Optimising the Geometry of a Breakwater Connected to Large Floating Structures

Abstract

The development of floating islands is an attractive option to provide living/working spaces at sea, as it would be a more economical solution for many locations at sea where the water depth is high. However, large second-order wave forces cause the floating island mooring system to become expensive as the wave height increases. So, in many locations with an intermediate water depth, land reclamation is still a more economical solution. A breakwater connected to the wave-ward side of the floating island can reduce the mean wave drift force of the entire structure by attenuating wave energy and thereby lowering the mooring costs. In this thesis, the optimal geometry of this breakwater is designed.

An optimisation is performed to find the ideal geometry of this breakwater such that it attenuates the maximum amount of wave energy while experiencing a low mean wave drift force. A parametric design of a breakwater is made, with six varying factors/parameters that define its shape, such that the geometry could range from a flat plate just below the water line, a large box-type breakwater at the water surface, a deeply submerged wedge-type breakwater, or anything in between. ComFLOW (a simulation method for free-surface flow) is used to determine the mean wave drift force and wave attenuation performance of all the breakwaters in the design space for two different regular wave conditions: Wave Condition 1 with a wave height of 3.0 metres and a peak period of 6.0 seconds, and Wave Condition 2 with a wave height of 9.0 metres and a peak period of 10.4 seconds. After all ComFLOW results are gathered, an optimisation method Design of Experiments is used to map the dependency of the six input factors that define the geometry, on the performance of the breakwaters, to come up with the geometry of the optimal breakwater.

To obtain the most accurate representation of reality in the numerical environment of ComFLOW, a validation of the programme is performed in two phases. Firstly, ComFLOW results are compared to analytical formulas, derived from linear wave theory. And secondly, ComFLOW dissipation characteristics are compared with the results of a physical experiment involving a regular wave plunging over a barred beach profile. From this followed, a minimum of twenty cells is required at the height of the structure to give reliable results of the mean wave drift forces on the structure. ComFLOW results for the wave transmission, wave reflection and forces on the structure followed the same trend as linear wave theory, with a converging offset. The wave energy dissipation characteristics of ComFLOW of all different grid sizes used in comparison with the experiment in which waves were plunging over a breaker bar, showed results that were in compliance with the experiment.

In Design Iteration 1, 94 different geometries were simulated in ComFLOW, of which 46 were completely submerged. Around 80\% of all submerged breakwaters experienced a mean wave drift force in the opposite direction of wave propagation. An explanation for this negative mean wave drift force is sought by the set-up and set-down of the water level, which occur around breaking waves. This results in a difference in hydrostatic pressure, and if the breakwater is positioned in between, it will experience a mean wave drift force in the opposite direction of wave propagation. The length of the sloping beach of the breakwater needs to be shorter than the wave length; otherwise, the set-up will be above the beach, and this results in a contribution to the mean wave drift force in the same direction of the wave propagation. The optima found by \acrshort{doe} based on minimising the mean wave drift force were either a shallow box-type structure relatively far below the water surface or a large structure closer to the waterline with a sloping beach on its wave-ward side, which induces the waves to break and thus dissipate wave energy. For maximal wave attenuation performance, the height and length of the breakwater must be maximised.

A cost function is developed that computes the reduction in captical expenditures (\acrshort{capex}) the breakwater provides to the floating island. Therefore, the construction costs of the breakwaters and the reduction in the mooring costs of the floating island are calculated. The difference between the two is the total cost reduction that the breakwater provides. An optimisation is done on maximising this total cost reduction for Wave Condition 1, which resulted in an optimal design of a breakwater with a length of 10.0 metres, a depth of 9.6 metres, a draught of 6.2 metres and its wave-ward side is a sloping beach that induces the incoming waves to break. It can provide a cost reduction of 24.4 k\texteuro per unit width. Compared with a floating island designed by the 3-year Space@Sea project for a location in the North Sea, this breakwater would deliver a 51% mooring cost reduction and a 7.7% reduction in total costs.