The low-order LRB model has been developed to rapidly distinguish the performance of arbitrary configurations of VAWT arrays. Comparison with field measurements validated that the LRB model is able to not only asses differences among individual turbines within an array but also to predict the ranking of the average performance of unique VAWT arrays with better than 95% statistical certainty. The LRB model is conservative in that it overpredicts the losses caused by the turbine wakes. In conjunction with the field data, the LRB model also provides insight into the physical mechanisms that determine individual turbine dynamics and array performance. A key conclusion that can be drawn from the present results is that there are two primary competing fluid dynamic mechanisms within
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the array that contribute to the overall performance. The first is turbine blockage, which can locally accelerate the flow adjacent to a turbine and, perhaps surprisingly, can thereby increase the performance of neighboring turbines above their performance in isolation. The other effect is that of the turbine wake, which locally decelerates the flow and leads to a decrease in performance for downstream turbines. The combined effect is captured by the LRB model, and therefore it achieves a reasonable estimate of performance based on the average wind speed directly ahead of each turbine.
It is prudent to note that this simplified model is not intended to capture the complex structure and dynamics of the three-dimensional turbulent flow that occurs in wind farms, e.g., the vertical shear of the incoming atmospheric boundary layer, or the dynamics of the energy exchange between the atmospheric boundary layer and the array. Rather, the model is intended to serve as a tool that can rapidly assess, to a first approximation, the viability of one wind farm configuration relative to another. This approach is akin to the work of Betz, which, despite assumptions of inviscid flow among other simplifications, can be quite useful for performing engineering calculations of wind turbines. Additionally, the benefit of the current approach is that optimal array configurations can be found with significantly less computational expense than higher fidelity numerical simulations such as LES and much more rapidly than in experiments.
As follow up to this work, recent wind tunnel experiments have demonstrated that the LRB model is quite robust in its ability to predict the ranking of array configurations among VAWTs with completely different geometry than those of the original field experiments (I. Brownstein, personal communication). Further work has also been undertaken to use the model in an evolutionary algorithm seeking to find optimal array configurations, with support from additional field measurements (Dabiri & Brownstein, 2015). Still, the model is inherently limited in many respects, including in its inability to characterize the dynamics of the VAWT wake. For this, more detailed and controlled experiments are needed, which are laid out in the next two chapters.
Chapter 3
A comparison of measurements in motor-driven and flow-driven
turbine experiments
The material presented in this chapter was authored by Araya & Dabiri (2015) and published inExp. Fluids56: 7. Its purpose is to introduce the laboratory-scale VAWT experiments by an account of determining the appropriate use of a motorized turbine, a necessary constraint on some of the subsequent experiments presented in Chapter 4. Some minor revisions have been made to the published text, references, and formatting of figures in accordance with the rest of this thesis.
3.1 Introduction
When studying flow phenomena in a scaled laboratory experiment or in a computational simulation, it is often not possible to achieve dynamic similarity with the full-scale flow of interest. In the case of wind and water turbine experiments, a scaled model turbine may not perform as well as in the field, or perhaps not at all, due to a mismatch of Reynolds number and other scaling difficulties such as increased bearing friction. Grant & Parkin (2000) note that in very small-scale model turbine experiments the blades may operate below their design Reynolds number, causing extensive flow separation, which can limit the extrapolation of these model tests to full scale rotors. Despite this, both wind and water tunnel experiments are used as a practical means to study the flow characteristics of tur- bines even when dynamic similarity cannot be achieved.
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Recent progress has been made in understanding the aerodynamics of VAWTs, also known as cross-flow turbines. Bachant & Wosnik (2014) examined the effect of Reynolds number on the near-wake characteristics of VAWTs. They found that turbine performance becomes nearly independent of Reynolds number at turbine diameter Reynolds number of ReD = 8×105. They also observed that near-wake statistics, such as mean velocity and turbulence intensity, showed only slight differences across the full range of Reynolds number that was examined, i.e.,ReD = 3−13×105. Fujisawa & Shibuya (2001) as well as Ferreira et al.(2009) investigated the dynamic stall characteristics of VAWTs using an isolated tur- bine blade. To mimic the VAWT dynamics, they used a motor to rotate the blade about a central axis within a freestream flow and observed the successive generation and shedding of vortices from the blade as it was rotated. Both studies concluded that the development of these vortices changed as the tip speed ratio, λ, the ratio of blade speed to freestream flow speed, was increased, but neither made reference as to whether such observations were physical with respect to a functional VAWT whose rotation is only driven by the oncoming flow.
This practice of prescribing the motion of turbine blades within a flow is common among both experimental and numerical turbine investigations. A survey of previous literature is tabulated in appendix B, with a distinction made between studies that used ‘flow-driven’
and ‘motor-driven’ turbines, details of which are provided in Section 3.2. The compilation highlights the frequent use of the motor-driven technique and also inconsistencies in report- ing power or torque measurements, which is shown in the current work to be an important aspect of matching the wake characteristics of flow-driven turbines.
Intuitively, one might anticipate that a motor-driven turbine whose geometry, shaft torque, andλmatches that of a flow-driven turbine would also share the same performance and wake characteristics. However, this conjecture has not been experimentally tested. A computational study by Leet al.(2014) compared the performance of a flow-driven turbine subject to a given load with that of one whereλwas specified. Their results show reasonable agreement in the measured power coefficient of the two configurations, which is consistent with the aforementioned hypothesis. Still, it remains unclear how the prescribed motion af-
fects the resulting flow field measurements, e.g., the wake velocity profile and power spectra.
To address this, two-dimensional particle image velocimetry is used to measure the velocity in the near wake region of a 3-bladed VAWT. From this, the average velocity is examined as well as the velocity power spectra, wake circulation, and measurements of shaft torque among various flow-driven and motor-driven configurations.