Center for Environmental and Applied Fluid Mechanics

Weekly Seminar
Weekly Seminar

Annual Symposium
CEAFM Dual Degree Program

Special Seminar : Spring 2014

Speaker: Dr. Raúl Bayoán Cal (Portland State University)
Title: "Markov Process and Fokker-Planck Equation to Describe a Wind Turbine Array Boundary Layer"

Date: Wednesday, June 4, 2014 (Special Date)
Time: 2:00 p.m. (Special Time)
Location: Latrobe Hall 106 (Special Location)


The Markovian properties within a wind turbine array boundary layer are explored for data taken in a wind tunnel containing a model wind turbine array. A stochastic analysis of the data is carried out using the mathematics of Markov processes. The data were obtained using hot-wire anemometry thus providing point velocity statistics. The theory of Markov process is applied to obtain a statistical description of longitudinal velocity increments inside the turbine wake. Comparison of two and three-scale conditional probability density functions indicates the existence of Markovian properties in longitudinal velocity increments for scale differences larger than the Taylor microscale. 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. The results show that directly behind the tips of the rotor and the hub, the complex turbulent interactions and large scale structures of the near-wake affect the Markovian nature of the field. In confirming Markovian properties, a description of the evolution of the probability density function of velocity increments via a Fokker-Planck equation is attained. A Fokker-Planck equation is possible due to the direct computation of the drift and diffusion coefficients. The results serve as a tool for improved estimation of wind velocity within the array.


Raúl Bayoán Cal is an assistant professor in the Department of Mechanical and Materials Engineering at Portland State University. He received his Ph.D. in Mechanical Engineering from Rensselaer Polytechnic Institute in Troy, NY in 2006. He also holds an M.S. Degree in Experimental and Computational Turbulence from Chalmers University of Technology attained in 2006. During 2006 to 2008, he was a postdoctoral fellow at Johns Hopkins University. Dr. Cal joined Portland State faculty in 2009. Dr. Cal’s area of research is focused on understanding hydrodynamic turbulence and complexity in fluid mechanics in general. He uses theoretical and experimental tools to assess the behavior of the flow. Emphasis is placed on topics such as interactions of wind turbine arrays and urban canopies with the atmospheric boundary layer as well as external effects on the turbulent boundary layer. Experimental techniques such as particle image velocimetry, laser Doppler velocimetry and hot-wire anemometry are used to quantify such flows in scaled environments.

Upcoming Seminar

Speaker: Prof. Beverley McKeon (California Institute of Technology)
Title: "Systems analysis of wall turbulence: Characterizing natural and synthetic self-sustaining processes"

Date: Friday, February 24, 2016
Time: 11:00 a.m.
Location: Gilman Hall 132

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