# A Comparison of Numerical Modelling Techniques for Tidal Stream Turbine Analysis

^{*}

## Abstract

**:**

## 1. Introduction

## 2. BEMT

**Figure 1.**Blade geometries for the (

**top**) Liverpool, (

**middle**) IFREMER and (

**bottom**) Manchester turbines. Chord length (distance from the section leading edge to the trailing edge) is shown with solid lines and the twist angle with dashed lines (90° meaning the section is parallel to the rotor plane).

^{4}; for the NACA 63418 section, data were taken from standard tables [1] for moderate angles of attack with Re = 9 × 10

^{6}, with flat-plate theory used for extreme angles of attack; for the Göttingen foil, data were taken from a wind tunnel study [13] at Re = 3 × 10

^{4}. Data for the Göttingen foil are much less complete than those for the other sections; additionally, the section stalls very abruptly and at an unusually low angle of 8°. To ensure a fast runtime, the data are not smoothed, and linear interpolation is used to estimate lift and drag between data points. As a result of the sparse data and the interpolation, the BEMT results contain many small discontinuities, since in many cases, a relatively small change in inflow angle results in a large jump in the lift and drag properties of the foil. This is also noticeable in the BEMT work carried out at Manchester, as can be seen in the studies that report their experimental results [10].

_{L}decreased by 10% at all inflow angles), one with increased drag (i.e., C

_{D}increased by 50% at all inflow angles) and one with both lift and drag altered. These cases are intended as a simple representation of the degradation of section performance due to factors such as biofouling or surface pitting due to cavitation, and the magnitude of the changes are in line with those found in experimental investigations [14]. Note that an earlier numerical investigation by Batten et al. [15] treated drag in a similar fashion, but did not consider the effects of roughness on lift. These results are presented graphically in Figure 2, along with experimental data for the IFREMER and Manchester turbines.

**Figure 2.**Power (C

_{P}) and axial force (C

_{Fa}) coefficients for (top) Liverpool, (middle) IFREMER and (bottom) Manchester turbines. In all cases, the upper cluster of lines shows C

_{Fa}, and the lower shows C

_{P}. Black dashed lines show original turbine performance; red lines show the 90% C

_{L}case; blue lines show the 150% C

_{D}case; green lines show the combined lift decrease and drag increase case. Experimental results are also shown for the IFREMER and Manchester turbines (in grey), with data taken from [9,11], respectively. Note that for the range of TSR values investigated, both the Liverpool and Manchester turbines go beyond the freewheeling state (i.e., C

_{P}= 0); in a real turbine, this operating condition cannot be reached.

_{P}terms, the IFREMER rotor is more sensitive to lift/drag changes than the Liverpool rotor, although their C

_{Fa}sensitivities are very similar. The Manchester rotor C

_{P}drops more significantly with degradation of section performance, particularly when drag is increased. It should be remembered that the Manchester rotor was designed in order to replicate full-scale thrust characteristics, rather than power characteristics, and so, changes in its C

_{P}curve are likely to be atypical. It is clear from this table, and from Figure 1, that across all rotor geometries, C

_{P}is more affected by an increase in sectional drag, whereas sectional lift has a greater influence on C

_{Fa}.

_{P}that is altered by these changes in blade profile properties, but also the TSR at which this optimum is attained. An increase in sectional drag coefficient always results in a downwards shift of the optimum TSR, while a decrease in lift has different effects: for the Manchester rotor, the optimum TSR shifts slightly downwards, but for the IFREMER and Liverpool rotors, the shift is upward. A sophisticated control scheme, then, may be able to use sensitivity analyses, such as those presented here, to partially compensate for blade degradation by altering the TSR at which the turbine is operated.

**Table 1.**Changes to maximum power and thrust coefficients and optimum TSR for Liverpool, IFREMER and Manchester turbines in response to small changes in the lift and drag properties of blade sections.

Liverpool | IFREMER | Manchester | ||
---|---|---|---|---|

Max C_{P} | Original | 0.4431 | 0.4122 | 0.3350 |

C_{L} − 10% | 0.4377 (−1.22%) | 0.4035 (−2.12%) | 0.3119 (−6.88%) | |

C_{D} + 50% | 0.4287 (−3.26%) | 0.3848 (−6.66%) | 0.2157 (−35.62%) | |

Both | 0.4213 (−4.92%) | 0.3736 (−9.37%) | 0.1866 (−44.3%) | |

Max C_{Fa} | Original | 0.8018 | 0.7531 | 0.9761 |

C_{L} − 10% | 0.7707 (−3.88%) | 0.7224 (−4.07%) | 0.9175 (−6.00%) | |

C_{D} + 50% | 0.8024 (+0.08%) | 0.7540 (+0.13%) | 0.9643 (−1.21%) | |

Both | 0.7714 (−3.79%) | 0.7234 (−3.95%) | 0.9185 (−5.90%) | |

Optimum TSR | Original | 3.64 | 4.52 | 4.64 |

C_{L} − 10% | 3.84 (+5.50%) | 4.62 (+2.21%) | 4.54 (−2.15%) | |

C_{D} + 50% | 3.52 (−3.30%) | 4.32 (−4.42%) | 4.10 (−11.64%) | |

Both | 3.70 (+1.65%) | 4.50 (−0.44%) | 4.40 (−5.17%) |

_{Fa}value would change by more than 1.4%, and no C

_{P}value by more than 2.2%. Overall, the agreement between BEMT predictions and experimental results allows us to be confident in our numerical model.

## 3. CFD and BEM-CFD

^{−1}or TSR 3.64, the design optimum rotational speed for the rotor in normal operation. Note that this is identical to the optimum TSR found in BEMT simulations of the Liverpool rotor (see Table 1). The zone that represents the rotation of the rotor is set to have a 17 m diameter and a 6 m width. The properties of the mesh for this model are discussed in detail in [6].

_{P}and C

_{Fa}for both models shows that the BEM-CFD method predicts a slightly higher C

_{P}value of 0.44 compared to 0.40 for the BRG-CFD, and the C

_{Fa}for the BEM-CFD and BRG-CFD is 0.81 and 0.83, respectively. The BRG-CFD results are published in [18] and also have good agreement with the BEMT results shown in the top panel of Figure 2. It should be borne in mind that for simplicity, this comparison is done in a uniform flow above a flat bed; in the real environment, non-uniform flows and sloped surfaces will influence the results [9,26]. Figure 4 shows the velocity deficit and the turbulent kinetic energy for each of the models.

**Figure 3.**Comparison of the velocity deficit in the rotor wake from BEM-CFD and blade-resolved geometry (BRG) models at a range of downstream locations.

**Figure 4.**Comparisons of the velocity deficit between BRG (

**top right**) and BEM-CFD (

**top left**) and between turbulent kinetic energy (TKE) for BRG (

**middle**) and BEM-CFD (

**bottom**) in the Cardiff 10-m rotor wake.

**Figure 5.**BEM-CFD model of IFREMER wake characteristics: axial velocity slice taken at the hub centre. Free stream velocity is 0.8 m·s

^{−1}; TSR is 3.67; and background turbulence intensity is set at 3%. The top panel shows the full wake to the end of the domain, while the bottom panel is staged to compare with Figure 9a from [9] and includes isolines at 0.5, 0.6 and 0.7 normalised axial velocity.

**Figure 6.**Comparison of IFREMER rotor results for C

_{P}(coefficient of power) between BEM-CFD and BEMT for a range of TSRs. Blockage corrected BEM-CFD results are included for reference.

**Figure 7.**Comparison of IFREMER rotor results for C

_{Fa}(coefficient of axial thrust) between BEM-CFD and BEMT for a range of TSRs. Blockage-corrected BEM-CFD results are included for reference.

## 4. Coastal Area Modelling

^{−1}velocity parallel to the shoreline and a still water level of zero (hence, a water depth of 30 m). The BEM-CFD model has a fixed lid at the zero water level, whereas the coastal area model has a free surface apart from the specified level at the boundary. In both models, bed resistance is set to zero.

_{D}is calculated as:

_{w}is the density of water, α is a correction factor that is equal to one in this study, C

_{D}is the drag co-efficient, A

_{e}is the effective area of the turbine and V is the velocity. A constant drag co-efficient was specified as 0.9, which was equivalent to the thrust coefficient reported from the BEM-CFD simulation results. This co-efficient varied between devices in the BEM-CFD results, and thus, the average value across the fence was used in the coastal area model. The drag force, calculated by Equation (1), is then used to implement a sink in the momentum equations using an extra source term. No additional turbulence is generated by the energy extraction process in the coastal area model. Conversely, the BEM-CFD mesh has sufficiently fine resolution to capture the turbulence generation [26]. Full details of the representation of the turbines in the BEM-CFD model are described in Section 3.

^{2}, such that a 10-m diameter rotor fits within one triangle. By contrast, the BEM-CFD model has 50,000 elements representing each rotor.

**Figure 8.**Meshes used in the headland case example: (

**a**) the coastal area model; (

**b**) the BEM-CFD model; and (

**c**) a close up of the BEM-CFD mesh showing the gradation to finer regions around the turbines.

**Figure 9.**Horizontal flow fields for the headland fence case: The images show velocity magnitude at hub height from: (

**a**) the BEM-CFD model; and (

**b**) the coastal area model. Flow is from left to right in the images.

**Figure 10.**Differences in horizontal flow for the headland fence case: the images show the difference in velocity magnitude at hub height for: (

**a**) the BEM-CFD model domain; and (

**b**) a close up around the six turbines. Negative values indicate that velocity magnitude is lower in the coastal area model and positive values that velocity magnitude is higher in the coastal area model. Black lines indicate the turbine locations in (

**b**).

^{−1}lower than the BEM-CFD results in the wake region. This is still a substantial difference given that the input boundary velocity is 3 m·s

^{−1}. It is uncertain how much of this difference is due to differences in the vortex affecting the wake structure: differences in wake velocities approach zero for the wakes of the two turbines located furthest from the headland at around 20 diameters downstream of the turbines. Given that the vortex is not identical in the two simulations, flows landward of the turbine array are dissimilar, which provides different lateral conditions and, hence, will affect wake recovery. Figure 11 shows that the difference at the downstream extent is unlikely to be due to the free surface given that the difference in water depth in this region of the domain is less than 2% of the total water depth.

**Figure 11.**A plot showing the difference in water level between the coastal area model and the BEM-CFD model (fixed lid at a 30-m water depth).

## 5. Conclusions

_{P}, the differences between the numerical model and empirical measurements are only 2.9% and 0.3%, respectively. This gives us confidence in our predictions regarding the effects of hydrofoil degradation on rotor performance, which we can briefly summarise by saying that rotor thrust is more sensitive to decreases in sectional lift and rotor power more sensitive to increases in sectional drag. The BEM-CFD has been shown to capture the wake dynamics well, both in comparison to experimental results (Figure 5, bottom panel) and to BRG-CFD (Figure 3 and Figure 4). In addition, the direct comparison of the BEMT and BEM-CFD models is reasonably satisfactory, with predictions of peak C

_{P}differing by only 5.4%.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Abbott, I.H.; von Doenhoff, A.E. Theory of Wing Sections, Including a Summary of Airfoil Data; Dover Publications Inc.: New York, NY, USA, 1959. [Google Scholar]
- Glauert, H. Airplane Propellers. In Aerodynamic Theory; Durand, W.F., Ed.; California Institute of Technology: Pasedena, LA, USA, 1934. [Google Scholar]
- Burton, T.; Sharpe, D.; Jenkins, N.; Bossanyi, E. Wind Energy Handbook; John Wiley & Sons, Ltd.: New York, NY, USA, 2001. [Google Scholar]
- Masters, I.; Chapman, J.C.; Orme, J.A.C.; Willis, M.R. A robust blade element momentum theory model for tidal stream turbines including tip and hub loss corrections. Proc. Inst. Mar. Eng. Sci. Tech. Part A
**2011**, 10, 25–35. [Google Scholar] - Chapman, J.C.; Masters, I.; Togneri, M.; Orme, J.A.C. The Buhl correction factor applied to high induction conditions for tidal stream turbines. Renew. Energy
**2013**, 60, 472–480. [Google Scholar] [CrossRef] - Mason-Jones, A. Performance assessment of a horizontal axis tidal turbine in a high velocity shear environment. Ph.D. Thesis, Cardiff University, Cardiff, UK, 2010. [Google Scholar]
- Tedds, S.C.; Owen, I.; Poole, R.J. Near-wake characteristics of a model horizontal axis tidal stream turbine. Renew. Energy
**2014**, 63, 222–235. [Google Scholar] [CrossRef] - Henriques, T.A.D.; Tedds, S.C.; Botsari, A.; Najafian, G.; Hedges, T.S.; Sutcliffe, C.J.; Owen, I.; Poole, R.J. The effects of wave-current interaction on the performance of a model horizontal axis tidal turbine. Int. J. Mar. Energy
**2014**, 8, 17–35. [Google Scholar] [CrossRef] - 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] - Fernandez-Rodriguez, E.; Stallard, T.J.; Stansby, P.K. Experimental study of extreme thrust on a tidal stream rotor due to turbulent flow and with opposing waves. J. Fluid. Struct.
**2014**, 51, 354–361. [Google Scholar] [CrossRef] - Stallard, T.; Feng, T.; Stansby, P.K. Experimental study of the mean wake of a tidal stream rotor in a shallow turbulent flow. J. Fluid. Struct.
**2015**, 54, 235–246. [Google Scholar] [CrossRef] - Togneri, M.; Masters, I.; Malki, R.; Rio, A. Flume measurements of lift and drag for selected tidal turbine blade sections. Int. J. Mar. Energy
**2015**. submitted for publication. [Google Scholar] - Hassan, U. A Wind Tunnel Investigation of the Wake Structure within Small Wind Turbine Farms; Technical Report ETSU WN 5113; Energy Technology Support Unit: London, UK, 1993. [Google Scholar]
- Walker, J.M.; Flack, K.A.; Lust, E.E.; Schultz, M.P.; Luznik, L. Experimental and numerical studies of blade roughness and fouling on marine current turbine performance. Renew. Energy
**2014**, 66, 257–267. [Google Scholar] [CrossRef] - Batten, W.M.J.; Bahaj, A.S.; Molland, A.F.; Chaplin, J.R. The prediction of the hydrodynamic performance of marine current turbines. Renew. Energy
**2008**, 33, 1085–1096. [Google Scholar] [CrossRef] - Afgan, I.; McNaughton, J.; Rolfo, S.; Apsley, D.D.; Stallard, T.; Stansby, P. Turbulent flow and loading on a tidal stream turbine by LES and RANS. Int. J. Heat Fluid Flow
**2013**, 43, 96–108. [Google Scholar] [CrossRef] - O’Doherty, D.; Mason-Jones, A.; Morris, C.; O’Doherty, T.O.; Byrne, C.; Prickett, P.; Grosvenor, R. Interaction of marine turbines in close proximity. In Proceedings of the 9th European Wave and Tidal Energy Conference, Southampton, UK, 5–9 September 2011.
- Mason-Jones, A.; O’Doherty, D.; Morris, C.E.; O’Doherty, T.; Byrne, C.; Prickett, P.W.; Grosvenor, R.I.; Owen, I.; Tedds, S.; Poole, R.J. Non-dimensional scaling of tidal stream turbines. Energy
**2012**, 44, 820–829. [Google Scholar] [CrossRef] - Willis, M.; Masters, I.; Thomas, S.; Glalie, R.; Loman, J.; Cook, A.; Ahmadian, R.; Falconer, R.; Lin, B.; Gao, G.; et al. Tidal turbine deployment in the Bristol Channel: A case study. Proc. ICE Energy
**2010**, 163, 93–105. [Google Scholar] [CrossRef] - Harrison, M.E.; Batten, W.M.J.; Bahaj, A.S. A blade element actuator disc approach applied to tidal stream turbines. In Proceedings of the OCEANS 2010, Seattle, WA, USA, 20–23 September 2010.
- Malki, R.; Williams, A.J.; Croft, T.N.; Togneri, M.; Masters, I. A coupled blade element momentum-computational fluid dynamics model for evaluating tidal stream turbine performance. Appl. Math. Model.
**2013**, 37, 3006–3020. [Google Scholar] [CrossRef] - Williams, A.J.; Croft, T.N.; Masters, I.; Bennet, C.R.; Patterson, S.G.; Willis, M.R. A combined BEM-CFD model for tidal stream turbine. In Proceedings of the 3rd International Conference on Ocean Energy, Bilbao, Spain, 6–8 October 2010.
- McCombes, T.R. An Unsteady Hydrodynamic Model for Tidal Current Turbines. Ph.D. Thesis, Univeristy of Strathclyde, Glasgow, UK, 2013. [Google Scholar]
- Malki, R.; Masters, I.; Williams, A.J.; Croft, T.N. Planning tidal stream turbine array layouts using a coupled blade element momentum—Computational fluid dynamics model. Renew. Energy
**2014**, 63, 46–54. [Google Scholar] [CrossRef] - Edmunds, M.; Malki, R.; Williams, A.J.; Masters, I.; Croft, T.N. Aspects of tidal stream turbine modelling in the natural environment using a coupled BEM-CFD model. Int. J. Mar. Energy
**2014**, 7, 20–42. [Google Scholar] [CrossRef] - Masters, I.; Malki, R.; Williams, A.J.; Croft, T.N. The influence of flow acceleration on tidal stream turbine wake dynamics: A numerical study using a coupled BEM-CFD model. Appl. Math. Model.
**2013**, 37, 7905–7918. [Google Scholar] [CrossRef] - Neill, S.P.; Hashemi, M.R.; Lewis, M.J. The role of tidal asymmetry in characterizing the tidal energy resource of Orkney. Renew. Energy
**2014**, 68, 337–350. [Google Scholar] [CrossRef] - Lewis, M.; Neill, S.P.; Robins, P.E.; Hashemi, M.R. Resource assessment for future generations of tidal-stream energy arrays. Energy
**2015**, 83, 403–415. [Google Scholar] [CrossRef] - Fairley, I.; Evans, P.; Wooldridge, C.; Willis, M.; Masters, I. Evaluation of tidal stream resource in a potential array area via direct measurements. Renew. Energy
**2013**, 57, 70–78. [Google Scholar] [CrossRef] - Ahmadian, R.; Falconer, R.; Bockelmann-Evans, B. Far-field modeling of the hydro-environmental impact of tidal stream turbines. Renew. Energy
**2012**, 28, 107–116. [Google Scholar] [CrossRef] - Ahmadian, R.; Falconer, R.A. Assessment of array shape of tidal stream turbines on hydro-environmental impacts and power output. Renew. Energy
**2012**, 44, 318–327. [Google Scholar] [CrossRef] - Chatzirodou, A.C.; Karunarathna, H. Impacts of tidal energy extraction on sea bed morphology. In Proceedings of the 34th International Conference on Coastal Engineering, Seoul, Korea, 15–20 June 2014.
- Neill, S.P.; Jordan, J.R.; Couch, S.J. Impact of tidal energy converter (TEC) arrays on the dynamics of headland sand banks. Renew. Energy
**2012**, 37, 387–397. [Google Scholar] [CrossRef] - Robins, P.E.; Neill, S.P.; Lewis, M.J. Impact of tidal-stream arrays in relation to the natural variability of sedimentary processes. Renew. Energy
**2014**, 72, 311–321. [Google Scholar] [CrossRef] - Fairley, I.; Masters, I.; Karunarathna, H. The cumulative impact of tidal stream turbine arrays on sediment transport in the Pentland Firth. Renew. Energy
**2015**, 80, 755–769. [Google Scholar] [CrossRef] - Wolf, J.; Prandle, D. Some observations of wave-current interaction. Coast. Eng.
**1999**, 37, 471–485. [Google Scholar] [CrossRef] - Hashemi, M.R.; Neill, S.P.; Robins, P.E.; Davies, A.G.; Lewis, M.J. Effect of waves on the tidal energy resource at a planned tidal stream array. Renew. Energy
**2015**, 75, 626–639. [Google Scholar] [CrossRef] - Fairley, I.; Ahmadian, R.; Falconer, R.A.; Willis, M.R.; Masters, I. The effects of a Severn Barrage on wave conditions in the Bristol Channel. Renew. Energy
**2014**, 68, 428–442. [Google Scholar] [CrossRef] - Lewis, M.J.; Neill, S.P.; Hashemi, M.R.; Reza, M. Realistic wave conditions and their influence on quantifying the tidal stream energy resource. Appl. Energy
**2014**, 136, 495–508. [Google Scholar] [CrossRef] - Kadiri, M.; Hashemi, M.R.; Bockelmann-Evans, B.; Rauen, W.; Falconer, R. A review of the potential water quality impacts of tidal renewable energy systems. Renew. Sustain. Energy Rev.
**2012**, 16, 329–341. [Google Scholar] [CrossRef] - Neill, S.P.; Hashemi, M.R.; Lewis, M.J. Optimal phasing of the European tidal stream resource using the greedy algorithm with penalty function. Energy
**2014**, 73, 997–1006. [Google Scholar] [CrossRef] - Martin-Short, R.; Hill, J.; Kramer, S.C.; Avdis, A.; Allison, P.A.; Piggott, M.D. Tidal resource extraction in the Pentland Firth, UK: Potential impacts on flow regime and sediment transport in the Inner Sound of Stroma. Renew. Energy
**2015**, 76, 596–607. [Google Scholar] [CrossRef] - Vogel, C.R.; Willden, R.H.J.; Houlsby, G.T. A correction for depth-averaged simulations of tidal turbine arrays. In Proceedings of the 10th European Wave and Tidal Energy Conference (EWTEC), Aalborg, Denmark, 2–5 September 2013.
- Takafumi, N.; Willden, R.H.J. The efficiency of an array of tidal turbines partially blocking a wide channel. J. Fluid Mech.
**2012**, 708, 596–606. [Google Scholar] - Baston, S.; Waldman, S.; Side, J. Modelling Energy Extraction in Tidal Flows. MASTS Position Paper. Available online: http://www.masts.ac.uk/media/126430/140828_position_paper_tidal_energy_extraction_rev2.1.pdf (accessed on 15 May 2015).
- Roc, T.; Conley, D.; Greaves, D. Methodology of tidal turbine representation in ocean circulation model. Renew. Energy
**2013**, 51, 448–464. [Google Scholar] [CrossRef] - Draper, S.; Stallard, T.; Stansby, P.; Way, S.; Adcock, T. Laboratory scale experiments and preliminary modelling to investigate basin scale tidal stream energy extraction. In Proceedings of the 10th European Wave and Tidal Energy Conference (EWTEC), Aalborg, Denmark, 2–5 September 2013.
- MIKE 21 and MIKE 3 Flow Model FM—Hydrodynamic and Transport Module—Scientific Documentation; Danish Hydraulic Insitute: Hørsholm, Denmark, 2012.
- Draper, S.; Borthwick, A.; Houlsby, G. Energy potential of a tidal fence deployed near a coastal headland. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci.
**2013**, 371. [Google Scholar] [CrossRef] [PubMed] - Kramer, S.; Piggott, M.D.; Hill, J.; Kregting, L.; Pritchard, D.; Elsaesser, B. The modelling of tidal turbine farms using multi-scale, unstructured mesh models. In Proceedings of the 2nd International Conference on Environmental Interactions of Marine Renewable Energy Technologies, Stornoway, UK, 28 April–2 May 2014.

© 2015 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 license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Masters, I.; Williams, A.; Croft, T.N.; Togneri, M.; Edmunds, M.; Zangiabadi, E.; Fairley, I.; Karunarathna, H.
A Comparison of Numerical Modelling Techniques for Tidal Stream Turbine Analysis. *Energies* **2015**, *8*, 7833-7853.
https://doi.org/10.3390/en8087833

**AMA Style**

Masters I, Williams A, Croft TN, Togneri M, Edmunds M, Zangiabadi E, Fairley I, Karunarathna H.
A Comparison of Numerical Modelling Techniques for Tidal Stream Turbine Analysis. *Energies*. 2015; 8(8):7833-7853.
https://doi.org/10.3390/en8087833

**Chicago/Turabian Style**

Masters, Ian, Alison Williams, T. Nick Croft, Michael Togneri, Matt Edmunds, Enayatollah Zangiabadi, Iain Fairley, and Harshinie Karunarathna.
2015. "A Comparison of Numerical Modelling Techniques for Tidal Stream Turbine Analysis" *Energies* 8, no. 8: 7833-7853.
https://doi.org/10.3390/en8087833