**2. Materials and Methods**

#### *2.1. Sediment Transport Theory*

When sediments at the tunnel bed are subjected to shear stresses higher than what is required to loosen them from the bed load, the sediments will be suspended and transported with the flow. Sediment transport can be divided into two main categories, depending on the shear velocity to settling velocity ratio of the particles, *u*∗ > *w* [15]. These categories are suspended load and bed load. Suspended load consists of finer particles that have low inertia and settling velocities due to their low mass. They are therefore transported further by the flow before settling compared with bed load sediments. Bed load usually consists of rocks and larger grains of sand that are too heavy to be suspended in water for longer durations. They are instead transported by sliding, saltating, or rolling along the sediment bed, as illustrated in Figure 2.

In order to determine if the upgrades improve sediment settling, it is necessary to measure the sand trap efficiency. The most straightforward method to compute the efficiency is a sediment-mass-based approach. Here, the ratio of the total mass of sediments injected at the inlet and escaped through the outlet is found. The efficiency can then be calculated as in Equation (1)

$$\eta = 1 - \frac{\Phi\_{s,out}}{\Phi\_{s,in}} \, ^\prime \tag{1}$$

where *η* is the sand trap efficiency and Φ represents the mass of sediment. Time-integrated particle mass flow reports created at the end of simulations will be used to find the inflow and outflow of sediments and then calculate sand trap efficiencies.

**Figure 2.** Types of sediment transport.

#### *2.2. Head Loss*

Installing new structures in the waterways could increase energy losses in the flow. This is mainly due to increased friction. This will affect the total head loss and, ultimately, the performance of the power plant. The head loss should therefore be minimised. Losses due to friction are determined by using the Darcy–Weisbach friction factor, seen in Equation (2).

$$h\_f = f \frac{L \times v^2}{D \times 2g'} \tag{2}$$

where *hf* (m) is the head loss, *f* is the dimensionless Darcy friction factor, *L* (m) is the length of the pipe, *v* (m/s) is the mean velocity of the flow, *D* (m) is the diameter of the tunnel, and *g* (m/s2) is the gravitational acceleration. To ensure correct head loss calculations, it is important to find the correct Darcy friction factor. Using a Moody diagram, the friction factor can be found by determining the Reynolds number and relative roughness of the flow situation. In the present work, the Darcy–Weisbach equation form based on the pressure drop (Equation (3)) will be used to find the head loss caused by the upgrades.

$$
\Delta h\_L = \frac{\Delta p}{\rho \mathcal{g}}\tag{3}
$$

where Δ*hL* is the head loss, Δ*p* (Pa) is the pressure difference between two points, and *ρ* (kg/m3) is the fluid density. The head loss in each of the geometries will be measured in post-processing. The head loss in the base case will be subtracted from each of the other cases, where the difference is the increased head loss caused by the upgrades.
