Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session L13: Wind Turbines: Wakes |
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Chair: Paolo Luzzatto-Fegiz, UC Santa Barbara Room: 201 |
Monday, November 23, 2015 4:05PM - 4:18PM |
L13.00001: Modelling wind turbine wakes using the turbulent entrainment hypothesis Paolo Luzzatto-Fegiz Simple models for turbine wakes have been used extensively in the wind energy community, both as independent tools, as well as to complement more refined and computationally-intensive techniques. Jensen (1983; see also Kati\'{c} \textit{et al.} 1986) developed a model assuming that the wake radius grows linearly with distance $x$, approximating the velocity deficit with a top-hat profile. While this model has been widely implemented in the wind energy community, recently Bastankhah {\&} Port\'{e}-Agel (2014) showed that it does not conserve momentum. They proposed a momentum-conserving theory, which assumed a Gaussian velocity deficit and retained the linear-spreading assumption, significantly improving agreement with experiments and LES. While the linear spreading assumption facilitates conceptual modeling, it requires empirical estimates of the spreading rate, and does not readily enable generalizations to other turbine designs. Furthermore, field measurements show sub-linear wake growth with $x$ in the far-wake, consistently with results from fundamental turbulence studies. We develop a model by relying on a simple and general turbulence parameterization, namely the entrainment hypothesis, which has been used extensively in other areas of geophysical fluid dynamics. Without assuming similarity, we derive an analytical solution for a circular turbine wake, which predicts a far-wake radius increasing with $x^{1/3}$, and is consistent with field measurements and fundamental turbulence studies. Finally, we discuss developments accounting for effects of stratification, as well as generalizations to other turbine designs. [Preview Abstract] |
Monday, November 23, 2015 4:18PM - 4:31PM |
L13.00002: Similarity considerations for a turbulent axisymmetric wake with rotation subjected to a boundary layer flow Martin Wosnik Recently an analytical and experimental investigation of the turbulent axisymmetric wake with rotation found a new asymptotic scaling function for the mean swirl, $W_{max}\propto U_o^{3/2}\propto x^{-1}$ (Dufresne and Wosnik, {\em Mar Technol Soc J}, \textbf{47}, no.4, 193-205, 2013). An equilibrium similarity theory derived scaling functions from the conditions for the existence of similarity directly from the equations of motion. Axial and azimuthal (swirl) velocities were measured in the wake of a single 3-bladed wind turbine in a free stream up to 20 diameters downstream, and the data were found to support the theoretical results. The scaling implies that the mean swirl decays faster, with $x^{-1}$, than the mean velocity deficit, with $x^{-2/3}$. Real wind turbines, however, operate in the atmospheric boundary layer. They are subjected to mean shear and turbulence, both have been observed to improve wake recovery. Similarity considerations are extended to place a turbulent axisymmetric wake with rotation in a boundary layer flow, and the scaling implications are examined. Corresponding experiments were carried out in the UNH Flow Physics Facility, using model wind turbines of various sizes as swirling wake generators. [Preview Abstract] |
Monday, November 23, 2015 4:31PM - 4:44PM |
L13.00003: Dynamic Mode Decomposition Analysis of Wind Turbine Wakes Vaughan Thomas, Claire VerHulst, Charles Meneveau, Dennice Gayme In this work we explore the use of dynamic mode decomposition (DMD) to analyze three dimensional large eddy simulations (LES) of wind farms in order to isolate the temporal characteristics of key flow structures. There are a number of variants of DMD that each produce a reduced order linear system that approximates the dynamics of the original system. Here, we are interested in finding the lowest order system which captures the wake dynamics and other essential flow features. When DMD is applied to wake regions of LES of wind farms, the results isolate the mean wake and flow structures whose oscillation determines the meandering behavior of the wake. This ability to capture the wake dynamics has important implications for wind farm modeling and control as they permit the construction of time-varying wake models that can capture time-varying effects such as wake meandering. [Preview Abstract] |
Monday, November 23, 2015 4:44PM - 4:57PM |
L13.00004: Optimal control of wind farms for power tracking using simplified one-dimensional convection-diffusion equation Carl Shapiro, Pieter Bauweraerts, Johan Meyers, Charles Meneveau, Dennice Gayme Coordinated control of wind turbines within a wind farm, accounting for wake interactions and associated flow phenomena, has the potential to provide a number of important services to the power grid. In this work we develop a simple time-dependent extension of a standard steady-state wake model that is used to obtain an optimal control strategy for tracking a time-varying power signal. First, we introduce a one-dimensional convection-diffusion equation for wind turbine wakes that is based on the Jensen wake model and the actuator disk model. This equation is tested during wind farm start up by comparing to large-eddy simulations of wind farms with both aligned and staggered turbine arrangements. Second, we investigate optimal control for power tracking applications, where turbines are controlled via the local thrust coefficient. The control strategy is designed to minimize the squared difference between the modeled farm power and a given power reference signal. Finally, the control strategies obtained are tested using large-eddy simulations. [Preview Abstract] |
Monday, November 23, 2015 4:57PM - 5:10PM |
L13.00005: Investigation on the near-wake flow structures of a utility-scale wind turbine using snowflake based flow visualization Teja Dasari, Mostafa Toloui, Michele Guala, Jiarong Hong Super-large-scale particle image velocimetry and flow visualization techniques using natural snow particles have been shown as an effective tool to probe the structure of the flow around full-scale wind turbines (Hong et al. \textit{Nature Comm.} 2014). Here we present a follow-up study based on the data collected during a deployment around the 2.5 MW wind turbine at EOLOS Wind Energy Research Station on April, 4$^{\mathrm{th}}$, 2014. The dataset includes the snow visualization of flow fields from different perspectives in the near wake of the turbine. The motions of the dominant coherent structures including tip, blade root, hub and tower vortices, represented by the snow voids, are examined with the objective of quantifying and correlating their behavior with the meteorological and turbine operating conditions. Some preliminary studies on flow-structure interaction are also performed by correlating the data from strain gauges, accelerometers mounted on the turbine blades, with the flow measurements. The statistical analysis of the motions of blade induced vortices shows a clear impact of atmospheric turbulence and vortex interaction on flow development in the near wake. The result further indicates a strong connection between near-wake vorticity field, turbine operation and structure deformations. [Preview Abstract] |
Monday, November 23, 2015 5:10PM - 5:23PM |
L13.00006: Studying Wake Deflection of Wind Turbines in Yaw using Drag Disk Experiments and Actuator Disk Modeling in LES Michael Howland, Juliaan Bossuyt, Johan Meyers, Charles Meneveau Recently, there has been a push towards the optimization in the power output of entire large wind farms through the control of individual turbines, as opposed to operating each turbine in a maximum power point tracking manner. In this vane, the wake deflection by wind turbines in yawed conditions has generated considerable interest in recent years. In order to effectively study the wake deflection according to classical actuator disk momentum theory, a 3D printed drag disk model with a coefficient of thrust of approximately 0.75 -- 0.85 and a diameter of 3 cm is used, studied under uniform inflow in a wind tunnel with test section of 1 m by 1.3 m, operating with a negligible inlet turbulence level at an inflow velocity of 10 m/s. Mean velocity profile measurements are performed using Pitot probes. Different yaw angles are considered, including 10, 20, and 30 degrees. We confirm earlier results that (e.g.) a 30 degree yaw angle deflects the center of the wake around 1/2 of a rotor diameter when it impinges on a downstream turbine. Detailed comparisons between the experiments and Large Eddy Simulations using actuator disk model for the wind turbines are carried out in order to help validate the CFD model. [Preview Abstract] |
Monday, November 23, 2015 5:23PM - 5:36PM |
L13.00007: A Stereo PIV Study on the Wake Characteristics behind Dual-Rotor Wind Turbines Hui Hu, Zhenyu Wang, Wei Tian We report an experimental study to investigate the aeromechanics and wake characteristics of dual-rotor wind turbines (DRWTs) with co- and counter-rotating configurations, in comparison to those of a conventional single-rotor wind turbine (SRWT). The experiments were performed in a large-scale Aerodynamic/Atmospheric Boundary Layer (AABL) wind tunnel under neutral stability conditions. In addition to measuring the power outputs and dynamic wind loads acting on the SRWT and DRWT systems, a stereoscopic PIV was used for detailed wake flow field measurements (free-run and phase-locked) to quantify the characteristics of the turbulent turbine wake flow and to reveal visualize the evolution of the unsteady vortex structures in the wakes of DRWTs, in comparison with those behind a conventional SRWT systems. The detailed flow field measurements are correlated with the dynamic wind loads and power output measurements to elucidate underlying physics for higher total power yield and better durability of the wind turbines. [Preview Abstract] |
Monday, November 23, 2015 5:36PM - 5:49PM |
L13.00008: Effect of nacelle on wake meandering in a laboratory scale wind turbine using LES Daniel Foti, Xiaolei Yang, Michele Guala, Fotis Sotiropoulos Wake meandering, large scale motion in the wind turbine wakes, has considerable effects on the velocity deficit and turbulence intensity in the turbine wake from the laboratory scale to utility scale wind turbines. In the dynamic wake meandering model, the wake meandering is assumed to be caused by large-scale atmospheric turbulence. On the other hand, Kang \emph{et al.} (\emph{J. Fluid Mech.}, 2014) demonstrated that the nacelle geometry has a significant effect on the wake meandering of a hydrokinetic turbine, through the interaction of the inner wake of the nacelle vortex with the outer wake of the tip vortices. In this work, the significance of the nacelle on the wake meandering of a miniature wind turbine previously used in experiments (Howard \emph{et al.}, \emph{Phys. Fluid}, 2015) is demonstrated with large eddy simulations (LES) using immersed boundary method with fine enough grids to resolve the turbine geometric characteristics. The three dimensionality of the wake meandering is analyzed in detail through turbulent spectra and meander reconstruction. The computed flow fields exhibit wake dynamics similar to those observed in the wind tunnel experiments and are analyzed to shed new light into the role of the energetic nacelle vortex on wake meandering. [Preview Abstract] |
Monday, November 23, 2015 5:49PM - 6:02PM |
L13.00009: Dynamic Gaussian wake meandering in a restricted nonlinear simulation framework Joel Bretheim, Fernando Porte-Agel, Dennice Gayme, Charles Meneveau Wake meandering can significantly impact the performance of large-scale wind farms. Simplified wake expansion (e.g., Jensen/PARK) models, which are commonly used in industry, lead to accurate predictions of certain wind farm performance characteristics (e.g., time- and row-averaged total power output). However, they are unable to capture certain temporal phenomena such as wake meandering, which can have profound effects on both power output and turbine loading. We explore a dynamic wake modeling framework based on the approach proposed by Larsen et al. (Wind Energy 11, 2008) whereby turbine ``wake elements'' are treated as passive tracers and advected by an averaged streamwise flow. Our wake elements are treated as Gaussian velocity deficit profiles (Bastankhah and Porte-Agel, Renew. Energy 70, 2014). A restricted nonlinear (RNL) model is used to capture the turbulent velocity fluctuations that are critical to the wake meandering phenomenon. The RNL system, which has been used in prior wall-turbulence studies, provides a computationally affordable way to model atmospheric turbulence, making it more reasonable for use in engineering models than the more accurate but computationally intensive approaches like large-eddy simulation. [Preview Abstract] |
Monday, November 23, 2015 6:02PM - 6:15PM |
L13.00010: An Immersed Boundary - Adaptive Mesh Refinement solver (IB-AMR) for high fidelity fully resolved wind turbine simulations Dionysios Angelidis, Fotis Sotiropoulos The geometrical details of wind turbines determine the structure of the turbulence in the near and far wake and should be taken in account when performing high fidelity calculations. Multi-resolution simulations coupled with an immersed boundary method constitutes a powerful framework for high-fidelity calculations past wind farms located over complex terrains. We develop a 3D Immersed-Boundary Adaptive Mesh Refinement flow solver (IB-AMR) which enables turbine-resolving LES of wind turbines. The idea of using a hybrid staggered/non-staggered grid layout adopted in the Curvilinear Immersed Boundary Method (CURVIB) has been successfully incorporated on unstructured meshes and the fractional step method has been employed. The overall performance and robustness of the second order accurate, parallel, unstructured solver is evaluated by comparing the numerical simulations against conforming grid calculations and experimental measurements of laminar and turbulent flows over complex geometries. We also present turbine-resolving multi-scale LES considering all the details affecting the induced flow field; including the geometry of the tower, the nacelle and especially the rotor blades of a wind tunnel scale turbine. [Preview Abstract] |
Monday, November 23, 2015 6:15PM - 6:28PM |
L13.00011: Wind tunnel measurements of the power output variability and unsteady loading in a micro wind farm model Juliaan Bossuyt, Michael Howland, Charles Meneveau, Johan Meyers To optimize wind farm layouts for a maximum power output and wind turbine lifetime, mean power output measurements in wind tunnel studies are not sufficient. Instead, detailed temporal information about the power output and unsteady loading from every single wind turbine in the wind farm is needed. A very small porous disc model with a realistic thrust coefficient of 0.75 - 0.85, was designed. The model is instrumented with a strain gage, allowing measurements of the thrust force, incoming velocity and power output with a frequency response up to the natural frequency of the model. This is shown by reproducing the -5/3 spectrum from the incoming flow. Thanks to its small size and compact instrumentation, the model allows wind tunnel studies of large wind turbine arrays with detailed temporal information from every wind turbine. Translating to field conditions with a length-scale ratio of 1:3,000 the frequencies studied from the data reach from $10^{-4}$ Hz up to about $6.10^{-2}$ Hz. The model's capabilities are demonstrated with a large wind farm measurement consisting of close to 100 instrumented models. A high correlation is found between the power outputs of stream wise aligned wind turbines, which is in good agreement with results from prior LES simulations. [Preview Abstract] |
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