Prediction of the hub vortex instability in a wind turbine wake: stability analysis with eddy-viscosity models calibrated on wind tunnel data

The instability of the hub vortex observed in wind turbine wakes has recently been studied by Iungo etal.(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 flow

Flow fluctuations and vorticity dynamics in the near-wake of a triangular prism in cross-flow

The results are described of experiments carried out to investigate on the connection between the flow fluctuations and the dynamics of different vorticity structures in the wake of a prism with equilateral triangular cross-section, aspect-ratio h/w = 3 (where h and w are the prism height and width, respectively), and placed vertically on a plane with its apex edge against the incoming flow. Flow visualizations, hot-wire velocity surveys and pressure measurements are analysed for the model in the original configuration and with geometrical modifications along its edges, conceived in order to interfere with the evolution of the various vorticity structures. In the wake of the original model, fluctuations at three prevailing frequencies are present, with different relative intensities depending on the wake region. In particular, the frequency connected with alternate vortex shedding from the lateral vertical edges of the prism, with a Strouhal number St = fw/U ≈ 0.16 (HF), dominates in the zones outside the lateral boundary of the wake, for vertical positions below z/h = 0.9. A lower frequency, at St ≈ 0.05 (LF), is found to prevail in the velocity fluctuations in the whole upper wake, for downstream distances x/w ≥ 1.5; this frequency is associated with a vertical, in-phase, oscillation of the vorticity structures detaching from the free-end. Fluctuations are also observed at an intermediate frequency St ≈ 0.09 (IF), and prevail in positions corresponding to the downstream boundary of the recirculation region in the central part of the near wake. Measurements of the mean and fluctuating pressures over the upper and rear surfaces of the model confirm the suggestion that the origin of the IF may be an oscillation of the transversal vorticity sheet bounding the recirculation region behind the body. Geometrical modifications to the lateral edges of the model, introduced to alter the vortex shedding, produce a lowering of the HF, directly related to the increase of the mean wake width, and the IF is found to follow a similar decreasing trend. Conversely, small plates inserted along the front edges of the model free-end do not alter the frequency, energy and regularity of the LF fluctuations in the upper part of the wake; this result probably derives from the fact that, in spite of the highly irregular free-end edge, the mechanism of roll-up of the vorticity shed from the sides of the plates is still strong enough to generate the axial vortices, even if with a different formation process. The forces acting on the various models are also measured

Experimental investigation on the influence of wind direction on the aerodynamic loads acting on low aspect-ratio prisms

The results are described of measurements of the mean and fluctuating forces acting on low aspect-ratio triangular prisms placed vertically on a plane, having isosceles triangular crosssection with 60° or 90° apex angles and aspect ratios ranging from 1:0 to 3:0. The tests are carried out in a wind-tunnel by varying the wind direction between 0° and 180°, at a Reynolds number Re = 1:2 x 10^5. Furthermore, for the model with apex angle of 60° and aspect ratio 3:0, flow visualizations with tufts and hot-wire measurements are performed, which permit to characterize the wake morphology as a function of wind direction and to assess that an alternate vortex shedding always exists, with a frequency that is roughly inversely proportional to the wake width. The force measurements show that large variations in the mean values of the drag and cross-flow forces occurby varying µ, in strict connection with changes in wake flow features. The intensity of the fluctuating cross-flow forces, directly connected with vortex shedding, is found to vary significantly with flow orientation and aspect ratio, and to be approximately proportional to the streamwise projection of the body surface immersed in the separated wake. Finally, an increase in vortex shedding frequency is generally found with decreasing aspect ratio

Experimental investigation on the aerodynamic loads and wake flow features of low aspect-ratio triangular prisms at different wind directions

The results are described of measurements of the mean and fluctuating forces acting on low aspect ratio triangular prisms placed vertically on a plane, having isosceles triangularcross-section with 60° or 90° apex angles and aspect ratios ranging from 1.0 to 3.0. The tests are carried out in a wind-tunnel by varying the wind direction, y, between 0° and 180°, at a Reynolds number Re ≈ 1.2 x 105. Furthermore, for the model with apex angle of 60° and aspect ratio 3.0, flow visualizations with tufts and hot-wire measurements are performed, which permit to characterize the wake morphology as a function of wind direction and to assess that an alternate vortex shedding always exists, with a frequency that is roughly inversely proportional to the wake width. The force measurements show that large variations in the mean values of the drag and cross-flow forces occur by varying y, in strict correspondence with changes in wake flow features. The intensity of the fluctuating cross-flow forces, directly connected with vortex shedding, is found to vary significantly with flow orientation and aspect ratio, and to be approximately proportional to the streamwise projection of the body surface immersed in the separated wake. Finally, an increase in vortex shedding frequency is generally found with decreasing aspect ratio

Experimental investigation on the wake generated from a low aspect-ratio triangular prism in cross-flow

The velocity fluctuations experimentally detected in the wake of a prism ha- ving triangular cross-section and an aspect ratio H/w = 3.0 are characterized. It is shown that, besides the fluctuations induced by an alternate vortex shedding with Strouhal number St ≈ 0.16, further components are present, with different relative intensities in different wake regions. A spectral contribution at St ≈ 0.05 is found to dominate all the velocity signals in the upper-wake and it is attributed to a vertical, in-phase oscillation of a couple of counter-rotating axial vortices de- taching from the front edges of the model free-end. An intermediate component is also ascertained occurring at St ≈ 0.09. The analysis of a previously available LES simulation was fundamental for the interpretation of the physical mechanism giving rise to this flow fluctuation, which is associated with the oscillations of a transversal shear layer detaching from the rear edge of the model free-end. Pro- ceeding downstream it bends downwards into the wake in such a way to be reversed upstream impinging the rear surface of the model. Consequently, a recirculation region is delimited by this transversal shear layer. This feature is also assessed from the pressure measurements carried out on the model surfaces; indeed, a pres- sure maximum was ascertained on the rear surface at z/H = 1/3 and fluctuations at St ≈ 0.09 are singled out just at the locations below the recirculation region. Furthermore, the statistics of this frequency are comparable to the ones related to the same spectral component singled out in proximity to rear edge of the free-end, and thus most probably are generated from the same vorticity structure, viz. the transversal shear layer. From the numerical visualizations of the vorticity field it is observed that the fluctuations of the recirculation region are strictly connected with the vortex shedding. Lateral vorticity sheets are dragged in the upper wake generating in correspondence to the wake symmetry plane a vertical \action" on the transversal shear layer directly. Most probably this intricate wake morphology is the physical mechanism giving rise to the oscillations of the recirculation region. Furthermore, it is experimentally assessed that modifications on the vertical edges of the model generate a variation of the vortex shedding frequency comparable to the one produced on the fluctuation frequency of the transversal shear layer. Howe- ver, no variations were found in the fluctuations at the lower frequency in the upper part of the wake, which suggests that they are likely to be essentially connected with an instability of the axial vortices originating from the free-end

Wing-tip vortex wandering: comparison between pressure probe rapid scanning and static hot-film measurements

Wandering is a typical feature of wind-tunnel generated vortices and it consists in random fluctuations of the vortex core. Vortices measured by static measuring techniques appear to be more di®use than in reality. Rapid scanning of a tip vortex generated from a tapered NACA 0012 half-wing was performed with a five hole pressure probe. The aim of this measuring technique is to obtain velocity signals theoretically not affected by wandering by means of sufficiently fast scans performed through the vortex core in order to consider the vortex itself fixed during each scan. The vortex centre position distributions evaluated from each rapid scanning test at a specific downstream location were found to be accurately represented through bi-variate normal probability density functions. The comparison of the rapid scan- ning data, not affected by wandering, with static measurements carried out through a three-component hot-film probe allowed the smoothing effects of wandering on static measurements to be evaluated. Furthermore, the rapid-scanning data high- lighted flow features otherwise hidden from the static measurements. For instance, it was found that a switch from a wake flow to jet flow by increasing the wing angle of attack, proposed by several authors, does not seem to be a proper representa- tion of the axial velocity field of a wing-tip vortex, but rather to be the result of wandering smoothing effects on the actual velocity field. During the roll-up of a vortex an excess of the axial velocity should always be present in correspondence of the vortex centre due to a negative axial pressure gradient. Proceeding down- stream a decay due to viscosity can occur, so that the axial velocity excess can be reversed in a defect surrounded by axial velocity overshoots in correspondence of the core radius. More downstream, a predominant axial velocity defect is singled out without any other surrounding velocity excesses. Consequently, the wing angle of attack only influences the downstream distance where the axial velocity excess is reversed in a deficit; indeed, a delayed switch occurs by increasing the vortex strength, and thus the wing angle of attack. Tests were performed to investigate on the behaviour of wandering by varying the streamwise distance, the wing angle of attack or the Reynolds number. The largest wandering amplitude was generally found along an outboard-upwards to inboard-downwards direction. Furthermore, wandering was found to be not a self-induced phenomenon, as its amplitude is in- creased for more diffuse vortices or with reduced strength. The vortex strength seems to be the principal vortex parameter controlling the wandering; indeed, nei- ther the downstream distance, the wing angle of attack or the free-stream velocity have an absolute influence on wandering. In other words, the wandering amplitude can be reduced by increasing the wing angle of attack, the free-stream velocity or by reducing the streamwise distance from the wing, but if the vortex is sufficiently strong or concentrated it may be completely insensitive to the variation of these parameters