Wall-resolved large eddy simulations (LES) and linear stability analyses of the flow on a rotating wind turbine blade section are performed to study the effects of rotation on laminar-turbulent transition on the suction surface. A chord Reynolds number of 100,000 and angles of attack (𝐴𝑜𝐴) of 12.8^◦, 4.2^◦, and 1.2^◦ are considered. For comparison, simulations with and without rotation at the same angles of attack are carried out. The rotating simulations displayed a flow toward the root outside the boundary layer. For 𝐴𝑜𝐴 = 12.8^◦, in which the flow is subject to a strong adverse pressure gradient (APG), rotation accelerates downstream the laminar attached and weakly separated flows, stabilizing them. However, the effect is the opposite in the high reverse flow region in the LSB, where rotation leads to a reverse flow of -16% compared to -7% in the non-rotating case. Rotation fosters an oblique transition mechanism that leads to a fast breakdown to small-scale turbulence. However, the stabilization of the attached flow overcomes this effect, leading to downstream shifts of 3% in transition and 4% in reattachment. For 𝐴𝑜𝐴 = 4.2^◦ and 𝐴𝑜𝐴 = 1.2^◦, which are subject to a long region of favorable pressure gradient (FPG), rotation decelerates the attached flow, rendering TS waves more unstable. This effect is reversed upon separation, and rotation starts to accelerate the flow slightly. Traveling and stationary crossflow modes are triggered by the rotation-induced crossflow towards the blade tip, especially in the front part of the LSB. However, the TS/KH mode remains the most amplified mechanism, governing the stability of the separation bubble. The rolls attributed to this mode develop a steady spanwise modulation with one or two spanwise wavelengths in the non-rotating cases. Rotation is found to reduce this spanwise modulation. The transition locations are insensitive to rotation in the 𝐴𝑜𝐴 = 4.2^◦ and 𝐴𝑜𝐴 = 1.2^◦ cases, which may be due to the dominance of the TS/KH mode and the identified region of absolute instability in the LSB.

Free-stream turbulence (FST) alters the boundary layer of wind turbine blades, changing the hydrodynamic stability and near wake. Large-eddy simulations (LES) of a blade section with a laminar separation bubble for several turbulence intensities (TI) and a Reynolds number of 100,000 are performed. The effects of boundary-layer streaks generated by FST on Tollmien-Schlichting (TS) and Kelvin-Helmholtz (KH) instabilities are analyzed with a model based on the parabolized stability equations (PSE). Two competing effects on flow stability are identified. The spanwise-averaged mean-flow distortion stabilizes primary TS/KH modes for increasing TI. However, this contribution seems dominant only for TI ≥ 8.6%. For lower TI, the spanwise-oscillating distortion caused by streaks destabilizes the flow, and the growth rates of secondary modal instabilities increase with the streak amplitude. The destabilization occurs mainly at spanwise locations with negative streaks since the inflection point shifts away from the wall, enhancing inviscid instabilities. Inflection points in the spanwise direction formed by the streaks also contribute to the destabilization. The modal structures from PSE and LES agree. Finally, the trailing-edge near-wake coherent structures are more energetic for TI ≥ 8.6% due to the partial stabilization of modal instabilities, delaying the turbulent breakdown.

The interaction of several instabilities and the influence of free-stream turbulence on laminar-turbulent transition on a 20% thick wind-turbine blade section with a laminar separation bubble (LSB) are investigated with wall-resolved large-eddy simulations (LES). Turbulence intensities (TI) of 0%, 2.2%, 4.5%, 8.6%, and 15.6% at chord Reynolds number 100,000 are considered. Linear receptivity occurs for the most energetic disturbances; high-frequency perturbations are excited via non-linear mechanisms for  TI≥8.6%⁠. Unstable Tollmien–Schlichting (TS) waves appear in the inflectional flow region for  TI≤4.5%⁠, shifting to inviscid Kelvin–Helmholtz (KH) modes upon separation and forming spanwise rolls. Sub-harmonic secondary instability occurs for  TI=0%⁠, with rolls intertwining before transition. Streaks spanwise modulate the rolls and increase their growth rates with TI for  TI≤4.5%⁠, reducing separation and shifting transition upstream. The  TI=4.5% case presents the highest perturbations, leading to the smallest LSB and most upstream transition. Earlier inception of TS/KH modes occurs on low-speed streaks, inducing premature transition. However, for  TI=8.6%⁠, the effect of the streaks is to stabilize the attached mean flow and front part of the LSB. This occurs due to the near-wall momentum deficit alleviation, leading to the transition delay and larger LSB than  TI=4.5%⁠. This also suppresses separation and completely stabilizes TS/KH modes for  TI=15.6%⁠. Linear stability theory predicts well the modal evolution for  TI≤8.6%⁠. Optimal perturbation analysis accurately computes the streak development upstream of the inflectional flow region but indicates higher amplification than LES downstream due to the capture of low-frequency, oblique modal instabilities from the LSB. Only low-amplitude [ O(1%)] streaks displayed exponential growth in the LES since non-linearity precludes the appearance of these modes.

Laminar-turbulent transition on a wind turbine blade section at 𝑅𝑒_𝑐 = 1,000,000 under anisotropic inflow turbulence is studied with wall-resolved large-eddy simulations and linear stability theory. The turbulence intensities (𝑇𝐼) are 0, 0.6, 1.2, 2.4, 4.5 and 7%. The laminar separation bubble (LSB) for 𝑇𝐼 = 0% develops two spanwise lobes upon reattachment due to the strong amplification of disturbances generated in the upstream attached boundary layer. Transition occurs via the breakdown of Kelvin-Helmholtz vortices in this case. Considering even modest turbulence levels (𝑇𝐼 = 0.6%) leads to the suppression of the LSB due to the strong streak growth. Inner modes, which in the limit of zero FST tends to Tollmien-Schlichting (TS) waves, are present for 𝑇𝐼 ≤ 2.4%, where Mack’s correlation agrees well with the simulations. Furthermore, linear receptivity occurs in this range of 𝑇𝐼, with the initial streak growth well predicted by optimal perturbation analysis. The breakdown of streaks arises predominantly through an inner varicose instability for 𝑇𝐼 ≤ 2.4%. For 𝑇𝐼 ≥ 4.5%, non-linear receptivity is found, and narrower streaks dominate the flow. These streaks are not the most energetic, and SPOD fails to identify them. The streaks break down via an outer varicose instability in this range of 𝑇𝐼, leading to bypass transition. The transition location displays a variation ∝ exp(𝑇𝐼⁻¹) for 𝑇𝐼 ≤ 2.4% and ∝ 𝑇𝐼⁻² for 2.4% < 𝑇𝐼 ≤ 7.0%, which can be explained by receptivity arguments. Finally, a model for a low-frequency cut-off for computing the effective 𝑇𝐼 in atmospheric turbulence isderived considering TS waves.

This work aims to develop a simple framework for transition prediction over wind-turbine blades, including effects of the blade rotation and spanwise velocity without requiring fully three-dimensional simulations. The framework is based on a set of boundary-layer equations (BLEs) and parabolized stability equations (PSEs), including rotation effects. An important element of the developed BL method is the modeling of the spanwise velocity at the boundary-layer edge. The two analyzed wind-turbine geometries correspond to a constant airfoil and the DTU 10-MW Reference Wind Turbine blades. The BL model allows an accurate prediction of thechordwise velocity profiles. Further, for regions not too close to the stagnation point and root of the blade, profiles of the spanwise velocity agree with those from Reynolds-averaged Navier–Stokes (RANS) simulations.The model also allows predicting inflectional velocity profiles for lower radial positions, which may allow cross-flow transition. Transition prediction is performed at several radial positions through an “envelope-of-envelopes” methodology. The results are compared with the eN method of Drela and Giles, implemented in the EllipSys3D RANS code. The RANS transition locations closely agree with those from the PSE analysis of a 2D mean flow without rotation. These results also agree with those from the developed model for cases with low 3D and rota-tion effects, such as at higher radial positions and geometries with strong adverse pressure gradients where 2D Tollmien–Schlichting (TS) waves are dominant. However, the RANS and PSE 2D models predict a later transition in the regions where 3D and rotation effects are non-negligible. The developed method, which accounts for these effects, predicted earlier transition onsets in this region (e.g., 19 % earlier than RANS at 26 % of theradius for the constant-airfoil geometry) and shows that transition may occur via highly oblique modes. These modes differ from 2D TS waves and appear in locations with inflectional spanwise velocity. However, except close to the root of the blade, crossflow transition is unlikely since the crossflow velocity is too low. At higher radial positions, where 3D and rotation effects are weaker and the adverse pressure gradient is more significant, modes with small wave angles (close to 2D) are found to be dominant. Finally, it is observed that an increase in the rotation speed modifies the spanwise velocity and increases the Coriolis and centrifugal forces, shifting the transition location closer to the leading edge. This work highlights the importance of considering the blade rotation and the three-dimensional flow generated by that in transition prediction, especially in the inner part of the blade.

The stability of the boundary layer over a section of a rotating wind turbine blade at Re_c = 300,000 is studied with direct numerical simulations and linear stability analyses.The results indicate that the transition location is not significantly affected by rotation in the outboard region of the blade for low rotation numbers Ro_c = Ω^∗𝑐/𝑈_∞. The relative insensitivity to rotation is due to a laminar separation bubble (LSB) near the leading edge, significantly spanwise-deformed by a primary self-excited instability, leading to the secondary absolute instability of the Kelvin-Helmholtz (KH) vortices and rapid transition. Moderate increases in the rotation rates and moving towards lower radii promote a stabilising effect due to the counteraction of the adverse pressure gradient (APG) in the attached flow region. This leads to the downstream displacement of theseparation point. Furthermore, competition with crossflow modes may also reduce the growth rates of KH waves. Higher increases in the rotation rate lead to a temporary transition delay in the blade inboard region. Nevertheless, stationary and travelling crossflow modes are triggered, spanwise modulating the KH rolls in the LSB and shifting the transition to the leading edge. Crossflow velocities as high as 50% of the free-stream velocity directed towards the blade tip are reached at the transition location. Considering a lower rotation number based on the radius 𝑅𝑜_𝑟 = Ω^∗𝑟/𝑈_∞, crossflow transition is also triggered inside the LSB. However, due to the stabilisation of the attached flow by rotation, the transition point is more downstream than the non-rotating case.

Numerical simulations of a wind turbine airfoil of the FFA-W3 series corresponding to a section of the DTU 10-MW Reference Wind Turbine are performed. Wall-resolved large eddy simulations (LESs) are carried out with the solvers Nek5000 and EllipSys3D for a chord Reynolds number of 100,000 and effective angle of attack 𝐴𝑜𝐴 = 3.1^◦ − 3.3^◦. It is shown that a domain width of 10% of the chord is enough to capture the evolution of the main disturbances besides reproducing well the time-averaged flow. EllipSys3D is validated against Nek5000 for LESs, indicating close results for the mean flow and most amplified perturbations. EllipSys3D underpredicts the amplitude of Tollmien-Schlichting waves in the attached boundary layer due to a higher numerical dissipation but closely predicts the evolution of the Kelvin-Helmholtz (KH) mode in the laminar separation bubble. The latter is in close agreement with the predictions from parabolized stability equations (PSE). The shape of the mode is obtained with spectral proper orthogonal decomposition (SPOD), clearly showing the wavepacket of the KH mode forming in the LSB. The long-term evolution of the flow is computed with EllipSys3D. A slow modulation of the normal force coefficient is identified with an amplitude of 10.5% and a period of 48 flowthroughs or equivalently a frequency 𝑓 = 𝑓^∗𝑐/𝑈_∞ = 0.021 or Strouhal number 𝑆𝑡 = 𝑓 sin 𝐴𝑜𝐴 = 0.0012. This frequency corresponds to low-frequency oscillations (LFOs) observed in several airfoil studies. However, 𝑆𝑡 is lower than previously noticed and occurs at a smaller 𝐴𝑜𝐴. In the DTU 10-MW Reference Wind Turbine, the period of these oscillations corresponds to 7.7 blade rotations. The periodic stalling and unstalling of the flow could trigger the LFO. The reverse flow on both sides of the airfoil is high enough to allow absolute instability, which may be responsible for the periodic bubble bursting.