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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

## Abstract

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, $ΔS⟨uiuj⟩$, 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.

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## Figures

Fig. 1

Conditional sampling of the fluctuating components of velocity

Fig. 2

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

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.

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.

Fig. 5

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

Fig. 6

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

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⟩.

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.

Fig. 9

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

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