# Computational Fluid Dynamics and Visualisation of Coastal Flows in Tidal Channels Supporting Ocean Energy Development

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theory and Method

#### 2.1. Standard k-ϵ Turbulence Model

_{i}is the ith component of the velocity vector, µ

_{l}and µ

_{t}are the laminar and turbulent dynamic viscosities respectively, and S

_{i}includes any additional sources [28,29].

_{1}

_{ϵ}, C

_{2}

_{ϵ}, σ

_{k}, and σ

_{ϵ}, are the closure constants, which are found empirically and are 1.44, 1.92, 1.0 and 1.3 respectively [29,30]. The turbulent generation rate G is defined by:

_{µ}is a constant with the value of 0.09. The coupling between turbulence and momentum equations is achieved through the dynamic viscosity which is a sum of the laminar and turbulent values. In all of the equations, since the flow is incompressible, the derivative of density over time is zero [32].

#### 2.2. Large Eddy Simulation (LES)

_{ij}is the filtered stress tensor and σ

_{ij}is the subgrid-scale Reynolds stresses.

_{t}is the turbulent viscosity, ∆ is the length scale of the filter, S

_{ij}is the filtered strain-rate tensor, C

_{s}is the Smagorinsky constant. The length scale of the filter, ∆, is usually considered to be the cube root of the volume of the cell [34].

#### 2.3. Visualisation Technique

## 3. Domain

^{2}. The bathymetry data was collected during the “Celtic Odyssey Operation”, using an echosounder [44] and then MATLAB

^{®}V4 grid data method which uses the Green functions of the biharmonic operator to find the minimum curvature interpolation of irregularly spaced data points was employed to generate the seabed geometry [46].

^{®}. This satellite data has a resolution of 30 m which means that the surface that is created by this dataset is very smooth and does not include the pinnacles and small rocks. The second dataset used was a historic dataset made available by the Royal Navy and was measured using a lead line in the early 20th century. In the regions where less information was available from the other two datasets, this was used to confirm the geometry of the seabed.

^{®}dataset to construct that region. The same evaluation was done for the other regions and the final geometry of the seabed was constructed. Afterwards the proposed geometry of the seabed was discussed with the locals and boat skippers who were familiar with the area and the bathymetry was finalised. The result gives us a bathymetry which is not only relatively simple to mesh but also resembles the key features of the region accurately, see Figure 2.

^{®}. The inlet velocity for the k-ϵ case is set to be 1.5 m/s with a turbulent intensity of 20% and turbulent viscosity ratio of 100. For the bed boundary condition a no slip wall with roughness height (k

_{s}) of 5.4 m and roughness constant of 0.9 is selected. In ANSYS FLUENT

^{®}the roughness constant is a value to define how uniformly the sand grains are distributed on the surface. A suitable value is usually between 0.5 and 1.0 and the smaller number means that the sand grains (here rocks) are placed on the surface more uniformly [47]. ANSYS FLUENT

^{®}uses the following equation to calculate the roughness height: Roughness Height = (9.793 × Roughness Length)/Roughness Constant. In which the roughness constant is a value to define how uniformly the sand grains are distributed on the surface, the roughness length is calculated based on the Nikuradse Sand Roughness. Based on this equation the size of the grains on the seabed is averaged to be roughly 0.5 m.

^{®}uses the logarithmic law of wall to solve the wall-bounded turbulent flows [33]. The reason for selecting these values (5.4 for roughness height and 0.9 for roughness constant) is that the model has simplifications in terms of the exact shape of the bed and also in terms of the inlet boundary condition. In the real world, the inlet has a very turbulent boundary condition because of the big rocks located in the south of the sound (known as the bitches).

## 4. Results

^{3}for density and 9763 N/m

^{2}for the pressure drop, h is calculated to be 0.995 m at a distance of 61 m downstream of Horse Rock. The samples are taken at x = 449, y = 5, z = 361, where p = −9014 and x = 449, y = 5, z = 300, where p = 749. Given the scale of the model and the small amount of blockage we can assume that the results are not significantly affected by the rigid lid. Therefore, the significant computational overhead of a free surface is not required in this case.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**This illustration demonstrates a simple stream surfaces seeded in front of a cuboid, and capturing the flow characteristics, i.e., vortices, emanating downstream from the cuboid. This visualisation is constructed using the framework described in [41].

**Figure 2.**The bathymetry (

**bottom**) created with the combination of the Boat (

**Top left**), SeaZone

^{®}(

**Top Centre**) and Royal Navy (

**Top Right**) data sets (The elevation was exaggerated to show the features clearly).

**Figure 4.**Comparison of the velocity profile across the channel at 775 m from the inlet (k-ϵ, LES, Boat data).

**Figure 5.**The Eddies forming behind the horse rock. The separation point is also visible (Large Eddy Simulation (LES) method).

**Figure 7.**Three different views of the big eddies forming as water from both sides of the channel joins together in the deeper section (LES method fine mesh).

**Figure 8.**Pressure plots (Pa) of the sea surface (

**top**) and seabed (

**bottom**), paying particular attention to the Horse rock region of the domain.

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**MDPI and ACS Style**

Zangiabadi, E.; Edmunds, M.; Fairley, I.A.; Togneri, M.; Williams, A.J.; Masters, I.; Croft, N.
Computational Fluid Dynamics and Visualisation of Coastal Flows in Tidal Channels Supporting Ocean Energy Development. *Energies* **2015**, *8*, 5997-6012.
https://doi.org/10.3390/en8065997

**AMA Style**

Zangiabadi E, Edmunds M, Fairley IA, Togneri M, Williams AJ, Masters I, Croft N.
Computational Fluid Dynamics and Visualisation of Coastal Flows in Tidal Channels Supporting Ocean Energy Development. *Energies*. 2015; 8(6):5997-6012.
https://doi.org/10.3390/en8065997

**Chicago/Turabian Style**

Zangiabadi, Enayatollah, Matt Edmunds, Iain A. Fairley, Michael Togneri, Alison J. Williams, Ian Masters, and Nick Croft.
2015. "Computational Fluid Dynamics and Visualisation of Coastal Flows in Tidal Channels Supporting Ocean Energy Development" *Energies* 8, no. 6: 5997-6012.
https://doi.org/10.3390/en8065997