To maximize the effectiveness of the rapidly increasing capacity of installed wind energy resources, new models must be developed that are capable of more nuanced control of each wind turbine so that each device is more responsive to inflow events. Models used to plan wind turbine arrays and control behavior of devices within the farm currently make questionable estimates of the incoming atmospheric flow and update turbine configurations infrequently. As a result, wind turbines often operate at diminished capacities, especially in arrays where wind turbine wakes interact and inflow conditions are far from ideal. New turbine control and wake prediction models must be developed to tune individual devices and make accurate power predictions. To that end, wind tunnel experiments are conducted detailing the turbulent flow in the wake of a wind turbine in a model-scale array. The proper orthogonal decomposition (POD) is applied to characterize the spatial evolution of structures in the wake. Mode bases from distinct downstream locations are reconciled through a secondary decomposition, called double proper orthogonal decomposition (DPOD), indicating that modes of common rank in the wake share an ordered set of sub-modal projections whose organization delineates underlying wake structures and spatial evolution. The doubly truncated basis of sub-modal structures represents a reduction to 0.015% of the total degrees of freedom of the wind turbine wake. Low-order representations of the Reynolds stress tensor are made using only the most dominant DPOD modes, corrected to account for energy excluded from the truncated basis with a tensor of constant coefficients defined to rescale the low-order representation of the stresses to match the original statistics. Data from the wind turbine wake are contrasted against simulation data from a fully-developed channel flow, illuminating a range of anisotropic states of turbulence. Complexity of flow descriptions resulting from truncated POD bases is suppressed in severe basis truncations, exaggerating anisotropy of the modeled flow and, in extreme cases, can lead to the loss of three dimensionality. Constant corrections to the low-order descriptions of the Reynolds stress tensor reduce the root-mean-square error between low-order descriptions of the flow and the full statistics as much as 40% and, in some cases, reintroduce three-dimensionality to severe truncations of POD bases. Low-dimensional models are constructed by coupling the evolution of the dynamic mode coefficients through their respective time derivatives and successfully account for non-linear mode interaction. Deviation between time derivatives of mode coefficients and their least-squares fit is amplified in numerical integration of the system, leading to unstable long-time solutions. Periodic recalibration of the dynamical system is undertaken by limiting the integration time and using a virtual sensor upstream of the wind turbine actuator disk in to read the effective inflow velocity. A series of open-loop transfer functions are designed to inform the low-order dynamical system of the flow incident to the wind turbine rotor. Validation data shows that the model tuned to the inflow reproduces dynamic mode coefficients with little to no error given a sufficiently small interval between instances of recalibration. The reduced-order model makes accurate predictions of the wake when informed of turbulent inflow events. The modeling scheme represents a viable path for continuous time feedback and control that may be used to selectively tune a wind turbine in the effort to maximize power output of large wind farms.

A wind turbine array was constructed in the wind tunnel at Portland State University in a standard Cartesian arrangement. Configurations of the turbine array were tested with rotor blades set to rotate in either a clockwise or counter-clockwise sense. Measurements of velocity were made with stereo particle-image velocimetry. Mean statistics of velocities and Reynolds stresses clearly show the effect of direction of rotation of rotor blades for both entrance and exit row turbines. Rotational sense of the turbine blades is visible in the mean spanwise velocity W and the Reynolds shear stress -[macron over vw]. The normalized anisotropy tensor was decomposed yielding invariants [lowercase eta] and [lowercase xi], which are plotted onto the Lumley triangle. Invariants of the normalized Reynolds stress anisotropy tensor indicate that distinct characters of turbulence exist in regions of the wake following the nacelle and the rotor blade tips. Eigendecomposition of the tensor yields principle components and corresponding coordinate system transformations. Characteristic spheroids are composed with the eigenvalues from the decomposition yielding shapes predicted by the Lumley triangle. Rotation of the coordinate system defined by the eigenvectors demonstrates streamwise trends, especially trailing the top rotor tip and below the hub of the rotors. Direction of rotation of rotor blades is evidenced in the orientation of characteristic spheroids according to principle axes. The characteristic spheroids of the anisotropy tensor and their relate alignments varies between cases clearly seen in the inflows to exit row turbines. There the normalized Reynolds stress anisotropy tensor shows cumulative effects of the rotational sense of upstream turbines. Comparison between the invariants of the Reynolds stress anisotropy tensor and terms from the mean mechanical energy equation indicate a correlation between the degree of anisotropy and the regions of the wind turbine wakes where turbulence kinetic energy is produced. The flux of kinetic energy into the momentum-deficit area of the wake from above the canopy is associated with prolate characteristic spheroids. Flux upward into the wake from below the rotor area is associate with oblate characteristic spheroids. Turbulence in the region of the flow directly following the nacelle of the wind turbines demonstrates more isotropy compared to the regions following the rotor blades. The power and power coefficients for wind turbines indicate that flow structures on the order of magnitude of the spanwise turbine spacing that increase turbine efficiency depending on particular array configuration.

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.

Vortex identification techniques are used to analyze the flow structure in a 4 x 3 array of scale model wind turbines. Q-criterion, Δ-criterion, and λ2-criterion are applied to Particle Image Velocimetry data gathered fore and aft of the last row centerline turbine. Q-criterion and λ2-criterion provide a clear indication of regions where vortical activity exists while the Δ-criterion does not. Galilean decomposition, Reynolds decomposition, vorticity, and swirling strength are used to further understand the location and behavior of the vortices. The techniques identify and display the high magnitude vortices in high shear zones resulting from the blade tips. Using Galilean and Reynolds decomposition, swirling motions are shown enveloping vortex regions in agreement with the identification criteria. The Galilean decompositions are 20% and 50% of a convective velocity of 7 m/s. As the vortices convect downstream, these vortices weaken in magnitude to approximately 25% of those present in the near wake. A high level of vortex activity is visualized as a result of the top tip of the wind turbine blade; the location where the highest vertical entrainment commences.

An experimental investigation was performed to measure Reynolds stresses in the turbulent flow downstream of a large-scale linear turbine cascade. A rotatable X-wire hot-wire probe that allows redundant data to be taken with solution for mean velocities and turbulence quantities by least-squares fitting procedures was developed. This measurement technique was verified in a fully-developed turbulent pipe flow; the results show the accuracy of the probe when used in an end-flow orientation at various incidence angles and with a multiple number of angular settings. Traverses with a single hot-wire at mid-span near the blade row exit show very high levels of turbulence locally in the blade wake near the trailing edge which quickly lessen in magnitude downstream. The rotatable X-wire was used to obtain the Reynolds stresses on a measurement plane located 10% of an axial chord downstream of the trailing edge. Here the turbulence kinetic energy exhibits a distribution resembling the contours of total pressure loss obtained previously, but is highest in the blade wake where losses are relatively low. The turbulent shear stresses obtained are consistent in sign and magnitude with the gradients of mean velocity. The mass-averaged turbulence kinetic energy accounts for 21% of the total pressure loss at this measurement plane. / Master of Science

This thesis focuses on generating real world turbulence levels in a water tunnel rotor test using fractal grids and characterizing the effect of the fractal grid generated-turbulence on the performance of hydrokinetic turbines. The research of this thesis is divided into three studies: one field study and two laboratory studies. The field study was conducted at the Canadian Hydro Kinetic Turbine Test Centre (CHTTC) on the Winnipeg River. An Acoustic Doppler Velocimeter (ADV) was used in the field study to collect flow measurements in the river. The laboratory studies were conducted at the University of Victoria (UVic) fluids research lab and the Sustainable Systems Design Lab (SSDL). In addition, the Particle Image Velocimetry (PIV) technique was used in the experiential studies to obtain quantitative information about the vector flow field along the test section, both upstream and downstream of the rotor’s plane. The first study is a field study aiming to provide real flow characteristics and turbulence properties at different depths from the free-surface to boundary layer region of a fast river current by conducting a field study in the Winnipeg River using ADV. A novel technique to deploy and control an ADV from free-surface to boundary layer in a fast-current channel is introduced in this work. Flow characteristics in the river, including mean flow velocities and turbulence intensity profiles are analyzed. The obtained results indicate that the maximum mean velocity occurs below the free-surface, suggesting that the mean velocity is independent of the channel depth. From the free-surface to half depth, it was found that changes in both the mean velocity and turbulence intensity are gradual. From mid-depth to the river bed, the mean velocity drops rapidly while the turbulence intensity increases at a fast rate. The turbulent intensity varied from 9% at the free-surface to around 17.5% near the river bed. The results of this study were used in the second lab study to help designing a fractal grid for a recirculating water flume tank. The goal was to modify the turbulence intensity in the water tunnel such that the generated turbulence was similar to that in the river at a location typical of a hydrokinetic device. The properties of fractal-generated turbulence were experimentally investigated by means of 2D Particle Image Velocimetry (PIV). The streamwise turbulent intensity profiles for different grids along the channel are presented. Additionally, visualization of the average and fluctuating flow fields are also presented. The results are in good agreement with results in literature. The third and final study investigated the power coefficient of a scale hydrokinetic turbine rotor in controlled turbulent flow (7.4 % TI), as well as in the low-turbulence smooth flow (0.5% TI) typical of lab scale testing. PIV was employed for capturing the velocity field. The results show that using realistic TI levels in the water tunnel significantly decrease the turbine’s power coefficient compared to smooth flow, highlighting the importance of considering this effect in future experimental campaigns. / Graduate

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<p dir="ltr">In this thesis, an experimental procedure for assessing unsteady fluctuations in flow velocity inside an annular low pressure turbine test facility using constant temperature anemometry is established. This procedure is then applied to two test cases in order to validate the methodology and build expertise with the measurement techniques involved. The results of these experiments appear to be reasonable and in good agreement with the body of literature documenting such cases. After the procedure is validated, the experiments in the annular test section are conducted and the results are processed according to the same methodology as previous. The results provide spatial and temporal understanding of the flow at a plane downstream of the blade row. The uncertainties of measured quantities are computed and the experimental results are contextualized with a comparison to a numerical study. The body of work is assessed to determine whether the research objective has been met and recommendations for future studies are given.</p>

Measuring the liquid velocity and turbulence parameters in multiphase flows is a challenging task. In general, measurements based on optical methods are hindered by the presence of the gas phase. In the present work, it is shown that this leads to a sampling bias. Here, particle image velocimetry (PIV) is used to measure the liquid velocity and turbulence in a bubble column for different gas volume flow rates. As a result, passing bubbles lead to a significant sampling bias, which is evaluated by the mean liquid velocity and Reynolds stress tensor components. To overcome the sampling bias a window averaging procedure that waits a time depending on the locally distributed velocity information (hold processor) is derived. The procedure is demonstrated for an analytical test function. The PIV results obtained with the hold processor are reasonable for all values. By using the new procedure, reliable liquid velocity measurements in bubbly flows, which are vitally needed for CFD validation and modeling, are possible. In addition, the findings are general and can be applied to other flow situations and measuring techniques.