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.

A global transient linear stability analysis of the three-dimensional time-dependent flow around an aerofoil undergoing small-amplitude pitching motion is performed using the optimally time-dependent (OTD) framework. The most salient linear instabilities associated with the instantaneous basic state are computed and tracked over time. The resulting OTD modes reflect the variations in the basic state and can be used as predictors of its spatial and temporal evolution, including the formation of a laminar separation bubble and its gradual spanwise modulation via primary global instability, leading to secondary instability and finally rapid breakdown to turbulence. The study confirms and expands upon earlier stability analyses of the same case based on the local properties of spanwise averaged velocity profiles in the bubble that predicted the onset of absolute instability soon followed by rapid breakdown of the separation bubble. The three-dimensional structure of the most unstable OTD mode is extracted, which compares well with both the locally absolutely unstable mode and the evolution of the basic state itself.

A linearized formulation for fluid-structure-interaction problems exhibiting rigid-body-motion is presented. The linearized equations are evaluated on a stationary grid and require no mesh motion. Numerical tests are performed to validate the derived formulation by comparing the time evolution between the linear and non-linear equations. In all cases both the growth rate and angular frequency of the instability matches to within 0.1% accuracy. The derived formulation is used to predict the phenomenon of symmetry breaking for a rotating cylinder with an attached splitter-plate, the onset of aeroelastic pitch-oscillations for a NACA0012 airfoil at transitional Reynolds numbers, and investigate the structural sensitivity of the least stable eigenvalue for an oscillating cylinder.

Global linear stability analysis is performed for a coupled fluid-structure-interaction problem of a NACA0012 airfoil at transitional Reynolds numbers to investigate the phenomenon of spontaneous pitch-oscillations. It is shown that the spontaneous onset of aeroelastic instability is due to a linearly unstable mode of the coupled fluid-structure-interaction problem. The parameter range of instability predicted by the global stability analysis is consistent with the observations of previous experimental and numerical investigations. However, the results show that the onset of instability and the frequency selection mechanisms are decoupled. The onset of pitch-oscillations is caused due to a zero frequency divergence instability while the frequency selection is likely due to a sub critical mode which is non-linearly excited. In addition the stability results provide an explanation for the absence of the von-Karman modes' frequencies in the pitch response, based on the shape of the eigenvectors of the system.

Large-eddy simulations are performed to investigate the dynamic response of a natural laminar flow airfoil undergoing harmonic small-amplitude pitch oscillations at a chord based Reynolds number of Rec=750,000. Large changes in the transition location as well as trailing-edge separation are observed throughout the pitch cycles, which leads to a nonlinear response of the aerodynamic forces. Despite the highly nonlinear nature of the flow, the evolution of the boundary layer over the airfoil can be modeled by using a simple phase-lag concept, which suggests a quasi-steady evolution of the boundary layer. A simple empirical model is developed based on this phase-lag assumption, which fits very well with the measured experimental data and identifies the primary source of non-linearities in the unsteady aerodynamic forces.

A rigorous derivation and validation for linear fluid–structure-interaction (FSI) equations for a rigid-body motion problem is performed in an Eulerian framework. We show that the ‘added stiffness’ terms arising in the formulation of Fanion et al. (Revue Européenne des Éléments Finis, vol. 9, issue 6–7, 2000, pp. 681–708) vanish at the FSI interface in a first-order approximation and can be neglected when considering the growth of infinitesimal disturbances. Several numerical tests with rigid-body motion are performed to show the validity of the derived formulation by comparing the time evolution between the linear and nonlinear equations when the base flow is perturbed by identical small-amplitude perturbations. In all cases both the growth rate and angular frequency of the instability matches within $0.1\,\%$ accuracy. The derived formulation is used to investigate the phenomenon of symmetry breaking for a rotating cylinder with an attached splitter plate. The results show that the onset of symmetry breaking can be explained by the existence of a zero frequency linearly unstable mode of the coupled FSI system. Finally, the structural sensitivity of the least stable eigenvalue is studied for an oscillating cylinder, which is found to change significantly when the fluid and structural frequencies are close to resonance.

Large eddy simulations are performed to investigate the possibility of bypass transition delay in spatially developing boundary layers. An open loop wall control mechanism is employed which consists of either spatial or temporal oscillations of the spanwise wall velocity. Both spatial and temporal oscillations show a delay in the sharp rise in skin friction coefficient which is characteristic of laminar-turbulent transition. An insight into the mechanism is offered based on a secondary filtering of the continuous Orr-Sommerfeld-Squire (OSQ) modes provided by the Stokes layer, and it is shown that the control mechanism selectively affects the low-frequency penetrating modes of the OSQ spectrum. This perspective clarifies the limitations of the mechanism's capability to create transition delay. Furthermore, we extend the two-mode model of bypass transition proposed by T. Zaki and P. Durbin [j Fluid Mech. 531, 85 (2005)] to cases with wall control and illustrate the selective action of the wall oscillations on the penetrating mode in this simplified case.

A rigorous derivation and validation for linear fluid-structure-interaction (FSI) equations for a rigid-body-motion problem is performed in an Eulerian framework. We show that the “added-stiffness” terms arising in the formulation of Fanion et al. (2000) vanish at the FSI interface in a first-order approximation. Several numerical tests with rigid-body motion are performed to show the validity of the derived formulation by comparing the time evolution between the linear and non-linear equations when the base flow is perturbed by identical small-amplitude perturbations. In all cases both the growth rate and angular frequency of the instability matches within 0.1% accuracy. The derived formulation is used to investigate the phenomenon of symmetry breaking for a rotating cylinder with an attached splitter-plate. The results show that the onset of symmetry breaking can be explained by the existence of a zero-frequency linearly unstable mode of the coupled fluid-structure-interaction system. Finally, the structural sensitivity of the least stable eigenvalue is studied for an oscillating cylinder, which is found to change significantly when the fluid and structural frequencies are close to resonance.

Large-eddy simulations are performed to investigate the dynamic response of a natural laminar flow airfoil undergoing harmonic pitch oscillations at a chord based Reynolds number of Rec= 750, 000. Large changes in the transition location are observed throughout the pitch cycles which leads to a non-linear response of the aerodynamic force coefficients. Preliminary results show that the evolution of the boundary layer over the airfoil can be modeled by using a simple phase-lag concept which implies that the boundary-layer evolution is quasi-steady in nature. A simple empirical model is developed based on this quasi-steady, phase-lag assumption which fits very well with the measured experimental data.

Reynolds-number effects in the adverse-pressure-gradient (APG) turbulent boundary layer (TBL) developing on the suction side of a NACA4412 wing section are assessed in the present work. To this end, we analyze four cases at Reynolds numbers based on freestream velocity and chord length ranging from Re-c = 100, 000 to 1,000,000, all of them with 5 degrees angle of attack. The results of four well-resolved large-eddy simulations (LESs) are used to characterize the effect of Reynolds number on APG TBLs subjected to approximately the same pressure-gradient distribution (defined by the Clauser pressure-gradient parameter beta). Comparisons of the wing profiles with zero pressure-gradient (ZPG) data at matched friction Reynolds numbers reveal that, for approximately the same beta distribution, the lower-Reynolds-number boundary layers are more sensitive to pressure-gradient effects. This is reflected in the values of the inner-scaled edge velocity U-e(+), the shape factor H, the components of the Reynolds-stress tensor in the outer region and the outer-region production of turbulent kinetic energy. This conclusion is supported by the larger wall-normal velocities and outer-scaled fluctuations observed in the lower-Re-c cases. Thus, our results suggest that two complementing mechanisms contribute to the development of the outer region in TBLs and the formation of large-scale energetic structures: one mechanism associated with the increase in Reynolds number, and another one connected to the APG. Future extensions of the present work will be aimed at studying the differences in the outer-region energizing mechanisms due to APGs and increasing Reynolds number.