Delft3D has no dedicated implementation of tidal turbines. However, these, along with their support structures, may be approximated by porous plates, which can be specified on the boundary between any two given cells of the grid. However, for this purpose, Delft3D has some specific limitations.

First, the model does not support variable drag coefficients for the plates, so a characteristic fixed coefficient has to be chosen.

Second, drag is only applied perpendicular to the direction of the porous plate, which is fixed in time. This prevents simulating turbines with horizontal axis rotating over time, and produces an underestimation of drag unless the flow remains mostly perpendicular to the plate.

Lastly, as previously mentioned, in 3D mode the program uses a “sigma” coordinate system, and the vertical layers move following the changes in free surface elevation. The position of the porous plate is specified as covering some or all of these layers, so that the modelled turbines will appear to grow and shrink in the water column depending on whether the tide rises or falls. This is especially problematic if the change in water surface elevation is large in relation to the mean water depth. Under these conditions, for the current case of study, there is little precision to be gained from simulating flow in 3D, as the porous plate loss would be applied to incorrect portions of the vertical velocity profile most of the time. That is the reason why a 2D treatment has been used so far for the Nalón estuary.

To evaluate the effect of an installation of tidal microturbines, an example based on [7] composed of 14 vertical axis (VAT) hydrokinetic microturbines was selected. Each unit have a swept area of 1 m^{2} (diameter of 0.7 m and length of 1.5 m). The microturbines are arranged in a row located in the normal direction to the river current.

The effect of the microturbines in the river flow has been modelled with the momentum sink term of Delft3D for porous plates [15].

$$\begin{array}{}{\displaystyle {M}_{\epsilon}=-{C}_{loss}\phantom{\rule{thinmathspace}{0ex}}\cdot \phantom{\rule{thinmathspace}{0ex}}\frac{1}{\mathit{\Delta}\mathit{x}}\phantom{\rule{thinmathspace}{0ex}}\cdot \phantom{\rule{thinmathspace}{0ex}}{V}_{(x,y)}\phantom{\rule{thinmathspace}{0ex}}\cdot \phantom{\rule{thinmathspace}{0ex}}|{V}_{(x,y)}|}\end{array}$$(2)

Where, *M*_{∊}, is the acceleration that represents the change in the momentum, *C*_{loss} is the quadratic friction coefficient, and *Δx* is cell size in the flow direction. By the application of the porous plate theory, the coefficient can be determined by [16],

$$\begin{array}{}{\displaystyle {C}_{loss}=\frac{{C}_{d}\phantom{\rule{thinmathspace}{0ex}}\cdot \phantom{\rule{thinmathspace}{0ex}}N\phantom{\rule{thinmathspace}{0ex}}\cdot \phantom{\rule{thinmathspace}{0ex}}A}{2\phantom{\rule{thinmathspace}{0ex}}\cdot \phantom{\rule{thinmathspace}{0ex}}\mathit{\Delta}\mathit{y}\phantom{\rule{thinmathspace}{0ex}}\cdot \phantom{\rule{thinmathspace}{0ex}}\mathit{H}}}\end{array}$$(3)

Table 1 Results from the study cells.

Where, *C*_{d} is the turbine drag coefficient, *N* is the number of microturbines assigned to the boundary between cells, *A* is the area swept by each microturbine, *Δy* is the size (in the direction normal to the flow) and *H* is the mean height of the porous plate, which, for a 2D calculation, is the mean water depth in the cells.

For the current case, the row of microturbines is 11.5 m wide, covering the width of two cells of *Δy* = 5.75 m each, *C*_{d} = 0.85 for a Gorlov microturbine, *H* =2.5 m and *N* · *A* = *Δy* 1.5 m = 8.27 m^{2}. Consequently, *C*_{loss} = 0.255.

The water depth oscillates between 1.5 m and 3.5 m for this zone, which, as mentioned above, is a big fluctuation relative to the mean water depth of 2.5 m.

The numerical model modified to include the effect of the microturbine simulated a whole year (2013). The values of power and energy per turbine were obtained (Figure 6).

Figure 6 Average power per turbine.

Additionally, the effect of the microturbine row in the river flow, was obtained as the average velocity change in each cell,

$$\begin{array}{}{\displaystyle \mathit{\Delta}U=\int \frac{(|{V}_{b}(x,y)|\phantom{\rule{thinmathspace}{0ex}}-\phantom{\rule{thinmathspace}{0ex}}|{V}_{a}(x,y)|)}{{t}_{f}\phantom{\rule{thinmathspace}{0ex}}-\phantom{\rule{thinmathspace}{0ex}}{t}_{i}}dt}\end{array}$$(4)

Where, *V*_{b}(*x*, *y*), is the depth-averaged velocity field without microturbines, *V*_{a} (*x*, *y*) is the depth-averaged velocity field with microturbines, *t*_{i} and *t*_{f} are the initial and final times of the simulation. In this case, in one year The results for this case for one year are shown in Figure 7.

Figure 7 Average velocity change (annual).

As for the economic analysis and according to a study of similar characteristics [17], with 20 turbines farm, the viability of the projects is achieved with investments around 1500 €/ Kw, with a payback period of 6 years.

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