The Effect of Plenum Chamber Volume and Air Turbine Hysteresis on the Optimal Performance of Oscillating Water Columns

It is well known that air compressibility is likely to influence the performance of oscillating water columns (OWC’s) and this has previously been modelled and estimated using linear aero-hydrodynamic lump-mass models. In addition, the optimum performance of specific OWC’s has been determined, with the effect of air compressibility included within the optimisation. This paper extends this work to determine the optimum performance of any OWC, defined by its hydrodynamic coefficients and serves as a reminder to experimentalists of the importance of considering air compressibility in their models. Moreover, the optimisation is analytical and so produces explicit expressions for maximum power capture, optimum damping, etc. The results indicate that for the majority of OWC’s the maximum power capture decreases with increasing plenum chamber volume, accompanied by a reduction in the optimum turbine damping and an increase in optimum water column motion. However, the results also show that air compressibility will increase maximum power capture for OWC’s when the incident wave period is shorter than the natural period of the water column. To date, air turbine hysteresis has been studied as a purely aerodynamic phenomenon and its effect on the optimum hydrodynamic performance of OWC’s has not been investigated. This paper uses a linearised phase shift to model an approximation of turbine hysteresis that shows that turbine hysteresis will have a small but significant influence on hydrodynamic performance, where the magnitude of influence is similar to the effect of subtle blade profile and blade sweep angle modifications on aerodynamic performance. The results indicate that hysteresis should be considered in turbine design, especially if a turbine modification improves aerodynamic performance whilst reducing hydrodynamic performance due to a change in the turbine hysteresis.