Stability and transition on wind turbine blades

QC 231002

Abstract

Transition on wind turbine blades is a highly complex phenomenon due to the myriad effects influencing the process. This thesis studies some of them, namely free-stream turbulence (FST), rotation, and three-dimensionality. The investigations employ large eddy simulations (LES) with and without (implicit or wall-resolved LES) a subgrid-scale model. The role of FST in the modal and non-modal stability of the flow on the suction side of a wind turbine section at a Reynolds number 𝑅𝑒_𝑐 = 100,000 is studied. This involved several simulations at varying turbulence intensity (𝑇𝐼) and primary and secondary linear stability analyses. The separated shear layers strongly govern the flow stability with the characteristic Kelvin-Helmholtz (KH) modes. Low FST levels increase the growth rates of the secondary instability of Tollmien-Schlichting (TS) and KH modes, leading to an upstream shift of transition and shrinking of the LSB. High enough 𝑇𝐼 stabilizes the flow to these modes, leading to an unexpected increase in the LSB. However, further rises in the turbulence level suppress separation. The spanwise-averaged part of the mean-flow distortion causes the stabilizing effect. The increase in the turbulence intensity also leads to a monotonic drop in the energy of coherent structures, shed from the separated shear layer, passing near the trailing edge. In the case of 𝑅𝑒_𝑐 = 1,000,000, streak growth is much more intense, and even low levels of 𝑇𝐼 are enough to suppress the LSB present in the absence of FST. For 𝑇𝐼 ≤ 2.4%, transition is caused by inner modes, which in the limit of zero FST tend to TS waves. This range of 𝑇𝐼 presents linear receptivity, good agreement of the 𝑁 factor from Mack’s correlation with simulation data, and an exponential dependency of the transition location with 𝑇𝐼. For 2.4% < 𝑇𝐼 ≤ 7.0%, bypass transition occurs, characterized by the predominance of the outer varicose mode. In this regime, the transition location displays a variation ∝ 𝑇𝐼⁻². A low-frequency cut-off for the free-stream turbulence is proposed to allow the computation of an effective turbulence intensity for wind turbine blades. Regarding the role of rotation, a model is developed to compute the quasi-three-dimensional base flow for stability analyses over a blade. The flow in the inboard region is highly three-dimensional and significantly affected by rotation. Highly oblique modes are the most unstable in this region, leading to a transition up to 19% earlier than the widely used two-dimensional semi-empirical 𝑒^𝑁 transition model of Drela and Giles, used in the RANS simulations. A transition-prediction framework based on the boundary layer and parabolized stability equations accounting for these effects was developed. It indicates that rotation shifts transition upstream if the Reynolds number is allowed to increase with the reference velocity. Subsequent LES indicated that rotation stabilizes the flow for a fixed Reynolds number in the attached flow region and front part of the LSB for low rotation rates, delaying transition and reattachment. Even though rotation delays these phenomena, rotation may act as an adverse pressure gradient after separation occurs, leading to an increase in the growth rates of the KH modes and reverse flow. Furthermore, crossflow transition may be triggered for higher rotation rates and towards the inboard blade region, leading to an upstream shift of the transition point. Crossflow transition leads to a rise in the pressure difference between the two sides of the airfoil, generating a higher lift. In the outboard blade region, a self-excited type of instability may occur in an LSB forming near the leading edge, promoting an early transition that may cause a sudden shift of the separation line to the leading edge after a certain critical radius, as observed in experiments. Finally, a low-frequency oscillation in the normal force coefficient, with an amplitude of 10.5% around the mean, was identified in a wind turbine airfoil. The period of these oscillations was long, corresponding to several turns of a wind turbine at rated rotation speed. The occurrence of such a phenomenon in real wind turbines should be assessed and considered in the structural design of the rotor.

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