A multi-scale analytical model for the performance of a tidal stream array in a tidal channel

Assessing the tidal resource is central to the feasibility analysis of any development of tidal stream turbines. This is true for the CoTide project which seeks to optimise the design of tidal stream turbines by building an integrated design tool considering hydrodynamics, structural effects, fatigue, environmental impact, etc. However, there is no closed-form analytical solution for the tidalresource assessment. Motivated by this, this paper proposes a multi-scale framework for tidal resource assessment for the Co-Tide project. The key element of this framework is to model the system, i.e. an array of turbines (arranged in a row) partially occupying a tidal channel, at differentscales (channel-scale, array-scale, turbine-scale), and then coupling them together through the net resistance of the turbine array solved by a drag model that might be derived from laboratory experiments or numerical simulations. The channel-scale flow dynamics is described by the Garrett& Cummins (2005) model [1] whereas based on the scale separation model of Nishino & Willden (2012) [2] the array-scale and turbine-scale flows are modelled separately by the Garrett & Cummins (2007) model [3] and then coupled together. Using characteristics representative of a tidal site (including tidal flow characteristics, channel geometry and turbine geometry) as inputs, we have employed the framework to predict the velocity in the channel, velocity through the array and the power generated by the array over time. Only two principal tidal constituents are considered here as increasing the number of tidal constituents significantly increases the computational cost.The model can be adapted for other tidal energy projects and has flexibility to incorporate more detailed sub-models in future.