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Wind turbine simulations using spectral elements
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.ORCID iD: 0000-0003-2687-8148
2017 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Understanding the flow around wind turbines is a highly relevant research question due to the increased interest in harvesting energy from renewable sources. This thesis approaches the topic by means of numerical simulations using the actuator line method and the incompressible Navier–Stokes equations in the spectral element code Nek5000. The aim is to gain enhanced understanding of the wind turbine wake structure and wind turbine wake interaction. A verification study of the method and implementation is performed against the finite volume solver EllipSys3D using two types of turbines, an idealized constant circulation turbine and the Tjæreborg turbine. It is shown that Nek5000 requires significantly lower resolution to accurately compute the wake development, however, at the cost of a smaller time step.The constant circulation turbine is investigated further with the goal of establishing guidelines for the use of the actuator line method in spectral element codes, where the mesh is inherently non-equidistant and currently used guidelines of force distribution based on Gaussian kernels are difficult to apply. It is shown that Nek5000 requires a larger kernel width in the fixed frame of reference to remove numerical instabilities. Further, the impact of different Gaussian widths on the wake development is investigated in the rotating frame of reference, showing that the convection velocity and the breakdown of the spiral tip and root vortices are dependent on the Gaussian width. In the second part, the flow around single and multiple wind-turbine setups at different operating conditions is investigated and compared with experimental results. The focus is placed on comparing the power and thrust coefficients and the wake development based on the time-averaged streamwise velocity and turbulent stresses. Further the influence of the tower model is investigated both upstream and downstream of the turbine. The results show that the wake is captured accurately in most cases. The loading exhibits a significant dependence on the Reynolds number at which the airfoil data is extracted. When the helical tip vortices are stable the turbulent stresses at the tip vortices are underestimated in the numerical simulations. This is due to the finite resolution and the projection of the actuator line forces in the numerical domain using a prescribed Gaussian width, which leads to lower induced velocities in the helical vortices.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2017. , 32 p.
Series
TRITA-MEK, ISSN 0348-467X ; 17/07
Keyword [en]
wind turbine, wakes, wake interaction, computational fluid dynamics, actuator line method, spectral elements, free-stream turbulence
National Category
Fluid Mechanics and Acoustics
Research subject
Engineering Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-207630ISBN: 978-91-7729-448-1 (print)OAI: oai:DiVA.org:kth-207630DiVA: diva2:1097822
Presentation
2017-06-07, E2, Lindstedtsvägen 3, Stockholm, 10:15 (English)
Opponent
Supervisors
Funder
Swedish Energy Agency
Note

QC 20170523

Available from: 2017-05-23 Created: 2017-05-22 Last updated: 2017-05-23Bibliographically approved
List of papers
1. Actuator line simulations of a Joukowsky and Tjæreborg rotor using spectral element and finite volume methods
Open this publication in new window or tab >>Actuator line simulations of a Joukowsky and Tjæreborg rotor using spectral element and finite volume methods
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2016 (English)In: Journal of Physics, Conference Series, ISSN 1742-6588, E-ISSN 1742-6596, Vol. 753, no 8, 082011Article in journal (Refereed) Published
Abstract [en]

The wake structure behind a wind turbine, generated by the spectral element code Nek5000, is compared with that from the finite volume code EllipSys3D. The wind turbine blades are modeled using the actuator line method. We conduct the comparison on two different setups. One is based on an idealized rotor approximation with constant circulation imposed along the blades corresponding to Glauert's optimal operating condition, and the other is the Tjffireborg wind turbine. The focus lies on analyzing the differences in the wake structures entailed by the different codes and corresponding setups. The comparisons show good agreement for the defining parameters of the wake such as the wake expansion, helix pitch and circulation of the helical vortices. Differences can be related to the lower numerical dissipation in Nek5000 and to the domain differences at the rotor center. At comparable resolution Nek5000 yields more accurate results. It is observed that in the spectral element method the helical vortices, both at the tip and root of the actuator lines, retain their initial swirl velocity distribution for a longer distance in the near wake. This results in a lower vortex core growth and larger maximum vorticity along the wake. Additionally, it is observed that the break down process of the spiral tip vortices is significantly different between the two methods, with vortex merging occurring immediately after the onset of instability in the finite volume code, while Nek5000 simulations exhibit a 2-3 radii period of vortex pairing before merging.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2016
Keyword
Actuators, Codes (symbols), Finite volume method, Merging, Torque, Turbine components, Turbomachine blades, Wakes, Wind turbines, Domain differences, Finite volume code, Helical vortices, Numerical dissipation, Onset of instabilities, Optimal operating conditions, Spectral element method, Wind turbine blades, Vortex flow
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-201777 (URN)10.1088/1742-6596/753/8/082011 (DOI)2-s2.0-84995394418 (Scopus ID)
Conference
5 October 2016 through 7 October 2016
Note

QC 20170217

Available from: 2017-02-17 Created: 2017-02-17 Last updated: 2017-05-23Bibliographically approved
2. Parametric study of the actuator line method in high-order codes
Open this publication in new window or tab >>Parametric study of the actuator line method in high-order codes
2017 (English)Report (Other academic)
Abstract [en]

The high accuracy of spectral element methods combined with low computationalcost and a high level of parallelization, makes them appealing for large-scale investigations of wind turbines and wind turbine interaction using the state-of-the-art actuator line method by Sørensen & Shen (2002). While the spectral element code Nek5000 has already been used for wind turbine simulations by e.g. Peet et al. (2013), Chatterjee & Peet (2015), Chatterjee & Peet (2016) and Kleusberg et al. (2016) for investigations of wind turbine wakes and wake interaction, the implications of the actuator line method in a high-order code and the effect of the involved parameters have not been studied in detail. This paper investigates the constant circulation turbine in the fixed and rotatingframe of reference. In the rotating frame of reference several wake parameters previously discussed e.g. by Ivanell et al. (2009) and Sarmast (2013) are revisitedand analyzed. Further, parametric studies are conducted in the fixed frame ofreference to investigate an observed instablility related to the spectral element width. The instablity is not a property of the spectral element discretization as it is also observed in other research using finite volume techniques. However, the decreased numerical dissipation and the non-equidistant grid used in spectral element methods leads to amplification of the instability. The parameters are investigated on a reduced two-dimensional test case and the conclusions transfered to the full actuator line setup. It is established that a Gaussian width of approximately five times the average grid spacing is necessary to reduce the effect of the instability related to the spectral element width when investigating sensitive flow cases. A force projection method proposed by Pinelli et al. (2010) is investigated as an alternative to the typically used Gaussian kernel. Finally, the influence of this instability is investigated when perturbations are applied tothe flow. Both small-scale perturbations that are introduced at the blade tips and low inflow turbulence which is imposed as an inlet condition are investigated.It is shown that when perturbations are introduced to the flow the large-scale wake behavior in the rotating and fixed frame of reference are similar and a Gaussian width which is 2.4 times the averaged grid spacing is sufficient.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2017. 35 p.
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-207629 (URN)
Funder
Swedish Energy Agency
Note

QC 20170523

Available from: 2017-05-22 Created: 2017-05-22 Last updated: 2017-05-23Bibliographically approved
3. High-order numerical simulations of wind turbine wakes
Open this publication in new window or tab >>High-order numerical simulations of wind turbine wakes
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2017 (English)Report (Other academic)
Abstract [en]

Previous attempts to describe the structure of wind turbine wakes and their mutual interaction were mostly limited to large-eddy and Reynolds-averaged Navier-Stokes simulations using finite volume solvers. We employ the higher-order spectral element code Nek5000 to study the influence of numerical aspects on the prediction of the wind turbine wake structure and the wake interaction between two turbines. The spectral element method enables an accurate representation of the vortical structures, with much lower numerical dissipation than the more commonly used finite volume codes. The blades are modeled as body forces using the actuator line method (ACL) in the incompressible Navier-Stokes equations. Both tower and nacelle are represented with appropriate body forces. An inflow boundary condition is used which emulates the homogeneous isotropic turbulence of wind tunnel flows. We validate the implementation with results from experimental campaigns undertaken at the Norwegian University of Science and Technology, investigate parametric influences and compare computational aspects with the existing finite volume codes. The results show good agreement between the experiments and the numerical simulations.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2017. 17 p.
Keyword
wind turbine wakes, wake interaction, spectral elements, Nek5000
National Category
Fluid Mechanics and Acoustics
Research subject
Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-207628 (URN)
Funder
Swedish Energy Agency
Note

QC 20170523

Available from: 2017-05-22 Created: 2017-05-22 Last updated: 2017-05-23Bibliographically approved

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