A New Streamwise Scaling for Wind Turbine Wake Modeling in the Atmospheric Boundary Layer

Abstract

In this study, we aim to investigate if there is a scaling of the streamwise distance from a wind turbine that leads to a collapse of the mean wake velocity deficit under different ambient turbulence levels. For this purpose, we perform large-eddy simulations of the wake of a wind turbine under neutral atmospheric conditions with various turbulence levels. Based on the observation that a higher atmospheric turbulence level leads to faster wake recovery and shorter near-wake length, we propose the use of the near-wake length as an appropriate normalization length scale. By normalizing the streamwise distance by the near-wake length, we obtain a collapse of the normalized wake velocity deficit profiles for different turbulence levels. We then explore the possibility of using the relationship obtained for the normalized maximum wake velocity deficit as a function of the normalized streamwise distance in the context of analytical wake modeling. Specifically, we investigate two approaches: (a) using the new relationship as a stand-alone model to calculate the maximum wake velocity deficit, and (b) using the new relationship to calculate the wake advection velocity within a physics-based wake expansion model. Large-eddy simulation of the wake of a wind turbine under neutral atmospheric conditions is used to evaluate the performance of both approaches. Overall, we observe good agreement between the simulation data and the model predictions, along with considerable savings in terms of the models’ computational costs.

Effect of tip speed ratio on coherent dynamics in the near wake of a model wind turbine

“…Sharp gradients exist near the wake edge as coherent tip vortices are still present. In the presence of freestream turbulence, however, the wake profile approaches a Gaussian nature earlier (see Wu & Porté-Agel 2012; Vahidi & Porté-Agel 2022), leading to a better agreement with the model. Another important thing to note is that the wake centreline, defined as the location where the velocity deficit is maximum, drifts from the geometric centreline () towards .…”

“…Various attempts have been made to define the near wake systematically. Sørensen et al (2015) and Vahidi & Porté-Agel (2022) defined the near wake as the distance from the rotor at which the mean velocity profile becomes approximately Gaussian. De Cillis et al (2021) defined the near wake's extent as the distance where the time-averaged coherent kinetic energy dropped to a certain level.…”

“…Sørensen et al. (2015) and Vahidi & Porté-Agel (2022) defined the near wake as the distance from the rotor at which the mean velocity profile becomes approximately Gaussian. De Cillis et al.…”

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“…El efecto de estela (wake turbulence) generado en la energía con grandes fluctuaciones de amplitud por las turbinas eólicas, representan una alta carga dinámica sobre los aerogeneradores ubicados corriente abajo del arreglo o parque eólico. Por lo tanto, la comprensión de la dinámica de la estela turbulenta y el desarrollo de modelos de ingeniería para una predicción rápida de su evolución aguas abajo son esenciales para el avance de las tecnologías eólicas, este tema es abordado a detalle en (Zhang et al, 2023) donde se explica la dinámica de la estela cercana y lejana sobre el flujo eólico, proponiendo una fórmula empírica para describir sus variaciones a favor del viento en diferentes posiciones de la envergadura de los captadores, ampliamente tratado en (Vahidi et al, 2022). Lo cual es insumo para la determinación del modelo de control adaptativo de los ángulos de entrada y salida, en la trayectoria de desplazamiento del captador a través de una secuencia de corrimiento coordinado de manera colaborativa, a fin de cancelar el efecto y mejorar la eficiencia e impacto sobre el entorno.…”

Dynamic response of a wind turbine wake subjected to surge and heave step motions under different inflow conditions

“…However, considering the reduced wind speed within the wake, the advection velocity is likely lower than the incoming free wind speed. Therefore, alternatives include setting it at a lower value, such as 0.8U hub [9,10], or at an average value between the mean free-stream velocity and the mean wake velocity [8,[11][12][13].…”