# Numerical Investigation of a Hydropower Tunnel: Estimating Localised Head-Loss Using the Manning Equation

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Setup

#### 2.1. Gävunda-Tunnel

#### 2.2. Determining Rough Surface Statistics

#### 2.3. Discretization and Simulation Setup

## 3. Results and Discussion

#### Head Loss

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**A top-view (

**left**) and cut-through (

**right**) schematic of the tunnel, both drawings made pre-excavation. The flow is from right to left according to the left figure. Units are given in m.

**Figure 2.**(

**a**) The local hydraulic radius as a function of the tunnel length. The black line represents the average. (

**b**) 45 cross sections of the tunnel. the red line represent the average cross section. Section 2.2 details the procedure on how to attain data on the cross sections.

**Figure 3.**(

**a**) depicts a section of the tunnel. The black points represent the point-cloud, the red points are all points within 0.10 m of the perpendicular plane, the red line is the centreline of the tunnel. (

**b**) depicts the cross section resulting from averaging the red points in (

**a**).

**Figure 4.**(

**Left**) the solid line represents the pressure modelled at the centre of the tunnel, while the dotted line represents the ideal case with no variation in hydraulic radius. The data represented by diamonds is the static pressure area-averaged over each of the cross-sections. (

**Right**) area averaged velocity from the entrance to the outlet of the tunnel.

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

## Share and Cite

**MDPI and ACS Style**

Andersson, L.R.; Hellström, J.G.I.; Andreasson, P.; Lundström, T.S.
Numerical Investigation of a Hydropower Tunnel: Estimating Localised Head-Loss Using the Manning Equation. *Water* **2019**, *11*, 1562.
https://doi.org/10.3390/w11081562

**AMA Style**

Andersson LR, Hellström JGI, Andreasson P, Lundström TS.
Numerical Investigation of a Hydropower Tunnel: Estimating Localised Head-Loss Using the Manning Equation. *Water*. 2019; 11(8):1562.
https://doi.org/10.3390/w11081562

**Chicago/Turabian Style**

Andersson, L. Robin, J. Gunnar I. Hellström, Patrik Andreasson, and T. Staffan Lundström.
2019. "Numerical Investigation of a Hydropower Tunnel: Estimating Localised Head-Loss Using the Manning Equation" *Water* 11, no. 8: 1562.
https://doi.org/10.3390/w11081562