Abstract: Wind turbines are often deployed in arrays of hundreds of units, where wake interactions can lead to drastic losses in power output. Remarkably, while the theoretical “Betz” maximum has long been established for the output of a single turbine, no corresponding theory appears to exist for a generic, large-scale energy extraction system. We develop a model for an array of energy-extracting devices of arbitrary design and layout, first focusing on the fully-developed regime, which is relevant for large wind farms. When tailoring our model to reflect current designs, the predicted power output is consistent with data from field measurements, experiments and simulations. Furthermore, by leveraging turbulence parametrizations originally developed in oceanography, we successfully extend our theory to account for the strong effect that atmospheric stability can have on power output. To provide a more stringent test of our model, we also expand it to describe spatially-developing flow in arrays of rigid or flexible obstacles, finding good agreement with laboratory measurements. Having tested our model in detail, we consider again flows in large turbine arrays. By defining a suitable ideal limit, we establish an upper bound on the performance of a large wind farm. This is an order of magnitude larger than the output of existing arrays, thus supporting the notion that large performance improvements may be possible.
Biosketch: Paolo Luzzatto-Fegiz graduated with a BEng in Aerospace Engineering from the University of Southampton. After a summer working with the ATLAS Magnet Team at CERN, he completed an MSc in Applied Mathematics at Imperial College, and an MS and a PhD in Aerospace Engineering at Cornell University. Upon leaving Cornell, he was awarded a Devonshire Postdoctoral Scholarship from the Woods Hole Oceanographic Institution, as well as a Junior Research Fellowship from Churchill College, Cambridge. He is currently an Assistant Professor in Mechanical Engineering at UCSB. His interests include large-scale fluid energy harvesting, drag reduction using superhydrophobic surfaces, and developing open-source instruments for oceanography.
Date/Time:
Date(s) - Mar 10, 2017
12:00 pm - 1:00 pm
Location:
38-138 Engineering IV
420 Westwood Plaza Los Angeles CA 90095