Actuator Disc Theory (ADT) is a classical theory in fluid mechanics to explain the limit of power extraction by an ideal turbine, which was studied independently by Lanchester, Betz and Joukowsky in the early 20th century. It is well known that the maximum power extracted by an ideal horizontal-axis wind turbine is 59.3% of the power of (undisturbed) wind passing through the rotor swept area, often referred to as the Betz limit.

To understand the limit of power extraction by marine turbine arrays, however, we need to consider several important factors that are not considered in the classical ADT, such as the effects of blockage (of local as well as global flow passages), wake mixing, seabed-induced shear and turbulence. In this study we are trying to extend ADT to explain theoretically the basic mechanisms deciding the maximum performance of marine turbines.

One of our major achievements so far in this area is the derivation of theoretical upper limits to the power extracted by a large number (say, more than 10) of marine turbines placed side-by-side as a single row. By considering the separation of scales for each turbine and for the entire row, we have shown that the limit of power extraction from a laterally unbounded flow, for example, may increase from the Betz limit of 59.3% to another limit of 79.8% as the spacing between turbines is optimised.

References:

[1] Nishino, T. & Willden, R. H. J. (2012) “The efficiency of an array of tidal turbines partially blocking a wide channel,” Journal of Fluid Mechanics, Vol. 708. pp. 596-606. http://dx.doi.org/10.1017/jfm.2012.349

[2] Nishino, T. & Willden, R. H. J. (2013) “Two-scale dynamics of flow past a partial cross-stream array of tidal turbines,” Journal of Fluid Mechanics, Vol. 730, pp. 220-244. http://dx.doi.org/10.1017/jfm.2013.340

[3] Draper, S. & Nishino, T. (2014) “Centred and staggered arrangements of tidal turbines,” Journal of Fluid Mechanics, Vol. 739, pp. 72-93. http://dx.doi.org/10.1017/jfm.2013.593

[4] Nishino, T. (2013) "Beyond the Betz theory - blockage, wake mixing and turbulence," 2nd Oxford Tidal Energy Workshop (OTE 2013), Oxford, UK, March 2013.