Comparative assessment of the harmonic balance Navier-Stokes technology for horizontal and vertical axis wind turbine aerodynamics

Several important wind turbine unsteady flow regimes, such as those associated with the yawed wind condition of horizontal axis machines, and most operating conditions of all vertical axis machines, are predominantly periodic. The harmonic balance Reynolds-averaged Navier-Stokes technology for the rapid calculation of nonlinear periodic flow fields has been successfully used to greatly reduce runtimes of turbomachinery periodic flow analyses in the past fifteen years. This paper presents an objective comparative study of the performance and solution accuracy of this technology for aerodynamic analysis and design applications of horizontal and vertical axis wind turbines. The considered use cases are the periodic flow past the blade section of a utility-scale horizontal axis wind turbine rotor in yawed wind, and the periodic flow of a H-Darrieus rotor section working at a tip-speed ratio close to that of maximum power. The aforementioned comparative assessment is based on thorough parametric time-domain and harmonic balance analyses of both use cases. The paper also reports the main mathematical and numerical features of a new turbulent harmonic balance Navier-Stokes solver using Menter's shear stress transport model for the turbulence closure. Presented results indicate that (a) typical multimegawatt horizontal axis wind turbine periodic flows can be computed by the harmonic balance solver about ten times more rapidly than by the conventional time-domain analysis, achieving the same temporal accuracy of the latter method, and (b) the harmonic balance acceleration for Darrieus rotor unsteady flow analysis is lower than for horizontal axis machines, and the harmonic balance solutions feature undesired oscillations caused by the wide harmonic content and the high-level of stall predisposition of this flow field type.