In a combined experimental and numerical effort, we investigate the generation and reduction of airfoil tonal noise. The means of noise control are streak generators in the form of cylindrical roughness elements. These elements are placed periodically along the span of the airfoil at the mid-chord streamwise position. Experiments are performed for a wide range of Reynolds numbers and angles of attack in a companion work (Alva et al., AIAA Aviation Forum, 2023). In the present work, we concentrate on numerical investigations for a further investigation of selected cases. We have performed wall-resolved large-eddy simulations for a NACA 0012 airfoil at zero angle of attack and Mach 0.3. Two Reynolds numbers (0.8 × 10⁵ and 1.0 × 10⁵) have been investigated, showing acoustic results consistent with experiments at the same Reynolds but lower Mach numbers. Roughness elements attenuate tones in the acoustic field and, for the higher Reynolds number, suppress them. Through Fourier decomposition and spectral proper orthogonal decomposition analysis of streamwise velocity data, dominating structures have been identified. Further, the coupling between the structures generated by the surface roughness and the instability modes (Kelvin–Helmholtz) of the shear layer has been identified through stability analysis, suggesting stabilisation mechanisms by which the sound generation by the airfoil is reduced by the roughness elements.

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.

Linear global stability analysis is performed on a laminar separation bubble formed dueto surface waviness. The eigenspectrum shows a globally unstable mode, responsiblefor the three-dimensionalisation of the bubble, and a family of low-frequency globallystable modes. An adjoint sensitivity analysis shows high sensitivity of the stable modesupstream of the bubble’s reattachment point. Direct numerical simulation (DNS)alongside with a linear impulse response analysis are performed. DNS shows that, whentransition occurs due to self-excited mechanisms, low-frequency upstream propagatingwaves form inside the bubble; this is not the case in linear impulse analysis. It isconjectured that these upstream propagating waves correspond to the low-frequencystable modes in the spectrum which become active through nonlinearity when transitionoccurs.

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.

The instability characteristics and laminar-Turbulent transition of a series of laminar separation bubbles (LSBs) formed due to a single sinusoidal surface waviness are investigated in the absence of external disturbances or forcing. A scaling based on the geometrical parameters of the waviness and flow Reynolds number is found that enables the prediction of flow separation on the wall leeward side. The analysis of three-dimensional instabilities of two-dimensional base flows reveals a relation between the number of changes in the curvature sign of the recirculating streamlines and the number of unstable centrifugal modes that coexist for the same flow. When multiple curvature changes occur, in addition to the usual steady mode reported for two-dimensional recirculation bubbles, a new self-excited mode with a higher growth rate emerges, localised near the highest streamline curvature, close to the reattachment point. A detailed analysis of the mode growth and saturation using DNS reveals that the localised mode only disturbs the LSB locally, while the usual one leads to a global distortion of the bubble in the spanwise direction; this has a distinctive impact on the self-excited secondary instabilities. Then, the complete transition scenario is studied for two selected LSB cases. The first one only presents an unstable eigenmode, namely the usual centrifugal mode in recirculating flows. The second case presents three unstable eigenmodes: Two centrifugal eigenmodes (the usual and the localised ones) and a two-dimensional eigenmode associated with the self-sustained Kelvin-Helmholtz waves. These results show how completely different transition scenarios can emerge from subtle changes in the LSB characteristics.

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.

This work demonstrates that linear stability analysis can be used to study the effect of a smooth hump on secondary instabilities in incompressible swept-wing boundary layers. Two-dimensional Local Stability Theory (LST-2D) and three-dimensional Parabolised Stability Equations (PSE-3D) are employed to investigate how secondary crossflow instabilities are affected by the presence of a hump, compared to the reference (without hump) case. Comparisons between PSE-3D and DNS results, for the dominant instability induced by the hump, show good agreement. These findings confirm the capability of PSE-3D as an efficient tool for analysing secondary instabilities in boundary layers affected by smooth surface humps.