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Actuator line simulations of a Joukowsky and Tjæreborg rotor using spectral element and finite volume methods
KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. Uppsala University, Wind Energy Section, Campus Gotland, SE-621 67 Visby, Sweden.
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2016 (English)Conference proceedings (editor) (Refereed)
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. Vol. 753, no 8, article id 082011
Keywords [en]
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: urn:nbn:se:kth:diva-201777DOI: 10.1088/1742-6596/753/8/082011Scopus ID: 2-s2.0-84995394418OAI: oai:DiVA.org:kth-201777DiVA, id: diva2:1075305
Conference
5 October 2016 through 7 October 2016
Note

QC 20170217

Available from: 2017-02-17 Created: 2017-02-17 Last updated: 2019-06-18Bibliographically approved
In thesis
1. Wind turbine simulations using spectral elements
Open this publication in new window or tab >>Wind turbine simulations using spectral elements
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. p. 32
Series
TRITA-MEK, ISSN 0348-467X ; 17/07
Keywords
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:nbn:se:kth:diva-207630 (URN)978-91-7729-448-1 (ISBN)
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
2. Wind-turbine wakes - Effects of yaw, shear and turbine interaction
Open this publication in new window or tab >>Wind-turbine wakes - Effects of yaw, shear and turbine interaction
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Vindturbinsvakar –Effekten av girning, skjuvning och turbininteraktion
Abstract [en]

The actuator-line method is used together with the incompressible Navier–Stokes equations to investigate the flow development behind wind turbines. Initial investigations focus on providing a thorough validation of the implementation in the spectral-element flow solver Nek5000 against existing numerical and experimental datasets. It is shown that the current implementation gives an accurate representation of the flow field for different turbine geometries, inflow conditions, yaw misalignment, and when considering multiple turbines. This enables an in-depth study of the wake physics in these configurations.

The yawed wind-turbine wake development is shown to depend on the tip-speed ratio, both in terms of the wake deficit and the generation of the counter-rotating vortices known to occur in yawed turbine wakes. For lower tip-speed ratios the wake deficit exhibited significant asymmetries with respect to the horizontal plane due to the advancing/retreating effect. At high tip-speed ratios this effect became negligible compared to the skewed wake effect, which affects the symmetry with respect to the vertical plane. These inhomogeneities in the averaged wake development also affect the tip-vortex breakdown, leading to different locations of the tip-vortex breakdown along the wake azimuth due to the significant azimuthal variations of the tip-vortex strength and convection velocity. An analysis of the interaction of a yawed wind-turbine wake with a sheared inflow exposed a dependency of the wake deflection and recovery on the yaw orientation, which then resulted in significant differences in the combined power output of a two-turbine setup. More detailed studies of the tip-vortex breakdown in sheared flows using single-frequency perturbations revealed that a sheared inflow changes the spatial growth rate of the tip vortices along the vertical axis, due to the varying tip-vortex convection velocity. However, by applying a scaling based on local vortex parameters, the growth rates collapse to the canonical case of an infinite row of point vortices. Finally, an idealized scenario of two in-line turbines with a steady tip-vortex development is investigated. By applying a range of controlled perturbations, modes were excited, which exhibited in-phase or out-of-phase displacement between the vortex system of the upstream and the downstream turbine for certain frequencies.

Abstract [sv]

Den så kallade actuator line-metoden används tillsammans med inkompressibla Navier–Stokes ekvationer för att undersöka strömningens utveckling bakom vindturbiner. Inledande studier syftar till att utförligt validera implementationen i spektralelementkoden Nek5000 mot befintliga numeriska och experimentella datamängder. Det visas att den nuvarande implementationen ger en noggrann representation av strömningsfältet för alla undersökta turbingeometrier. Vidare fångas utvecklingen hos vaken väl för en rad olika inflödesvillkor, förturbingirning, och under interaktion mellan flera turbiner.

Vakutvecklingen för en girad turbin visas bero signifikant på kvoten mellan vingspetsens och friströmmens hastighet, både när det gäller hastighetsunderskottet i vaken och bildningen av de motroterande vakvirvlarna. För låga hastighetskvoter mellan vingspetsen och friströmmen uppvisar vakens hastighetsunderskott en betydande asymmetri med avseende på horisontalplanet genom en så kallad avancerande/retirerande effekt. För höga hastighetskvoter blir denna effekt däremot försumbar i jämförelse med vakens skevhet som påverkar symmetrin med avseende på vertikalplanet. Dessa inhomogeniteter i den medelvärdesbildade vakutvecklingen påverkar också det turbulenta nedbrottet hos vingspetsvirvlarna, vilket inträffar vid olika positioner i vinkelled på grund av signifikanta vinkelvariationer hos virvelstyrkan och konvektionshastigheten. En analys of interaktionen mellan en girad turbinvak och en inkommande skjuvströmning avslöjar ett beroende hos vakens förskjutning och återhämtning på girningens riktning, vilket resulterar i betydande skillnader i den sammantagna effekten hos två turbiner. Mer detaljerade studier av spetsvirvlarnas nedbrott i skjuvströmningar med enfrekvensstörningar visar att ett skjuvat inflöde förändrar den spatiella tillväxtgraden längs den vertikala axeln på grund av varierande konvektionshastighet hos spetsvirvlarna.Tillväxtgraderna sammanfaller dock med motsvarande värde för det klassiska fallet med två oändliga virvelrader, om de skalas med lokala virvelparametrar. Slutligen studeras en stationär virvelutveckling för ett idealiserat fall bestående av två turbiner i linje med varandra. Genom att applicera en rad kontrollerade störningar, exciteras moder som beroende på frekvens uppvisar förskjutningar i eller ur fas med virvelsystemen från turbinen uppströms och nedströms.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2019. p. 58
Series
TRITA-SCI-FOU ; 2019:29
Keywords
wind-turbine wakes, yaw, tip-vortex breakdown, shear, computational fluid dynamics, actuator-line method, spectral-element method, Vindturbinsvakar, girning, turbulent nedbrott hos spetsvirvlar, skjuvning, vakinteraktion, beräkningsströmningsdynamik, actuator line-metod, spektralelementmetod
National Category
Fluid Mechanics and Acoustics
Research subject
Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-251450 (URN)
Public defence
2019-06-04, H1, Teknikringen 33, Stockholm, 13:50 (English)
Opponent
Supervisors
Funder
Swedish Energy Agency
Note

QC20190514

Available from: 2019-05-14 Created: 2019-05-14 Last updated: 2019-05-14Bibliographically approved

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