Performance of the porous disk wind turbine model at a high Reynolds number: Solidity distribution and length scales effects

Abstract

A new design methodology for porous disk wind turbine modeling is proposed, where a disk is matched to a horizontal axis wind turbine (HAWT) on (i) thrust coefficient, (ii) radial solidity distribution, and (iii) length scale criteria. Three disk designs are tested, allowing for isolation of the effects of each criterion, with performance evaluated through experimental wake comparisons with a model HAWT at a diameter-based Reynolds number of 4 × 106 and free-stream turbulence intensity of 1.2%. Wake velocity measurements reveal excellent agreement on mean profiles in the near wake (as early as 112 diameters downstream) when the rotor’s radial solidity distribution is incorporated into the disk design. Higher order velocity statistics can also be matched farther downstream (312 diameters). To match the higher order moments, the disk must generate near wake turbulence of similar characteristics to the rotor, since this turbulence dominates the development of the wake in a high Reynolds number, low free-stream turbulence environment. This is achieved by the third design criterion, where physical features that match the rotor length scales are incorporated. Thus, including all three criteria in a single porous disk yields a model that performs well at field-relevant Reynolds numbers, is not performance dependent on the free-stream turbulence intensity, and does not require iterative tuning.