Wake

Table of Contents

• 1. Wake   wake
  • 1.1. Researchers
  • 1.2. Theory
    • 1.2.1. entrainment of kinetic energy
  • 1.3. Near vs Far wake
  • 1.4. FAQ
    • 1.4.1. what is wake?
    • 1.4.2. why momentum is reduced?
    • 1.4.3. Who is the first author study wind/tidal turbine wake?
  • 1.5. Turbulent wake state
    • 1.5.1. turbulent wake of a circular cylinder
    • 1.5.2. Reference
  • 1.6. Wake Models
    • 1.6.1. References
  • 1.7. Numerical modelling
    • 1.7.1. Turbulence model for turbine wake
  • 1.8. Dynamic wake model   Dynamic_Wake
  • 1.9. Turbulence in wakes and wind farms
    • 1.9.1. free stream/wake mixing
    • 1.9.2. Thrust vs Velocity Reduction
    • 1.9.3. Turbulence Intensity VS Blade Design
  • 1.10. wake structure
  • 1.11. Wake of a wind/Tidal turbine :Turbine:   wake
    • 1.11.1. experimental study
    • 1.11.2. Reference
  • 1.12. Visualization
  • 1.13. Quantities Analysis
    • 1.13.1. pressure along streamwise direction
  • 1.14. References
    • 1.14.1. Dissertation

1 Wake   wake

wake

a region where the velocity is still lower than the free-stream value

wake

a region with momentum decifit compared with free stream

(no term)

the cause:

the flow separates form the body surface

Features:

• lower velocity compared with U_∞
• recirculating flow

1.1 Researchers

Matthew Churchfield, NREL, USA

1.2 Theory

1.2.1 entrainment of kinetic energy

1.3 Near vs Far wake

• near wak, 4-5D
  • not accurate if you put pressure outlet at near wake
• far wake: 20-40D

1.4 FAQ

1. How does the tip-vortex instability influence the wake flow and its re-energising process?

1.1. What is the effect on the mean velocity field in the wake? 1.2. What is the effect on the flow turbulence and on the wake re-energising process?

1. What are the key turbulence phenomena in the wake of a wind turbine rotor?

2.1. What is the amount of kinetic energy transported and dissipated by the most relevant flow structures? 2.2. What is the role of the tip-vortices, their instability and their breakdown in the turbulent mixing process?

1. What are the main differences between the near wake of a wind turbine and an actuator disc?

3.1. What are the key differences in the wind turbine and actuator disc near wake and how do they affect the transport of mean-flow kinetic-energy? 3.2. To what extent is the actuator disc assumption valid for the representation of the near wake?

1. What is the level of accuracy of the state-of-the-art numerical models in reproducing the near wake features highlighted in the experiments?

> Refer to Lignarolo 2016 Dissertation

1.4.1 what is wake?

wake

a region with momentum decifit compared with free stream

1.4.2 why momentum is reduced?

-the reason is the force from object on fluid the present of an object (e.g. cylinder. airfoil,wing) change to flow streamline, the fluid gives a force on the object, meanwhile, the object gives an reaction force on the fluid. Force = rate of change of momentum, thus the momentum of fluid is changed.

1.4.3 Who is the first author study wind/tidal turbine wake?

1.5 Turbulent wake state

the wake behind the front rotor is far from turbulent (leishman, 2009) what is turbulent wake?

• when Turbulent intensity, I, is higher than 5% (Eldad)

Ct vs a [fig. 4.5 (hansen)] 0.5<a<1 at turbulent wake state

When does it happen? at high TSR

• for fixed rotational speed turbine, at low inflow speed
• for fixed inflow speed, at high rotational speed

Why does it happen?

• a velocity jump at the edge of the wake ( fig. 4.7 hansen)

baseline: 1D momentum theory,

when 0.5 <a<1 the velocity jump at wake is high and eddies are formed ( P33 fig. 4.6 hansen) ( fig. 4.7 hansen)

Figure 1: Schematic view of the turbulent-wake state induced by the unstable shear flow at the edge of the wake

1.5.1 turbulent wake of a circular cylinder

• Cantwell and Coles 1983

[43] Fabris, G., 1979. Conditional sampling study of the turbulent wake of a cylinder. Part 1. Journal of Fluid Mechanics 94, 673-709 [50] Ghaemi, S., Scarano, F., 2011. Counter-hairpin vortices in the turbulent wake of a sharp trailing edge. Journal of Fluid Mechanics 689, 317-356 Nishino, T., Willden, R.H.J., 2012. Effects of 3-D channel blockage and turbulent wake mixing on the limit of power extraction by tidal turbines. International Journal of Heat and Fluid Flow 37, 123-135

1.5.2 Reference

1. Dissertation
   

   refer to Johansson 2002 (PhD Dissertation) Johansson, Peter BV. axisymmetric turbulent wake behind a disk . Chalmers University of Technology, 2002.

2. Others
   

   Steffen et al 2007 "3D-simulation of the turbulent wake behind a wind turbine." Journal of Physics: Conference Series. Vol. 75. No. 1. IOP Publishing,

   B. Sanderse 2011 Review of computational fluid dynamics for wind turbine wake aerodynamics

   N Sedaghatizadeh et al 2018 Ren. Energy, Modelling of wind turbine wake using large eddy simulation

   Sørensen 2013 "Analysis of turbulent wake behind a wind turbine." International Conference on aerodynamics of Offshore Wind Energy Systems and wakes (ICOWES 2013). Technical University of Denmark (DTU), 2013.

1.6 Wake Models

• Park model (N.O. Jensen 1983)¹
  • Simplest model
  • park model is used in Ch5, Dual Rotor cases

1.6.1 References

a review slides >> title: A Review of Wind Turbine Wake Models and Future Directions file name: 2013 NREL A Review of Wind Turbine Wake Models and Future Directions.pdf 2013 North American Wind Energy Academy (NAWEA) Symposium Matthew J. Churchfield Boulder, Colorado August 6, 2013 NREL/PR-5200-60208

1.7 Numerical modelling

methods? parametric study? Quantities? challenges?

• Jens Sorensen, Numerical Modeling of Wind Turbine Wakes, J. Fluids Eng 2002
• Comparison of Engineering Wake Models with CFD Simulations S J Andersen et al 2014 J. Phys.: Conf. Ser. 524 01216

1.7.1 Turbulence model for turbine wake

1.8 Dynamic wake model   Dynamic_Wake

1.9 Turbulence in wakes and wind farms

Features:

• reduced velocity
• increased turbulence level

causes of turbulence in the wake:

• blade tip vortex
• shear at edge of wake

For a turbine operating in the wake ( there are turbine in upstream) VS a turbine operating in the free stream

• Cp is lower than free stream case
• Ct is higher tahn free stream turbine

from 1D momentum theory

1.9.1 free stream/wake mixing

keywords: wake mixing, HAWT, particle image velocity, tip vortex instability

as there is a velocity difference in the edge of wake, an unstable mixing process exits at edge of wake

> 3.6.1 Free-stream/wake mixing > Lignarolo 2016 PhD Dissertation, TUDelft, On the Turbulent Mixing in Horizontal Axis Wind Turbine Wakes

1.9.2 Thrust vs Velocity Reduction

Thrust on blade is: T= ρ u A (U_∞ -u) (4.10, hansen)

• u: velocity at rotational plane

thus Thrust is directly related to velocity reduction (U_∞ -u)

1.9.3 Turbulence Intensity VS Blade Design

• Turbulence intenstiy within a wind farm is not included in wind turbine design

> 2.10 Turbulence in Wakes and Wind Farms (Burton)

1.10 wake structure

• increases n tangential velocity is balanced by a loss of static pressure
• The radial pressure gradient balances the centrigugal force

> 3.3.4 Wake structure (Burton) Glauert, H., (1935a). ‘Airplane propellers’. Aerodynamic theory (ed. Durand, W. F.). Julius Springer, Berlin, Germany.

Glauert, H., (1935b). ‘Windmills and fans’. Aerodynamic theory (ed. Durand, W. F.). Julius Springer, Berlin, Germany

1.11 Wake of a wind/Tidal turbine :Turbine:   wake

why do we study wake?

1.11.1 experimental study

the wake recovery of two model horizontal-axis tidal stream turbines measured in a laboratory flume with Particle Image Velocimetry ~\cite{simmons2017investigation}

1.11.2 Reference

ZHANG Y. Q. 2017 Experimental Analysis and Evaluation of the Numerical Prediction of Wake Characteristics of Tidal Stream Turbine

> chapter 6 , James thesis

> Turnock SR, Phillips AB, Banks J, Nicholls-Lee R. Modelling tidal current turbine wakes using a coupled RANS-BEMT approach as a tool for analysing power capture of arrays of turbines. Ocean Eng 2011;38(11e12):1300e7. http://dx.doi.org/10.1016/j.oceaneng.2011.05.018.

> McNaughton J, Rolfo S, Apsley DD, Stallard T, Stansby PK. CFD power and load prediction on a 1MW tidal stream turbine with typical velocity profiles from the EMEC test site. In: Proceedings of the 10th European Wave and Tidal Energy Conference. 2nde5th September, Aalborg; 2013.

1.12 Visualization

Dual Rotor Inline and offline Interaction of horizontal-axis turbine wakes Georgios Deskos, Imerial College London https://www.youtube.com/watch?v=jbr7cf5J3A0

1.13 Quantities Analysis

1.13.1 pressure along streamwise direction

1.14 References

Schepers, J. G. and Snel, H. (1995) Dynamic Inflow: Yawed Conditions and Partial Span Pitch Control, ECN-C- -95-056, Petten, The Netherlands

Snel, H. and Schepers, J. G. (1995) Joint Investigation of Dynamic Inflow Effects and Implementation of an Engineering Method, ECN-C- -94-107, Petten, The Netherlands

1.14.1 Dissertation

> Lignarolo 2016 PhD Dissertation, TUDelft, On the Turbulent Mixing in Horizontal Axis Wind Turbine Wakes

Footnotes:

¹

Jensen, Niels Otto. "A note on wind generator interaction." (1983).

Created: 2018-07-18 Wed 14:30

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