comparison of the actuator line model with fully resolved...

Institute of Aerodynamics and Gas Dynamics

Comparison of the Actuator Line Model with

Fully Resolved Simulations in Complex

Environmental Conditions

Pascal Weihing, Christoph Schulz,

Thorsten Lutz, Ewald Krämer

• Wake Conference

2017

Complex Terrain

• Effects of orography:

• Inclination, yaw, local over-speed

• Roughness / forest

• Stratification

• Atmospheric turbulence

Offshore

• Atmospheric turbulence

• Stratification

• Coriolis force

• Yaw misalignment

• Wake turbine interaction

Challenges in modeling the flow around wind turbines

Motivation

30/05/2017 University of Stuttgart 3

Non-uniform velocity distribution in the rotor plane unsteady aerodynamic effects

Accuracy of the ACL in such conditions?

[1]

University of Stuttgart 4

Numerical Modeling of Wind Turbines in FLOWer

Fully resolved rotor (FR)

• Boundary layer of the airfoil is resolved 𝑦+ ≈ 1

• Turbine components are separately meshed and integrated

using the overset grid technique

Detailed view into flow phenomena around the rotor

Accurate prediction of loads and power including unsteady

aerodynamic effects without need for further modeling

Disadvantages:

• Time consuming meshing

• High computational effort

Only suitable for simulation of wind farms to a limited extent

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• Effect of the blades on the flow modeled by a momentum source term

𝝏

𝝏𝒕𝑽

𝑾𝒅𝑽 + 𝑭 𝑺

⋅ 𝒏𝒅𝑺 = 𝑺 𝑾 𝒅𝑽𝑽

• Aerodynamic forces: 𝒇𝟐𝑫 =1

2𝜌𝑣𝑟𝑒𝑙

2 𝑐 𝑐𝑙 𝛼 𝒆𝑳, 𝑐𝑑 𝛼 𝒆𝒅

• Iterative calculation of the angle of attack

• Sampling of the velocity upstream of the AL point

• Gaussian smearing 𝑓 = 𝑓2𝐷⊗𝜂𝜖,3𝐷, 𝜂𝜖,3𝐷 =1

𝜖3𝜋3/2exp −

𝑑

𝜖

2


The Actuator Line Method

Modeling of the rotor

𝜙 = tan−1𝑢𝐴𝐿

𝑣𝐴𝐿 + Ω𝑟 𝑢𝐴𝐿 = 𝑢𝑠𝑎𝑚𝑝 − 𝑢𝑖 d𝑠𝑎𝑚𝑝 𝛼 𝑐𝑎 , Γ Biot-Savart

iteration

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• Calculation of overall drag force using specified

𝑐𝐷 and area

• Break down into volume force increments

• Insert as momentum sink in Navier-Stokes

Equations

• Sinusoidal force to mimic bluff bodies:

𝐹𝑠𝑓 = 𝑘𝑓𝐹𝐷 sin2𝜋𝑆𝑟𝑈∞𝐿

𝑡


The Actuator Line Method

Modeling of the nacelle

Nacelle wake:

FR ACL 𝑐𝐷 = 0.8 ACL 𝑐𝐷 = 0.8, sin

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• 5M wind turbine located in Alpha-Ventus, Germany

• Diameter 126m

• Hub height: 95m

• Tilt /Cone angle: 6°, -4°

• TSR: 8.5

• Total of 80M cells for FR, 42M cells for ACL, wake: Δ = 1𝑚3

• 100 ACL points, nacelle modeled by source term

• −180° < 𝛼 < 180° polars XFOIL/Viterna

• Higher order WENO scheme in the background mesh

Lower dissipation settings for ACL compared to FR


caseOffshore

Investigated cases

Overset Meshing

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• 2.4M wind turbine located on an escarpment in Stötten, Germany

• Diameter 109m

• Hub height: 70m

• Tilt /Cone angle: 5°, -2°

• TSR: 6.64

• Total of 180M cells for FR, wake: Δ = 1𝑚3

• 100 ACL points, nacelle also meshed

• −180° < 𝛼 < 180° polars XFOIL/Viterna

• Higher order WENO scheme in the background mesh


caseTerrain

Investigated cases

Part of the computational domain

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[3]

• WRF and LiDAR based LES simulations by

ForWind using PALM

• Almost neutral stratification

• Wind speed at hub height: 8 m/s

• Turbulence intensity: 4.5%

• Signal made periodic over 60s


caseOffshore

Inflow Conditions

Velocity profile at the inlet

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• UAV and LiDAR measurements approximated by

• Steady power law profile 𝛼 = 0.14

• Synthetic turbulence by Mann model:

• 𝐿 = 40𝑚; Γ = 3.9; 𝛼𝜖2/3 = 0.035; 𝜎𝑢 = 0.9𝑚/𝑠

• Introduced as body forces with model of Troldborg [2]

• Velocity at hub height 11m/s

• Turbulence intensity ≈ 10%


caseTerrain

Inflow Conditions

Velocity profile at the turbine

position (LiDAR □; UAV▲) [1]

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caseOffshore

• Linear loading over wide range

• Higher loads of ACL in the outer part

caseTerrain

• Higher loading in the mid part

of the rotor

• Good agreement of ACL and FR


Loads

Results

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• AoA vs. Lift coefficient

• Unsteady aerodynamic effects

present in the inner and mid portion

• ACL predicts 2D polar as expected

• ACL shows higher lift at lower AoA

XFOIL polars inacurrate


Unsteady aerodynamics caseOffshore

Results

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Vorticity contour for caseOffshore – FR

Results

• Tilt angle

Drivers of Instability:

+

• Shear +

larger scale

Turbulence

• High TSR

Effects:

• Vortex pairing

• Large scale motion

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Vorticity contour for caseOffshore – ACL

Results

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Instantaneous velocity field: caseTerrain

Investigation of a single wind turbine wake

Wake of the ACL rotor

Wake of the FR turbine

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[3]


Vorticity contour for caseTerrain

Results

FR

ACL

Drivers of Instability:

+

• Shear +

high level

Turbulence

• Inclination

Effects:

• Quicker disordering

• More homogeneous

turbulence

• Upward deflection

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[3]


Mean velocity profiles caseOffshore

Results

FR

ACL • “Linear” velocity deficit, with high induction

• Recovery process initiated by turbulent mixing with the surrounding flow

• Wake deflection in vertical direction

• Overall good agreement of ACL and FR

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Standard deviation of velocities caseOffshore

Results

• Higher standard deviation in the mid part of the wake by ACL

• Growing shear layer in the tip region yields higher standard deviation

• Mixing with high kinetic energy fluid from outside for x/R>4

FR

ACL

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Mean velocity profiles caseTerrain

Results

FR

ACL • “Bell”-shaped velocity deficit

• Higher velocity near the ground

• Turbine “footprint” blurred by high ambient turbulence level

• Slight over prediction of deficit by ACL

• Gaussian shaped velocity field for x/R>7

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Standard deviation of velocities caseTerrain

Results

• Higher turbulence levels compared to caseOffshore

• Fluctuations still present near the ground

• Peaks of the tip more pronounced in the horizontal plane

FR

ACL

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Velocity spectra caseOffshore

Results

FR

ACL

• Distinct 3P frequency peaks in the near wake, sharper for ACL

• In the farther wake ACL shows higher to amplitudes due to less dissipative scheme

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x/R=0.1 x/R=6


Velocity spectra caseTerrain

Results

FR

ACL

• In the near wake the peaks of the ACL are smeared to neighboring frequencies

Vortices are disintegrated by high level of turbulence

• In the farther wake only slightly higher fluctuations in the higher frequencies by ACL

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x/R=0.1 x/R=7

• Comparison of ACL and FR for typical offshore and complex terrain case

• Unsteady aerodynamic effects present

• Wake development offshore determined by operational conditions, shear and large scale

turbulence

• Wake development in complex terrain dominated by inclination and high turbulence

• ACL predicts well:

• Wake instability

• Mean deficit


Conclusions

• ACL depends on high quality polars

• Seems to over predict fluctuations in the near wake

[1] Schulz C, Hofsäß M, Anger J, Rautenberg A, Lutz T, Cheng P W and Bange J 2016 Journal of

Physics:

[2] Troldborg N, Sørensen J N, Mikkelsen R and Sørensen N N 2014 Wind Energy 17 657–669

[3] Schulz C 2017 Numerische Untersuchungen des Verhaltens von Windenergieanlagen im komplexen

Gelände


References

e-mail

phone +49 (0) 711 685-

fax +49 (0) 711 685-

University of Stuttgart

Thank you!

Pascal Weihing

69974

69974

Institut für Aerodynamik und Gasdynamik

[email protected]

Pfaffenwaldring 21

Institute of Aerodynamics and Gas Dynamics


Instantaneous velocity field: caseOffshore

Results

Wake of the ACL rotor Wake of the FR turbine

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comparison of the actuator line model with fully resolved...

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