Wind tunnel measurements were performed for the wake produced by a three-bladed wind turbine immersed in uniform flow. These tests show the presence of a vorticity structure in the near-wake region mainly oriented along the streamwise direction, which is denoted as the hub vortex. The hub vortex is characterized by oscillations with frequencies lower than that connected to the rotational velocity of the rotor, which previous works have ascribed to wake meandering. This phenomenon consists of transversal oscillations of the wind turbine wake, which might be excited by the vortex shedding from the rotor disc acting as a bluff body. In this work, temporal and spatial linear stability analyses of a wind turbine wake are performed on a base flow obtained with time-averaged wind tunnel velocity measurements. This study shows that the low-frequency spectral component detected experimentally matches the most amplified frequency of the counter-winding single-helix mode downstream of the wind turbine. Then, simultaneous hot-wire measurements confirm the presence of a helicoidal unstable mode of the hub vortex with a streamwise wavenumber roughly equal to that predicted from the linear stability analysis.

The instability of the hub vortex observed in wind turbine wakes has recently been studied by Iungo et al. (J. Fluid Mech., vol. 737, 2013, pp. 499–526) via local stability analysis of the mean velocity field measured through wind tunnel experiments. This analysis was carried out by neglecting the effect of turbulent fluctuations on the development of the coherent perturbations. In the present paper, we perform a stability analysis taking into account the Reynolds stresses modelled by eddy-viscosity models, which are calibrated on the wind tunnel data. This new formulation for the stability analysis leads to the identification of one clear dominant mode associated with the hub vortex instability, which is the one with the largest overall downstream amplification. Moreover, this analysis also predicts accurately the frequency of the hub vortex instability observed experimentally. The proposed formulation is of general interest for the stability analysis of swirling turbulent flows.

The steady engulfment regime in a fully three-dimensional micro T-mixer is investigated. This regime is of significant interest for applications since it implies high mixing between the flow streams entering the device. Direct numerical simulations are first used to characterize this regime. In particular, the main vortical structures typical of the engulfment regime and their effects on mixing are investigated. Three-dimensional linear stability analysis is successively applied to the characterization of the instability leading to the engulfment regime. The critical Reynolds number and the global unstable mode are first computed for a configuration characterized by fully-developed inlet velocity conditions. The sensitivity of this instability to a generic modification of the base flow is then investigated, thanks to the computation of the mode adjoint to the direct unstable one. Finally, this kind of analysis is specialized to investigate the effect of a perturbation of the velocity distribution at the inlet of the T-mixer. Sensitivity analysis shows that non-fully developed inlet velocity conditions lead to an increase of the critical Reynolds number. More generally, the sensitivity maps can be used for the design of control strategies aimed at promoting or inhibiting the engulfment. An example is provided for a control based on blowing/suction through the mixer walls.

The different flow regimes occurring in T-mixers are investigated by means of direct numerical simulations. Three different values of the aspect ratio of the inlet channels, ki, that is their width to height ratio, are considered, namely ki= 0.75, 1 and 2. For the configurations with ki= 0.75 and 1, the same behavior as previously described in the literature, is found. In particular, as the Reynolds number is increased, the flow evolves from vortical to engulfment steady regimes, then to unsteady asymmetric and symmetric periodic regimes, until, finally, it becomes chaotic. All the critical values of the Reynolds number, at which the transitions between the different regimes occur, are found to be very similar for ki= 0.75 and 1, while some differences are highlighted in the vorticity dynamics and characteristic frequencies of the unsteady regimes. The observed scenario is completely different for ki= 2. Indeed, in this case, the flow evolves directly from the vortical regime to an unsteady symmetric behavior, with a vorticity dynamics that is significantly different from those observed for the other aspect ratios

The laminar flow past a square cylinder symmetrically placed between two parallel walls is considered. A classical vortex wake is shed from the cylinder, but three-dimensional instabilities are present and they develop in complicated flow patterns. The possibility of extracting an accurate low-order model of this flow is explored.

An overview of the mixing performances of micro T-mixers operating with a single fluid is presented. The focus is on the relationship between flow features and mixing. Indeed, T-mixers are characterized by a variety of regimes for increasing Reynolds numbers; they are briefly described, in particular in terms of the three-dimensional vorticity field, which can explain the different mixing performances. The effects of changes in the aspect ratios of the channels are also reviewed. The role of instability and sensitivity analyses in highlighting the mechanisms of onset of the different regimes is then described. These analyses also suggest possible geometrical modifications to promote mixing. We focus on that consisting in the downward tilting of the inlet channels (arrow-mixers). Arrow-mixers are interesting because the onset of the engulfment regime is anticipated at lower Reynolds numbers. Hence, the mixing performances of arrow-mixers with varying Reynolds number are described.