8th GRACM International Congress on Computational Mechanics Volos, 12 July – 15 July 2015

NUMERICAL SIMULATION OF FLUID-STRUCTURE INTERACTION BETWEEN SEA WAVES AND A SPAR-BUOY WIND TURBINE PLATFORM

Giorgos K. Makrygiannis1 and Athanassios A. Dimas

1

1Department of Civil Engineering University of Patras

Patras, GR-26500, Greece e-mail: adimas@upatras.gr

Keywords: floating wind turbine, spar-buoy platform, fluid-structure interaction, VOF, RANS equations.

Abstract. The objective of this study was the investigation of the fluid-structure interaction (FSI) due to the motion of a floating wind turbine under wave loading. In general, a floating wind turbine undergoes translational (surge, sway, heave) and rotational (pitch, roll, yaw) motions in space with respect to all three axes (x, y, z). In this study, the spar-buoy concept was chosen to support the wind turbine on the floating platform, and its heave and pitching motions were examined. The methodology is based on the numerical solution of the U-RANS equations under the ANSYS FLUENT software. The incident waves were approximated with the third order Stokes wave theory. The free surface is tracked using the volume of fluid (VOF) method, while turbulence was closed with the shear-stress transport (SST-kω) turbulence model. At every timestep, remeshing was achieved whenever certain criteria of mesh quality were exceeded due to the wind turbine platform motion. We studied the behavior of the wind turbine platform in three different wave conditions: (i) wave height H = 2 m and wave period T = 6 s, (ii) wave height H = 5.42 m and wave period T = 7.55 s and (iii) wave height H = 8.23 m and wave period T = 7.55 s. The last loading case corresponds to an extreme wave condition in the Aegean Sea with a return period of fifty (50) years. In each case, the results include the corresponding velocity, pressure and vorticity fields with emphasis on their effect on the operation of the wind turbine. 1 INTRODUCTION

Renewable energy sources such as the wind could be the key-factor in our efforts to generate “clear” energy due to the fact that they occur naturally and they are non-polluting and inexhaustible. There are different approaches in the construction of marine wind turbines and thus there are floating or stationary structures. Moreover, for the offshore wind turbines there are several floating support platforms configurations such as the spar-buoy concept or the tension leg platform. These configurations differ from each other in the way of achieving the desired stability for the structure.

In present study we considered the spar-buoy concept in order to support the floating wind turbine and we examined its behaviour in the translational motion (heave) along the vertical z-axis, as well as in the rotational motion (pitch) about the lateral y-axis. The diameter of the spar-buoy is 6 m and its draft is 70 m. Moreover, the construction weights 1975.64 tn, while the moments of inertia are Ixx = Iyy = 5.3·109 Kg·m2 and Izz = 8.9·106 Kg·m2. The methodology which was followed is based on the numerical solution of the U – RANS equations with the aid of the ANSYS FLUENT software. We studied the behaviour of the wind turbine platform in three different wave conditions: (i) wave height of H = 2 m and wave period of T = 6 s, (ii) wave height of H = 5.42 m and wave period of T = 7.55 s and (iii) wave height of H = 8.23 m and wave period of T = 7.55 s. The last loading case corresponds to an extreme wave condition in the Aegean Sea with a return period of fifty (50) years. The incoming waves in our simulation were approximated using the third order Stokes wavy theory, while the free surface was tracked by the volume of fluid (VOF) method of the ANSYS FLUENT programme and turbulence was closed with the shear-stress transport (SST-kω) turbulence model. Additionally, in every timestep remeshing was achieved, whenever certain criteria of mesh quality were exceeded due to the wind turbine platform motion. 2 METHODOLOGY The method, which was followed in order to investigate the fluid-structure interaction (FSI) due to the motion of a floating wind turbine under wave loading, is based on the numerical simulation of the three dimensional equations U - RANS under the ANSYS FLUENT software. [2, 3] We used this specific methodology in order to determine with greater accuracy the forces that were developed on the floating platform

Giorgos K. Makrygiannis, Athanassios A. Dimas.

as well as the fields of velocity, pressure and vorticity in comparison with the results which would have been ensued if the Morison equation was solved.

From the available numerical methods in ANSYS FLUENT, we chose the pressure – based segregated algorithm since it is much more flexible from the alternative solving algorithm and demands a smaller computing memory. Furthermore, the discretization schemes we used for the convection terms and pressure were the Second Order Upwind and Body Force Weighted, respectively. The last discretization scheme was chosen on one hand due to the great forces which were developing on the body of the wind turbine and on the other hand due to the vorticity which would probably occurred in the flow. Given that this specific flow was unsteady, for the coupling of pressure and velocity we used the PISO algorithm. Moreover, we utilized the Volume of Fraction (VOF) method of ANSYS FLUENT software in order to track the free surface during simulation. Finally, we applied the dynamic mesh technique because of the relevant motion between the floating platform and the fluid. This technique and the equations that mark it are described below. 2.1 Dynamic mesh

In ANSYS FLUENT the dynamic mesh model is used in cases where there is relevant motion between a fluid and a solid body during simulation. This model can be applied for both single flows and multiphase flows whether fluids are intermixed or not. It can be applied not only in steady flows but also in unsteady flows. The feature of this type of volume mesh is that it can follow the motion made by a solid body whether this is a prescribed or it is an unprescribed motion. Prescribed motion is considered the motion in which the user has defined from the beginning the linear and angular velocities of the gravity center of the solid body for every temporal moment of the simulation. On the other hand in the unprescribed motion these values are estimated through the force balance in the solid body with the aid of a fluent solver, such as the six degree of freedom (6DOF) solver. The process of the volume mesh update is made at the beginning of each time step automatically by the programme itself, on the basis of the new position of the boundaries. If we are going to use the dynamic mesh model we must at first define a starting volume mesh (that is the control volume) and afterwards determine on one hand the zones which it will be applied and on the other hand the type of motion in these zones. Nevertheless, independently of the type of motion which is finally chosen, the programme demands that the definition of the motion to be made on a zone surface or in a cell zone. In ANSYS FLUENT this motion can be described by using either the characteristics of a boundary profile or a function adequately defined by the user which is called user – defined function (UDF) or the six degree of freedom (6DOF) solver which is provided by the programme itself. [1] In this study the last method of determination was chosen.

2.1.1 Conservation equations

In the dynamic mesh model the conservation equation for a general scalar, Φ, on an arbitrary control volume V, can be written as:

where

ρ: is the fluid density

: is the flow velocity vector

: is the mesh motion velocity vector

Γ: is the diffusion coefficient

: is the source term of Φ

In the above equation the symbolism is used to represent the boundary of the arbitrary control volume V. By using a first - order backward difference formula, we are able to express the time derivative term which is

comprised in the above equation as:

where n and n + 1 indicate the quantity of the current and the next simulation step, respectively. The control volume for the time step is calculated from the equation:

Giorgos K. Makrygiannis, Athanassios A. Dimas.

where dV/dt is the time derivative of the control volume V. In order to satisfy the conservation equation for the volume mesh (eqn (1)), the time derivative of the control

volume V should be equalled to:

where nf is the number of faces on the control volume and is the vector which is vertical on the face at j -

direction. The term for each control volume is calculated by the equation:

where is the volume swept out by the control volume face j during the time step Δt. 2.1.2 Theory of the six degree of freedom (6DOF) solver

This specific ANSYS FLUENT solver by using the forces and moments which are exerted on a body, calculates the values for the translational and angular motion of its gravity center.

For an inertia co - ordinate system the translational motion of the gravity center is given by the equation:

where is the acceleration of the body gravity center, m is the mass and is the force vector due to gravity. The angular motion of a body is determined by calculating its angular velocities. The programme uses the

local co - ordinates of the reference system and determines the angular acceleration through the equation:

where L is the inertia tensor, is the vector of the moments which act on the body and is the angular velocity vector of the body.

The moments, , of the inertia system are transformed in the local body’s co - ordinate system according to the equation:

The R term in the above equation represents the following transformation matrix:

where, generally, Cx = cos(x) and Sx = sin(x), whereas φ, θ and ψ are Euler angles representing the following angular motions:

Rotation about x - axis (roll).

Rotation about y - axis (pitch).

Rotation about z - axis (yaw). After determining the translational and angular accelerations through the process which was described

earlier, the programme goes on to calculate the requisite values of translational and angular velocities with numerical integration. 

Giorgos K. Makrygiannis, Athanassios A. Dimas.

3 SIMULATION CONDITIONS 3.1 Computational modelling of the floating support platform

The computational geometry mesh in this study was created using the ANSYS Meshing application of the ANSYS v.13 software. Initially, we defined the surfaces which represent a boundary in our geometry, such as the inlet and outlet of the domain, its walls, as well as the outer walls of the wind turbine; then we set the parameters concerning the creation of the computational mesh. First, we created the dense hexahedral mesh in the interface of the two fluids (air and water) and then the tetrahedral mesh in the body of the wind turbine as well as in the remaining domain occupied by the two fluids. The creation of the dense hexahedral mesh in the interface of the two fluids was done using the Inflation method of ANSYS Meshing application. The mesh that was finally created for the geometry of the specific problem is depicted in Figure 1.

Figure 1. Computational geometry mesh of the entire volume

Figure 2 shows some of the mesh aspects in the inlet and outlet of the domain, as well as a focus on the wind turbine’s body which is close to the free surface. It is also worth mentioning that before the desired numerical simulations are performed with the aid of the ANSYS FLUENT software, there was a check on the quality of the mesh created using the ANSYS Meshing application. This was made by calculating the parameter referred to cell skewness which must have a value of less than 0.98. For the mesh created in this study, the value of this parameter was 0.92.

Finally, it should be mentioned that the mesh which resulted through the above process consisted of 560,992 nodes and 1,997,038 elements and it was a hybrid one, since it consisted of tetrahedral and hexahedral elements.

Giorgos K. Makrygiannis, Athanassios A. Dimas.

Figure 2. (a) Domain inlet, (b) Domain outlet, (c) Zoom – in the body of the wind turbine close to the free surface

4 RESULTS - DISCUSSION

For each of the three different wave conditions examined, both in the translational and the rotational motion of the wind turbine, we obtained results for the total simulation time presenting the translation of the wind turbine during its heave motion and its rotation angle during the pitch motion, respectively. Additionally, in all simulations we created figures showing the velocity vectors and the streamlines that were developed around the body of the wind turbine. It should be noted that all figures were created while the body of the wind turbine was at the crest of the incoming wave so that the extracted results would relate to the most adverse flow conditions developed in each case.

The wind turbine behaviour during its rotational motion around the lateral y-axis for the three different wave conditions is shown in Figure 3. It should be noted that clockwise direction is considered as positive and counter – clockwise as negative. Consequently, a positive value in the rotation angle means a clockwise rotation of the wind turbine, while a negative value in the rotation angle means a counter-clockwise rotation of the wind turbine. In Figure 3 we can see that the maximum “negative” value of the turbine rotation angle was recorded during the first period of each wave for all three load conditions, while, correspondingly, the maximum “positive” value of the turbine rotation angle was recorded during the last period. The largest values of the wind turbine rotation angle were obtained for the largest wave height (H = 8.23 m) and it was 7o to the positive of the rotation axis and 4o to its negative, while the smaller values of the wind turbine rotation angle – 0.7o to the positive of the rotation axis and 0.6o to its negative – were recorded for the smaller wave height (H = 2 m) as expected. At the wave height of H = 5.42 m, it was observed that the recorded values for the clockwise and counter-clockwise rotation angles of the wind turbine were similar and equal to 4o to the positive of the rotation axis and 3o to its negative.

Giorgos K. Makrygiannis, Athanassios A. Dimas.

Figure 3. Rotational motion of the wind turbine as a function of time for (a) wave height of H = 2 m, (b) wave

height of H = 5.42 m and (c) wave height of HS = 8.23 m

Figure 4 shows the wind turbine behaviour during its translational motion along the vertical z-axis for the two wave conditions with the largest wave heights. It appears that in both cases the change in the wind turbine position during the total simulation time presented a certain periodicity, with a frequency that differed from the incoming wave frequency. It was also observed that for both H = 8.23 m and H = 5.42 m, the maximum translational movement of the wind turbine from its balance position was 2 m. Finally, it is worth mentioning the fact that, in both wave conditions, the maximum value of the translational movement was recorded at approximately the same instant of time, while the total behaviour of the wind turbine in general was similar for both load conditions. Therefore, the increase in wave height from 5.42 m to 8.23 m did not affect the translational motion along the vertical z-axis of the wind turbine as much as the rotational motion described above.

Figure 4. Translational motion of the wind turbine as a function of time for (a) wave height of H = 5.42 m and (b) wave height of HS = 8.23 m

Figures 5, 6 and 7 show the streamlines and the velocity vectors that were developed both in translational and rotational motion for the wave heights of H = 2 m, H = 5.42 m and H = 8.23 m, respectively. It is observed that no flow separation occurs even for H = 8.23 m. It is also observed that the heave motion causes more significant wave diffraction than the pitch motion.

Giorgos K. Makrygiannis, Athanassios A. Dimas.

Figure 5. Streamlines and velocity vectors for H = 2 m in pitch motion (a,b) and heave motion (c,d)

Figure 6. Streamlines and velocity vectors for H = 5.42 m in pitch motion (a,b) and heave motion (c,d)

Giorgos K. Makrygiannis, Athanassios A. Dimas.

Figure 7. Streamlines and velocity vectors for H = 8.23 m in pitch motion (a,b) and heave motion (c,d)

5 CONCLUSION

The coupled fluid-structure interaction of a spar-buoy wind turbine and incident waves were examined for typical wave conditions in the Aegean Sea. It was found that no flow separation occurs even for extreme wave conditions with a return period of 50 years since typical wind turbine diameters are larger or of the same order with wave heights. It was also found that the heave motion of the spar-buoy platform depends weakly on the wave characteristics. ACKNOWLEDGEMENT

This research has been co-financed by the European Union (European Social Fund - ESF) and Hellenic national funds through the Operational Program "Competitiveness and Entrepreneurship" of the National Strategic Reference Framework (NSRF 2007-2013) - Research Funding Program: Bilateral R&D Cooperation between Greece and China 2012-2014, under project SEAWIND with code 12CHN184. REFERENCES [1] ANSYS FLUENT Theory Guide, (2011), ANSYS, Inc., Southpointe, Canonsburg [2] Rammohan, RS. (2012), “Coupled fluid structure interaction analysis on a cylinder exposed to ocean wave

loading”, Chalmers University of Technology, Goteborg, Sweden. [3] Thanhtoan, T., Donghyun, K., Jinseop, S. (2014), “Computational fluid dynamics analysis of a floating

offshore wind turbine experiencing platform pitching motion”, Energies, Vol. 7, pp. 5011-5026.