CONCLUSION

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the different way the two softwares treat the upper surface of the geometries studied, i.e. the surface at z = 0, the free water surface.

AQWA does not consider it since the geometries it uses are thin hollow surfaces obtained cutting solid bodies.

BEMUse, on the other hand, discretizes and creates panels on the top surface of each geometry, which then obviously are considered in the calculations. Subsequently, since the most significant contribution to the hydrodynamic parameters under investigation comes from near the free water surface, the difference between the two results surely depends on this.

For the same reason, as the mesh in AQWA is automatically generated and cannot be controlled by the user, the greater contribution near the body’s edges and the water surface cannot be adequately taken into account as it is impossible to increase the mesh refinement near these particularly important areas.

Finally, it can be noted how the plots generated by AQWA show in some cases the effects of a non-optimal removal of irregular frequencies. These sudden peaks are not to be seen in BEMUse, as its removal procedure is, like the one in WAMIT, much more efficient.

The comparison with Jonkman (2007) [32] is considered successful and of particular importance, as it validates BEMUse on a geometry with practical applications in the field of FOWTs, against a paper published by one of the leading experts at NREL, the National Renewable Energy Laboratory in the USA.

Summarizing, the validation of BEMUse as a reliable hydrodynamic analysis software can be considered successful, as the results compare quite nicely with both WAMIT and AQWA. This is just the first step though, as there is plenty of work to be done before the library can be successfully and confidently incorporated inside QBlade. In the next chapter, the future objectives to be achieved in the development of BEMUse are briefly illustrated.

6.3 F

The work of validation carried out in this thesis is just the first step in the development of a well-established and acknowledged hydrodynamic analysis model. However, the encouraging results of this study demonstrate the potential of BEMUse as an open-source, easy-to-use alternative to expensive softwares like AQWA and WAMIT.

Before being able to include it in QBlade, giving the users the possibility to simulate the behavior and the performance of FOWTs like they nowadays do with fixed-bottom turbines, BEMUse needs to undergo significant additional development. In this chapter, the next steps in its development are briefly assessed.

First, the issues faced during this work of validation need to be corrected. It’s fundamental to understand why the exciting force for the heave motion is always wrong, and especially where is the issue with the RAOs for the rotational motions. Until then, this whole work of validation cannot be considered completely successful.

For the moment, all the simulations are carried out in the infinite-depth configuration, which does not consider the effect of the seafloor on the velocity potential. This is because the

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depth case requires another form of the Green function, which is much more challenging to implement on a software.

Numerous researchers in recent years have faced this issue, and various solutions have been proposed. Liu, Iwashita, and Hu (2015) [33] suggests using different equations depending on the ratio between the characteristic length of the body to be studied and the water depth h. The four equations become progressively challenging to implement numerically as h increases, and the ratio consequently decreases.

Newman (1985) [15], on the other hand, proposes one single equation to be used, no matter how deep the water is. The problem is that for reasons of computational efficiency, he transforms the integral of the Green function in a sum, whose rate of convergence depends again on the ratio L/h. This series is practically useless for small values of L/h since each summand contains a logarithmic singularity when L/h tends to 0. Moreover, it’s been proven that the number of terms required in the sum for a given accuracy is proportional to h/L, which means that the computational cost of the calculation increases rapidly.

Chen (2018) [34] recently proposed a new and improved formulation of the sum computed by Newman, but the issues are not solved, and therefore, the computational cost is still very high.

Additionally, Chen proposed a sum formulation also for the derivative of the Green’s functions both in the horizontal direction and in the vertical one. When trying to implement Chen’s sums in BEMUse, the results were quite correct even though they didn’t converge to 0 when the wave angular frequency ω was 0.

For the moment, BEMUse only calculates first-order forces and moments. Once the previous two improvements will be completed, the second-order problem also needs to be implemented in the model. Second-order waves are generated from the quadratic interaction of two linear wave components in the discrete spectrum. The second-order problem is much more challenging to study and implement because of the increased complexity of the solving equations.

There are a lot of other features that need to be added in BEMUse before it could confidently be used in place of other hydrodynamic modeling softwares. This chapter only gave an idea of where the work at Hermann-Föttinger-Institut will focus in the near future to soon provide a reliable, efficient and free-to-use hydrodynamic analysis model.

Humanity cannot afford to wait anymore to change the energy sources on which to rely on, and my hope is that BEMUse will soon help with the research on FOWTs, which have the potential to become one of the leading technologies in the urgent transition to a fossil-free world.

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