In this work, Direct Numerical Simulation is performed on a low-pressure turbine blade with parallel end-walls, in a linear cascade environment at an exit Reynolds number of 1.5 · 10⁵. Our simulations are performed with Neko, a framework for high-order spectral elements for heterogeneous computing architectures. Secondary flow structures and associated losses are presented in configurations with and without free-stream turbulence and with a Blasius boundary layer inflow profile. Instantaneous and mean flow visualizations validate the classical secondary flow structures reported in the literature. The results highlight strong vortex cores at the outflow and large contributions to losses from the passage vortex and trailing shed vortex (or counter vortex). The application of turbulent structures at the inflow does not affect the formation of the horseshoe vortex nor the vortex cores at the outlet, but still suppresses the shedding at midspan. Proper Orthogonal Decomposition (POD) is applied to provide an overall picture of the flow structures in the entire domain. Without free-stream turbulence, the most energetic modes are found to be linked to the shedding at mid span and the secondary flow structures. Fourier analysis of the POD times series show low frequencies associated with the secondary structures. POD modes for the simulation with free-stream turbulence shows identical secondary flow structures, with additional streamwise-elongated streaky structures in the blade boundary layer and without any modes related to shedding.

This work presents results of direct numerical simulations (DNS) of a one-bladed vertical-axis wind turbine (VAWT). The flow field around the turbine blade is simulated at two different tip-speed ratios λ = 1.5 and 3.0, to capture different dynamic stall scenarios. The phase-averaged flow fields and unsteady aerodynamic loads obtained from the DNS are compared with the experimental measurements. The results demonstrate a high level of consistency in the flow field development and the evolution of aerodynamic coefficients. However, the high-fidelity simulation additionally captures the interaction between the dynamic stall vortex and the turbine blade, which was not seen in experiments due to the three-dimensional effect from the tip vortices of turbine blade and the background disturbance. The interaction of separated dynamic stall vortex and turbine blade, as well as some smaller vortices generated at the upwind side, convect downstream and interact with the blade at the downwind side. This contributes to the difference to the experimental results, such as the total force coefficient having the second peak in the downwind cycle. The proper orthogonal decomposition (POD) analysis not only provides detailed insights into the three-dimensional flow structures around the turbine blade but also facilitates comparison with the aerodynamic loads, offering a clear indication of the dynamic stall evolution on the vertical-axis wind turbine. The high-fidelity simulations and modal analysis of the VAWT provide deeper insights into dynamic stall phenomena and help identify potential strategies for improving performance through enhanced flow control methods.

A reactive control strategy is implemented to attenuate the streaks formed on a wing boundary layer due to free-stream turbulence (FST). Numerical simulations are performed on a section of a NACA0008 profile, considering its leading edge, while forced by FST with turbulence intensities of 0.5 % and 2.5 %. The controller is composed of localised sensors and actuators, with the control law consisting of a linear quadratic Gaussian regulator designed on a reduced-order model based only on the impulse responses of the system. Three configurations are evaluated by considering three different numbers of sensors/actuators along the spanwise direction. It is found that all configurations are effective in damping the streaks inside the boundary layer, whose effect is sustained downstream of the objective function location. However, distinct behaviours are observed when comparing the capability of the controllers with delay transition, where the best performance is attained for the case with larger number of sensors/actuators. This is attributed to the effectiveness of the controller in damping the streaks that will later break down, which in this case are associated with relatively short spanwise wavelength. This observation is confirmed by analysing the stability of the flow before the appearance of turbulent spots. Our results suggest that for an effective transition delay, efforts should not only be put into control of streaks with average spanwise wavelength, but also in the short spanwise wavelength associated with breakdown.

This work investigates the receptivity mechanisms of a NACA0008 airfoil to a level of free-stream turbulence (FST) through a direct numerical simulation (DNS) and an associated linearised simulation on the same mesh. By comparing velocity perturbation fields between the two simulations, the study reveals that the streaky structures that degenerate into turbulent spots are predominantly influenced by nonlinear convective terms, rather than the linear amplification of inflow perturbations around the laminar base flow. A power spectral analysis shows differences in the energy distribution between the DNS and linearised simulation, with the DNS containing more energy at higher wavenumbers, for structures located near the airfoil's leading edge. Representative wavenumbers are identified through modal analysis, revealing a dynamics dominated by streak-like structures. The study employs the Nek5000 numerical solver to distinguish between linear and nonlinear receptivity mechanisms over the NACA0008 airfoil, highlighting their respective contributions to the amplification of perturbations inside the boundary layer. In the high FST case studied, it is observed that the energy of the incoming turbulence is continuously transferred into the boundary layer along the length of the wing. The nonlinear interactions generate streaks with higher spanwise wavenumbers compared with those observed in purely linearised simulations. These thinner streaks align with the spanwise scales identified as susceptible to secondary instabilities. Finally, the procedures presented here generalise the workflow of previous works, allowing for the assessment of receptivity for simulations with arbitrary mesh geometries.

A collection of secondary instability calculations in streaky boundary layers is presented. The data are retrieved from well-resolved numerical simulations of boundary layers forced by free-stream turbulence (FST), considering different geometries and FST conditions. The stability calculations are performed before streak breakdown, taking place at various $Rey_x$ the Reynolds number based on the streamwise coordinate. Despite the rich streak population of various sizes, it is found that breaking streaks have similar aspect ratios, independently of the streamwise position where they appear. This suggests that wider streaks will break down further downstream than thinner ones, making the appearance of secondary instabilities somewhat independent of the streak's wavelength. Moreover, the large difference in the integral length scale among the simulations suggests that this aspect ratio is also independent of the FST scales. An explanation for this behaviour is provided by showing that these breaking streaks are in the range of perturbations that can experience maximum transient growth according to optimal disturbance theory. This could explain why, at a given streamwise position, there is a narrow spanwise wavelength range where streak breakdown is more likely to occur.

This study employs spectral proper orthogonal decomposition (SPOD) on direct numerical simulation data from a low-pressure turbine (LPT) operating under high freestream turbulence levels. The impacts of upstream wakes on the transition process are assessed by considering both cases with and without wakes, modeled by a moving cylinder placed upstream of the LPT blade. In the absence of upstream wakes, the SPOD eigenvalues decreases almost monotonically as frequency increases. At high frequencies, the spectra reveal a broadband interval with minimal elevation, corresponding to the Kármán vortex streets formed downstream of the blade's trailing edge. The SPOD modes in this inflow condition show fully attached boundary layers across the entire blade, suggesting that the boundary layers may be transitional. When subjected to upstream wakes, however, the SPOD spectra display several intense peaks linked to the wake passage frequencies. The associated SPOD modes reveal turbulent spots and lambda vortices on the rear suction side of the blade, typical indicators of turbulent boundary layers. Between the fundamental passage frequency and its harmonics, a series of tones emerge, representing the Doppler-shifted wakes. Triadic interactions between modes involving upstream wakes and their translation induce a cascade of these intermediate components, as verified by the bispectrum map. The SPOD modes capture interactions of structures carried by upstream wakes and the freestream flow with the blade boundary layers, manifested as low- and high-velocity streaks whose breakdown promotes the transition. High-frequency modes describe coherent structures break down into the vortex streets at the trailing edge.

It is well understood that spanwise arrays of roughness elements can be used to generate steady streaks in boundary layers. This modulation of the boundary layer has the potential to attenuate the growth of Tollmien–Schlichting (TS) waves which can lead to the transition to turbulence in low turbulence intensity environments, such as those experienced by an aircraft's fuselage in atmospheric flight. This article applies density based topology optimization in order to design roughness elements capable of exploiting the aforementioned stabilizing effect as a means of passive flow control. The geometry of the roughness elements are represented using a Brinkman penalization when conducting Direct Numerical Simulations (DNS) to simulate the streaky boundary layer flow. Similarly, the unsteady linearized Navier–Stokes equations are evolved to assess the spatial growth of the TS waves across the flat plate. The optimization procedure aims to minimize the TS wave amplitude at a given downstream position while a novel constraint is used promoting a stable baseflow. The optimization problem is solved with gradient descent algorithms where the adjoint-variable method is used to compute gradients. This method has been applied to three initial material distributions yielding three distinct and novel designs capable of damping the downstream growth of the TS wave significantly more than a reference Minature Vortex Generator (MVG) of comparable size. The optimized designs and streaky baseflows they induce are then studied using an energy budget analysis and local stability analysis.

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.

Under the action of free-stream turbulence (FST), elongated streamwise streaky structures are generated inside the boundary layer, and their amplitude and wavelength are crucial for the transition onset. While turbulence intensity is strongly correlated with the transitional Reynolds number, characteristic length scales of the FST are often considered to have a slight impact on the transition location. However, a recent experiment by Fransson and Shahinfar [J. Fluid Mech. 899, A23 (2020)] shows significant effects of FST scales. They found that, for higher free-stream turbulence levels and larger integral length scales, an increase in the length scale postpones transition, contrary to established literature. Here, by performing well-resolved numerical simulations, we aim at understanding why the FST integral length scale affects the transition location differently at low- and high turbulence levels. We found that the integral length scales in Fransson and Shahinfar's experiment are so large that the introduced wide streaks have substantially lower growth in the laminar region, upstream of the transition to turbulence, than the streaks induced by smaller integral length scales. The energy in the boundary layer subsequently propagate to smaller spanwise scales as a result of the nonlinear interaction. When the energy has reached smaller spanwise scales, larger amplitude streaks results in regions where the streak growth are larger. It takes longer for the energy from wider streaks to propagate to the spanwise scales associated with the breakdown to turbulence, than for those with smaller spanwise scales. Thus, there is a faster transition for FST with lower integral length scales in this case.

Thin airfoil dynamic stall at moderate Reynolds numbers is typically linked to the sudden bursting of a small laminar separation bubble close to the leading edge. Given the strong sensitivity of laminar separation bubbles to external disturbances, the onset of dynamic stall on a NACA0009 airfoil section subject to different levels of low-amplitude free stream disturbances is investigated using direct numerical simulations. The flow is practically indistinguishable from clean inflow simulations in the literature for turbulence intensities at the leading edge of Tu = 0.02 %. At slightly higher turbulence intensities of Tu = 0.05 %, the bursting process is found to be considerably less smooth and strong coherent vortex shedding from the laminar separation bubble is observed prior to the formation of the dynamic stall vortex (DSV). This phenomenon is considered in more detail by analysing its appearance in an ensemble of simulations comprising statistically independent realisations of the flow, thus proving its statistical relevance. In order to extract the transient dynamics of the vortex shedding, the classical proper orthogonal decomposition method is generalised to include time in the energy measure and applied to the time-resolved simulation data of incipient dynamic stall. Using this technique, the dominant transient spatiotemporally correlated features are distilled and the wave train of the vortex shedding prior to the emergence of the main DSV is reconstructed from the flow data exhibiting dynamics of large-scale coherent growth and decay within the turbulent boundary layer.