Vortex-induced vibrations in OTEC

Abstract

As climate change seems to become more and more of a serious issue, a sudden surge of interest in clean and renewable energy sources is inevitable. Ocean Thermal Energy Conversion (OTEC), or the process of harnessing energy from the temperature difference between the warm upper ocean layer and the cold bottom ocean layer, is one of these renewable energy production methods. In order to pump up this cold water, a large diameter pipe of a length in the order of 1000 m is deployed. A pipe of such large properties will indubitably suffer from problems related to production, installation and drag forces. Up till now these problems have all largely been evaluated. One phenomenon that has been explored less frequently is VIV in OTEC, and this is therefore the main scope of this research.
Vortex-induced vibrations (VIV) are the vibrations that occur when a current flows past a cylinder, shedding vortices at higher Reynolds numbers, leading to an asymmetrical pressure distribution. For this research, the pipe is modelled as a slender Euler-Bernoulli beam conveying fluid, with gravity and ambient flow considered. The model is discretised and rewritten into state-space representation, in order to make it suitable for Python’s odeint ordinary differential equation-solver. A wake oscillator model is introduced to model the VIV phenomenon, and the complete model is used to evaluate multiple scenarios to evaluate the influence of variables as pipe diameter, ballast mass and current velocity.
A typical cold water pipe is made of a light material as for example HDPE, has a length in the order of 1000 m and a diameter of around 2.5 m, kept under tension by a ballast mass in the order of magnitude of 350 tonnes. For this research, this typical cold water pipe is taken as a starting point and subjected to a uniform current flow of 0.4 m/s. The VIV response of the pipe is then evaluated with a range of different variables. First, the pipe is evaluated in steel, FRP and HDPE to establish which material is most suitable. HDPE shows the best fatigue resistance, and is therefore chosen as the material in which the further research will be conducted. The pipe diameter is varied between 2.0 and 6.0 m, the diameter to wall thickness ratio between 12 and 26, the effect of the magnitude of the ballast mass is evaluated and the inflow velocity is changed between 1.0 and 6.0 m/s. Finally, the current flow is varied between a uniform current of 0.1 m/s and 0.8 m/s and a location specific sheared current profile is applied, in order to check whether VIV in the OTEC cold water pipe might occur in a realistic setting.
Depending on the chosen variables, in general the pipe will experience a maximum cross-flow displacement per diameter ranging between 0.6 and 1.0. Furthermore, for each set of variables the pipe will vibrate in a different normal mode, which might lead to the fact that a pipe with less maximum displacement will still experience more fatigue damage. Pipes in larger diameters will definitely suffer from a higher fatigue, however the maximum experienced damage per year was in the order of 10-15, meaning that this is insignificant. The wall thickness will not have a lot of effect. The ballast mass however, can better be chosen high since it prevents vibrations at a high mode and it seems that HDPE is strong enough in terms of yield strength to survive a large mass. Finally, when the pipe is subdued to high currents, it seems as if in-line displacement will become a larger problem then VIV, as the in-line bending reaches dangerously high levels when subjected to a current of 0.8 m/s. It has to be noted however that certain measures can be taken against this displacement.
It is very likely that VIV occurs in a cold water pipe of an OTEC plant as it is subjected to certain current flows, but in the case HDPE is used, this does not seem a large concern.