A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

Digital wavefront measuring interferometer for testing optical surfaces and lenses

Wind energy, together with other renewable energy sources, are expected to grow substantially in the coming decades and play a key role in mitigating climate change and achieving energy sustainability. One of the main challenges in optimizing the design, operation, control, and grid integration of wind farms is the prediction of their performance, owing to the complex multiscale two-way interactions between wind farms and the turbulent atmospheric boundary layer (ABL). From a fluid mechanical perspective, these interactions are complicated by the high Reynolds number of the ABL flow, its inherent unsteadiness due to the diurnal cycle and synoptic-forcing variability, the ubiquitous nature of thermal effects, and the heterogeneity of the terrain. Particularly important is the effect of ABL turbulence on wind-turbine wake flows and their superposition, as they are responsible for considerable turbine power losses and fatigue loads in wind farms. These flow interactions affect, in turn, the structure of the ABL and the turbulent fluxes of momentum and scalars. This review summarizes recent experimental, computational, and theoretical research efforts that have contributed to improving our understanding and ability to predict the interactions of ABL flow with wind turbines and wind farms.

https://link.springer.com/content/pdf/10.1007/s10546-019-00473-0.pdf

Wind-Turbine and Wind-Farm Flows: A Review

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.

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

Comprehensive wind tunnel experiments were carried out to study the interaction of a turbulent boundary layer with a wind turbine operating under different tip-speed ratios and yaw angles. Force and power measurements were performed to characterize the variation of thrust force (both magnitude and direction) and generated power of the wind turbine under different operating conditions. Moreover, flow measurements, collected using high-resolution particle-image velocimetry as well as hot-wire anemometry, were employed to systematically study the flow in the upwind, near-wake, and far-wake regions. These measurements provide new insights into the effect of turbine operating conditions on flow characteristics in these regions. For the upwind region, the results show a strong lateral asymmetry under yawed conditions. For the near-wake region, the evolution of tip and root vortices was studied with the use of both instantaneous and phase-averaged vorticity fields. The results suggest that the vortex breakdown p...

Wind tunnel study of the wind turbine interaction with a boundary-layer flow: Upwind region, turbine performance, and wake region

We present experimental data to demonstrate that the far wake of a vertical-axis wind turbine (VAWT) exhibits features that are quantitatively similar to that of a circular cylinder with the same aspect ratio. For a fixed Reynolds number (Re ≈ 0.8 × 10^5) and variable tip-speed ratio, two-dimensional particle image velocimetry (PIV) is used to measure the velocity field in the wake of four different laboratory-scale models: a 2-bladed, 3-bladed and 5-bladed VAWT, as well as a circular cylinder. With these measurements, we use spectral analysis and proper orthogonal decomposition (POD) to evaluate statistics of the velocity field and investigate the large-scale coherent motions of the wake. In all cases, we observe three distinct regions in the VAWT wake: (i) the near wake, where periodic blade vortex shedding dominates; (ii) a transition region, where growth of a shear-layer instability occurs; (iii) the far wake, where bluff-body wake oscillations dominate. We define a dynamic solidity parameter, σ_D , that relates the characteristic scales of the flow to the streamwise transition location in the wake. In general, we find that increasing σ_D leads to an earlier transition, a greater initial velocity deficit and a faster rate of recovery in the wake. We propose a coordinate transformation using σ_D in which the minimum velocity recovery profiles of the VAWT wake closely match that of the cylinder wake. The results have implications for manipulating VAWT wake recovery within a wind farm.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/23E8DEA61FDDF9D2ECF0B02EB333A867/S0022112016008624a.pdf/div-class-title-transition-to-bluff-body-dynamics-in-the-wake-of-vertical-axis-wind-turbines-div.pdf

Transition to bluff-body dynamics in the wake of vertical-axis wind turbines

The flow behind a model of a wind turbine rotor is investigated experimentally in a water flume using particle image velocimetry (PIV) and laser Doppler anemometry (LDA). The study performed involves a three-bladed wind turbine rotor designed using the optimization technique of Glauert (Aerodynamic Theory, vol. IV, 1935, pp. 169–360). The wake properties are studied for different tip speed ratios and free stream speeds. The data for the various rotor regimes show the existence of a regular Strouhal number associated with the development of an instability in the far wake of the rotor. From visualizations and a reconstruction of the flow field using LDA and PIV measurements it is found that the wake dynamics is associated with a precession (rotation) of the helical vortex core.

A regular Strouhal number for large-scale instability in the far wake of a rotor

The vortex breakdown bubble in the confined flow generated by a rotating lid in closed containers with polygonal cross sections was analysed both experimentally and numerically for the height/radius aspect ratio equal to 2. The stagnation point locations of the breakdown bubble emergence and the corresponding Reynolds number were determined experimentally and in addition computed numerically by STAR-CCM+ CFD software for square, pentagonal, hexagonal, and octagonal cross section configurations. The flow pattern and the velocity were observed and measured by combining the seeding particle visualization and the temporal accuracy of laser Doppler anemometry. The vortex breakdown size and position on the container axis were determined for Reynolds numbers, ranging from 1450 to 2400. The obtained results were compared with the flow structure in the closed container of cubical and cylindrical configurations. It is shown that the measured evolution of steady vortex breakdown is in close agreement with the numerical results.

Vortex breakdown in closed containers with polygonal cross sections

The present work investigates local flow structures and the downstream evolution of the core of helical tip vortices generated by a three-bladed rotor. Earlier experimental studies have shown that the core of a helical tip vortex exhibits a local helical symmetry with a simple relation between the axial and azimuthal velocities. In the present study, a self-similarity scaling argument further describes the downstream development of the vortex core. Self-similarity has up to now only been investigated for longitudinal vortices and it is the first time that helical vortices have become the subject of such an analysis. Combining symmetry arguments from previous studies on helical vortices with novel experiments and knowledge regarding the self-similarity evolution of the core of longitudinal vortices, a new model describing what is referred to as ‘helical self-similarity’ is proposed. The generality of the model is verified and supported by experimental data. The proposed model is important for fundamental understanding of the behaviour of helical vortices, with a range of applications in both industry and nature. Examples of this are tip vortices behind aerodynamic devices, such as vortex generators, and fixed and rotary aircraft, and in combustion chambers and cyclone separators.

/pdf/helical-self-similarity-of-tip-vortex-cores-48k7msd69z.pdf

Helical self-similarity of tip vortex cores

This chapter comprises the review of new methods of phase triangulation, which allow 3D geometry measurements under the conditions of arbitrary measured object surface light-scattering properties, varying measurement setting external illumination, and limited depth of field of optical elements of the source and receiver of optical radiation. The application of the proposed methods provides higher metrological characteristics of measuring systems and expands the functionality and the range of application of optical-electronic systems for geometric control in the production environment.

Advanced Phase Triangulation Methods for 3D Shape Measurements in Scientific and Industrial Applications

The flow behind the model of wind turbine rotor is investigated experimentally in a water flume using Particle Image Velocimetry. The study carried out involves rotors of three bladed wind turbine designed using Glauert's optimization. The transitional regime, generally characterized as in between the regime governed by stable organized vortical structures and the turbulent wake, develops from disturbances of the tip and root vorticies through vortex paring and further complex behaviour towards the fully turbulent wake. Our PIV measurements pay special attention to the onset of the instabilities. The near wake characteristics (development of expansion, tip vortex position, deficit velocity and rotation in the wake) have been measured for different tip speed ratio to compare with main assumptions and conclusions of various rotor theories.

/pdf/experimental-investigation-of-the-wake-behind-a-model-of-1jyifgoge6.pdf

I. K. Kabardin

Papers

A regular Strouhal number for large-scale instability in the far wake of a rotor

Vortex breakdown in closed containers with polygonal cross sections

Helical self-similarity of tip vortex cores

Advanced Phase Triangulation Methods for 3D Shape Measurements in Scientific and Industrial Applications

Experimental investigation of the wake behind a model of wind turbine in a water flume