# Hydrodynamics of Wave-Power Extraction

**Principal Investigator**
Chiang Mei

**Project Website**
http://web.mit.edu/mit-tdp/www/ad-research-technology-2.html

This research is focused on the extraction of mechanical energy from ocean surface waves, without including the specifics of mechanical to electrical energy conversion, to predict wave power absorption rate, wave forces on and motion of wave-energy absorbers. Our objectives are to construct mathematical models to predict the hydrodynamic aspects of two types of wave-energy absorbers, buoys and oscillating water columns, in the following areas: (1) mutual interaction of neighboring absorbers in a wave farm, which is an array of many point absorbers, (2) energy loss in the neighborhood of absorbers, (3) nonlinearity of waves and absorber motion, (4) randomness of waves, and (5) variation of sea depth.

We are currently investigating the items (1) absorber arrays, and (2) dissipation loss, employing theoretical fluid dynamics, wave theories, perturbation and asymptotic methods.

Two classes of absorber arrays are investigated: (1) small buoys separated at distances smaller than a typical wave length, (2) medium to large buoys, with each on top of a vertical cylinder, separated by approximately a wavelength. As a necessary first step to study the arrays, the linear dynamics of a single buoy is studied to find the added mass and radiation damping coefficients as well as the force due to diffraction.

For accurate prediction of net wave power absorption, realistic estimation of dissipation loss is essential. There are two important causes of dissipation. One is inside the turbulent boundary layers on the structural surface and the other is vortex shedding. As an initial step to examine the effect of friction on waves, we have extended the asymptotic theory for resonant scattering of water waves by an array of fixed vertical cylinders. The asymptotic theory employs certain general tools in solid-state physics and crystallography. Method of multiple scales is used to find the amplitude of the resonated waves. To account for the effect of dissipation, we impose a fictitious boundary condition on the cylinder walls which can be adjusted to treat the two types of dissipation.

Linear dynamics of a single small buoy of cylindrical shape has been studied analytically. Numerical computations have also been performed to find the necessary coefficients in order to predict the motion of the buoy and the power output.

Linear dynamics of a single buoy on top of a vertical cylinder has been examined theoretically. Numerical computations are in progress.

Having extended the theory of Li & Mei (2007), we modified their analytical solutions for a long strip of cylinder array attacked by waves from the left side of the strip, for both normal and oblique incidence involving two or three resonantly coupled waves to investigate the effect of energy loss on the attenuation of the wave amplitude along the array.

We have defined the fictitious boundary condition on the cylinder walls to incorporate the effect of dissipation in the boundary layer near the cylinder walls. Incorporating the effect of dissipation due to vortex shedding is ongoing.