Analysis of Turbulent Flow Around Horizontal Axis Wind Turbines Using Algebraic Stress Model
Authors: Beyhaghi Saman , Amano Ryoichi S. 
Published: March 2016

Due to the problems associated with increase of greenhouse gases, and the limited supply of fossil fuels, switching to clean and renewable sources of energy seems necessary. Wind energy is a very suitable form of renewable energy which can be a good choice for those areas around the world with sufficient amount of wind annually. However, in order for the commercial wind turbines to be cost-effective, they need to operate at very high elevations, and therefore, blades with the length as high as 60–70 m are common. Because of the high manufacturing and transportation costs of the wind turbine components, it is necessary to evaluate and predict the performance of the turbine prior to shipping it to the installation site.
Computational Fluid Dynamics (CFD) has proven to be a simple, cheap and yet relatively accurate tool for prediction of wind turbine performance, where suitability of different designs can be evaluated at a low cost. Total lift and drag forces can be calculated, from which one can estimate the torque, and ultimately the output power. Reynolds Stress Model (RSM) is a well-known Reynolds Averaged Navier-Stokes (RANS) turbulence model, which is typically more accurate than eddy viscosity models, but it comes with higher computational cost.
In the present work, turbulent flow of air around a horizontal axis wind turbine blade is modeled computationally by using a modified version of RSM, known as Algebraic Stress Model (ASM) for the near-blade region.
Because of the periodicity nature of the flow domain, only one of three blades is modeled by applying the periodic conditions on the sides of a 120 degree sector of the domain. While the flow is solved in the bulk fluid using the k-epsilon model, in order to better capture the near-wall effects and to make the computations cost effective, it is proposed to apply ASM only in the locations very close to the blade surface.
A number of reasonable assumptions are made in ASM in order to convert the transport differential equations of the Reynolds stresses into an algebraic form. The highly coupled system of non-linear equations is then solved concurrently for six Reynolds stress components. Turbulent kinetic energy, turbulent dissipation rate, and mean velocity gradients are calculated from the k-epsilon model and used as initial values and iterated through the ASM computations. To the best of our knowledge, this is the first time that ASM is used for analysis of Reynolds stress for flow around rotating wind turbines blades.
Reynolds stresses are obtained at several locations (heights) along the blade, and at different radial distances from the blade. Different variations of implicit and explicit ASM are examined and compared in terms of accuracy. Results indicate that the implicit ASM method using the full form of pressure-strain term tends to show predictions that are closer to the predictions of the fully-resolved RSM simulation, as compared to the other ASM models examined. Therefore, there seems to be a good potential for reducing computational costs for determination of near wall Reynolds stresses and ultimately calculating torque and power generated from wind turbines without sacrificing the accuracy.