Laminar-turbulent transition on the suction surface of the LM45.3p blade (thickness) was investigated using wall-resolved large eddy simulation (LES) at a chord Reynolds number of and angle of attack. The effects of anisotropic free stream turbulence (FST) with intensities - were examined, with integral length scales scaled down from atmospheric measurements. At, a laminar separation bubble (LSB) forms and transition is initiated by Kelvin-Helmholtz vortices. At low FST levels , robust streak growth via the lift-up mechanism suppresses the LSB, while transition dynamics shifts from two-dimensional Tollmien-Schlichting (TS) waves to predominantly varicose inner and outer instabilities (and) induced by the wall-normal shear and inflectional velocity profiles. The critical disturbance kinetic energy scales with, compared with from Mack's correlation. For, bypass transition dominates, driven by high-frequency boundary layer perturbations and streak breakdown via outer sinuous modes induced by the spanwise shear and inflectional velocity profiles. The scaling of streak amplitudes with becomes sub-linear and spanwise non-uniformity characterises the turbulent breakdown. The critical disturbance kinetic energy reduces to, marking a transition regime distinct from modal mechanisms. The onset of bypass transition aligns with prior studies of separated and flat-plate flows. A proposed turbulence spectrum cutoff links atmospheric measurements to wind tunnel data and Mack's correlation, offering a framework for effective estimation in practical environments.

Wall-resolved large eddy simulations of the flow on a rotating wind turbine blade section are conducted to study the rotation effects on laminar-turbulent transition on the suction surface. A chord Reynolds number of 1x10(5) and angles of attack (AoA) of 12.8 degrees, 4.2 degrees, and 1.2 degrees are considered. Simulations with and without rotation are performed for each AoA. For AoA=12.8 degrees, rotation increases the reverse flow from 7% of the free-stream velocity in the non-rotating case to 16% of it in the rotating case in the laminar separation bubble (LSB), triggering an oblique instability mechanism in the latter, leading to a faster breakdown to small-scale turbulence. However, rotation delays transition and reattachment in 3%-4% of the chord due to the acceleration of the boundary layer upstream of the LSB, which is subject to a strong adverse pressure gradient (APG), stabilizing Tollmien-Schlichting (TS) waves. Regarding AoA=4.2 degrees and 1.2 degrees, rotation slightly decelerates the attached boundary layer since the APG is very mild but accelerates the separated flow downstream, stabilizing Kelvin-Helmholtz (KH) modes. This mitigates the oblique instability mechanism and slows down the breakdown of KH vortices in the rotating case. In these cases, the transition location is little affected by rotation, possibly due to a rotation-independent absolute instability. Rotation also generates a spanwise tip-flow in the LSB for AoA=4.2 degrees and 1.2 degrees, which is highly unstable and triggers stationary and traveling crossflow modes. Nevertheless, the amplitudes of these modes remain too low to trigger transition.

The boundary-layer stability on a section of a rotating wind turbine blade with an FFA-W3 series aerofoil at a chord Reynolds number of 3 × 105, with varying rotation and radii, is studied with direct numerical simulations and linear stability analyses. Low rotation does not significantly affect transition in the outboard blade region. The relative insensitivity to rotation is due to a laminar separation bubble near the leading edge, spanwise-deformed by a primary self-excited instability, promoting the secondary absolute instability of the Kelvin–Helmholtz (KH) vortices and rapid transition. Moderate increases in rotation, or moving inboard, stabilise the flow by accelerating the attached boundary layer and possibly inducing competition between cross-flow and KH modes. This delays separation and transition. Initially, for high rotation rates or radial locations close to the hub, transition is delayed. Nevertheless, strong stationary and travelling cross-flow modes are eventually triggered, spanwise modulating the KH rolls and shifting the transition line close to the leading edge. Cross-flow velocities as high as 56 % of the free stream velocity directed towards the blade tip are reached at the transition location. For radial locations farther from the hub, the effective angle of attack is decreased, and cross-flow transition occurs at lower rotation rates. The advance or delay of the transition line compared with a non-rotating configuration depends on the competing rotation effects of stabilising the attached boundary layer and triggering cross-flow modes in the separation flow region.

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.

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.

Laminär-turbulent omslag på vindturbinblad är ett mycket komplext fenomen på grund av de många faktorer som påverkar processen. I denna avhandling studerar vi några av dem, nämligen hur friströmsturbulens (FST), rotation och tredimensionalitet påverkar strömningen. Analysen är baserad på det så kallade large eddy simulation (LES) med och utan en modell för subgrid-skala (implicit eller väggupplöst LES). FST:s roll i den modala och icke-modala stabiliteten av flödet på sugsidan av en vindturbinsektion vid ett Reynolds nummer Re_c=100.000 studeras. Detta involverade flera simuleringar med varierande turbulensintensitet (TI) och primära och sekundära linjära stabilitetsanalyser. De separerade skjuvskikten styr flödesstabiliteten via de karakteristiska Kelvin-Helmholtz (KH) virvlarna. Låga FST-nivåer ökar tillväxthastigheten för den sekundära instabiliteten i Tollmien-Schlichting (TS) och KH-fallet, vilket leder till en uppströmsförskjutning av omslaget till turbulens och en minskning av LSB. Tillräckligt hög TI stabiliserar flödet i dessa lägen, vilket leder till en oväntad ökning av LSB. Ytterligare höjningar av turbulensnivån undertrycker emellertid avlösningen. Den spännvidds medelvärdesbildade delen orsakar den stabiliserande effekten. Ökningen av turbulensintensiteten leder också till en monoton minskning av energin hos koherenta strukturer, bakom det separerade skjuvskiktet. I fallet med Re_c=1.000.000 är stråktillväxten mycket mer intensiv, och även låga nivåer av TI är tillräckligt för att undertrycka LSB som finns i frånvaro av FST. För TI≤ 2,4% orsakas övergången av inre moder som liknar TS-vågor i gränsen mot noll FST. Detta intervall av TI visar god överensstämmelse mellan N-faktorn från Macks korrelation med simuleringsdata och ett exponentiellt beroende av omslaget med TI. För 2,4%<TI≤7,0% sker sk  bypass omslag, kännetecknad av dominansen symmetriska stråk. En lågfrekvent cut-off för friströmsturbulensen möjliggör beräkning av en effektiv turbulensintensitet för vindturbinblad. När det gäller rotationens roll utvecklas en modell för att beräkna det kvasi-tredimensionella basflödet för stabilitetsanalyser över ett blad. Flödet är mycket tredimensionellt och påverkas avsevärt av rotation. Mycket sneda vågor är de mest instabila i denna region, vilket leder till ett omslag upp till 19% tidigare än den allmänt använda tvådimensionella semi-empiriska e^N omslagsmodellen av Drela och Giles, som används i RANS-simuleringarna. Ett ramverk för omskagsprediktion baserat på gränsskiktet och paraboliserade stabilitetsekvationer som står för dessa effekter utvecklades. Det indikerar att rotation skiftar övergång uppströms om Reynolds-talet tillåts öka med referenshastigheten. Efterföljande LES indikerade att rotation stabiliserar flödet för ett fast Reynolds-tal i flödesområdet och främre delen av LSB för låga rotationshastigheter, vilket fördröjer övergång och återlaminarisering. Även om rotation fördröjer dessa fenomen, kan rotation verka som en negativ tryckgradient efter att separation inträffar, vilket leder till en ökning av tillväxthastigheterna för KH-moden och återcircirkulerande flöde. Vidare kan omslag till turbulens utlösas för högre rotationshastigheter och mot det inre bladområdet, vilket leder till en uppströmsförskjutning av omslagspunkten. Crossflow-övergång leder till en ökning av tryckskillnaden mellan de två sidorna av vingytan, vilket genererar en högre lyftkraft. I andra områden kan en självexciterad typ av instabilitet uppstå i en LSB som bildas nära framkanten, vilket främjar en tidigt omslag som kan orsaka en plötslig förskjutning av separationslinjen till framkanten efter en viss kritisk radie, som också observerats i experiment. Slutligen identifierades en lågfrekvent oscillation i normalkraftskoefficienten, med en amplitud på 10,5% runt medelvärdet, i ett vindkraftverks vingprofil. Perioden för dessa svängningar var lång, motsvarande flera varv av ett vindturbin med nominell rotationshastighet. Förekomsten av ett sådant fenomen i verkliga vindkraftverk bör bedömas och beaktas i den strukturella designen av rotorn.

Direct numerical simulations of the flow around an FFA-W3 series airfoil at a chord Reynolds number of 100,000 are performed to study the effects of rotation on flow over a section of a rotating wing. In order to achieve this goal, three simulations with different rotation speeds (and corresponding angles of attack) are carried out. Three additional simulations with the same angles of attack of the former but without including Coriolis and centrifugal forces are also computed. It is shown that rotation moves the transition location upstream on the suction side for low angles of attack, and on the pressure side, due to the enhancement of the shear-layer instability and its spanwise modulation. Nevertheless, rotation delays transition on the suction side for larger angles of attack. The reason for this change is most likely the fact that the shear-layer instability is much stronger in this case, and it is not bypassed by instabilities generated by rotation such as that from the inflectional spanwise velocity profiles. However, the latter can reduce the shear in the separation bubble, mitigating the rapid growth of the former. The onset of separation is not changed by rotation, but the trailing edge of the separation bubble is displaced downstream because of an enhanced reverse flow. The lift is only significantly affected by rotation when there are large separation regions on both suction and pressure surfaces, promoting its reduction.

The present work investigates the laminar-turbulent transition of the flow around a typical section of a wind turbine blade under different levels of isotropic inflow turbulence at a Reynolds number of Rec = 105. Wall-resolved large-eddy simulations are performed under different turbulence intensities (TI) up to TI = 2.8 %. The results are analyzed with tools based on the linear stability and optimal-perturbation theory. At TI = 0%, transition to turbulence via the breakdown of Kelvin-Helmholtz (KH) rolls formed over the laminar separation bubble (LSB) is seen. These modes start to grow upstream of the LSB as an inflectional instability. At TI = 1.4 % rolls are also seen; but, instabilities formed by the interaction between streaks and the LSB also contribute to transition. The streaks are estimated to have a spanwise wavenumber around β = 100 (βδ∗ = 0.19 at 20 % chord; δ∗ is the displacement thickness) and a frequency in the range f = 5-8 (f δ∗/ue = (1.4-2.3) × 10-2 at 40 % chord; ue is the boundary layer edge velocity), close to that of the shear-layer instability. In the TI = 2.8 % case, the flow is heavily influenced by the presence of streaks, which stabilize the flow concerning inflectional/KH instabilities, but, at the same time, undergoes varicose-type instabilities and breakdown to turbulence.

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.

We present a two-point model to investigate the underlying source mechanisms for broadband shock-associated noise (BBSAN) in shock-containing supersonic jets. In the model presented, the generation of BBSAN is assumed to arise from the nonlinear interaction between downstream-propagating coherent structures with the quasi-periodic shock cells in the jet plume. The turbulent perturbations are represented as axially extended wavepackets and the shock cells are modelled as a set of stationary waveguide modes. Unlike previous BBSAN models, the physical parameters describing the hydrodynamic components are not scaled using the acoustic field. Instead, the source characteristics of both the turbulent and shock components are extracted from the hydrodynamic region of large-eddy simulation and particle image velocimetry datasets. Apart from using extracted data, a reduced-order description of the wavepacket structure is obtained using parabolised stability equations. The validity of the model is tested by comparing far-field sound pressure level predictions to azimuthally decomposed experimental acoustic data from a cold Mach 1.5 underexpanded jet. At polar angles and frequencies where BBSAN dominates, encouraging comparisons of the radiated noise spectra for the first three azimuthal modes, in both frequency and amplitude ( at peak frequency), reinforce the suitability of using reduced-order wavepacket sources for predicting BBSAN peaks. On the other hand, wavepacket jitter is found to have a critical role in recovering sound amplitude at interpeak frequencies. The paper presents a quantitative demonstration that the wavepacket-shock interaction, carefully reconstructed by extracting components from data or linearised models, contains the correct essential flow physics that accounts for most features of the far-field BBSAN spectra.