Hydrodynamics

Why Modelling PSP?

The choice of PSP, or Pneumatically Stabilised Platform, is covered in detail in Why PSP?. While this concept is not yet proven at full scale, the potential to significantly reduce the displacements (in particular the heave motion) due of the waves impacting it make it interesting from both design and research perspectives. As the literature suggests, a series of resized scale models have been experimentally proven through academic research, and the results got seem to perfectly follow the expected mathematical predictions developed on the software. So why modelling it “again”?

Every design and every sea state together determine the dynamic response of a device, or in this case platform. The initial aim of the modelling and analysis was to prove the dynamic stabilising effect of the PSP would perform as expected considering the overall design and wave climate differed from those previously researched. However, it quickly became apparent that the number of assumptions and simplifications required to carry out this analysis in the time frame of the project would lead to invalid results. Therefore the decision was taken to simply the analysis scope to assessing the dynamic response of the platform ignoring the stabilising cylinders. As such, if the motions were acceptable – the true design should be even more sable.

Literature Review and Scope of the Model

A small but detailed body of literature and academic papers already exist on PSPs and on modelling them (since their behaviour is based substantially on the behaviour of an Oscillating Water Column – OWC), with some modifications for the air transfer between the columns. It is analogous to an array of OWC connected together in a solid structure.

One approach to modelling this system, as used by Cheung [2] would be to represent each cylinder as individual spring-mass-damper systems. Parameters would need to be estimated for the inputs to the 6 degree of freedom system that would be assessed. Each individual cylinder would be singularly modelled as a mass-spring-damper system with the same properties, using as an input a series of regular waves with different amplitude frequency or phase, or more properly, a spectrum (JONSWAP). Finally, the overall response would be evaluated as a superposition of the single responses.

In their study, Cheung et. al compared their numerical results with scale model tank test motions in analogous waves – the results were comparable and very promising with regards to motion reduction.

As such, it appears that this approach is rigorous; however, the proper estimation of the parameters and validation of the model would require significant investments of time and resources and, as such, this approach was discarded for the purpose of this project. This is the approach recommended for further analysis of this concept.

Float Incorporated, one of the main proponents of PSP technology, used an alternative approach of continually distributed impedance properties – in contrast to the lumped-mass-spring damper approach already discussed. Their numerical results also correlated well with empirical tank testing, finding reductions of transmitted waves of between 50% and 90% and low platform motions [2], [7] & [8].

Methodology

It has been shown that it was necessary to develop a model of the PSP design and to analytically study the response of the platform, using the relevant annual average sea state conditions for the chosen location. First there is an explanation of the model construction, which assumptions have been made, what has been left outside the scope for further and future improvements. Second, the results are detailed and, finally, some guidance on the interpretation of these results is given.

From the “design part” of the model, we can see that our platform is nothing more than a series of array of cylinders of a specified dimension, or for an overall saying “a tablet”.

A 3D model was created to allow both the hydrostatics and hydrodynamics analyses to be carried out. As previously mentioned, the geometry was simplified to a monolithic block. The model was imported into “MaxSurf Motion Advanced” [6] to study the response.

Figure 1. Geometry of Tethys, MaxSurf Motion Advanced, meshed with the Panel Method

To ascertain the dynamic behaviour, the forcing function must be found, which is derived from the wave energy spectrum. The JONSWAP model was used to generate wave spectra for the specified location [5] and this was subdivided into six sea states. A wave scatter diagram was generated to graphically represent the wave climate (shown in the following table and Figure 2).

Figure 2. Wave scatter diagram

The calculated RAOs (Response Amplitude Operators) for the corresponding six motions of the platform (heave, surge, sway, pitch, roll andThe calcula yaw), were then used to obtain the resultant Root Mean Square (RMS) motions over the different sea states.

Assumptions

Results

A table with all the RMS responses over the six motions follows.

It can be observed in the previous table that the two highest RMS motions are heave and sway, with responses of 1.9m RMS and 2.0 m RMS respectively. These occur in Sea State 7 which corresponds to significant wave heights (Hs) of 7.5 m. Clearly the sheer size and layout of the platform result in a design that is not overly susceptible to wave motion. Surge, pitch roll and yaw motions are all very low, to the point of being almost insignificant.

With regards to the ultimate aim of the platform providing a stable base for the OWC wave Energy Converters, the heave, or vertical motion is the most important. The heave motion is depicted in Figure 3, while the RMS heave response for the heave motion in all 6 sea states is shown in Figure 4.

Figure 3. Heave Motion

Figure 4. Wave height reduction over the six different sea states (Heave motion)

What can be observed, is that, despite the necessary simplifications, the platform is stable and the motions are low in all expected sea states.

Conclusions

Due to the limited time and resources, it was not possible to fully explore the intricacies of the PSP design and there remains huge scope for further research. However, using a simplified model it has been shown that, mainly due to the overall size and shape, the platform remains stable even discounting the influence of the PSP cylinders and air transfer, which are designed to further improve the stabilisation and wave dissipation, characteristics which have been shown to work effectively in wave tanks.

It is clear that as good as it can be, our model still doesn’t take into account the interaction and the motion of the water within the individual cylinders, it doesn’t consider the interstices between them and of course (but this can’t be solved) suffers always for some kind of simplifications that have to be made in order to represent the chaotic motion of the waves in a real state (spectrum representation).

A deeper kind of study that we would suggest would be, with a proper theoretical research on the exact input parameters, a multi-degree of freedom (most likely three, as the floating oscillating water column devices) model using mass-spring-damper systems. The system would be represented by second order differential equations, using frequency dependant coefficients, in either in the time, or frequency domain. As a first pass this could be carried out for the PSP, but mostly (because of the lack of data on it) on the Wave Energy Collectors in the front, to make a proper estimation of the wave energy harvested, and to give a proper idea of the overall cost of energy provided by the synergy of wind and waves.

Many studies have analysed wave energy devices, but a lack of specific literature on this unique platform design is evident. However, our results add further weight to the previous theoretical and empirical studies on the individual components, but Float inc and other researchers, showing that this is a highly promising design which warrants further study.