Experimental Investigation and Similarity Solution of the Axisymmetric Turbulent Wake With Rotation

ABSTRACT An experimental and analytical investigation of an axisym-metric turbulent wake with rotation was carried out. The axialand azimuthal (swirl) velocity ﬁelds were measured in the wakeof a single 3-bladed model wind turbine with rotor diameter of0.91m, up to 20 diameters downstream. The turbine was posi-tioned in the free stream, near the entrance of the 6 m x 2.7 mcross section of the UNH Flow Physics Facility. Measurementswere conducted at different rotor loading conditions with bladetip-speed ratios from 2.0 to 2.8. A pitot-static tube and constanttemperature hot-wire anemometry with a multi-wire sensor wereused to measure velocity ﬁelds. An equilibrium similarity theoryfor the turbulent axisymmetric wake with rotation was outlined,and ﬁrst evidence for a new scaling function for the decay ofthe mean swirling velocity component, W max µ x 1 µU 3=2o , wasfound. INTRODUCTION Energy production data from existing offshore and onshorewind farms indicate that the wakes of upwind turbines interactwith downwind turbines. The performance of downwind turbinesis highly sensitive to alignment with respect to upwind turbinesrelative to wind direction, and turbines located downstream ofthe front row experience a signiﬁcant reduction in power outputwhen compared to the output of the ﬁrst row.The energy production losses due to these wind turbine wakeeffects can be dramatic, and when averaged over a year and allwind directions, typically range from 5% to over 15%, depend-ing on the wind farm layout [1]. However, losses have beenmeasured as high as 20% in large off-shore wind farms withregularly-spaced wind turbines [2, 3]. Improved array spacingis necessary to obtain the maximum possible energy per unit cost(cost is driven by ocean or land area used) and reduce turbu-lence loads on downstream rotors. Wind turbine array spacingoptimization is still an active research area, e.g. [4], since muchabout the downstream velocity deﬁcit, turbulence intensities, andwake-wake interactions remains unknown. Barthelmie et al. [2]summarize the state of knowledge in modelling and measuringwind turbine wakes in large offshore wind farms as having a“fundamental lack of understanding about the behavior...”.The cost of this limited understanding is signiﬁcant. For ex-ample, consider an offshore wind farm with a capacity factor of0.4: income loss per year is $3.46M (million) for each percentwake loss per installed GW capacity based on an average retailprice of $0.116 per kWh [5]. Further, the increased levels of tur-bulence created by upstream turbines causes fatigue loading ofdownstream rotors and play a signiﬁcant role in turbine servicelife. Gearboxes with a projected service life of 20 years havebeen observed to wear out in half that time [6]. The turbulent op-erating environment results in varying loads, accelerations, andvibration levels that are believed to promote this wear [7].Vermeer et al. 2003 [8] presented a thorough summaryof wind tunnel studies of wind turbines. However, many ofthem were either affected by blockage due to small tunnel cross-sectional area or suffered from low Reynolds number due to asmall turbine size. Where experiments were conducted with rea-sonable size turbines in large wind tunnels, detailed ﬂow mea-surements were typically not made far downstream, usually dueto facility limitations imposed by test section length or cross sec-1 Copyright c 2013 by ASME