Far-wake meandering induced by atmospheric eddies in flow past a wind turbine

• Published in: Journal of fluid mechanics 2018-07, Vol.846, p.190-209
• Main Authors: Mao, X., Sørensen, J. N.
• Format: Article
• Language: English
• Subjects: Algorithms; Computational fluid dynamics; Eddies; Energy; Fluid flow; Fluid mechanics; Incompressible flow; Inflow; JFM Papers; Mathematical models; Meandering; Navier-Stokes equations; Perturbation methods; Reynolds number; Rivers; Stochasticity; Strouhal number; Three dimensional flow; Turbine engines; Turbines; Velocity; Vortex rings; Vortices; Wavelengths; Wind farms; Wind power; Wind speed; Wind turbines
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2018.275

A novel algorithm is developed to calculate the nonlinear optimal boundary perturbations in three-dimensional incompressible flow. An optimal step length in the optimization loop is calculated without any additional calls to the Navier–Stokes equations. The algorithm is applied to compute the optimal inflow eddies for the flow around a wind turbine to clarify the mechanisms behind wake meandering, a phenomenon usually observed in wind farms. The turbine is modelled as an actuator disc using an immersed boundary method with the loading prescribed as a body force. At Reynolds number (based on free-stream velocity and turbine radius) $Re=1000$ , the most energetic inflow perturbation has a frequency $\unicode[STIX]{x1D714}=0.8$ –2, and is in the form of an azimuthal wave with wavenumber $m=1$ and the same radius as the actuator disc. The inflow perturbation is amplified by the strong shear downstream of the edge of the disc and then tilts the rolling-up vortex rings to induce wake meandering. This mechanism is verified by studying randomly perturbed flow at $Re\leqslant 8000$ . At five turbine diameters downstream of the disc, the axial velocity oscillates at a magnitude of more than 60 % of the free-stream velocity when the magnitude of the inflow perturbation is 6 % of the free-stream wind speed. The dominant Strouhal number of the wake oscillation is 0.16 at $Re=3000$ and keeps approximately constant at higher $Re$ . This Strouhal number agrees well with previous experimental findings. Overall the observations indicate that the well-observed stochastic wake meandering phenomenon appearing far downstream of wind turbines is induced by large-scale (the same order as the turbine rotor) and low-frequency free-stream eddies.