Portland State University. Department of Mechanical and Materials Engineering
Raúl Bayoán Cal
Date of Award
Master of Science (M.S.) in Mechanical Engineering
Mechanical and Materials Engineering
1 online resource (vi, 52 pages)
Markov processes, Wind power -- Mathematical models, Turbulence -- Measurement -- Data processing
The Markovianity within a wind turbine array boundary layer is explored for data taken in a wind tunnel containing a model wind turbine array. A stochastic analysis of the data is carried out using Markov chain theory. The data were obtained via hot-wire anemometry thus providing point velocity statistics. The theory of Markovian processes is applied to obtain a statistical description of longitudinal velocity increments inside the turbine wake using conditional probability density functions. It is found that two and three point conditional probability density functions are similar for scale differences larger than the Taylor micro-scale. This result is quantified by use of the Wilcoxon rank-sum test which verifies that this relationship holds independent of initial scale selection outside of the near-wake region behind a wind turbine. Furthermore, at the locations which demonstrate Markovian properties there is a well defined inertial sub-range which follows Kolmogorv's -5/3 scaling behavior. Results indicate an existence of Markovian properties at scales on the order of the Taylor micro-scale, λ for most locations in the wake. The exception being directly behind the tips of the rotor and the hub where the complex turbulent interactions characteristic of the near-wake demonstrate influence upon the Markov process. The presence of a Markov process in the remaining locations leads to characterization of the multi-point statistics of the wind turbine wakes using the most recent states of the flow.
Melius, Matthew Scott, "Identification of Markov Processes within a Wind Turbine Array Boundary Layer" (2013). Dissertations and Theses. Paper 1422.