# Lagrangian Vortex Computations of a Four Tidal Turbine Array: An Example Based on the NEPTHYD Layout in the Alderney Race

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Method

#### 2.1. Vortex Particle Method

- A rotational velocity component ${\mathit{u}}^{\psi}$ accounting for particle–particle interaction, the core of any Lagrangian Vortex method. The component ${\mathit{U}}^{\psi}$ is the discrete solution of the continuous equation:$$\Delta \mathit{\psi}=-\mathit{\omega},$$$${\mathit{U}}^{\psi}\left(M\right)=\frac{1}{4\pi}\sum _{i=1}^{{N}_{P}}\frac{{\mathit{MX}}_{\mathit{i}}}{|{\mathit{MX}}_{\mathit{i}}{|}^{3}}\wedge {\mathbf{\Omega}}_{i}.$$
- A potential velocity component ${\mathit{u}}^{\varphi}$, representing the influence of a solid body. There are many applications for the use of such a component, such as the simulation of the nozzle of jet [49], of a sail [50], or of a monofin [51]. In the present study, the potential velocity component represents the influence of the rotor of a turbine [9], as will be demonstrated in the following sections. This velocity component ${\mathit{u}}^{\varphi}$ derives from a scalar potential $\varphi $, which must satisfy:$$\Delta \varphi =0.$$
- A velocity component ${\mathit{u}}_{\infty}$ representing the upstream velocity field at infinity, generally treated as a constant vector. The focus of this paper will be to adapt the upstream velocity component ${\mathit{u}}_{\infty}$ in order to account for ambient turbulence in the surrounding flow.

#### 2.2. Synthetic Eddy Method

#### 2.3. Numerical Parameters

## 3. Computation of a Single Tidal Turbine

#### 3.1. Numerical Set-Up and Tested Configurations

#### 3.2. Taking into Account the Nacelle

#### 3.3. Influence of the Filling Ratio R_{f}

#### 3.4. Influence of the Turbulent Structure Size λ

## 4. Four Tidal Turbine Array: The NEPTHYD Layout

#### 4.1. Description of the Selected Configuration: The NEPTHYD Project

#### 4.2. Initial Configuration

#### 4.3. Yawed Flows

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

LES | Large Eddy Simulation |

PSE | Particle Strength Exchange |

SEM | Synthetic Eddy Method |

TSR | Tip Speed Ratio |

## References

- EnFAIT. Enabling Future Arrays in Tidal. Available online: https://www.enfait.eu/ (accessed on 14 June 2021).
- SIMEC Atlantis Energy. Tidal Stream Projects MeyGen. Available online: https://simecatlantis.com/projects/meygen/ (accessed on 14 June 2021).
- Karsten, R.; Swan, A.; Culina, J. Assessment of arrays of in-stream tidal turbines in the Bay of Fundy. Philos. Trans. R. Soc. A Math. Eng. Sci.
**2013**, 371. [Google Scholar] [CrossRef] [Green Version] - Divett, T.; Vennell, R.; Stevens, C. Optimization of multiple turbine arrays in a channel with tidally reversing flow by numerical modelling with adaptive mesh. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci.
**2013**, 371. [Google Scholar] [CrossRef] - Gerris Flow Solver. Available online: http://gfs.sourceforge.net/wiki/index.php/Main_Page (accessed on 14 June 2021).
- Churchfield, M.J.; Li, Y.; Moriarty, P.J. A large-eddy simulation study of wake propagation and power production in an array of tidal-current turbines. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci.
**2013**, 371. [Google Scholar] [CrossRef] [Green Version] - Mycek, P.; Gaurier, B.; Germain, G.; Pinon, G.; Rivoalen, E. Experimental study of the turbulence intensity effects on marine current turbines behaviour. Part II: Two interacting turbines. Renew. Energy
**2014**, 68, 876–892. [Google Scholar] [CrossRef] [Green Version] - Mycek, P. Étude Numérique et Expérimentale du Comportement d’Hydroliennes. Ph.D. Thesis, Université du Havre, Le Havre, France, 2013. [Google Scholar]
- Pinon, G.; Mycek, P.; Germain, G.; Rivoalen, E. Numerical simulation of the wake of marine current turbines with a particle method. Renew. Energy
**2012**, 46, 111–126. [Google Scholar] [CrossRef] [Green Version] - Osalusi, E.; Side, J.; Harris, R. Structure of turbulent flow in EMEC’s tidal energy test site. Int. Commun. Heat Mass Transf.
**2009**, 36, 422–431. [Google Scholar] [CrossRef] - Osalusi, E.; Side, J.; Harris, R. Reynolds stress and turbulence estimates in bottom boundary layer of Fall of Warness. Int. Commun. Heat Mass Transf.
**2009**, 36, 412–421. [Google Scholar] [CrossRef] - Thomson, J.; Polagye, B.; Durgesh, V.; Richmond, M. Measurements of Turbulence at Two Tidal Energy Sites in Puget Sound, WA. IEEE J. Ocean. Eng.
**2012**, 37, 363–374. [Google Scholar] [CrossRef] - Milne, I.A.; Sharma, R.N.; Flay, R.G.J.; Bickerton, S. Characteristics of the turbulence in the flow at a tidal stream power site. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci.
**2013**, 371. [Google Scholar] [CrossRef] [PubMed] - McCaffrey, K.; Fox-Kemper, B.; Hamlington, P.E.; Thomson, J. Characterization of turbulence anisotropy, coherence, and intermittency at a prospective tidal energy site: Observational data analysis. Renew. Energy
**2015**, 76, 441–453. [Google Scholar] [CrossRef] [Green Version] - Thiébaut, M.; Filipot, J.F.; Maisondieu, C.; Damblans, G.; Duarte, R.; Droniou, E.; Chaplain, N.; Guillou, S. A comprehensive assessment of turbulence at a tidal-stream energy site influenced by wind-generated ocean waves. Energy
**2020**, 191, 116550. [Google Scholar] [CrossRef] - Sentchev, A.; Thiébaut, M.; Guillou, S. Turbulence characterization at tidal-stream energy site in Alderney Race. In Developments in Renewable Energies Offshore; Soares, C.G., Ed.; CRC Press: Boca Raton, FL, USA, 2020. [Google Scholar] [CrossRef]
- Mercier, P.; Thiébaut, M.; Guillou, S.; Maisondieu, C.; Poizot, E.; Pieterse, A.; Thiébot, J.; Filipot, J.F.; Grondeau, M. Turbulence measurements: An assessment of Acoustic Doppler Current Profiler accuracy in rough environment. Ocean Eng.
**2021**, 226, 108819. [Google Scholar] [CrossRef] - Furgerot, L.; Sentchev, A.; Bailly du Bois, P.; Lopez, G.; Morillon, M.; Poizot, E.; Méar, Y.; Bennis, A.C. One year of measurements in Alderney Race: Preliminary results from database analysis. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci.
**2020**, 378. [Google Scholar] [CrossRef] [PubMed] - Sentchev, A.; Nguyen, T.D.; Furgerot, L.; Bailly du Bois, P. Underway velocity measurements in the Alderney Race: Towards a three-dimensional representation of tidal motions. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci.
**2020**, 378. [Google Scholar] [CrossRef] [PubMed] - Thiébaut, M.; Filipot, J.F.; Maisondieu, C.; Damblans, G.; Jochum, C.; Kilcher, L.F.; Guillou, S. Characterization of the vertical evolution of the three-dimensional turbulence for fatigue design of tidal turbines. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci.
**2020**, 378. [Google Scholar] [CrossRef] [PubMed] - Thiébaut, M.; Filipot, J.F.; Maisondieu, C.; Damblans, G.; Duarte, R.; Droniou, E.; Guillou, S. Assessing the turbulent kinetic energy budget in an energetic tidal flow from measurements of coupled ADCPs. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci.
**2020**, 378. [Google Scholar] [CrossRef] - Bourgoin, A.C.L.; Guillou, S.S.; Thiébot, J.; Ata, R. Turbulence characterization at a tidal energy site using large-eddy simulations: Case of the Alderney Race. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci.
**2020**, 378. [Google Scholar] [CrossRef] - Guillou, N.; Neill, S.P.; Thiébot, J. Spatio-temporal variability of tidal-stream energy in north-western Europe. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci.
**2020**, 378. [Google Scholar] [CrossRef] [PubMed] - Lopez, G.; Bennis, A.C.; Barbin, Y.; Sentchev, A.; Benoit, L.; Marié, L. Surface currents in the Alderney Race from high-frequency radar measurements and three-dimensional modelling. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci.
**2020**, 378. [Google Scholar] [CrossRef] - Bailly du Bois, P.; Dumas, F.; Morillon, M.; Furgerot, L.; Voiseux, C.; Poizot, E.; Méar, Y.; Bennis, A.C. The Alderney Race: General hydrodynamic and particular features. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci.
**2020**, 378. [Google Scholar] [CrossRef] - Jarrin, N.; Benhamadouche, S.; Laurence, D.; Prosser, R. A Synthetic-Eddy-Method for Generating Inflow Conditions for Large-Eddy Simulations. Int. J. Heat Fluid Flow
**2006**, 27, 585–593. [Google Scholar] [CrossRef] [Green Version] - Jonkman, B.J.; Kilcher, L. TurbSim User’s Guide: Version 1.06.00 (Draft Version); Technical Report; National Renewable Energy Laboratory: Golden, CO, USA, 2012.
- Bernard, P.; Viré, A.; Moureau, V.; Lartigue, G.; Beaudet, L.; Deglaire, P.; Bricteux, L. Large-Eddy Simulation of wind turbines wakes including geometrical effects. Comput. Fluids
**2018**, 173, 133–139. [Google Scholar] [CrossRef] - Ahmed, U.; Apsley, D.; Afgan, I.; Stallard, T.; Stansby, P. Fluctuating loads on a tidal turbine due to velocity shear and turbulence: Comparison of CFD with field data. Renew. Energy
**2017**, 112, 235–246. [Google Scholar] [CrossRef] [Green Version] - Mercier, P.; Grondeau, M.; Guillou, S.; Thiébot, J.; Poizot, E. Numerical study of the turbulent eddies generated by the seabed roughness. Case study at a tidal power site. Appl. Ocean Res.
**2020**, 97, 102082. [Google Scholar] [CrossRef] - Pinon, G.; Carlier, C.; Fur, A.; Gaurier, B.; Germain, G.; Rivoalen, E. Account of ambient turbulence for turbine wakes using a Synthetic-Eddy-Method. J. Phys. Conf. Ser.
**2017**, 854, 012016. [Google Scholar] [CrossRef] [Green Version] - Choma Bex, C.; Carlier, C.; Fur, A.; Pinon, G.; Germain, G.; Rivoalen, É. A stochastic method to account for the ambient turbulence in Lagrangian Vortex computations. Appl. Math. Model.
**2020**, 88, 38–54. [Google Scholar] [CrossRef] - Chatelain, P.; Backaert, S.; Winckelmans, G.; Kern, S. Large Eddy Simulation of Wind Turbine Wakes. Flow Turbul. Combust.
**2013**, 91, 587–605. [Google Scholar] [CrossRef] - Bossy, M.; Espina, J.; Moricel, J.; Paris, C.; Rousseau, A. Modeling the wind circulation around mills with a Lagrangian stochastic approach. SMAI J. Comput. Math.
**2016**, 2, 177–214. [Google Scholar] [CrossRef] [Green Version] - Mycek, P.; Pinon, G.; Lothodé, C.; Dezotti, A.; Carlier, C. Iterative solver approach for turbine interactions: Application to wind or marine current turbine farms. Appl. Math. Model.
**2017**, 41, 331–349. [Google Scholar] [CrossRef] [Green Version] - Autorité Environnementale. Projet Nepthyd. Technical report, Conseil Général de l’environement et du développement durable. Available online: http://www.cgedd.developpement-durable.gouv.fr/IMG/pdf/160406_-_Hydroliennes_Raz_Blanchard_-_Nepthyd_50_-_delibere_cle05849f.pdf (accessed on 9 March 2021).
- Rehbach, C. Calcul numérique d’écoulements tridimensionnels instationnaires avec nappes tourbillonaires. La Rech. Aérosp.
**1977**, 5, 289–298. [Google Scholar] - Lewis, R. Vortex Element Methods for Fluid Dynamic Analysis of Engineering Systems; Cambridge University Press: Cambridge, UK, 1991. [Google Scholar]
- Cottet, G.; Koumoutsakos, P. Vortex Methods: Theory and Practice; Cambridge University Press: Cambridge, UK, 2000. [Google Scholar]
- Degond, P.; Mas-Gallic, S. The weighted particle method for convection-diffusion equations. Part I: The case of an isotropic viscosity. Math. Comp.
**1989**, 53, 485–507. [Google Scholar] [CrossRef] - Choquin, J.; Huberson, S. Particles simulation of viscous flow. Comput. Fluids
**1989**, 17, 397–410. [Google Scholar] [CrossRef] - Sagaut, P. Large Eddy Simulation for Incompressible Flows: An Introduction; Scientific Computation; Springer: Berlin/Heidelberg, Germany, 2006. [Google Scholar]
- Mansour, N.; Ferziger, J.; Reynolds, W. Large-Eddy Simulation of a Turbulent Mixing Layer; Technical Report, Report TF-11; Thermosciences Div., Dept. of Mech. Eng., Stanford University: Stanford, CA, USA, 1978. [Google Scholar]
- Ogami, Y.; Akamatsu, T. Viscous flow simulation using the discrete vortex model—The diffusion velocity method. Comput. Fluids
**1991**, 19, 433–441. [Google Scholar] [CrossRef] - Mycek, P.; Pinon, G.; Germain, G.; Rivoalen, E. Formulation and analysis of a diffusion-velocity particle model for transport-dispersion equations. Comput. Appl. Math.
**2016**, 35, 447–473. [Google Scholar] [CrossRef] - Leonard, A. Vortex methods for flow simulation. J. Comput. Phys.
**1980**, 37, 289–335. [Google Scholar] [CrossRef] - Winckelmans, G.S.; Leonard, A. Contributions to Vortex Particle Methods for the Computation of Three-Dimensional Incompressible Unsteady Flows. J. Comput. Phys.
**1993**, 109, 247–273. [Google Scholar] [CrossRef] - Lindsay, K.; Krasny, R. A particle method and adaptive treecode for vortex sheet motion in three-dimensional flow. J. Comput. Phys.
**2001**, 172, 879–907. [Google Scholar] [CrossRef] [Green Version] - Pinon, G.; Bratec, H.; Huberson, S.; Pignot, G.; Rivoalen, E. Vortex method for simulation of a 3D round jet in a cross-stream. J. Turbul.
**2005**, 6, 1–25. [Google Scholar] [CrossRef] - Hauville, F.; Roux, Y. Réglage Dynamique d’une Voile par une Méthode d’Intéraction Fluide/Structure. 9èmes Journées de l’Hydrodynamique. 2003. Available online: http://website.ec-nantes.fr/actesjh/images/9JH/Annexe/16-04-05.pdf (accessed on 23 June 2021).
- Luersen, M.; Le Riche, R.; Lemosse, D.; Le Maître, O. A computationally efficient approach to swimming monofin optimization. Struct. Multidiscip. Optim.
**2006**, 31, 488–496. [Google Scholar] [CrossRef] - Carlier, C.; Pinon, G.; Gaurier, B.; Germain, G.; Rivoalen, E. Numerical and experimental study of elementary interactions in marine current turbines array. In Proceedings of the 11th European Wave and Tidal Energy Conference (EWTEC), Nantes, France, 6–11 September 2015. [Google Scholar]
- Lund, T.S.; Wu, X.; Squires, K.D. Generation of Turbulent Inflow Data for Spatially-Developing Boundary Layer Simulations. J. Comput. Phys.
**1998**, 140, 233–258. [Google Scholar] [CrossRef] [Green Version] - Jarrin, N. Synthetic Inflow Boundary Conditions for the Numerical Simulation of Turbulence. Ph.D. Thesis, University of Manchester, Manchester, UK, 2008. [Google Scholar]
- Mycek, P.; Gaurier, B.; Germain, G.; Pinon, G.; Rivoalen, E. Experimental study of the turbulence intensity effects on marine current turbines behaviour. Part I: One single turbine. Renew. Energy
**2014**, 66, 729–746. [Google Scholar] [CrossRef] [Green Version] - Choma Bex, C.; Pinon, G.; Slama, M.; Gaston, B.; Germain, G.; Rivoalen, E. Lagrangian Vortex computations of turbine wakes: Recent improvements using Poletto’s Synthetic Eddy Method (SEM) to account for ambient turbulence. J. Phys. Conf. Ser.
**2020**, 1618, 062028. [Google Scholar] [CrossRef] - Maganga, F.; Germain, G.; King, J.; Pinon, G.; Rivoalen, E. Experimental characterisation of flow effects on marine current turbine behaviour and on its wake properties. IET Renew. Power Gener.
**2010**, 4, 498–509. [Google Scholar] [CrossRef] [Green Version] - Harding, S.; Bryden, I. Directionality in prospective Northern UK tidal current energy deployment sites. Renew. Energy
**2012**, 44, 474–477. [Google Scholar] [CrossRef] - Frost, C.H.; Evans, P.S.; Harrold, M.J.; Mason-Jones, A.; O’Doherty, T.; O’Doherty, D.M. The impact of axial flow misalignment on a tidal turbine. Renew. Energy
**2017**, 113, 1333–1344. [Google Scholar] [CrossRef] - Maslov, N.; Charpentier, J.F.; Claramunt, C. A modelling approach for a cost-based evaluation of the energy produced by a marine energy farm. Int. J. Mar. Energy
**2015**, 9, 1–19. [Google Scholar] [CrossRef] [Green Version] - Guillou, N.; Neill, S.P.; Robins, P.E. Characterising the tidal stream power resource around France using a high-resolution harmonic database. Renew. Energy
**2018**, 123, 706–718. [Google Scholar] [CrossRef] [Green Version] - Baltazar, J.; Falcão de Campos, J.A.C. Hydrodynamic Analysis of a Horizontal Axis Marine Current Turbine With a Boundary Element Method. In Proceedings of the ASME 27th Conference on Offshore Mechanics and Arctic Engineering (OMAE), Estoril, Portugal, 15–20 June 2008; pp. 883–893. [Google Scholar] [CrossRef]
- Baltazar, J.; Falcão de Campos, J. An iteratively coupled solution of the cavitating flow on marine propellers using BEM. J. Hydrodyn. Ser. B
**2010**, 22, 838–843. [Google Scholar] [CrossRef] - Boujleben, A.; Ibrahimbegovic, A.; Lefrançois, E. An efficient computational model for fluid-structure interaction in application to large overall motion of wind turbine with flexible blades. Appl. Math. Model.
**2020**, 77, 392–407. [Google Scholar] [CrossRef] - Riziotis, V.A.; Voutsinas, S.G. Dynamic stall modelling on airfoils based on strong viscous–inviscid interaction coupling. Int. J. Numer. Methods Fluids
**2008**, 56, 185–208. [Google Scholar] [CrossRef] - Zanon, A.; Giannattasio, P.; Simão Ferreira, C. A vortex panel model for the simulation of the wake flow past a vertical axis wind turbine in dynamic stall. Wind Energy
**2013**, 16, 661–680. [Google Scholar] [CrossRef] - Salvatore, F.; Sarichloo, Z.; Calcagni, D. Marine Turbine Hydrodynamics by a Boundary Element Method with Viscous Flow Correction. J. Mar. Sci. Eng.
**2018**, 6, 53. [Google Scholar] [CrossRef] [Green Version] - Togneri, M.; Pinon, G.; Carlier, C.; Choma Bex, C.; Masters, I. Comparison of synthetic turbulence approaches for blade element momentum theory prediction of tidal turbine performance and loads. Renew. Energy
**2020**, 145, 408–418. [Google Scholar] [CrossRef]

**Figure 1.**Configuration of the NEPTHYD project: a four turbine precommercial farm developed by Engie in 2014 and supposed to be equipped with Alstom’s Oceade™ turbine. The image is reproduced and adapted from the report [36] of the Autorité Environnementale, an agency of the French Ministry of Energy and Environment.

**Figure 4.**Time-averaged wakes obtained for ${I}_{\infty}$ = 1.5%, TSR = 3.67, $\lambda =4.5$ m, $\sigma \left(\lambda \right)=0\%$ and ${R}_{f}$ = 1. (

**a**) with nacelle. (

**b**) without nacelle.

**Figure 5.**Comparison of the experimental velocity profiles with the numerical results obtained with and without nacelle, for ${I}_{\infty}$ = 1.5%, TSR = 3.67, $\lambda =4.5$ m, $\sigma \left(\lambda \right)=0\%$ and ${R}_{f}$ = 1.

**Figure 6.**Comparison of the experimental and numerical disc-averaged velocities (TSR = 3.67, $\lambda =4.5$ m, $\sigma \left(\lambda \right)=0\%$ and ${R}_{f}$ = 1). (

**a**) ${I}_{\infty}$ = 1.5%. (

**b**) ${I}_{\infty}$ = 15%.

**Figure 7.**Comparison of the numerical disc-averaged velocities obtained for three filling ratios ${R}_{f}$ and two turbulence intensities (TSR = 3.67, $\lambda =4.5$ m, $\sigma =0\%$). (

**a**) ${I}_{\infty}$ = 1.5%. (

**b**) ${I}_{\infty}$ = 15%.

**Figure 8.**Comparison of the numerical disc-averaged velocities obtained for three filling ratios ${R}_{f}$ and two standard deviations $\sigma \left(\lambda \right)$ (TSR = 3.67, $\lambda =4.5$ m, ${I}_{\infty}$ = 15%).

**Figure 9.**Comparison of the numerical disc-averaged velocities obtained for TSR = 4.1, ${I}_{\infty}$ = 10% and several $\lambda $. (

**a**) $\sigma \left(\lambda \right)=0\%$. (

**b**) $\sigma \left(\lambda \right)=75\%$.

**Figure 10.**Four tidal turbine array configurations: (

**a**) initial configuration (straight flow), (

**b**) configuration with a yawed flow, (

**c**) configuration with a yawed flow used for the simulation.

**Figure 12.**Time-averaged wakes obtained for two turbulence intensities and two integral length scales (TSR = 4.1, $\sigma \left(\lambda \right)=75\%$).

**Figure 13.**Time-averaged wake lines obtained for two turbulence intensities and two integral length scales (TSR = 4.1, $\sigma \left(\lambda \right)=75\%$). For each turbine, the corresponding line passes through its centre. The solid grey line depicts the incoming velocity ${U}_{\infty}=3.2$ m/s.

**Figure 14.**Time-averaged wakes obtained for several yaw angles (${I}_{\infty}=10\%$, $L=18$ m, $Rf\approx 229$, TSR = 4.1, $\sigma \left(\lambda \right)=75\%$).

**Figure 15.**Time-averaged wake lines obtained for four yaw angles (${I}_{\infty}=10\%$, $L=18$ m, $Rf\approx 229$, TSR = 4.1, $\sigma \left(\lambda \right)=75\%$). For each turbine, the corresponding line passes through its centre. The solid grey line depicts the incoming velocity ${U}_{\infty}=3.2$ m/s.

**Figure 16.**Velocity u measured by six numerical probes, for four yaw angles (${I}_{\infty}=10\%$, $L=18$ m, $Rf\approx 229$, TSR = 4.1, $\sigma \left(\lambda \right)=75\%$).

**Figure 17.**Time average and standard deviation of the velocity u (${I}_{\infty}=10\%$, $L=18$ m, $Rf\approx 229$, TSR = 4.1, $\sigma \left(\lambda \right)=75\%$). (

**a**) Time average of the velocity; (

**b**) Standard deviation of the velocity.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Slama, M.; Choma Bex, C.; Pinon, G.; Togneri, M.; Evans, I.
Lagrangian Vortex Computations of a Four Tidal Turbine Array: An Example Based on the NEPTHYD Layout in the Alderney Race. *Energies* **2021**, *14*, 3826.
https://doi.org/10.3390/en14133826

**AMA Style**

Slama M, Choma Bex C, Pinon G, Togneri M, Evans I.
Lagrangian Vortex Computations of a Four Tidal Turbine Array: An Example Based on the NEPTHYD Layout in the Alderney Race. *Energies*. 2021; 14(13):3826.
https://doi.org/10.3390/en14133826

**Chicago/Turabian Style**

Slama, Myriam, Camille Choma Bex, Grégory Pinon, Michael Togneri, and Iestyn Evans.
2021. "Lagrangian Vortex Computations of a Four Tidal Turbine Array: An Example Based on the NEPTHYD Layout in the Alderney Race" *Energies* 14, no. 13: 3826.
https://doi.org/10.3390/en14133826