A correction to the enhanced bottom drag parameterisation of tidal turbines

TL;DR

This paper identifies limitations in current hydrodynamic models of tidal turbines at small grid sizes and proposes a correction based on actuator disc theory to improve force and energy estimates across scales.

Contribution

It introduces a correction to the enhanced bottom drag parameterisation that maintains accuracy from coarse to turbine-scale grid resolutions using actuator disc theory.

Findings

Force calculation remains accurate across grid sizes with correction

Improved estimate of extractable energy using the correction

Demonstrated correction applied to MIKE 21 and Fluidity models

Abstract

Hydrodynamic modelling is an important tool for the development of tidal stream energy projects. Many hydrodynamic models incorporate the effect of tidal turbines through an enhanced bottom drag. In this paper we show that although for coarse grid resolutions (kilometre scale) the resulting force exerted on the flow agrees well with the theoretical value, the force starts decreasing with decreasing grid sizes when these become smaller than the length scale of the wake recovery. This is because the assumption that the upstream velocity can be approximated by the local model velocity, is no longer valid. Using linear momentum actuator disc theory however, we derive a relationship between these two velocities and formulate a correction to the enhanced bottom drag formulation that consistently applies a force that remains closed to the theoretical value, for all grid sizes down to the turbine scale. In addition, a better understanding of the relation between the model, upstream, and actual turbine velocity, as predicted by actuator disc theory, leads to an improved estimate of the usefully extractable energy. We show how the corrections can be applied (demonstrated here for the models MIKE 21 and Fluidity) by a simple modification of the drag coefficient.