# Coupled Fluid-Structure Interaction Modelling of Loads Variation and Fatigue Life of a Full-Scale Tidal Turbine under the Effect of Velocity Profile

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Simulation Conditions and Load Parameters

^{3}), and that the flow was free of cavitation. Therefore, the effects of cavitation are also not considered in the simulations. The turbine is simulated at the peak power condition of Tip Speed Ratio (TSR) 4.87 corresponding to the turbine rotational rate of 0.7 rad/s. This operational condition is selected because the largest bending moments occur when the turbine operates near peak power [32]. For the uniform velocity case, mean free stream velocity is set at 1.5 m/s, with a turbulence intensity of 5% and viscosity ratio of 10. For the velocity profile case, it is assumed that the velocity profile follows the 1/7th power law. While velocity profiles vary considerably from site to site depending on the local bathymetric conditions, these velocity profiles can typically be approximated using power laws. The 1/7th and 1/10th power laws have been used to estimate the velocity profiles for EPRI North American tidal in stream power feasibility demonstration project [40] and other previous research works [14,38]. The flow is assumed to only vary along the depth, and stays uniform across the width of the domain. The velocity profile is estimated using a simple 1/7th power law equation (${V}_{y}={V}_{0}\times {\left({y}_{i}/{y}_{D}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$7$}\right.}$). Here, ${V}_{0}$ is the velocity at the surface of fluid domain, ${y}_{i}$ is the depth at position $i$ and ${y}_{D}$ is the total domain depth. To enable direct comparison with the uniform velocity case, the velocity is distributed such that velocity at the hub height is 1.5 m/s. The mean velocity above the hub height is therefore greater than this value, while the velocity below the hub is smaller. The average velocity across the turbine swept area is 1.496 m/s, and the turbine rotational velocity is calculated using this velocity for an estimate of the optimum TSR. A plot of the mean velocity profile used at the inlet condition in this paper is provided in Figure 1. This velocity profile changes once the flow passes the turbine. The velocity profile at different downstream locations can be clearly visualized in the results and discussion section of this paper.

_{∞}

_{P}= P/0.5ρAU

_{∞}

^{3}

_{T}= T/0.5ρAU

_{∞}

^{2}

_{BM}= Bending Moment/0.5ρAU

_{∞}

^{2}R

_{θ}= Torque/0.5ρAU

_{∞}

^{2}R

_{P}is the power coefficient, C

_{T}is the thrust coefficient, C

_{BM}is the bending moment coefficient of the turbine, U

_{∞}(m/s) represent the free stream velocity, ω (rad/s) the angular speed of the rotor (assumed constant for the simulations conducted in this paper), R (m) the radius of the rotor, A (m

^{2}) the swept area of the rotor, P (watts) the total power available in the flow stream, T (N) is the stream-wise (thrust) force on the rotor, and Bending Moment (Nm) is the flap-wise bending moments caused by the moment of thrust force and acts along the chord line.

## 3. Computational Method

#### 3.1. Computational Fluid Dynamics Model

#### 3.2. Coupled Fluid Structure Interaction Model

#### 3.3. Computational Mesh

^{6}elements (7.6 × 10

^{5}nodes). The stationary rectangular domain is meshed with an element size of 2900 mm except the surface of the monopile support tower that is meshed with an element size of 100 mm. The total mesh count for the rectangular domain is 1.4 × 10

^{6}elements (2.7 × 10

^{5}nodes). For the structural analysis system in the coupled FSI simulations, the turbine model is meshed with a patch confirming the tetrahedral method. The turbine blades are meshed with a body sizing of 60 mm, hub and nacelle 300 mm, and tower 200 mm. For blades, the mesh size function is set to the curvature to properly resolve the leading edge. The hub, nacelle and tower had a uniform size function. The FEA model has a total mesh count of 4.4 × 10

^{5}elements (7.1 × 10

^{5}nodes), of which 67% of the elements are at the turbine blades.

## 4. Verification and Validation of the Numerical Method

^{6}elements (Grid 3) is selected for further simulations. To establish the temporal accuracy of the fluid dynamic model a time step sensitivity study is performed by utilizing the transient CFD model described in Section 3.1 with selected Grid 3. Three simulations at time steps corresponding to 2°, 4° and 6° of turbine rotations and total time corresponding to three turbine rotations are conducted at the optimum TSR 4.87 and each simulation is initialized by the steady flow solution. The difference between the torque values with respect to the 2° case is 0.08% and 0.32% for the 4° and 6° case respectively. The value of predicted torque is found to be less sensitive to the size of the time step. This observation is similar to the findings in other similar studies [47,49] and supported by the fact that ANSYS CFX is an implicit solver and does not require very small Courant numbers for stability [42]. Thus, a time step corresponding to 6° of turbine rotation is selected to ensure computational efficiency is achieved without compromising the accuracy and stability of the numerical solution.

_{T}) are not available. However, all the numerical models predicted similar values of thrust coefficient $({C}_{T})$. The turbine diameter-based Reynold number $\left({R}_{eD}={U}_{\infty}\times D/\nu \right)$ for the utilized turbine design in this study is 3 × 10

^{7}, whereas the turbine in the experiment has a Reynold number of 5.2 × 10

^{5}. But still the performance coefficients of full-scale model matched well with the scaled model experimental data. This observation is consistent with the findings in Reference [9] and supports the fact that performance in terms of non-dimensional parameters is independent of Reynold number beyond a critical value. To ensure the proper execution of data transfer between the fluid and structural dynamic models, the expert parameter “DumpInterfaceMeshes” in the FSI model setup is set to the CFD post. A summary of the data transfer report displayed on the solver run window of the coupled simulation and contour plot of “DumpInterfaceMeshes” showed that 100% of node data were successfully transmitted between the solvers.

## 5. Results and Discussion

#### 5.1. Effect of Velocity Profile on Variation of Structural Loads

#### 5.2. Effect of Velocity Profile on Variation of Stresses and Implications to Fatigue Life

_{Min}/σ

_{Max}) of 0.97 and 0.90 is used for the uniform velocity and velocity profile case respectively. Fatigue S-N curves for materials are mostly generated from fully reversed constant amplitude experimental tests. For in service application such loading condition is very rare and mostly a mean stress will exist that must be accounted for in the fatigue analysis. In the stress life fatigue model of the ANSYS fatigue module the mean stress effect can be taken into account through direct interpolation between experimental S-N data. But such experimental data is usually not available due to the cost of experimental tests. Empirical relations like Goodman, Soderberg and Gerber theories can be used as an alternative to the experimental data. These empirical relations use the static material properties together with the S-N data to account for the mean stress effects. The experimental data generally lies between the Goodman and Gerber relation. For brittle materials, the Goodman relation is considered as a better choice whereas for the ductile materials the Gerber relation is often preferred. The turbine blades for the current study are made from structural steel and therefore a Gerber equation is selected. Equivalent (VonMises) stress was used as the stress component for the fatigue analysis to convert from a multiaxial stress state obtained from FE analysis to the uniaxial stress state of the experimental fatigue data.

## 6. Conclusions and Prospects

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Milne, I.A.; Sharma, R.N.; Flay, R.G.; Bickerton, S. Characteristics of the turbulence in the flow at a tidal stream power site. Philos. Trans. R. Soc. A
**2013**, 371, 20120196. [Google Scholar] [CrossRef] [PubMed] - Jones, J.; Davies, A. Influence of wave-current interaction, and high frequency forcing upon storm induced currents and elevations. Estuar. Coast. Shelf Sci.
**2001**, 53, 397–413. [Google Scholar] [CrossRef] - Zeiner-Gundersen, D.H. Turbine design and field development concepts for tidal, ocean, and river applications. Energy Sci. Eng.
**2015**, 3, 27–42. [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 Gen.
**2010**, 4, 498–509. [Google Scholar] [CrossRef] [Green Version] - Barltrop, N.; Varyani, K.; Grant, A.; Clelland, D.; Pham, X. Investigation into wave—Current interactions in marine current turbines. Proc. Inst. Mech. Eng. Part A J. Power Energy
**2007**, 221, 233–242. [Google Scholar] [CrossRef] - Luznik, L.; Flack, K.A.; Lust, E.E.; Taylor, K. The effect of surface waves on the performance characteristics of a model tidal turbine. Renew. Energy
**2013**, 58, 108–114. [Google Scholar] [CrossRef] - Blackmore, T.; Myers, L.E.; Bahaj, A.S. Effects of turbulence on tidal turbines: Implications to performance, blade loads, and condition monitoring. Int. J. Mar. Energy
**2016**, 14, 1–26. [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 I: One single turbine. Renew. Energy
**2014**, 66, 729–746. [Google Scholar] [CrossRef] [Green Version] - Mason-Jones, A.; O’doherty, D.; Morris, C.; O’doherty, T.; Byrne, C.; Prickett, P.; Grosvenor, R.; Owen, I.; Tedds, S.; Poole, R. Non-dimensional scaling of tidal stream turbines. Energy
**2012**, 44, 820–829. [Google Scholar] [CrossRef] - Draper, S.; Nishino, T.; Adcock, T.; Taylor, P. Performance of an ideal turbine in an inviscid shear flow. J. Fluid Mech.
**2016**, 796, 86–112. [Google Scholar] [CrossRef] [Green Version] - Batten, W.; Bahaj, A.; Molland, A.; Chaplin, J. The prediction of the hydrodynamic performance of marine current turbines. Renew. Energy
**2008**, 33, 1085–1096. [Google Scholar] [CrossRef] - Lewis, M.; Neill, S.; Robins, P.; Hashemi, M. Resource assessment for future generations of tidal-stream energy arrays. Energy
**2015**, 83, 403–415. [Google Scholar] [CrossRef] [Green Version] - Blunden, L.; Bahaj, A. Tidal energy resource assessment for tidal stream generators. Proc. Inst. Mech. Eng. Part A J. Power Energy
**2007**, 221, 137–146. [Google Scholar] [CrossRef] - Mason-Jones, A.; O’doherty, D.; Morris, C.; O’doherty, T. Influence of a velocity profile & support structure on tidal stream turbine performance. Renew. Energy
**2013**, 52, 23–30. [Google Scholar] - Tatum, S.; Allmark, M.; Frost, C.; O’Doherty, D.; Mason-Jones, A.; O’Doherty, T. CFD modelling of a tidal stream turbine subjected to profiled flow and surface gravity waves. Int. J. Mar. Energy
**2016**, 15, 156–174. [Google Scholar] [CrossRef] [Green Version] - Yahagi, K.; Takagi, K. Moment loads acting on a blade of an ocean current turbine in shear flow. Ocean Eng.
**2019**, 172, 446–455. [Google Scholar] [CrossRef] - Muchala, S.; Willden, R.H. Influence of support structures on tidal turbine power output. J. Fluids Struct.
**2018**, 83, 27–39. [Google Scholar] [CrossRef] - Li, H.; Hu, Z.; Chandrashekhara, K.; Du, X.; Mishra, R. Reliability-based fatigue life investigation for a medium-scale composite hydrokinetic turbine blade. Ocean Eng.
**2014**, 89, 230–242. [Google Scholar] [CrossRef] - McCann, G. Tidal current turbine fatigue loading sensitivity to waves and turbulence—A parametric study. In Proceedings of the 7th European Wave and Tidal Energy Conference, Porto, Portugal, 11–13 September 2007. [Google Scholar]
- Bahaj, A.; Molland, A.; Chaplin, J.; Batten, W. Power and thrust measurements of marine current turbines under various hydrodynamic flow conditions in a cavitation tunnel and a towing tank. Renew. Energy
**2007**, 32, 407–426. [Google Scholar] [CrossRef] - Stallard, T.J.; Feng, T.; Stansby, P.K. Experimental study of the mean wake of a tidal stream rotor in a shallow turbulent flow. J. Fluids Struct.
**2015**, 54, 235–246. [Google Scholar] [CrossRef] - Draycott, S.; Payne, G.; Steynor, J.; Nambiar, A.; Sellar, B.; Venugopal, V. An experimental investigation into non-linear wave loading on horizontal axis tidal turbines. J. Fluids Struct.
**2019**, 84, 199–217. [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. Fluids Struct.
**2014**, 51, 354–361. [Google Scholar] [CrossRef] - Gaurier, B.; Davies, P.; Deuff, A.; Germain, G. Flume tank characterization of marine current turbine blade behaviour under current and wave loading. Renew. Energy
**2013**, 59, 1–12. [Google Scholar] [CrossRef] [Green Version] - Milne, I.; Day, A.; Sharma, R.; Flay, R. Blade loading on tidal turbines for uniform unsteady flow. Renew. Energy
**2015**, 77, 338–350. [Google Scholar] [CrossRef] - Milne, I.; Day, A.; Sharma, R.; Flay, R. The characterisation of the hydrodynamic loads on tidal turbines due to turbulence. Renew. Sustain. Energy Rev.
**2016**, 56, 851–864. [Google Scholar] [CrossRef] - Payne, G.S.; Stallard, T.; Martinez, R.; Bruce, T. Variation of loads on a three-bladed horizontal axis tidal turbine with frequency and blade position. J. Fluids Struct.
**2018**, 83, 156–170. [Google Scholar] [CrossRef] - Xia, Y.; Takagi, K. Effect of shear flow on a marine current turbine. In Proceedings of the Oceans, Shanghai, China, 10–13 April 2016; pp. 1–5. [Google Scholar]
- Kang, S.; Borazjani, I.; Colby, J.A.; Sotiropoulos, F. Numerical simulation of 3D flow past a real-life marine hydrokinetic turbine. Adv. Water Resour.
**2012**, 39, 33–43. [Google Scholar] [CrossRef] - Tedds, S.; Owen, I.; Poole, R. Near-wake characteristics of a model horizontal axis tidal stream turbine. Renew. Energy
**2014**, 63, 222–235. [Google Scholar] [CrossRef] [Green Version] - Ahmed, U.; Apsley, D.; Afgan, I.; Stallard, T.J.; Stansby, P.K. 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] - Ouro, P.; Harrold, M.; Stoesser, T.; Bromley, P. Hydrodynamic loadings on a horizontal axis tidal turbine prototype. J. Fluids Struct.
**2017**, 71, 78–95. [Google Scholar] [CrossRef] [Green Version] - Ouro, P.; Stoesser, T. Impact of Environmental Turbulence on the Performance and Loadings of a Tidal Stream Turbine. Flow Turbul. Combust.
**2018**, 102, 613–639. [Google Scholar] [CrossRef] [Green Version] - Grogan, D.M.; Leen, S.B.; Kennedy, C.; Brádaigh, C.Ó. Design of composite tidal turbine blades. Renew. Energy
**2013**, 57, 151–162. [Google Scholar] [CrossRef] [Green Version] - Suzuki, T.; Mahfuz, H. Analysis of large-scale ocean current turbine blades using Fluid–Structure Interaction and blade element momentum theory. Ships Off Shore Struct.
**2018**, 13, 451–458. [Google Scholar] [CrossRef] - Nicholls-Lee, R.; Turnock, S.; Boyd, S. Application of bend-twist coupled blades for horizontal axis tidal turbines. Renew. Energy
**2013**, 50, 541–550. [Google Scholar] [CrossRef] - Tatum, S.; Frost, C.; Allmark, M.; O’Doherty, D.; Mason-Jones, A.; Prickett, P.; Grosvenor, R.; Byrne, C.; O’Doherty, T. Wave-current interaction effects on tidal stream turbine performance and loading characteristics. Int. J. Mar. Energy
**2016**, 14, 161–179. [Google Scholar] [CrossRef] - Badshah, M.; Badshah, S.; Kadir, K. Fluid Structure Interaction Modelling of Tidal Turbine Performance and Structural Loads in a Velocity Shear Environment. Energies
**2018**, 11, 1837. [Google Scholar] [CrossRef] - Craig, H.; Vincent, S.N.; Budi, G.; Michele, G.; Fotis, S.U.S. Department of energy reference model program RM1: Experimental results. Dynamic Pose test, 2 December 2014. [Google Scholar]
- Hagerman, G.; Polagye, B. Methodology for estimating tidal current energy resources and power production by tidal in-stream energy conversion (TISEC) devices, EPRI North American Tidal In Stream Power Feasibility Demonstration Project. EPRI-TP-001 NA Rev 2. 2006. Available online: http://www.pstidalenergy.org/Tidal_Energy_Projects/Misc/EPRI_Reports_and_Presentations/EPRI-TP-001_Guidlines_Est_Power_Production_14Jun06.pdf (accessed on 11 June 2019).
- ANSYS Inc. ANSYS CFX-Solver Modelling Guide; ANSYS, Inc.: Southpointe 2600 ANSYS Drive Canonsburg, PA, USA, 2016. [Google Scholar]
- ANSYS Inc. ANSYS CFX-Solver Theory Guide; ANSYS, Inc.: Southpointe 2600 ANSYS Drive Canonsburg, PA, USA, 2016. [Google Scholar]
- Badshah, M.; VanZwieten, J.; Badshah, S.; Jan, S. CFD study of blockage ratio and boundary proximity effects on the performance of a tidal turbine. IET Renew. Power Gen.
**2019**. [Google Scholar] [CrossRef] - Sufian, S.F.; Li, M.; O’Connor, B.A. 3D modelling of impacts from waves on tidal turbine wake characteristics and energy output. Renew. Energy
**2017**, 114, 308–322. [Google Scholar] [CrossRef] [Green Version] - Tian, W.; VanZwieten, J.H.; Pyakurel, P.; Li, Y. Influences of yaw angle and turbulence intensity on the performance of a 20 kW in-stream hydrokinetic turbine. Energy
**2016**, 111, 104–116. [Google Scholar] [CrossRef] [Green Version] - O’Doherty, T.; Mason-Jones, A.; O’Doherty, D.; Byrne, C.; Owen, I.; Wang, Y. Experimental and computational analysis of a model horizontal axis tidal turbine. In Proceedings of the 8th European Wave and Tidal Energy Conference (EWTEC), Uppsala, Sweden, 7–10 September 2009. [Google Scholar]
- Nitin, K.; Arindam, B. Performance characterization and placement of a marine hydrokinetic turbine in a tidal channel under boundary proximity and blockage effects. Appl. Energy
**2015**, 148, 121–133. [Google Scholar] [CrossRef] - Davide, M.; Andreas, U. 2014 JRC Ocean Energy Status Report; Publications Office of the European Union: Luxembourg, Luxembourg, 2015; Available online: https://setis.ec.europa.eu/sites/default/files/reports/2014-JRC-Ocean-Energy-Status-Report.pdf (accessed on 11 June 2019).
- Lawson, M.J.; Li, Y.; Sale, D.C. Development and verification of a computational fluid dynamics model of a horizontal-axis tidal current turbine. In Proceedings of the ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering, Rotterdam, The Netherlands, 19–24 June 2011; American Society of Mechanical Engineers: Rotterdam, The Netherlands, 2011; pp. 711–720. [Google Scholar]
- Zahle, F.; Sørensen, N. Overset grid flow simulation on a modern wind turbine. In Proceedings of the 26th AIAA Applied Aerodynamics Conference, Honolulu, HI, USA, 18–21 August 2008; p. 6727. [Google Scholar]
- Zahle, F.; Sørensen, N.N.; Johansen, J. Wind turbine rotor-tower interaction using an incompressible overset grid method. Wind Energy
**2009**, 12, 594–619. [Google Scholar] [CrossRef]

**Figure 10.**Axial velocity (normalized by the free stream velocity) contour for (

**a**) uniform inlet velocity; (

**b**) velocity profile.

**Figure 11.**Velocity variation along depth of the channel at different downstream location for (

**a**) uniform velocity; (

**b**) velocity profile (the red dash dotted line represent location of turbine hub center and the black dashed lines represent the extent of blade tips).

**Figure 12.**Velocity deficit along the length of the channel at different channel depths for (

**a**) uniform velocity; (

**b**) velocity profile.

Density | 7850 | Kg/m^{3} |
---|---|---|

Young Modulus | 2 × 10^{11} | Pa |

Poisson’s Ratio | 0.3 | (-) |

Tensile Yield Strength | 2.5 × 10^{8} | Pa |

Compressive Yield Strength | 2.5 × 10^{8} | Pa |

Tensile Ultimate Strength | 4.60 × 10^{8} | Pa |

Grid | No. of Elements (× 10^{6}) | Torque Difference ^{1} | ||
---|---|---|---|---|

Inner Domain | Outer Domain | Total | (%) | |

1 | 1.34 | 0.72 | 2.07 | −3.2 |

2 | 2.23 | 1.07 | 3.30 | −1.1 |

3 | 3.10 | 1.40 | 4.50 | −0.5 |

4 | 5.02 | 2.39 | 7.42 | - |

^{1}% Torque difference denotes the difference of predicted torque value from each grid with respect to Grid 4.

TSR | Experiment | Steady State CFD | Transient CFD | Coupled FSI | |||
---|---|---|---|---|---|---|---|

C_{P} [39] | C_{P} | % Difference ^{1} | C_{P} | % Difference ^{1} | C_{P} | % Difference ^{1} | |

3.02 | 0.320 | 0.347 | 8.5 | 0.354 | 10.7 | - | - |

3.79 | 0.408 | 0.406 | 0.4 | 0.411 | 0.8 | - | - |

4.87 | 0.477 | 0.449 | 5.8 | 0.447 | 6.3 | 0.447 | 6.2 |

5.76 | 0.471 | 0.440 | 6.6 | 0.442 | 6.2 | - | - |

6.82 | 0.414 | 0.401 | 3.2 | 0.402 | 2.8 | - | - |

7.57 | 0.368 | 0.369 | 0.4 | 0.368 | 0.1 | - | - |

8.32 | 0.295 | 0.322 | 9.2 | 0.319 | 8.2 | - | - |

9.05 | 0.230 | 0.260 | 13.0 | 0.254 | 10.4 | - | - |

^{1}% Difference indicates the absolute percentage difference to the experimental value in Reference [39].

Parameter | Value | Uniform Velocity | Velocity Shear | ||
---|---|---|---|---|---|

Single Blade | Rotor | Single Blade | Rotor | ||

Thrust Coefficient | Peak | 0.437 | 0.877 | 0.445 | 0.869 |

Mean | 0.433 | 0.872 | 0.429 | 0.864 | |

Range | 0.012 | 0.011 | 0.039 | 0.012 | |

% Variation ^{1} | 2.8 | 1.3 | 9.0 | 1.4 | |

Torque Coefficient | Peak | 0.046 | 0.093 | 0.048 | 0.092 |

Mean | 0.045 | 0.092 | 0.045 | 0.091 | |

Range | 0.002 | 0.002 | 0.009 | 0.002 | |

% Variation ^{1} | 5.2 | 2.3 | 19.3 | 2.7 | |

Flap Wise Bending Moment Coefficient | Peak | 1.013 | - | 1.078 | - |

Mean | 1.0 | - | 1.0 | - | |

Range | 0.049 | - | 0.185 | - | |

% Variation ^{1} | 4.9 | - | 18.5 | - |

^{1}% Variation indicates the variation from mean cycle value during a rotation.

Parameter | Value | Uniform Velocity | Velocity Profile |
---|---|---|---|

Deformation [mm] | Peak | 40.9 | 41.9 |

Mean | 40.6 | 40.2 | |

Range | 1.0 | 3.9 | |

% Variation ^{1} | 2.5 | 9.8 | |

Stress [MPa] | Peak | 118.1 | 121.1 |

Mean | 117.1 | 116.0 | |

Range | 3.2 | 12.0 | |

% Variation ^{1} | 2.8 | 10.3 |

^{1}% Variation denotes variation from cycle mean value during a rotation cycle.

© 2019 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Badshah, M.; Badshah, S.; VanZwieten, J.; Jan, S.; Amir, M.; Malik, S.A.
Coupled Fluid-Structure Interaction Modelling of Loads Variation and Fatigue Life of a Full-Scale Tidal Turbine under the Effect of Velocity Profile. *Energies* **2019**, *12*, 2217.
https://doi.org/10.3390/en12112217

**AMA Style**

Badshah M, Badshah S, VanZwieten J, Jan S, Amir M, Malik SA.
Coupled Fluid-Structure Interaction Modelling of Loads Variation and Fatigue Life of a Full-Scale Tidal Turbine under the Effect of Velocity Profile. *Energies*. 2019; 12(11):2217.
https://doi.org/10.3390/en12112217

**Chicago/Turabian Style**

Badshah, Mujahid, Saeed Badshah, James VanZwieten, Sakhi Jan, Muhammad Amir, and Suheel Abdullah Malik.
2019. "Coupled Fluid-Structure Interaction Modelling of Loads Variation and Fatigue Life of a Full-Scale Tidal Turbine under the Effect of Velocity Profile" *Energies* 12, no. 11: 2217.
https://doi.org/10.3390/en12112217