Performance of two-dimensional tidal turbine arrays in free surface flow

TL;DR

This study extends classical tidal turbine array theory to include free surface effects and two-dimensional arrangements, demonstrating that smaller turbines in a 2D layout outperform traditional 1D arrays in power and efficiency, with optimal configurations identified.

Contribution

The paper introduces a two-dimensional array model with free surface effects, analyzing optimal turbine arrangements and demonstrating increased power coefficients over existing models.

Findings

2D turbine arrays outperform 1D arrays in power and efficiency.

Optimal turbine distribution depends on channel parameters.

Maximum power coefficient of 0.869 at Fr=0.2 significantly exceeds previous results.

Abstract

Encouraged by recent studies on the performance of tidal turbine arrays, we extend the classical momentum actuator disc theory to include the free surface effects and allow the vertical arrangement of turbines. Most existing literatures concern one dimensional arrays with single turbine in the vertical direction, while the arrays in this work are two dimensional (with turbines in both the vertical and lateral directions) and also partially block the channel which width is far larger than height. The vertical mixing of array scale flow is assumed to take place much faster than lateral one. This assumption has been verified by numerical simulations. Fixing the total turbine area and utilized width, the comparison between two-dimensional and traditional one-dimensional arrays is investigated. The results suggest that the two dimensional arrangements of smaller turbines are preferred to one dimensional arrays from both the power coefficient and efficiency perspectives. When channel dynamics are considered, the power increase would be partly offset according to the parameters of the channel but the optimal arrangement is unchangeable. Furthermore, we consider how to arrange finite number of turbines in a channel. It is shown that an optimal distribution of turbines in two directions is found. Finally, the scenario of arranging turbines in infinite flow, which is the limiting condition of small blockages, is analysed. A new maximum power coefficient 0.869 occurs when $Fr=0.2$, greatly increasing the peak power compared with existing results.