# 3-D Numerical Study of a Bottom Ramp Fish Passage Using Smoothed Particle Hydrodynamics

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Site

^{3}/s. It was estimated that typical and high flows would amount to approximately 0.4 and 0.6 m

^{3}/s, respectively. All the main input data for the model were measured. Channel width (B) water depth (H), and average velocity of the flow (u) were measured at the weir, average slope (I) of the stream was determined from existing geodetic data, while the shape, size, and distribution of substrate elements were measured upstream of the weir. Note that substrate elements in Figure 1 (i.e., rocks between sills, downstream of the weir) are larger than those present in the non-regulated sections of the stream.

#### 2.2. SPH Method and DualSPHysics

#### 2.2.1. Main Formulation of the SPH

_{a}reads [18]:

#### 2.2.2. DualSPHysics

## 3. Validation

#### 3.1. Validation against Experiments

- (1)
- eight straight transverse lines, each including six equal spheres (having a diameter d = 0.14 m and effective height 0.125 m above the bed), with spheres located 0.01 m apart (i.e., the gap between the surfaces of two neighboring spheres, measured in the plane of the spheres’ centers), lines located 0.9 m apart, slope 3%, and discharge Q = 0.060 m
^{3}/s (denoted “HOR“ by the authors), - (2)
- eight V-shaped formations, each including seven equal spheres (having a diameter d = 0.14 m and effective height 0.125 m above the bed), with V-formations located 0.9 m apart, slope 3%, and discharge Q = 0.120 m
^{3}/s (denoted “VUS“ by the authors).

^{−6}m

^{2}s, and the effect of viscosity at the boundaries through the parameter denoted α

_{bf}(the default value in this work being α

_{bf}= 0). Comparisons are given in Figure 3, Figure 4 and Figure 5.

^{2}= 0.88 and 0.81 for the HOR and VUS case, respectively.

^{−6}m

^{2}s are very similar. Furthermore, employing a boundary viscosity coefficient different from zero resulted in a poorer agreement between the model and the experiment. Based on the above considerations, the following settings were used in all the subsequent simulations: dp = 1.5 cm, α = 0.01, and α

_{bf}= 0.

#### 3.2. Validation against a Numerical Study

^{3}/s, slope 3%, depth H = 0.17 m, denoted as “Configuration I—simulation A4” by the authors (Figure 7).

## 4. Results

#### 4.1. Numerical Setup

_{x}= 0.147, g

_{y}= 0, and g

_{z}= −9.809 m/s

^{2}. In majority of cases, the slope was set to I = 1.5% to equal the average slope of the observed stream, while I = 3% and I = 5% cases were simulated to make the comparisons.

_{1}= 0.12 m (amounting to Q

_{1}= 0.24 m

^{3}/s), H

_{2}= 0.21 m (amounting to Q

_{2}= 0.42 m

^{3}/s), and H

_{3}= 0.30 m (amounting to Q

_{3}= 0.60 m

^{3}/s).

_{1}case (of which 2.2 million were fluid particles) to 6.1 million in the Q

_{3}case (of which 4.7 million were fluid particles). Simulations were performed on a single GPU (GeForce GTX 1080 Ti).

#### 4.2. Depth Calculation Tool

_{1}case, 0.27 m − 0.21 m = 0.06 m in the Q

_{2}case, and 0.35 m − 0.30 m = 0.05 m in the Q

_{3}case. Note that undulated surface (i.e., waves) of the main flow is visible in the Q

_{2}and Q

_{3}case (see arch-like shapes in the region x = 5 to 8 m, y = −0.75 to 0 m). The new depth tool can provide information on the depth of water flowing over the obstacles. These results can then be compared to the minimum water depth requirements of target fish species and thus contribute to the fish passage efficiency evaluation. However, to create a more close-to-nature ramp, substrate elements should be further repositioned to provide more diverse flow conditions.

#### 4.3. Velocity Field Tool

_{1}to Q

_{3}results in higher maximum velocities (from 1.5 to 2 m/s), larger jets, and smaller areas of low velocities (u < 0.4 m/s). It can be expected that a less uniform distribution of obstacles would lead to a more diverse flow pattern.

#### 4.4. Bed Roughness Tool

^{9}particles [49]. The input of GenCase is a XML (eXtensible Markup Language) file where geometry of boundaries, fluid areas, and other simulation parameters are defined. The basic boundary elements (e.g., boxes, spheres, cylinders…) are explicitly defined by indicating their position and dimensions, but more complex 3-D models can also be imported from format files STL, VTK, or PLY supported by design software such as Blender or AutoCAD. These options allow the creation of complex cases, but it is not easy to create non-regular cases closer to nature.

#### 4.5. Area–Velocity Tool

^{2}at x = 1.75 m to 0.25 m

^{2}at x = 10.5 m in the Q

_{1}case and from 0.4 m

^{2}at x = 1.75 m to 0.3 m

^{2}at x = 10.5 m in the Q

_{3}case. Furthermore, in these locations, maximum fluid velocity increases from 0.8 m/s at x = 1.75 m to 1.6 m/s at x = 10.5 m for the Q

_{1}case and from 1.2 m/s at x = 1.75 m to 2.2 m/s at x = 10.5 m in the Q

_{3}case.

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Plan view of the geometries used in the validation, taken from [45].

**Figure 3.**Centerline water-surface elevation along the selected section of HOR case for α = 0.01 and various dp.

**Figure 4.**Centerline water-surface elevation along the selected section of VUS case for α = 0.01 and various dp.

**Figure 5.**Centerline water-surface elevation along the selected section of HOR case for dp = 1.5 cm and various viscosity treatments.

**Figure 6.**Plan view of the horizontal velocity magnitude at z = 0.08 m plane. (

**a**) HOR experiment (

**b**) HOR model, (

**c**) VUS experiment, (

**d**) VUS model. Dots in (

**b**,

**d**) represent solid particles of spheres. Figure 6a,c are taken from the reference study.

**Figure 8.**Velocity field at z = H/2 plane. (

**a**) Results taken from the reference study [16] and (

**b**) our model results.

**Figure 9.**The model geometry (

**a**) with a smooth bed (dimensions in meters) and (

**b**) with bed roughness elements. Colors indicate bed roughness elements (blue), substrate spheres (red), and cylinders (green). Flow from left to right.

**Figure 11.**Depth of the flow over the solid boundary after 30 s of simulation. (

**a**) Q

_{1}case, (

**b**) Q

_{2}case, (

**c**) Q

_{3}case. Flow from left to right.

**Figure 12.**Longitudinal velocity u for the Q

_{2}case, looking in the downstream direction, at cross-sections. (

**a**) x = 1.5 m (i.e., upstream of the first row of obstacles), (

**b**) x = 3 m (i.e., first line of cylinders), (

**c**) x = 6 m (i.e., second line of cylinders), (

**d**) x = 9 m (i.e., third line of cylinders), and (

**e**) x = 11 m (i.e., downstream of the last line of obstacles).

**Figure 13.**Velocity field at z = H/2 plane after 30 s of simulation. (

**a**) Q

_{1}case, z = 0.05 m; (

**b**) Q

_{2}case, z = 0.10 m; (

**c**) Q

_{3}case, z = 0.15 m.

**Figure 14.**Velocities close to the bottom at z = 0.05 m plane for the Q

_{2}case (

**a**) with smooth bed and (

**b**) bed roughness.

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## Share and Cite

**MDPI and ACS Style**

Novak, G.; Domínguez, J.M.; Tafuni, A.; Silva, A.T.; Pengal, P.; Četina, M.; Žagar, D.
3-D Numerical Study of a Bottom Ramp Fish Passage Using Smoothed Particle Hydrodynamics. *Water* **2021**, *13*, 1595.
https://doi.org/10.3390/w13111595

**AMA Style**

Novak G, Domínguez JM, Tafuni A, Silva AT, Pengal P, Četina M, Žagar D.
3-D Numerical Study of a Bottom Ramp Fish Passage Using Smoothed Particle Hydrodynamics. *Water*. 2021; 13(11):1595.
https://doi.org/10.3390/w13111595

**Chicago/Turabian Style**

Novak, Gorazd, José M. Domínguez, Angelo Tafuni, Ana T. Silva, Polona Pengal, Matjaž Četina, and Dušan Žagar.
2021. "3-D Numerical Study of a Bottom Ramp Fish Passage Using Smoothed Particle Hydrodynamics" *Water* 13, no. 11: 1595.
https://doi.org/10.3390/w13111595