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A comparison between a simplified vortex model and actuator line simulations of a horizontal axis wind turbine
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0001-8667-0520
DTU wind energy.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
(English)Manuscript (preprint) (Other academic)
National Category
Mechanical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-120588OAI: oai:DiVA.org:kth-120588DiVA: diva2:615796
Funder
StandUp for Wind
Note

QS 2013

Available from: 2013-04-12 Created: 2013-04-12 Last updated: 2017-01-18Bibliographically approved
In thesis
1. 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
2013 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The optimization of new generation of the wind farms is dependent on our understanding of wind turbine wake development, wake dynamics and the interaction of the wakes. The overall goal of the optimization is decreasing the fatigue loading and increasing the power production of the wind farms. To this end, numerical simulations of the wake of wind turbine are performed by means of applying fourth order finite volume code, EllipSys3D along with the actuator line method. The basic idea behind such actuator line method is representing the blades  by employing the body forces in the Navier--Stokes equations. The forces are then determined through a combination of Blade Element Momentum (BEM) method and tabulated airfoil data.

In the first part of thesis, the dynamics of the tip vortices behind a single wind turbine is investigated. The generated wind turbine wake is perturbed using small amplitude disturbances. The amplification of the wave along the spiral triggers some modes leading to wake instability. The perturbed wake is then analyzed using modal decomposition in which  the dominant modes leading to the onset of instability can be identified. Two different cases are studied; symmetric configuration, in that the wake is excited by identical perturbation near each blade tip; and non-symmetric configuration, in which general perturbations are used. The corresponding result confirms that the instability is dispersive and the growth occurs only for specific frequencies in symmetric case. However in general non-symmetric case, all the modes have positive spatial growth rate. This can be explained through the fact that breaking the symmetry results in superposition of the unstable modes related to three-bladed, two-bladed and one-blade wind turbine wake.

A rotor experiment has been recently carried out at NTNU wind tunnel using horizontal axis model scale rotors, for detailed investigation of the wake development. A single rotor configuration was first tested and then a setup of two rotors inline was investigated.  Previous numerical investigation of single wind turbine wake using actuator line method shows that the quality of the result depend on the input tabulated airfoil data. Due to absence of the reliable data, a series of experiments using 2-D airfoil were carried out at DTU wind tunnel to obtain the tabulated airfoil data for the Reynolds number corresponding to NTNU rotor operating conditions. The numerical simulations using actuator line method together with the new experimental airfoil data were then carried out for studying the  phenomenon of wake interaction between the two wind turbines.

Different cases are simulated with various tip speed ratio of the downstream turbine specifically adjusted to match the NTNU experiments. The characteristics of the interacting wakes were extracted including the rotor performance and the averaged velocity and turbulence fields as well as the development of wake generated vortex structures. The obtained  results were in agreement of NTNU experimental data showing that  numerical computations are reliable tools for prediction of wind turbine aerodynamics.

The third aim of the project is to perform a comparison between an analytical vortex model and the actuator line of an isolated horizontal axis wind turbine (simulated with the ACL approach) to assess whether the predictions by the vortex model can substitute more expensive CFD approaches. The model is based on the constant circulation along three blade (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: one with constant circulation along the blade, to replicate the vortex method approximations, and the other with a realistic circulation distribution, to compare the outcomes of the vortex model with real operative wind turbine conditions (Tj\ae reborg wind turbine). The vortex model matched the numerical simulation of the turbine withconstant blade circulation in terms of the near wake structure and the local forces along the blade. The simple vortex codeis therefore able to provide an estimation of the flow around the wind turbine similar to the actuator line code but with anegligible computational effort. The results from the Tj\ae reborg turbine case showed some discrepancies between the twoapproaches although the overall agreement is qualitatively good. This could be considered as a validation for the analytical method for more general conditions.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. vi, 38 p.
Series
Trita-MEK, ISSN 0348-467X ; 2013:08
Keyword
Wind Turbines, CFD, EllipSys3D, Actuator Line, Stability, Wake, Vortex Model
National Category
Fluid Mechanics and Acoustics Applied Mechanics Energy Engineering
Research subject
SRA - E-Science (SeRC)
Identifiers
urn:nbn:se:kth:diva-120579 (URN)978-91-7501-706-8 (ISBN)
Presentation
2013-04-23, E3, Lindstedsvagen 3, KTH, Stockholm, 10:15 (English)
Opponent
Supervisors
Projects
Nordic Consortium: Optimization and Control of large wind farms
Funder
Swedish e‐Science Research Center, 76290
Note

QC 20130412

Available from: 2013-04-12 Created: 2013-04-11 Last updated: 2013-04-12Bibliographically 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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