A Numerical Study on the Development of Self-Similarity in a Wind Turbine Wake Using an Improved Pseudo-Spectral Large-Eddy Simulation Solver

Abstract

Large-eddy simulation (LES) is performed to investigate self-similarity in a wind turbine wake flow. The turbine is represented using an actuator line model in a pseudo-spectral method-based solver. A new hybrid approach of smoothed pseudo-spectral method and finite-difference method (sPSMFDM) is proposed to alleviate the Gibbs phenomenon caused by the jump of velocity and pressure around the turbine. The LES is validated with the mean velocity and turbulence statistics obtained from wind-tunnel measurement reported in the literature. Through an appropriate choice of characteristic scales of velocity and length, self-similarity is elucidated in the normalized mean velocity and Reynolds stress profiles at various distances. The development of self-similarity is categorized into three stages based on the variation in the characteristic scales and the spanwise distribution of normalized velocity deficit. The mechanisms responsible for the transition of self-similarity stages are analyzed in detail. The findings of the flow physics obtained in this study will be useful for the modeling and fast prediction of wind turbine wake flows.

Keywords

• wind turbine wake
• spectral method
• self-similarity
• boundary-layer equation