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

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.

Quantification of wake shape modulation and deflection for tilt and yaw misaligned wind turbines

“…Similar evaluation has been done in Hamilton & Cal (2015), Kadum et al. (2020), Kadum, Knowles & Cal (2018), Ali et al. (2019), Cortina, Calaf & Cal (2016) and Camp & Cal (2016).…”

“…The velocity terms of (3.8) are shown in figure 17. Similar evaluation has been done in , Kadum et al (2020), Kadum, Knowles & Cal (2018), Ali et al (2019), Cortina, Calaf & Cal (2016 and Camp & Cal (2016). In-plane spatial gradients (∂/∂y and ∂/∂z) are calculated with central differences after spatially smoothing by convolving a Gaussian kernel with a radius of 5 L, with L the PIV grid-size resolution.…”

Near Wake Development Behind Marine Propeller Model in Presence of Freestream Turbulence

“…In order to elucidate the behavior of these terms, conditional sampling of Reynolds stresses based on quadrant analysis is performed [4,20]. For example, conditional sampling for the phaseaveraged shear stress hu 0 v 0 i is defined as…”

“…To the best of the authors' knowledge, this is the first time that mean flow kinetic energy flux terms are reported for the marine propeller wake. In the near wake of wind turbines, it has been shown that ÀUhu 0 v 0 i flux is also the dominant term in the vertical transport of mean flow kinetic energy [5,20].…”