Sponsor
Portland State University. Department of Mechanical and Materials Engineering
First Advisor
Raul Bayoan Cal
Term of Graduation
Spring 2024
Date of Publication
5-31-2024
Document Type
Dissertation
Degree Name
Doctor of Philosophy (Ph.D.) in Mechanical Engineering
Department
Mechanical and Materials Engineering
Language
English
DOI
10.15760/etd.3774
Physical Description
1 online resource (xvii, 213 pages)
Abstract
Spatial heterogeneity is an fundamental property of natural systems. In fluid dynamics subtle variations in fluid motion give rise to chaotic turbulent flows. When a fluid passes an object it retains an imprint of the object as a momentum deficit known as a wake. The resulting spatial structure of the wake is intrinsically linked to the object responsible for its creation. The coupling between geometric complexity in wake producing entities and turbulent wake evolution is considered in terms of spatial heterogeneity from individual wakes through turbulent canopy flows. First a novel Lacunarity-based method is developed for quantifying spatial heterogeneity in one, two, and three dimensional systems. This method identifies the key physical length scales and facilitates quantitative comparisons between systems. The measure is applied to large eddy simulations of a single wind turbine wake and links the dynamics of misaligned wakes to their structure. Terms from the Reynolds Average Navier-Stokes equations are framed in terms of spatial heterogeneity and reveal the locations of key physics in the wake. Invariants of the Reynolds stress tensor illustrate the spatial organization of turbulent stresses at key points in wake development. The relationship between the formation of turbulent stresses in the wake and mean wake structure leads to the development of an analytic model for the evolution of eddy viscosity in a turbulent wake. Eddy viscosity in a wake is shown to vary with distance downstream of a turbine and is modeled as a Rayleigh function. The proposed model captures this behavior and demonstrates agreement with wake measurements from wind tunnel experiments and large eddy simulations. Analytic wake models provide the foundation for expanded studies on spatially complex systems containing multiple wind turbines and wind plants. Because turbines within a plant and wind plants themselves seldom operate in isolation, predicting wake impacts within and among turbine groups is critical for sustainable wind energy. Wake interactions between a parametric system of two neighboring wind plants show wake interactions are driven by plant arrangement and wind direction. The directed nature of wake interactions between turbines is captured through weighted directed graph networks where wind direction and wake expansion determine network structure. Graph network adjacency matrices reveal spatially coherent patterns of wake losses. Quantifying the spatial heterogeneity of the weighted average adjacency matrices demonstrates the complexity in wind plant layout is reflected in turbulent wake interactions. Modeling wake interactions among five neighboring wind plants using measured atmospheric conditions identifies wind direction frequency as the main determiner of wake interactions since wind direction determines when neighboring plants are aligned. Wake steering and axial induction control are evaluated as methods for mitigating wake interactions between the five plants. Controls settings are optimized with two analytic wake models and two models for turbine wear. Neither strategy improves plant performance due to the disconnect between single turbine actuation and plant wake dynamics. At this scale, wind plant wakes are characterized by spatial patterns of aggregate wake merging and the formation of large scale flow structures in a similar manner as heterogeneous canopy flows. The effects of spatial heterogeneity on canopy flow dynamics are quantified through a series of wind tunnel experiments with vegetated canopies including multiple model canopies of varying heterogeneity and a live moss canopy. Hot wire anemometry and four-dimensional particle tracking velocimetry show the flow over a vegetated canopy is driven by spatial heterogeneity at multiple scales. Lagrangian tracks of inertial particles and Pinus ponderosa pollen indicate canopy heterogeneity controls the formation of large scale flow structures with implications for particle transport.
Rights
In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
Persistent Identifier
https://archives.pdx.edu/ds/psu/42255
Recommended Citation
Scott, Ryan, "Consequences of Spatial Heterogeneity for Turbulent Wake Development" (2024). Dissertations and Theses. Paper 6642.
https://doi.org/10.15760/etd.3774