| dc.description.abstract | Ocean wave energy is a large, and mostly untapped potential source of renewable energy worldwide. The scope of engineering solutions for harvesting wave energy is vast, ranging from wave-induced oscillating bodies, to overtopping devices and oscillating water columns. One particularly interesting approach to energy harvesting is to use arrays of oscillating bodies. The advantage of such a solution lies in potential amplification of the wave field through the interactions of waves that are diffracted and radiated by the bodies. Recent examples from other fields of physics (e.g. photonics crystals) show that by carefully engineering the configuration of the array, it is possible to greatly improve its performance. This thesis studies the performance of large arrays of axisymmetric bodies through the use of multiple scattering formulation of wave interactions. The focus is on the energy extraction characteristics in particular, but the effects on mean drift force are also studied. The multiple scattering (MS) formulation for Wave Energy Converter (WEC) arrays is extended in three areas. First, the dynamical behavior of a body in an array is decoupled from the dynamics of the array as a whole. This allows for the dynamical characteristics of a body to be completely determined in isolation, and then used in an array setting through newly-formed dynamical transfer matrices. This approach is especially beneficial in optimization studies, where the changes in the spatial array configuration do not require the recalculation of the hydrodynamic characteristics of an array. Second, the non-linear mean drift force on an array is expressed in terms of newly-formed non-linear drift transfer matrices. Lastly, a theoretical formulation is developed for periodic arrays with closely-spaced rows of bodies so that they can be analyzed in an exact manner within the MS formulation. Based on these extensions, a fast computational algorithm is developed that is capable of handling large arrays (0(100) bodies) of different configurations (general finite-size arrays, periodic arrays, periodic arrays of subarrays). The algorithm imposes no constraints on the body-size-to-wavelength ratio or on the inter-body spacings. Using this algorithm, a series of systematic studies of energy extraction characteristics by different array configurations is performed (as a function of wavenumber and wave incoming angle). These array configurations can be described with at most two parameters. In particular, the study of periodic and uniformly spaced line arrays reveals that large gains occur before new scattering orders appear (at Rayleigh wavelength). The gains are particularly large for super-resonant wavenumbers where there is still significant energy extraction. The studies of rectangularly arranged arrays show that, while still related to Rayleigh wavelengths, the optimal spacing is governed by the emergence of higher scattering orders. In all cases, arrays arranged in the direction of array propagation (attenuator arrays) perform poorly, except for sub-resonant wavenumbers. The effect or spacing irregularity (linear, quadratic and random) is studied on terminator arrays. The performance of irregularly spaced arrays as a function of wavenumber is more uniform, without high peaks in performance, and it indicates that there is a trade-off between high array gain and broad-bandedness of array gain. Finally, optimization of spatial configuration of a series of large arrays (up to 200 bodies) is performed. The array configuration is parameterized such that it can be described by a small number of variables, but that still allows a large number of different configuration types (irregularities in body spacings). Gradients of objective functions (extracted energy, array gain, drift force) are obtained using the adjoint method that, by also employing matrix-free matrix-vector multiplications, leads to a fast, memory-efficient gradient-based optimization algorithm. The optimization is performed for regular and irregular seas. The optimized rectangular arrays lead to high array gains, especially for mildly super-resonant wavenumbers where it reaches values of over 4. Surprisingly, uniformly spaced rectangular arrays perform better than the irregularly spaced ones in both regular and irregular seas. For many optimized arrays, the array capture width (extraction cross-section) is equal to the geometrical extent (cross-section) of the array, indicating that these arrays harvest all the energy of a particular frequency incoming on the spatial area they occupy. The optimal configurations are analyzed from a physical standpoint and compared to other structured arrays in physics. The results overall provide guidelines on the possible future design of WEC arrays. | en_US |
