

_{FGS}= 49.31 m, which significantly increases the average time required for fish to find the bypass as well as the risk of undesired passage through the FGS. In this regard, Nordlund [91] suggested that multiple bypass entrances should be used if v

_{p}is not guiding the fish to the bypass within 60 s. An opportunity to decrease l

_{FGS}and use lower α at the same time are HPPs in the bay-type layout, but it should be considered that the approach flow can be deflected even further compared to block-type HPPs [92]. Finally, technical and economic issues must also be considered when implementing longer FGSs, e.g., higher investment costs. The addition of a bottom overlay in V7 significantly decreases v

_{n}near the riverbed. In previous ethohydraulic model tests considering bottom overlays [40,77,93], an improved FGE was reported. This can be explained, since the majority of fish examined in model tests migrated near the riverbed; for instance, 97% of rack passages were observed close to the riverbed when no bottom overlay at an HBR was used in Meister et al. [40]. However, the protective function of bottom overlays has not yet been confirmed in field studies [94]. Areas of low flow velocities, such as in front of the bottom overlay, can also be used by fish to maintain position in the current without actively swimming, allowing them to rest [95]. Moreover, in the case of no pronounced guiding effect towards the bypass near the bottom overlay (i.e., v

_{p}≤ 0 m/s), as shown close to the downstream end of the FGS in Figure 17, sediment deposition may occur at these locations, which can further deteriorate downstream fish migration, e.g., if delays occur as a result, increasing the probability of becoming a target for predators [35]. It should be mentioned that h

_{bo}used in V7 is lower than the recommended values in Ebel [28] (h

_{bo}/h

_{0}= 15 to 20% or h

_{bo}≥ 0.5 m). Nevertheless, it can be assumed that similar tendencies on the flow field occur at bottom overlays with h

_{bo}> 0.2 m. V8 shows that for the defined HPP designs, installing the FGS upstream of the headrace channel should be the preferred option due to the velocities in the headrace channel being so high that small fish in particular may not be able to swim against the flow. Consequently, they only drift with the flow, which can cause them to be pressed against or through the FGS or enter areas with highly complex flow conditions. Therefore, fish should be prevented from entering the headrace channel in this case, and instead should be guided to a bypass further upstream. Nevertheless, since the hydraulic parameters in front of the FGS provides the best FGE of all designs studied, V8 may be considered for existing HPPs or new construction with low flow velocities in the headrace channel. In addition, a variant not included in this paper was examined in which the FGS was constructed in the headrace channel, and the bypass was integrated into the dividing pier. However, this variant leads to similar results as V8 and is therefore not presented in this study. In summary, it can be expected that a combination of several variations, which also go beyond those presented in this study, can lead to significantly improved FGE at block-type HPPs.

#### 4.2. Limitations

#### 4.3. Engineering Application Considerations

## 5. Conclusions

- The block-type layout may lead to large flow deflections towards the turbines, resulting in spatially distinct approach flow conditions to FGSs. Therefore, the use of mean flow values in the design process (e.g., the mean rack normal flow velocity $\overline{{v}_{n}}$), as frequently applied in common guidelines, does not allow for an accurate assessment of actual conditions for downstream migrating fish.
- Complex flow conditions with relatively high values for the turbulent kinetic energy TKE and spatial velocity gradient SVG, which often caused avoidance responses in previous ethohydraulic experiments [12,48], can occur especially at the bypass entrance, but may be mostly negligible in the area upstream of the HBRs.
- The flow conditions at the bypass entrance are significantly affected by the bypass discharge Q
_{by}, which should be determined based on the hydraulic parameters at the bypass entrance rather than a fixed percentage of the total river discharge Q_{0}, as well as by the geometric design of the entrance area and the bypass itself. In terms of fish guidance efficiency (FGE) along the FGS, the effects are negligible. - Low rack angles α and the implementation of a bottom overlay can improve the FGE at block-type HPPs from a hydraulic point of view.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ASME | American Society of Mechanical Engineers |

CFD | Computational fluid dynamics |

DES | Detached eddy simulation |

FGE | Fish guidance efficiency |

FGS | Fish guidance structure |

GCI | Grid convergence index |

HBR | Horizontal bar rack |

HBR-BS | Horizontal bar rack bypass system |

HPP | Hydropower plant |

LES | Large eddy simulation |

L1–L5 | Locations 1 to 5 |

MFS | Maximum face sizing |

RANS | Reynolds-averaged Navier-Stokes |

SIMPLE | Semi-Implicit Method for Pressure-Linked Equations |

UDF | User-defined function |

VBR | Vertical bar rack |

V1–V8 | Variations 1 to 8 |

WFD | Water framework directive |

Notation | |

A_{FGS,hyd} | Hydraulically active area of the FGS [m^{2}] |

h_{bo} | Bottom overlay height [m] |

h_{0} | Approach water level upstream of the HPP [m] |

l_{FGS} | Length of the FGS [m] |

Q_{by} | Bypass discharge [m^{3}/s] |

Q_{by,rel} | Relative bypass discharge [-] |

Q_{d} | Design discharge [m^{3}/s] |

Q_{0} | (Assumed) total river discharge [m^{3}/s] |

r | Grid refinement factor [-] |

SVG | Spatial velocity gradient [1/s or cm/s/cm] |

SVG_{f} | Spatial velocity gradient experienced by a fish [1/s or cm/s/cm] |

T | Water temperature [°C] |

t | Swimming duration [s] |

TKE | Turbulent kinetic energy [m^{2}/s^{2}] |

TL | Total fish length [m] |

u’, v’, w’ | Local flow velocity fluctuations in x-, y-, and z-direction [m/s] |

u, v, w | Local flow velocities in x-, y-, and z-direction [m/s] |

v_{a} | Approach flow velocity to the FGS [m/s] |

v_{a}’ | Outflow velocity downstream of the FGS [m/s] |

v_{by} | Velocity at the bypass entrance [m/s] |

v_{f} | Fish swimming speed [m/s] |

v_{m} | Velocity magnitude [m/s] |

v_{n} | Rack normal velocity component [m/s] |

v_{p} | Rack parallel velocity component [m/s] |

v_{pro} | Prolonged swimming speed [m/s] |

v_{sus} | Sustained swimming speed [m/s] |

v_{0} | Mean approach flow velocity [m/s] |

w_{by} | Bypass width [m] |

w_{0} | River width [m] |

x, y, z | Coordinates [-] |

α | Horizontal rack angle [°] |

α_{w} | Water volume fraction parameter [-] |

Δh | Water level difference [m] |

Δp | Pressure drop [Pa] |

θ | Horizontal angle between the approach flow and FGS [°] |

θ’ | Horizontal angle between the outflow and FGS downstream of the FGS [°] |

ξ | Head loss coefficient [-] |

## Appendix A

**Table A1.**Mesh independency study using the mean flow velocity magnitude $\overline{{v}_{m}}$ at the locations 1–5 (L1–L5) from the results of the HPP on the alpine river with three different mesh resolutions, with MFS = maximum face sizing, r = grid refinement factor, and GCI = grid convergence index.

Mesh | MFS Outer/Inner Region [m] | Elements | r [-] | L1 | L2 | GCI [%] L3 | L4 | L5 |
---|---|---|---|---|---|---|---|---|

Fine | 0.2/0.1 | 4,039,279 | 2.152 1.864 | 1.902 16.305 | 0.507 3.599 | 1.453 11.614 | 1.714 3.436 | 0.275 1.477 |

Medium | 0.4/0.2 | 810,298 | ||||||

Coarse | 0.8/0.4 | 250,128 |

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**Figure 1.**Typical schematic layout of a block-type hydropower plant in Central Europe (

**a**) without and (

**b**) with measures for fish protection.

**Figure 2.**Schematic representation of the horizontal bar rack bypass system (HBR-BS) concept used in this study, adapted from Ebel [28] and Maddahi et al. [39], with α = horizontal rack angle, θ = horizontal angle between the approach flow and the rack, v

_{a}= approach flow velocity to the rack, v

_{n}= rack normal velocity component, v

_{p}= rack parallel velocity component, and v

_{0}= mean approach flow velocity.

**Figure 3.**Schematic workflow of the porous medium with the developed UDF during a numerical simulation, with v

_{a}= approach flow velocity to the FGS, v

_{a}’ = outflow velocity downstream of the FGS, and θ’ = horizontal angle between the outflow and FGS downstream of the FGS.

**Figure 4.**Sustained swimming speed v

_{sus}and prolonged swimming speed v

_{pro}depending on the total length TL, calculated with Equation (1), with t = swimming duration, and T = water temperature.

**Figure 5.**Velocity field at the HPP on the pre-alpine river at z = 2.0 m (z/h

_{0}= 0.5): (

**a**) velocity magnitude v

_{m}and normalized flow vectors with a length of 0.75 m in a rectangular grid of 1 m distance around the FGS, and (

**b**) velocity magnitude v

_{m}, normalized flow vectors with a length of 0.2 m in a rectangular grid of 0.2 m distance and selected values for the spatial velocity gradient experienced by a fish SVG

_{f}with total length TL = 0.2 m at the bypass entrance. The green line indicates the position of the FGS in the model.

**Figure 6.**Hydraulic parameters at the HPP on the pre-alpine river 0.1 m in front of the FGS: (

**a**) approach flow velocity to the FGS v

_{a}, (

**b**) rack normal velocity component v

_{n}, (

**c**) rack parallel velocity component v

_{p}(positive in the bypass direction, negative in the direction of the upstream end of the FGS), (

**d**) ratio of v

_{p}/v

_{n}, and (

**e**) turbulent kinetic energy TKE.

**Figure 7.**Hydraulic parameters at the downstream end of the FGS and the bypass entrance of the HPP on the pre-alpine river at z = 2.0 m (z/h

_{0}= 0.5): (

**a**) turbulent kinetic energy TKE, and (

**b**) spatial velocity gradient SVG. The green line indicates the position of the FGS in the model.

**Figure 8.**Velocity field at the bypass entrance of the HPP on the pre-alpine river (

**a**) near the riverbed (z = 0.1 m, z/h

_{0}= 0.025) and (

**b**) near the water surface (z = 3.5 m, z/h

_{0}= 0.875), including normalized flow vectors with a length of 0.2 m in a rectangular grid of 0.2 m distance and selected values for the spatial velocity gradient experienced by a fish SVG

_{f}with total length TL = 0.2 m. The green line indicates the position of the FGS in the model.

**Figure 9.**Velocity field at the bypass entrance of the HPP on the pre-alpine river at z = 2.0 m (z/h

_{0}= 0.5), including normalized flow vectors with a length of 0.2 m in a rectangular grid of 0.2 m distance and selected values for the spatial velocity gradient experienced by a fish SVG

_{f}with total length TL = 0.2 m for (

**a**) the initial design, and (

**b**) variation 1 (V1). The green line indicates the position of the FGS in the model.

**Figure 10.**Velocities at the HPP on the pre-alpine river for (

**a**,

**b**) the initial design, and (

**c**,

**d**) variation 1 (V1) 0.1 m in front of the FGS: (

**a**,

**c**) rack normal velocity component v

_{n}, and (

**b**,

**d**) rack parallel velocity component v

_{p}(positive in the bypass direction, negative in the direction of the upstream end of the FGS).

**Figure 11.**Velocity field at the bypass entrance of the HPP on the pre-alpine river at z = 3.5 m (z/h

_{0}= 0.875), including normalized flow vectors with a length of 0.2 m in a rectangular grid of 0.2 m distance and selected values for the spatial velocity gradient experienced by a fish SVG

_{f}with total length TL = 0.2 m for (

**a**) the initial design, and (

**b**) variation 2 (V2). The green line indicates the position of the FGS in the model.

**Figure 12.**Velocity field at the bypass entrance of the HPP on the pre-alpine river at z = 3.5 m (z/h

_{0}= 0.875), including normalized flow vectors with a length of 0.2 m in a rectangular grid of 0.2 m distance and selected values for the spatial velocity gradient experienced by a fish SVG

_{f}with total length TL = 0.2 m for (

**a**) the initial design, and (

**b**) variation 3 (V3). The green line indicates the position of the FGS in the model.

**Figure 13.**Velocity field at the bypass entrance of the HPP on the alpine river at z = 1.0 m (z/h

_{0}= 0.5), including normalized flow vectors with a length of 0.1 m in a rectangular grid of 0.1 m distance and selected values for the spatial velocity gradient experienced by a fish SVG

_{f}with total length TL = 0.1 m for (

**a**) the initial design, (

**b**) variation 4 (V4), and (

**c**) variation 5 (V5). The green line indicates the position of the FGS in the model.

**Figure 14.**Velocities at the HPP on the alpine river for (

**a**,

**b**) the initial design, and (

**c**,

**d**) variation 6 (V6) 0.1 m in front of the FGS: (

**a**,

**c**) rack normal velocity component v

_{n}, and (

**b**,

**d**) rack parallel velocity component v

_{p}(positive in the bypass direction, negative in the direction of the upstream end of the FGS).

**Figure 15.**Velocity field at the HPP on the alpine river at z = 1.0 m (z/h

_{0}= 0.5): velocity magnitude v

_{m}and normalized flow vectors with a length of 0.5 m in a rectangular grid of 0.5 m distance around the FGS for (

**a**) the initial design, and (

**b**) variation 6 (V6). The green line indicates the position of the FGS in the model.

**Figure 16.**Velocity field at the downstream end of the FGS and bypass entrance of the HPP on the alpine river at z = 0.1 m (z/h

_{0}= 0.05), including normalized flow vectors with a length of 0.1 m in a rectangular grid of 0.1 m distance and selected values for the spatial velocity gradient experienced by a fish SVG

_{f}with total length TL = 0.1 m for (

**a**) the initial design, and (

**b**) variation 7 (V7). The green line indicates the position of the FGS in the model.

**Figure 17.**Velocities at the HPP on the alpine river for (

**a**,

**b**) the initial design, and (

**c**,

**d**) variation 7 (V7) 0.1 m in front of the FGS: (

**a**,

**c**) rack normal velocity component v

_{n}, and (

**b**,

**d**) rack parallel velocity component v

_{p}(positive in the bypass direction, negative in the direction of the upstream end of the FGS).

**Figure 18.**Velocity field at the HPP on the pre-alpine river for variation 8 (V8) at z = 2.0 m (z/h

_{0}= 0.5): (

**a**) velocity magnitude v

_{m}and normalized flow vectors with a length of 0.75 m in a rectangular grid of 1 m distance around the FGS, and (

**b**) velocity magnitude v

_{m}, normalized flow vectors with a length of 0.2 m in a rectangular grid of 0.2 m distance and selected values for the spatial velocity gradient experienced by a fish SVG

_{f}with total length TL = 0.2 m at the bypass entrance. The green line indicates the position of the FGS in the model.

**Table 1.**Characteristics and main parameters of the studied hydropower plants (HPPs). Varied values of parameters that have been modified within the variations are marked with *.

Site | Pre-Alpine River | Alpine River |
---|---|---|

Fish Zonation | Grayling Region | Lower Trout Region |

HPP Construction Type | Block-Type | Block-Type |

Total river discharge Q_{0} [m^{3}/s] | 50 | 10 |

Design discharge Q_{d} [m^{3}/s] | 48 | 8 *, 9 *, 9.5 |

Bypass discharge Q_{by} [m^{3}/s] | 2 | 0.5, 1 *, 2 * |

Mean approach flow velocity v_{0} [m/s] | 0.36 | 0.25 |

Mean rack normal velocity component $\overline{{v}_{n}}$ [m/s] | 0.46 | 0.24 *, 0.45 |

River width w_{0} [m] | 35 | 20 |

Bypass width w_{by} [m] | 1 | 0.5 |

Length of the FGS l_{FGS} [m] | 23.34 *, 25.94 | 10.58, 20.19 * |

Approach water level upstream of the HPP h_{0} [m] | 4 | 2 |

Rack angle α [°] | 40 | 20 *, 40 |

Variation | Varied Component | Description | Schematic Illustration | HPP |
---|---|---|---|---|

V1 | Dividing pier (weir-side part) | Shifted 1.0 m in the upstream direction | Pre-alpine river | |

V2 | Dividing pier (weir-side part) | Modified the shape and width for smoother flow conditions around the pier | Pre-alpine river | |

V3 | Inlet gate | Installed at the turbine-side part of the dividing pier | Pre-alpine river | |

V4 | Sloping weir | Lowered to double the bypass discharge Q_{by} compared to the initial design | Alpine river | |

V5 | Sloping weir | Lowered to quadruple the bypass discharge Q_{by} compared to the initial design | Alpine river | |

V6 | Fish guidance structure | Modified the rack angle α to 20° | Alpine river | |

V7 | Fish guidance structure | Implementation of a bottom overlay with a height of 0.2 m | Alpine river | |

V8 | Fish guidance structure | Integrated into the headrace channel with the bypass on the orographic right side (cf. Figure 2) | Pre-alpine river |

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**MDPI and ACS Style**

Zöschg, H.; Dobler, W.; Aufleger, M.; Zeiringer, B.
Evaluation of Hydraulics and Downstream Fish Migration at Run-of-River Hydropower Plants with Horizontal Bar Rack Bypass Systems by Using CFD. *Water* **2023**, *15*, 1042.
https://doi.org/10.3390/w15061042

**AMA Style**

Zöschg H, Dobler W, Aufleger M, Zeiringer B.
Evaluation of Hydraulics and Downstream Fish Migration at Run-of-River Hydropower Plants with Horizontal Bar Rack Bypass Systems by Using CFD. *Water*. 2023; 15(6):1042.
https://doi.org/10.3390/w15061042

**Chicago/Turabian Style**

Zöschg, Hannes, Wolfgang Dobler, Markus Aufleger, and Bernhard Zeiringer.
2023. "Evaluation of Hydraulics and Downstream Fish Migration at Run-of-River Hydropower Plants with Horizontal Bar Rack Bypass Systems by Using CFD" *Water* 15, no. 6: 1042.
https://doi.org/10.3390/w15061042