The development of a Lagrangian dynamics model of an oscillating water column (OWC), wave energy converter (WEC)

An oscillating water-air column (OWC) is one of the most technically viable options for converting wave energy into useful electric power. The OWC system uses the wave energy to “push or pull” air through an air turbine, as illustrated simply in Fig. 1. The turbine is typically a bidirectional turbine, such as a Wells turbine, or an advanced Dennis-Auld turbine. The energy conversion from the water column to pneumatic power in an OWC system is affected by sinusoidal transients of volume flow rate and OWC chamber pressure through the turbine. The recovery of wave energy is also affected by the buoyancy of the floating OWC and its relative motion between the turbine and the wave front. A new math model of an OWC system has been developed by Concepts NREC (CN) that is based on Lagrangian Dynamics and can provide more insight into what parameters most affect the recovery of energy from water waves. The sketch shown in Fig. 2 depicts the model of an OWC with distances in relation to the sea-bed floor taken to be the inertial reference. The variable X1 represents the massless distance of the water wave front from the inertial reference which imparts a non-conservative force Ft into the OWC chamber, thus exciting the entrapped air. The variable X2 represents the distance of the OWC mass from the inertial reference and includes a non-conservative force, Fb, that is associated with the buoyancy of the OWC mass caused by the motion of the OWC as it responds to the non-conservative force, Ft. The variable X3 represents the distance of the virtual joint connecting the spring constant and the damping coef. The power extraction by the turbine and the air cavity within the OWC are thus modeled using a damping coef., C [Lbf/(ft/s)], and a spring constant, Ks [Lbf/ft] derived as a function of the OWC geometry. The primary objective for the analysis is to determine the amount of work extracted from the OWC system via the damping system, with damping constant C as a function of the OWC size and the wave period and amplitude, and to discern how the recovery of the energy from the wave may be improved upon by designing the OWC features when the incident wave climate changes. A secondary objective of the analysis was to compare the results from the Lagrangian Analysis with two other thermo-fluids models of an OWC system that were previously derived by Concepts NREC for a fixed OWC system. Ultimately, a solution derived from Lagrangian Dynamics would provide a greater insight into improving the capture of wave energy from a climate of waves with different frequency and amplitudes. This paper will provide the details of the solution of the Lagrangian Dynamics Solution and how they may be applied to an OWC design. The paper also provides a summary review of earlier computer models of an OWC that have been prepared by Concepts NREC.