A Numerical Study of Wind Turbine Wake by Large Eddy Simulation and Proposal for a New Analytical Wake Model

Guowei QIAN, Takeshi ISHIHARA
The University of Tokyo, Tokyo, Japan


The present work is devoted to developing a numerical wind tunnel to study the wind turbine wake in the offshore and onshore atmosphere boundary layer flow by using large eddy simulation (LES). Two kinds of operating conditions (rated power and maximum power) under two types of inflow with different ambient turbulence intensity (offshore and onshore) are simulated for a single miniature wind turbine. The turbine induced forces, including thrust and torque force, are modeled by using the actuator disk model with rotation (ADM-R). Firstly, characteristics of mean streamwise velocity and turbulence in the wake region are examined and compared well with the experiment data. Subsequently, based on the numerical simulation result, a new analytical wake model is proposed by systematical analysis of the ambient turbulence intensity and the thrust coefficient of the rotor. In general, the velocity deficits and added turbulence intensity in the wake predicted by the new wake model show good agreement with the LES data both in the near and far wake region.

Keywords: Wind turbine wake, Large eddy simulation, Actuator disk model, Analytical wake model


In this study, LES is adopted to solve the computational fluid dynamics, which can reproduce the unsteady turbulent flow in the wind turbine wake region. ADM-R is adopted to parameterize the turbine-induced forces, which can account for the effect of turbine rotation and uneven thrust force. The lift and drag forces acting on the turbine blades, which are parameterized by using the blade element momentum (BEM) theory, are implemented as source terms in the LES code. Simultaneously, the nacelle and tower are also modeled as porous media with 99.99% packing density instead of a rigid body. The numerical simulation setup generally follows the wind tunnel experiment, in which the atmosphere boundary layer is simulated by using the spire and fence.


Firstly, the main characteristics of wake effects, including the streamwise mean velocity and the turbulence intensity, are examined both in vertical and horizontal directions, which generally show good agreement with the experiment data.

Secondly, an analytical method to model the wake effects is proposed and validated. The mean velocity deficit and added turbulence intensity present favorable self-similarity properties following an assumed Gaussian distribution in the wake section, based on which the corresponding streamwise distribution functions are subsequently derived. Compared with the conventional wake models, the currently proposed wake model shows better agreement with LES data as well as experiment data both in streamwise and horizontal directions for each case.


Based on a series of numerical simulations of wind turbine wake, a new analytical wake model is proposed in this study. Following conclusions are obtained.

(1) The ADM-R model in combination with LES simulation is capable of providing a reliable description of the wake effect. The numerical wind tunnel and the wind turbine model built in this study show high prediction accuracy.

(2) The proposed wake model well predicts the velocity deficit and the added turbulence intensity in both near and far wake region, which can be an effective tool for the wind farm industry to predict the wake effect because of its simplicity of operation and universal applicability for the wind turbine with varying thrust coefficients under offshore and onshore conditions.


A number of wind farms are constructed near the coast, where the ambient turbulence varies considerably depending on the wind direction. In this study, a numerical approach to investigate the wake characteristics and an analytical method to model the wake effect for a single wind turbine under various operation and ambient turbulence conditions can be learned.