Experiments in the wind turbine far wake for the evaluation of - - PowerPoint PPT Presentation

Norwegian University of Science and Technology

Experiments in the wind turbine far wake for the evaluation of analytical wake models

Norwegian University of Science and Technology

Department of Energy and Process Engineering Luis García , Mari Vatn, Franz Mühle and Lars Sætran

Norwegian University of Science and Technology

Introduction

• Wakes in wind

farms:

– Lower efficiency – Fluctuating loads

2

Horns Rev offshore wind farm west of Denmark. Credit: Vattenfall

Norwegian University of Science and Technology

Introduction

• Important to know the evolution of the parameters

3

𝑉∞

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Velocity decay & Width development

4

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Analytical model

• Schlichting model

– Blunt bodies

• Objective

– Wind turbines

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Parameters

• Velocity Decay
• Width development

– Half depth width

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𝑉1 = 𝑉∞ − 𝑉 𝑐1 2

= 𝑔(𝑦, 𝑉1)

𝑉1 𝑐1 2

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Analytical description of wakes

• Analytical expressions in terms of the downstream distance.

Type of flow Width development Velocity decay 2-D wake Circular wake

𝑦1 2 𝑦−1 2 𝑦1 3 𝑦−2 3

𝑐1 2 𝐸 = 𝐷𝑐 ∙ 𝑦 𝐸

1 3

𝑉1 𝑉∞ = 𝐷𝑣 ∙ 𝑦 𝐸

−2 3

• Velocity distribution

𝑣1

𝑉∞ = 10 18𝛾 ∙ 𝑦 𝐷𝑈𝐵

−2 3

∙ 1 − 𝑨 𝑐

3 2 2

Norwegian University of Science and Technology

8

Analytical description of wakes

• Analytical expressions in terms of the downstream distance.

Type of flow Width development Velocity decay 2-D wake Circular wake

𝑦1 2 𝑦−1 2 𝑦1 3 𝑦−2 3

𝑐1 2 𝐸 = 𝐷𝑐 ∙ 𝑦 𝐸

1 3

𝑉1 𝑉∞ = 𝐷𝑣 ∙ 𝑦 𝐸

−2 3

ln 𝑐1 2 𝐸 = ln 𝐷𝑐 + 1 3 ln 𝑦 𝐸

• Velocity distribution

𝑣1

𝑉∞ = 10 18𝛾 ∙ 𝑦 𝐷𝑈𝐵

−2 3

∙ 1 − 𝑨 𝑐

3 2 2

Norwegian University of Science and Technology

9

Analytical description of wakes

• Analytical expressions in terms of the downstream distance.

Type of flow Width development Velocity decay 2-D wake Circular wake

𝑦1 2 𝑦−1 2 𝑦1 3 𝑦−2 3

𝑐1 2 𝐸 = 𝐷𝑐 ∙ 𝑦 𝐸

1 3

𝑉1 𝑉∞ = 𝐷𝑣 ∙ 𝑦 𝐸

−2 3

ln 𝑐1 2 𝐸 = ln 𝐷𝑐 + 1 3 ln 𝑦 𝐸

• Velocity distribution

𝑣1

𝑉∞ = 10 18𝛾 ∙ 𝑦 𝐷𝑈𝐵

−2 3

∙ 1 − 𝑨 𝑐

3 2 2

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Experimental setup

• Instrumentation

– Wind tunnel – Laser Doppler Velocimeter – Turbine

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• Full 2-D wakes
• Lines wakes
• 2 turbulence ambient

conditions

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Results of mean velocity 2 D full wakes

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• Downshift of the wake due to tower effect [1]

[1] Pirella F and Sætran L 2017 Wind tunnel investigation on the effect of the turbine tower on wind turbines wake symmetry. Wind Energy (2017)

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Results of mean velocity in the xz plane

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• Expansion of the wake •

Decrease of the velocity decay

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Discussion of the velocity decay

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Velocity decay Low TI

• Deviation of 2.0%

Velocity decay High TI

• Deviation of 2.5%

𝑉1 𝑉∞ = 𝐷𝑣 ∙ 𝑦 𝐸

−2 3

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Discussion of the width development

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Width development Low TI

• Deviation of 2.5%

Width development High TI

• Deviation of 3.0%

𝑐1 2 𝐸 = 𝐷𝑐 ∙ 𝑦 𝐸

1 3

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Discussion of the velocity distribution

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• High degree of

agreement

• Some deviations in

the edges

𝑣1 𝑉∞ = 10 18𝛾 ∙ 𝑦 𝐷𝑈𝐵

−2 3

∙ 1 − 𝑨 𝑐

3 2 2

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Turbulence intensity

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Turbulence intensity models

• Three different models

– Crespo and Hernandez – Quarton – Frandsen and Thogersen

• Input parameters

Parameter/Model

Input parameters Crespo and Hernandez 𝐽∞, a, D Quarton 𝐽∞, 𝐷𝑈, 𝜓𝑂 Frandsen and Thogersen D, 𝑊

ℎ𝑣𝑐

Norwegian University of Science and Technology

Results of turbulence intensity in the xz plane

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• Decrease of the added turbulence intensity

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Discussion of turbulence intensity

• Good agreement of

the measurements with the models

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Conclusion

• Investigation of the Schlichting model for wind turbines
• Good agreement between experiments and theory
• Gaussian shape prediction
• Fairly well prediction of the turbulence intensity of the

wake

• Analytical models can describe the wake characteristics

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Conclusion

Thank you for your attention, Questions, comments?

• Investigation of the Schlichting model for wind turbines
• Good agreement between experiments and theory.
• Gaussian shape prediction
• Fairly well prediction of the turbulence intensity of the

wake

• Analytical models can describe the wake characteristics