A.F. de O. Falcão

OWC wave energy devices with air flow control

A theoretical model is developed to simulate the energy conversion, from wave to turbine shaft, of an oscillating-water-column (OWC) plant equipped with a Wells air-turbine and with a valve (in series or in parallel with the turbine) for air-flow control. Numerical simulations show that the use of a control valve, by preventing or reducing the aerodynamic stall losses at the turbine rotor blades, may provide a way of substantially increasing the amount of energy produced by the plant, particularly at the higher incident wave power levels. From the hydrodynamic point of view, a by-pass valve or a throttle valve should be used depending on whether the wave energy absorbing system is over-damped or under-damped by the turbine.

Wave generation by an oscillating surface-pressure and its application in wave-energy extraction

A two-dimensional analysis, based on linear surface-wave theory, is developed for an oscillating-water-column wave-energy device in water of arbitrary constant depth. The immersed part of the structure is assumed of shallow draught except for a submerged vertical reflecting wall. Both the cases of linear and nonlinear power take-off are considered. The results show that air compressibility can be important in practice, and its effects may in general be satisfactorily represented by linearization. The analysis indicates that using a turbine whose characteristic exhibits a phase difference between pressure and flow rate may be a method of strongly reducing the chamber length and turbine size with little change in the capability of energy extraction from regular waves. It was found in two examples of devices with strongly nonlinear power take-off that the maximum efficiency is only marginally inferior to what can be achieved in the linear case.

Control of an oscillating-water-column wave power plant for maximum energy production

A stochastic model was applied to devise an optimal algorithm for the rotational speed control of an oscillating-water-column (OWC) wave power plant equipped with a Wells turbine and to evaluate the average power output of the plant. The hydrodynamic coefficients for the OWC are assumed known (as functions of frequency), as well as the turbine performance curves. The whole model is based on linear control theory of a stochastic process, it being assumed that the sea surface elevation has a Gaussian probability density function. The optimal control law is expressed in terms of a simple relationship between the instantaneous values of the electromagnetic torque (to be applied on the generator rotor) and the rotational speed. It is remarkable that the optimal control algorithm was found to be practically insensitive to wave climate. A simple additional algorithm, accounting for constraints imposed by the electrical grid on power oscillations, was derived in order to complement the optimal control law.

Stochastic modelling of OWC wave power plant performance

A stochastic method has been developed to evaluate the average performance of an oscillating water column wave energy device equipped with an (assumedly linear) Wells turbine. The wave climate is represented by a set of sea states, characterized by their power spectra, the free-surface elevation being a Gaussian random variable in each sea state. The variance and the probability distribution of the air pressure inside the chamber are computed for each sea state, it being assumed that the chamber hydrodynamic coefficients and the turbine curves are known. This allows the average performance of the turbine and of the plant to be obtained for each sea state and for the annual wave climate. Numerical examples are worked out for given chamber geometry and turbine shape, showing how the turbine size and rotational speed may be optimized for maximum energy production. Controllable rotational speed and the use of a valve system for turbine flow control are considered.

Aerodynamics of the wells turbine

Abstract The paper describes a theoretical and experimental investigation concerning the aerodynamic performance of the Wells turbine, a self-rectifying axial-flow turbine suitable for energy extraction from reciprocating air flow. The turbine consists essentially of a rotor with untwisted aerofoil blades of symmetrical cross section, set radially at 90° angle of stagger. Numerical results were computed from a streamline curvature throughflow method and compared with analytically obtained results from a linear actuator disk model. Unidirectional steady-flow measurements were performed with a turbine of about 0.6 m rotor diameter and several numbers of blades, and included flow rate, pressure drop and torque, as well as velocity and pressure distributions. Experimental results are compared with theoretical values.

Turbine-controlled wave energy absorption by oscillating water column devices☆

Abstract The paper deals with phase control as a method of increasing the energy absorption by oscillating water column (OWC) devices, from regular as well as from irregular waves. The power take-off machine considered is a modified version of the self-rectifying axial-flow Wells air turbine, whose rotor blades are of variable setting angle; this allows the air pressure and flow rate to be controlled independently from each other. Results of numerical simulations are presented for three different control strategies applied to energy absorption from irregular waves by an OWC device of simple, two-dimensional geometry. Experimental data from a turbine model are used in the simulation.

Wave-power absorption by a periodic linear array of oscillating water columns

Abstract This paper describes a theoretical analysis of the ocean wave energy absorption by a periodic linear array of oscillating water columns (OWCs) of arbitrary planform. The analysis is based on classical linear water wave theory and uses the expressions for the wave field resulting from time-harmonic pressure distributions on the free surface. The water depth is assumed finite and constant. The cases of oblique and normal incidence are analysed. A linear power take-off mechanism is assumed, but a complex characteristic constant (allowing for phase control) and air compressibility are considered. Special analytical expressions are derived for OWCs of rectangular and circular planforms. Numerical results for circular chambers show that the hydrodynamic interaction can substantially change the maximum energy absorption, depending on array and chamber geometry and on angle of incidence.

Aerodynamics of the wells turbine: Control by swinging rotor-blades

Abstract The paper describes a theoretical and experimental investigation of the aerodynamic performance of a version of the Wells turbine modified such that its rotor blades can be set at a varying angle. Unidirectional steady-flow measurements were performed with a turbine of about 0.6 m rotor diameter. The results show that the modified turbine can provide a way of increasing the amount of energy produced from ocean waves by efficiently phase-controlling an oscillating water column type of device.

Flow field due to a row of vortex and source lines spanning a conical annular duct

Analytical expressions are derived for the incompressible flow due to a row of vortex and source lines spanning a duct whose walls are coaxial conical surfaces of revolution with a common vertex. The singularity lines have the shape of an arc of circle meeting the walls perpendicularly, and are defined by the intersection of a spherical surface with a series of equally spaced meridional planes. Although source lines of spanwisely varying strength are in general assumed, only vortex lines of constant circulation are considered. Simpler expressions are derived for the limiting two-dimensional cases when the flow is axisymmetric (actuator disc), and when the angular distance between the conical walls becomes vanishingly small. The expressions for the latter case are used in an example to obtain numerical results by a panel method for the velocity distribution of the flow about the inlet guide vane system of a water turbine of bulb type.

Lifting-surface theory of straight cascades of swept blades

Abstract Lifting-line and lifting-surface expressions are derived for the steady irrotational incompressible flow through a straight cascade of swept blades of finite length and constant loading along the span, the main object being to study the three-dimensional perturbations arising from the presence of the end walls and to determine the warped shape of the blade camber surface. The blade axis is taken perpendicular to the blade-to-blade direction, as an approximation to conical flow with radially set blades. The solution, in terms of the velocity potential, is based on the authors analytical expressions for cascades of unswept blades of varying circulation along the span. Numerical results are presented for a wide range of cascade geometries, and the effects of several cascade parameters upon the wall-induced three-dimensional perturbations are discussed. In particular, it has been found, for most geometries used in practice, that a good approximation is obtained by superposing the disturbances due to the two walls separately.