An Analytical Model for Wind Turbine Wakes under Pressure Gradient

Abstract

In this study, we present an analytical modeling framework for wind turbine wakes under an arbitrary pressure gradient imposed by the base flow. The model is based on the conservation of the streamwise momentum and self-similarity of the wake velocity deficit. It builds on the model proposed by Shamsoddin and Porté-Agel, which only accounted for the imposed pressure gradient in the far wake. The effect of the imposed pressure gradient on the near wake velocity is estimated by using Bernoulli’s equation. Using the estimated near wake velocity as the starting point, the model then solves an ordinary differential equation to compute the streamwise evolution of the maximum velocity deficit in the turbine far wake. The model is validated against experimental data of wind turbine wakes on escarpments of varying geometries. In addition, a comparison is performed with a pressure gradient model which only accounts for the imposed pressure gradient in the far wake, and with a model that does not account for any imposed pressure gradient. The new model is observed to agree well with the experimental data, and it outperforms the other two models tested in the study for all escarpment cases.

Wind Tunnel Experimental Study on the Efficiency of Vertical-Axis Wind Turbines via Analysis of Blade Pitch Angle Influence

“…Several studies analyzed variations in loads, moments, angle of attack, vorticity, and boundary layer phenomena as functions of pitch angle using computational fluid dynamics (CFD) simulations [18][19][20][21]. The aim of most studies has been to gain insight into the aerodynamic behavior of VAWTs and identify optimal turbine configurations, including pitch angle settings, that can improve their overall efficiency [22][23][24]. One potential parameter for improving VAWT performance is the pitch angle; it has been confirmed by analyses that the right angle can provide an increase in turbine performance [25][26][27].…”

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

“…Due to the importance of developing accurate models for wind turbine wake flows, far wake self-similarity enables the development of computationally fast models that can predict the mean flow distribution in an accurate manner. Analytical wake models, such as the Gaussian wake model [4] and the model for axisymmetric wakes under pressure gradient [19,20], have shown that the concept of self-similarity can be used to develop accurate models for wind turbine wake flows.…”

Installation and Performance Study of a Vertical-Axis Wind Turbine Prototype Model

“…As mentioned above, a typical WT consists of mechanical, electrical, and structural components, apart from the supporting foundation [14]. A brief review of the existing literature reveals that there are significant past research contributions, including laboratory model studies [15][16][17], full-scale field investigations [18][19][20], analyses [21][22][23], and numerical [24][25][26] works, along with appropriate design recommendations [27,28]. Limited studies were carried out in the past on the performance analysis and parametric studies of small-scale wind turbines [29,30].…”