Numerical validation of the two-scale actuator disc theory for marine turbine arrays

The challenge in the hydrodynamic modelling of tidal and marine turbine farms is to take into account the interaction of flow events across a wide range of scales, such as the blade scale, turbine scale, array scale and regional scale. Whilst the interaction of the blade and turbine scales can be studied using the classical Blade-Element-Momentum (BEM) theory, no basic theory was available until recently to describe the interaction of the turbine and larger scales. The two-scale actuator disc theory (ADT), first proposed in 2012 by Nishino and Willden, explains the interaction of the turbine and array scales at a fundamental level; however, its validity or applicability to real problems has only partially been confirmed. Hence in this study we perform 3D RANS simulations of single and double rows of porous discs (8 discs for each row) in the middle of a shallow open channel with a vertically sheared flow. The simulation results are shown to agree qualitatively with the two-scale ADT and importantly, the optimal intra-disc spacing predicted by the simulations (to maximise the total power) agrees well with the theory, for both single- and double-row cases.