**3. Results and Discussions**

The results will mainly focus on how the velocity, vorticity, turbulence, and settling patterns vary between the three distinct models, as these are the key factors that affect sand trap efficiency in this case.

### *3.1. Sand Trap Efficiency*

The sand trap efficiencies of the different models were obtained by creating a timeintegrated particle mass flow report. This measures the total sediment mass entering the domain through the inlet and exiting through the outlet. The total time of 1000 s was found to be sufficient for all suspended sediments to exit the domain while remaining sediments are travelling along the bed. In the models with ribs implemented, sediments travelling along the bed are observed to pour into the gaps between ribs. At the end of simulation, not all sediments travelling along the bed have reached the ribs. However, a precedent is set by the sediments that do reach the ribs. These are all seen to pour into the the ribs instead of passing over them, indicating that this will also be the case for the remaining sediments. Due to limited computational resources, running the simulations for longer was not feasible. Running the simulations until all sediments are either completely settled or out of the domain could affect the sand trap efficiencies.

Using the model without upgrades as the base line, the mass of sediments exiting through the outlet is reduced by 24.5% from 2.5 × <sup>10</sup><sup>3</sup> to 1.9 × 103 kg by including the ribs. This indicates that the ribs are more effective at capturing and trapping bed load sediments than only the weir. By also adding the v-shaped rakes, the amount of sediments escaping the sand trap is increased by 48.5% from 2.5 × 103 to 3.7 × 103 kg compared with the model without upgrades. The amount of larger sediments trapped can be assumed to be similar before and after including the rakes, as larger sediments cannot be seen to escape the sand trap in neither particle track plots. The lack of performance from the model with rakes included can therefore be attributed to the turbulent vortices preventing smaller sediments to settle. This reduces sand trap efficiency. The sand trap efficiency of the different models are listed in Table 3.


**Table 3.** Sand trap efficiencies.

In all simulations, the divide between suspended load and bed load appears to be around 1 mm in diameter. The majority of sediments that remain suspended until escaping the sand trap are smaller than 1 mm, while the larger sediments travel along the bed by sliding, saltating, or rolling. Models for simulating sediment resuspension were not included in the simulations. The bed load sediments are therefore not observed to be resuspended. It has previously been shown that for classically dimensioned sand traps, sediment resuspension mostly occurs for sediments with grain sizes smaller than <sup>2</sup> × <sup>10</sup>−<sup>4</sup> <sup>m</sup> [21]. This is below the range of grain sizes used in the present work. Further analyses could be done with the resuspension models included and with smaller grain sizes to investigate the rate of sediment resuspension from the bed load. To further improve the sand trap efficiency, a flow calmer in the shape of horizontal bars, as suggested by Richter, should be tested. Instead of acting as a bluff body and inducing turbulence, this flow calmer could break up turbulence structures and improve settling characteristics for smaller sediments. Smoothing the transition between inlet and diffuser by reducing the inclination of the slope was suggested as an option to further increase the settling of smaller sediments [5]. However, it was found that this solution does not significantly improve the jet flow behaviour in the diffuser, thus not improving the settling of small sediments.

Looking at particle track plots of the different models, it appears that particles that reach the tunnel bed before passing over the ribs will indeed fall between them. This confirms the discovery from experiments by Richter et al. [4,5]. Sediments that remain suspended when passing the ribs will generally escape the sand trap. The amount of suspended sediments vary depending on if rakes are included in the diffuser or not. In the results where the rakes are not included, the suspended sediments are gathered closer towards the bottom of the tunnel. When rakes are included, the suspended sediments are of greater numbers and are more dispersed over the tunnel cross-section. This is believed to be caused by the turbulence from the rakes.

#### *3.2. Head Losses*

The head loss, Δ*hL*, of the different models was calculated from the steady-state simulations using the pressure-drop-based Darcy–Weisbach equation in Equation (3). The pressure difference, Δ*p*, is calculated between the inlet and outlet faces of the models. Using the head loss in the model with no upgrades as a base value, the increased head loss caused by the upgrades was calculated by finding the difference in head loss between each of the upgraded models and the base value.

As presented in Table 4, the head loss caused by including just the ribs is 0.003 m, equating to an increase of 1.8% for the whole sand trap. Combined with the better sand trap efficiency of this model, this speaks for the value of including ribs in the sand trap. The model with both ribs and rakes included sees an increase in head loss of 12.7% compared to the model with no upgrades. The large head loss and the relatively poor sand trap efficiency of this model make it possible to conclude that other types of improvements to the sand trap should be pursued instead.

**Table 4.** Head loss, Δ*hL*, is calculated using Equation (3). Increased head loss is found by comparison with the model with no upgrades.


#### *3.3. No Upgrades*

The model with no upgrades represents the sand trap as it stands today, with a diffuser near the inlet and a weir just upstream of the penstock. The simulation results on the model with no upgrades give a baseline with which results from the other models can be compared. In addition, the results on this model will be compared to PIV and ADCP measurements for validation [4,5]. The velocity contour plot in Figure 5 shows the separation occurring at the entrance of the diffuser and the jet forming above it. Large circulation zones develop both in the horizontal and vertical planes at the entrance of the diffuser. These phenomena were obtained in both PIV results and in other experimental results, thus validating the simulations in this work [13,20]. Field measurements by Almeland et al. showed that the main current follows the centre of the diffuser, which can also be seen in the present results [12].

The turbulence, which develops from the separation in the diffuser, is seen to propagate through the sand trap, see Figure 6. The turbulence appears to dissipate as the flow reaches the halfway point before increasing as it crosses the weir and enters the penstock. The slow dissipation of turbulence may be due to the relative smoothness of the tunnel walls. Increasing the wall roughness to closer resemble the rough unlined tunnel walls in the prototype would affect the simulation results. One possibility is that turbulence would dissipate faster because of the increased energy losses. This would lead to improved sediment settling characteristics in the downstream end of the sand trap. Another possibility is that the rough walls may introduce even higher turbulence, disturbing sediment settling.

**Figure 5.** Velocity distributions in the sand trap with no upgrades included at t = 1000 s. A highvelocity jet above vortices caused by flow separation can be seen in the diffuser. Further downstream, the velocity is more evenly distributed.

**Figure 6.** Sand trap without upgrades, symmetry plane at t = 1000 s. (**a**) Velocity contour. Flow separation occurs in the diffuser, which causes a higher flow velocity in the upper part of the diffuser. Separation is also seen to occur at the weir. (**b**) Vorticity contour. Flow separation in the diffuser and at the weir causes vortex generation. (**c**) Turbulence kinetic energy contour. Turbulence propagating from the diffuser starts to dissipate before reaching the penstock.

### *3.4. Sand Trap with Ribs*

The flow behaviour upstream of the ribs remains identical to the model without upgrades. Large vortex structures propagate from the diffuser, where flow separation occurs. The separation of the flow field around the ribs is presented in Figure 7. This results in low velocities in the space below the ribs, which improves sediment settling. It can also be seen that inflow occurs at the last rib. This causes circulation in the downstream end of the space below the ribs. Sediments begin to settle in the upstream end, and will therefore be less affected by this circulation. However, this could change as the space fills up with sediments. A turbulent boundary layer forms over the ribs from separation at the ramp. This will be beneficial for the settling of bed load sediments under the ribs, as these will slow down when entering the boundary layer. The chance of the sediments falling through the gaps is therefore increased. Flow into the penstock is more turbulent as a consequence of the turbulent boundary layer.

**Figure 7.** Extended view of ribs in the symmetry plane at t = 1000 s. (**a**) Velocity contour. Separation of the velocity field is visible. Low velocities below ribs increase the chances of sediment settling. Low-velocity inflow occurs between the last two ribs. This causes circulation in the downstream end below the ribs. Sediments will begin to settle in the upstream end, and will therefore be less affected by the circulation. However, this could change as the space fills up with sediments. (**b**) Vorticity contour. (**c**) Turbulence kinetic energy contour. A turbulent boundary layer forms over the ribs due to separation from the ramp. This will be beneficial for the settling of bed load sediments, as these will slow down when entering the boundary layer. Flow into the penstock is more turbulent as a consequence.
