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Mutual inductance instability of the tip vortices behind a wind turbine
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. Tech Univ Denmark.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. 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), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.ORCID iD: 0000-0001-9627-5903
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2014 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 755, 705-731 p.Article in journal (Refereed) Published
Abstract [en]

Two modal decomposition techniques are employed to analyse the stability of wind turbine wakes. A numerical study on a single wind turbine wake is carried out focusing on the instability onset of the trailing tip vortices shed from the turbine blades. The numerical model is based on large-eddy simulations (LES) of the Navier-Stokes equations using the actuator line (ACL) method to simulate the wake behind the Tj ae reborg wind turbine. The wake is perturbed by low-amplitude excitation sources located in the neighbourhood of the tip spirals. The amplification of the waves travelling along the spiral triggers instabilities, leading to breakdown of the wake. Based on the grid configurations and the type of excitations, two basic flow cases, symmetric and asymmetric, are identified. In the symmetric setup, we impose a 120 degrees symmetry condition in the dynamics of the flow and in the asymmetric setup we calculate the full 360 degrees wake. Different cases are subsequently analysed using dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD). The results reveal that the main instability mechanism is dispersive and that the modal growth in the symmetric setup arises only for some specific frequencies and spatial structures, e.g. two dominant groups of modes with positive growth (spatial structures) are identified, while breaking the symmetry reveals that almost all the modes have positive growth rate. In both setups, the most unstable modes have a non-dimensional spatial growth rate close to pi/2 and they are characterized by an out-of-phase displacement of successive helix turns leading to local vortex pairing. The present results indicate that the asymmetric case is crucial to study, as the stability characteristics of the flow change significantly compared to the symmetric configurations. Based on the constant non-dimensional growth rate of disturbances, we derive a new analytical relationship between the length of the wake up to the turbulent breakdown and the operating conditions of a wind turbine.

Place, publisher, year, edition, pages
2014. Vol. 755, 705-731 p.
Keyword [en]
instability, vortex interaction, wakes
National Category
Mechanical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-145662DOI: 10.1017/jfm.2014.326ISI: 000341128600036OAI: oai:DiVA.org:kth-145662DiVA: diva2:719486
Funder
Swedish e‐Science Research Center
Note

QC 20140930. Updated from manuscript to article in journal.

Available from: 2014-05-26 Created: 2014-05-26 Last updated: 2017-12-05Bibliographically approved
In thesis
1. Flow control and reduced-order modelling of transition in shear flows
Open this publication in new window or tab >>Flow control and reduced-order modelling of transition in shear flows
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis direct numerical simulation is used to investigate the possibility to delay the transition from a laminar to a turbulent flow in boundary layer flows. Furthermore, modal analysis techniques are used to identify the coherent structures in wind turbine wake.

Among different transition scenarios, the classical transition scenario is considered where the laminar-turbulent transition occursdue to Tollmien-Schlichting (TS) waves. These waves are convectively unstable and when triggered inside the boundary layer, they grow exponentially inamplitude as they are advected downstream of the domain. The aim is to suppressthese waves using flow control strategies based on a row of spatially localised sensors and actuators distributed near the wall inside the boundary layer. To avoid the high dimensionality arising from discretisation of the Navier–Stokes equations, a reduced order model (ROM) based on the Eigensystem Realisation Algorithm(ERA) is obtained and based on that a linear controller is designed. To manip-ulate the flow, a plasma actuator is modelled and implementedas an externalforcing. To account for the restrictions of the plasma actuators, several strategies are proposed and tested within the LQG framework. We studied also the design of a faster controller based on decentralised approach and compared the performance to a more expensive centralised controller. The outcomes revea lsuccessful performance in mitigating the energy of the disturbances inside the boundary layer and suppressing the TS waves.

To extract coherent features of the wind turbine wakes, modal decomposition techniques are employed. In this method a large dynamical system is reduced to a fewer number of degrees of freedom. Two decomposition techniques are employed, namely proper orthogonal decomposition and dynamic mode decomposition. In the former, the flow is decomposed into a set of orthogonal structures which are ranked according to their energy contents in a hierarchical manner. In the latter, the eigenvalues and eigenvectors of the underlying approximate linear operator of the system is evaluated. In particular each mode is associated with a specific frequency and growth rate. The results revealed the coherent structures which are dynamically significant for the onset of instability in the wind turbine wake

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2014. vii, 57 p.
Series
TRITA-MEK, ISSN 0348-467X ; 2014:14
Keyword
Flow control, plasma actuator, wing, leading edge, flat plate, wind turbine, optimal controller, model reduction, proper orthogonal decomposition, dynamic mode decomposition.
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-145631 (URN)978-91-7595-170-6 (ISBN)
Public defence
2014-06-10, Sal F3, Lindstedtsvägen 26. KTH, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20140526

Available from: 2014-05-26 Created: 2014-05-23 Last updated: 2014-05-26Bibliographically approved
2. Numerical study on instability and interaction of wind turbine wakes
Open this publication in new window or tab >>Numerical study on instability and interaction of wind turbine wakes
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Numerical simulations of the Navier-Stokes equations are conducted to achieve a better understanding of the behavior of wakes generated by the wind turbines. The simulations are performed by combining the in-house developed code EllipSys3D with the actuator line technique.

In step one of the project, a numerical study is carried out focusing on the instability onset of the trailing tip vortices shed from a 3-bladed wind turbine. To determine the critical frequency, the wake is perturbed using low-amplitude excitations located near the tip spirals. Two basic flow cases are studied; symmetric and asymmetric setups. In the symmetric setup a 120 degree flow symmetry condition is dictated due to the confining the polar computational grid to 120 degree or introducing identical excitations. In the asymmetric setup, uncorrelated excitations are imposed near the tip of the blades. Both setups are analyzed using proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). By analysing the dominant modes, it was found that in the symmetric setup the amplification of specific waves (traveling structures) traveling along the tip vortex spirals is responsible for triggering the instability leading to wake breakdown, while by breaking the symmetry almost all the modes are involved in the tip vortex destabilization. The presence of unstable modes in the wake is related to the mutual inductance (vortex pairing) instability where there is an out-of-phase displacement of successive helix turns. Furthermore, using the non-dimensional growth rate, it is found that the mutual inductance instability has a universal growth rate equal to Π/2. Using this relationship, and the assumption that breakdown to turbulence occurs once a vortex has experienced sufficient growth, an analytical relationship is provided for determining the length of the stable wake. This expression shows that the stable wake length is inversely proportional to thrust, tip speed ratio and the logarithmic of the turbulence intensity.

In second study, large eddy simulations of the Navier-Stokes equations are also performed to investigate the wake interaction. Previous actuator line simulations on the single model wind turbine show that the accuracy of the results is directly related to the quality of the input airfoil characteristics. Therefore, a series of experiments on a 2D wing are conducted to obtain high quality airfoil characteristics for the NREL S826 at low Reynolds numbers. The new measured data are used to compute the rotor performance. The results show that the power performance as well as the wake development behind the rotor are well-captured. There are, however, some difficulties in prediction of the thrust coefficients. The continuation of this work considers the wake interaction investigations of two turbines inline (full-wake interaction) and two turbines with spanwise offset (half wake interaction). It is demonstrated that the numerical computations are able to predict the rotor performances as well as the flow field around the model rotors, and it can be a suitable tool for investigation of the wind turbine wakes.

In the last study, an evaluation of the performance and near-wake structure of an analytical vortex model is presented. The vortex model is based on the constant circulation along the blades (Joukowsky rotor) and it is able to determine the geometry of the tip vortex filament in the rotor wake, allowing the free wake expansion and changing the local tip vortex pitch. Two different wind turbines have been simulated: a wind turbine with constant circulation along the blade and the other setup with a realistic circulation distribution, to compare the outcomes of the vortex model with real operative wind turbine conditions. The vortex model is compared with the actuator line approach and the presented comparisons show that the vortex method is able to approximate the single rotor performance and qualitatively describe the flow field around the wind turbine but with a negligible computational effort. This suggests that the vortex model can be a substitute of more computationally-demanding methods like actuator line technique to study the near-wake behavior.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2014. xi, 44 p.
Series
TRITA-MEK, ISSN 0348-467X ; 2014:23
Keyword
Wind turbine wakes, Stability, interaction, POD, DMD
National Category
Fluid Mechanics and Acoustics
Research subject
Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-153961 (URN)978-91-7595-298-7 (ISBN)
Public defence
2014-10-31, F3, Lindstedsvägen 26, KTH, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20141010

Available from: 2014-10-10 Created: 2014-10-10 Last updated: 2014-10-10Bibliographically approved

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Schlatter, PhilippHenningson, Dans S.

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