0
Research Papers: Fundamental Issues and Canonical Flows

Quantification of Preferential Contribution of Reynolds Shear Stresses and Flux of Mean Kinetic Energy Via Conditional Sampling in a Wind Turbine Array

[+] Author and Article Information
Hawwa Falih Kadum, Devin Knowles, Raúl Bayoán Cal

Department of Mechanical
and Materials Engineering,
Portland State University,
Portland, OR 97207

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 19, 2017; final manuscript received June 6, 2018; published online July 10, 2018. Assoc. Editor: Jun Chen.

J. Fluids Eng 141(2), 021201 (Jul 10, 2018) (9 pages) Paper No: FE-17-1598; doi: 10.1115/1.4040568 History: Received September 19, 2017; Revised June 06, 2018

Conditional statistics are employed in analyzing wake recovery and Reynolds shear stress (RSS) and flux directional out of plane component preference. Examination of vertical kinetic energy entrainment through describing and quantifying the aforementioned quantities has implications on wind farm spacing, design, and power production, and also on detecting loading variation due to turbulence. Stereographic particle image velocimetry measurements of incoming and wake flow fields are taken for a 3 × 4 model wind turbine array in a scaled wind tunnel experiment. Reynolds shear stress component is influenced by uv component, whereas vw is more influenced by streamwise advection of the flow; u, v, and w being streamwise, vertical, and spanwise velocity fluctuations, respectively. Relative comparison between sweep and ejection events, ΔSuiuj, shows the role of streamwise advection of momentum on RSS values and direction. It also shows their tendency to an overall balanced distribution. uw intensities are associated with ejection elevated regions in the inflow, yet in the wake, uw is linked with sweep dominance regions. Downward momentum flux occupies the region between hub height and top tip. Sweep events contribution to downward momentum flux is marginally greater than ejection events'. When integrated over the swept area, sweeps contribute 55% of the net downward kinetic energy flux and 45% is the ejection events contribution. Sweep dominance is related to momentum deficit as its value in near wake elevates 30% compared to inflow. Understanding these quantities can lead to improved closure models.

FIGURES IN THIS ARTICLE
<>
Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Lu, S. S. , and Willmarth, W. W. , 1973, “ Measurements of the Structure of the Reynolds Stress in a Turbulent Boundary Layer,” J. Fluid Mech., 60(3), pp. 481–511. [CrossRef]
Shen, S. , and Leclerc, M. , 1973, “ Modelling the Turbulence Structure in the Canopy Layer,” Agric. For. Meteorol., 87(1), pp. 3–25. [CrossRef]
Guan, D. , Agarwal, P. , and Chiew, Y. M. , 2018, “ Quadrant Analysis of Turbulence in a Rectangular Cavity With Large Aspect Ratios,” J. Hydraulic Eng., 144(7), p. 04018035.
Qi, M. , Li, J. , Chen, Q. , and Zhang, Q. , 2018, “ Roughness Effects on Near-Wall Turbulence Modeling for Open-Channel Flows,” J. Hydraulic Res., 37(2), pp. 1–14. [CrossRef]
Mo, Z. , and Liu, C. H. , 2018, “ A Wind Tunnel Study of Ventilation Mechanism Over Hypothetical Urban Roughness: The Role of Intermittent Motion Scales,” Building Environ., 135, pp. 94–103. [CrossRef]
Roussinova, V. , Shinneeb, A.-M. , and Balachandar, R. , 2009, “ Investigation of Fluid Structures in a Smooth Open-Channel Flow Using Proper Orthogonal Decomposition,” J. Hydraulic Eng., 136(10), pp. 143–154.
Viggiano, B. , Dib, T. , Ali, N. , Mastin, L. G. , Cal, R. B. , and Solovitz, S. A. , 2018, “ Turbulence, Entrainment and Low-Order Description of a Transitional Variable-Density Jet,” J. Fluid Mech., 836, pp. 1009–1049. [CrossRef]
Wu, Y. , and Christensen, K. T. , 2007, “ Outer-Layer Similarity in the Presence of a Practical Rough-Wall Topography,” Phys. Fluids, 19(8), p. 085108.
Volino, R. J. , Schultz, M. P. , and Pratt, C. M. , 2001, “ Conditional Sampling in a Transitional Boundary Layer Under High Free-Stream Turbulence Conditions,” ASME Paper No. 2001-GT-0192.
Nolan, K. P. , and Zaki, T. A. , 2013, “ Conditional Sampling of Transitional Boundary Layers in Pressure Gradients,” J. Fluid Mech., 728(7), pp. 306–339. [CrossRef]
Aksamit, N. O. , and Pomeroy, J. W. , 2018, “ The Effect of Coherent Structures in the Atmospheric Surface Layer on Blowing-Snow Transport,” Boundary-Layer Meteorol., 167(2), pp. 211–233.
Buckley, M. P. , and Veron, F. , 2018, “ The Turbulent Airflow Over Wind Generated Surface Waves,” Eur. J. Mech.-B/Fluids, (in Press).
Zhu, W. , Van Hout, R. , and Katz, J. , 2007, “ PIV Measurements in the Atmospheric Boundary Layer Within and Above a Mature Corn Canopy—Part II: Quadrant-Hole Analysis,” J. Atmospheric Sci., 64(8), pp. 2825–2838. [CrossRef]
Longo, S. , and Losada, M. A. , 2012, “ Turbulent Structure of Air Flow Over Wind-Induced Gravity Waves,” Exp. Fluids, 53(2), pp. 369–390. [CrossRef]
Pokrajac, D. , Campbell, L. J. , Nikora, V. , Manes, C. , and McEwan, I. , 2007, “ Quadrant Analysis of Persistent Spatial Velocity Perturbations Over Square-Bar Roughness,” Exp. Fluids, 42(3), pp. 413–423. [CrossRef]
Craig, A. E. , Dabiri, J. O. , and Koseff, J. R. , 2016, “ Flow Kinematics in Variable-Height Rotating Cylinder Arrays,” ASME J. Fluids Eng., 138(11), p. 111203. [CrossRef]
Chamorro, L. P. , and Porté-Agel, F. , 2011, “ Turbulent Flow Inside and above a Wind Farm: A Wind-Tunnel Study,” Energies, 4(11), pp. 1916–1936. [CrossRef]
Lu, H. , and Porté-Agel, F. , 2015, “ On the Impact of Wind Farms on a Convective Atmospheric Boundary Layer,” Boundary-Layer Meteorol., 157(1), pp. 81–96. [CrossRef]
Markfort, C. D. , Zhang, W. , and Porté-Agel, F. , 2012, “ Turbulent Flow and Scalar Transport Through and Over Aligned and Staggered Wind Farms,” J. Turbul., 13(1), p. N33. [CrossRef]
Zhang, W. , Markfort, C. D. , and Porté-Agel, F. , 2013, “ Experimental Study of the Impact of Large-Scale Wind Farms on Land-Atmosphere Exchanges,” Environ. Res. Lett., 8(1), p. 015002. [CrossRef]
Viestenz, K. , and Cal, R. B. , 2016, “ Streamwise Evolution of Statistical Events in a Model Wind-Turbine Array,” Boundary-Layer Meteorol., 158(2), pp. 209–227. [CrossRef]
Cal, R. B. , Lebron, J. , Castillo, L. , Kang, H. S. , and Meneveau, C. , 2010, “ Experimental Study of the Horizontally Averaged Flow Structure in a Model Wind-Turbine Array Boundary Layer,” J. Renewable Sustainable Energy, 2(1), p. 013106. [CrossRef]
Hamilton, N. , Kang, H. S. , Meneveau, C. , and Cal, R. B. , 2012, “ Statistical Analysis of Kinetic Energy Entrainment in a Model Wind Turbine Array Boundary Layer,” J. Renewable Sustainable Energy, 4(6), p. 063105. [CrossRef]
Raupach, M. R. , 1981, “ Conditional Statistics of Reynolds Stress in Rough-Wall and Smooth-Wall Turbulent Boundary Layers,” J. Fluid Mech., 108(1), pp. 363–382. [CrossRef]
Nolan, K. P. , Walsh, E. J. , and McEligot, D. M. , 2010, “ Quadrant Analysis of a Transitional Boundary Layer Subject to Free-Stream Turbulence,” J. Fluid Mech., 658, pp. 310–335. [CrossRef]
Shaw, R. H. , Tavangar, J. , and Ward, D. P. , 1983, “ Structure of the Reynolds Stress in a Canopy Layer,” J. Clim. Appl. Meteorol., 22(11), pp. 1922–1931. [CrossRef]
Hamilton, N. , Melius, M. , and Cal, R. B. , 2015, “ Wind Turbine Boundary Layer Arrays for Cartesian and Staggered Configurations-Part I, Flow Field and Power Measurements,” Wind Energy, 18(2), pp. 277–295. [CrossRef]
Ali, N. , Hamilton, N. , DeLucia, D. , and Cal, R. B. , 2018, “ Assessing Spacing Impact on Coherent Features in a Wind Turbine Array Boundary Layer,” Wind Energy Sci., 3(1), p. 43. [CrossRef]
Chamorro, L. P. , Arndt, R. E. A. , and Sotiropoulos, F. , 2012, “ Reynolds Number Dependence of Turbulence Statistics in the Wake of Wind Turbines,” Wind Energy, 15(5), pp. 733–742. [CrossRef]
Hamilton, N. , and Cal, R. B. , 2015, “ Anisotropy of the Reynolds Stress Tensor in the Wakes of Wind Turbine Arrays in Cartesian Arrangements With Counter-Rotating Rotors,” Wind Energy, 27(1), p. 015102.
Sciacchitano, A. , and Wieneke, B. , 2016, “ PIV Uncertainty Propagation,” Meas. Sci. Technol., 27(8), p. 084006. [CrossRef]
Thomsen, K. , and Sørensen, P. , 1999, “ Fatigue Loads for Wind Turbines Operating in Wakes,” J. Wind Eng. Ind. Aerodyn., 80(1–2), pp. 121–136. [CrossRef]
Camp, E. H. , and Cal, R. B. , 2016, “ Mean Kinetic Energy Transport and Event Classification in a Model Wind Turbine Array Versus an Array of Porous Disks: Energy Budget and Octant Analysis,” Phys. Rev. Fluids, 1(4), p. 044404. [CrossRef]
Katul, G. , Hsieh, C. I. , Kuhn, G. , Ellsworth, D. , and Nie, D. , 1997, “ Turbulent Eddy Motion at the Forest-Atmosphere Interface,” J. Geophys. Res.: Atmospheres, 102(D12), pp. 13409–13421. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Conditional sampling of the fluctuating components of velocity

Grahic Jump Location
Fig. 2

Diagram of the experimental setup as viewed from the side. The diagram is not to scale.

Grahic Jump Location
Fig. 3

Total ⟨uv⟩ Reynolds shear stresses. Units are m2s−2. The horizontal lines at y/D = 0.5, 1, and 1.5 refer to bottom tip, hub height, and top tip location, respectively.

Grahic Jump Location
Fig. 4

Stress fractions for ⟨uv⟩. Units are m2s−2: (a) inflow and (b) wake. Q1 is the top right contour, Q2 is the top left contour, Q3 is the bottom left contour, and Q4 is the bottom right contour.

Grahic Jump Location
Fig. 5

Stress fractions for ⟨uw⟩. conditionally sampled by ⟨uv⟩. Units are m2s−2: (a) inflow and (b) wake. Quadrants as in Fig.4.

Grahic Jump Location
Fig. 6

Stress fractions for ⟨uw⟩. conditionally sampled by ⟨uw⟩. Units are m2s−2: (a) inflow and (b) wake. Quadrants as in Fig.4.

Grahic Jump Location
Fig. 7

ΔS⟨uiuj⟩=S⟨uiuj⟩,4−S⟨uiuj⟩,2. The inflow to the left and the wake to the right: (a) ΔS⟨uv⟩, (b) ΔS⟨uw⟩, and (c) ΔS⟨uw⟩.

Grahic Jump Location
Fig. 8

The exuberance, E⟨uv⟩=(S1+S3)=(S2+S4). Momentum transfer is primarily upward for values of E < −1 and conversely momentum transfer is directed downward for E > −1.

Grahic Jump Location
Fig. 9

Conditionally averaged Fk=−⟨uv⟩kU for (a) incoming flow and (b) wake flow

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In